News Bulletin - Buckminster Fuller Institute

Or. to rescale to match the root = distances, you=20 can
multiply through by 1/root(2). So for root(1):

{1,1,0} = ->=20 {root(2)/2,root(2)/2,0}

When you do the permutations (all combos = of=20 {1,1,0}
including with negative signs), you get the 12 vertices
of = the=20 cuboctahedron, each sphere root(1) from the
origin.

For = root(2) I get:=20 {2,0,0} = meaning
(2,0,0)(0,2,0)(0,0,2)(-2,0,0)(0,-2,0)(0,0,-2)

If you=20 multiply through by 1/root(2), you get the 2nd
Waterman with ccp = spheres=20 root(2) from (0,0,0) --
an octahedron with spheres on the X,Y and Z=20 axes
(as you show so well=20 at:
http://www.dsuper.net/%7Etinom/ph2000/ROOT2.html = )

>>>=20 waterman.poly(3)
[[(2, 1, 1), (1, 2, 1), (1, 1, 2)]]

Those are = the 3=20 positive permutations of {2,1,1}.
{2,1,1} ->=20 (-2,1,1)(2,-1,1)(2,1,-1)(-2,-1,1)(-2,1,-1)
(2,-1,-1)(-2,-1,-1)(2,1,1)<= BR>
That's=20 8 vertices, for each of the above 3 -- a
total of 24 (as you show=20 at:
http://www.dsuper.net/%7Etinom/ph2000/ROOT3.html
)

this looks good.

................................................................= ........................
Anyway,=20 for root(10000), the kernel tuples (unpermuted) are:

>>> = waterman.poly(10000,0)
[(140, 16, 12), (140, 20, 0), (128, 60, 4), = (124, 60,=20 32),
(124, 68, 0), (116, 80, 12), (112, 84, 20),(108, 80, = 44),
(100, 80,=20 60), (100, 96, 28), (100, 100, 0)]

i have to take your word on this=20 one.
.................................................................= ....................
Each=20 of these would need to be permuted, both in the
positive octant, and = with=20 negative signs, to generate all
the vertices. Then, if you wanted to = scale it=20 to fit the
sphere diameter =3D 1 regimen, you'd want to = multiply
through by=20 1/root(2). It would take yet further
manipulations to convert the = resultant=20 coordinates into
the kind of tabular raw data you've used in the=20 past.

excellent=20 recap.
...............................................................= ...................
A=20 Pentium 133 with Windows is powerful enough to run
the little Python = programs=20 I've writing, should you
be interested.

yes.

www.python.org is where to = download
the=20 package (free).

my computer is just about to bust its = seams. i will=20 have to

prepare for my physics stuff soon and = probably will=20 not

get to do this...but i = may.

Or maybe you have all the tools
you = need right=20 now.

i start to get lost with all the = different systems=20 and

i generally am afraid to add others as = it might be=20 the straw.

i only do=20 stuff here when necessary....and rarely risk trying

to upgrade or add software . not that i = am=20 paranoid, i have

just had a lot of bad experiences here = and do=20 not

want to risk crashing my = system.

The Python'd be more fun if I = had
that convex=20 hull algorithm, in which case I'd be able
to go all the way through = to Povray=20 (a free ray tracer)
and generate the relevant graphics.

yes, i just downloaded it last = week.

But from your
website, I see you're = being=20 well-supplied from
Mathematica, so this project is likely=20 redundant.

if only,

after finding out that someone was = working on=20 waterman

hulls, and then seeing it on the net, i = wrote to=20 russell

and introduced myself. we talked shop a = bit=20 and

he sent me jpgs of what he had done so=20 far.

he had numbered all the roots = sequentially, so=20 that

r14 became r15, r15 became r16, r30 = became=20 r32..

so i requested that he change to = reflect the=20 missing numbers.

he said they where arbitrary numbers = and that he=20 would not.

i could have made these conversions = myself, but as=20 we were

still at the beginning, i wanted to = have the=20 numbering

system reflect the r = distance.

i mistakenly, then wrote a letter to = karl and asked=20 for his

support on the issue, informing russell = that i had=20 done so.

russell freaked, stopped writing = and never=20 sent another picture.

................................................................= .......................

PS: I'm appending the source code I'm = using=20 (better
algorithm than before), perhaps for later = reference.

you are the man here now, i have no=20 comments

at ALL on any program code. i cannot = answer=20 anything

in this field.

................................................................= .........................

some musing...

perhaps a standard should be set as to = the angle to=20 tilt

the depictions at, to remain = consistent.=20

i have wild speculation that i believe = is not true,=20 but i want to verify.

question, if a line is drawn = from ALL=20 prime number roots, do they

ever pass through another sphere center = having a=20 smaller root distance ?

for if not, then that would be a way to = determine=20 ALL ? prime numbers...

but i suspect greatly that this will = not=20 work.

a ccp starter kit.....spheres with 12 = touch points,=20 6 innies and 6 outies.

frequency 1 contains spheres at = r1

frequency 2 contains spheres at = r2,r3,and=20 r4.

F3 ? (can i call it this short ? ) = contains=20 spheres at r5,r6,r7,r9, but no r8

F4 contains spheres at r8, up to=20 r16...

F4 probably has r15 omitted, i could = figure it out,=20 however

it would like to see this = correlation....all=20 spheres

distances in Fuller frequencies to be = associated=20 with

their specific root = number.

the ccp unit cell stays the same as = currently=20 depicted

on most sites. personally, i view = that unit=20 cell as

"void centered". take that unit cell, = cut at the=20 equator,

flip the bottom 1/2 over, and place on = top of the=20 other piece.

this ccp unit cell, in my view, i refer = to as=20 sphere centered.

i suggest that if you take a unit cell, = of ANY type=20 packing,

it can be placed ANYWHERE and at any = orientation=20 within

the packing (ccp), and still be a = viable unit cell=20 depiction.

steve

------=_NextPart_000_0004_01C078B0.1CBD0220-- ========================================================================= Date: Sun, 7 Jan 2001 14:18:01 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: RD R and D MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0009_01C078B4.A45BCD20" This is a multi-part message in MIME format. ------=_NextPart_000_0009_01C078B4.A45BCD20 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable my take on the .... RD ....the rhombic dodecahedron... all waterman spheres can be made from RD. each face could be given a unique face color. all RD should maintain this color scheme so that when looking at it from the exterior, you would mostly be viewing all the same color(s) in my view, the RD is THE packing figure. i imagine them lodged in the interior of a ship at sea carrying simultaneously fuel, grain, other choices, packed into the hold. aligning top to bottom in aba ( i think ) allows for a feature, unlike normal containers, that "sinks" into the previous row. this radically decreases possible "shifting of the load". from an ecological view, oil spills could be reduced to almost zero, as the interior containers would all have to break individually to sink to the sea floor. from a much larger prospective, these than would be off-loaded by programmed machines and placed=20 on converted ( with a molded to ccp bottom) flatbeads,=20 trains or whatever. steve ------=_NextPart_000_0009_01C078B4.A45BCD20 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

my take on the ....

RD ....the rhombic = dodecahedron...

all waterman spheres can be made from=20 RD.

each face could be given a unique face=20 color.

all RD should maintain this color=20 scheme

so that when looking at it from the=20 exterior,

you would mostly be viewing all the = same=20 color(s)

in my view, the RD is THE packing=20 figure.

i imagine them lodged in the interior = of a=20 ship

at sea carrying simultaneously fuel,=20 grain,

other choices,=20 packed into the hold.

aligning top to bottom in aba ( i think = )

allows for a feature, unlike normal=20 containers,

that "sinks" into the previous = row.

this radically decreases possible = "shifting of=20 the load".

from an ecological view, oil spills = could be=20 reduced

to almost zero, as the interior = containers would=20 all

have to break individually to sink to = the sea=20 floor.

from a much larger prospective, these = than=20 would

be off-loaded by programmed machines = and placed=20

on converted ( with a molded to ccp = bottom)=20 flatbeads,

trains or whatever.

steve

------=_NextPart_000_0009_01C078B4.A45BCD20-- ========================================================================= Date: Sun, 7 Jan 2001 11:26:27 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: More on "missing numbers" (Waterman polys) In-Reply-To: <3.0.3.32.20010107021659.00a58140@pop.teleport.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Hi Steve -- As a further check on my algorithm to generate the positive (permuted or unpermuted) (x,y,z) coordinates of the Waterman polys, in a ccp with sphere radius = root(2), here's a filtering designed to return only the missing roots: >>> import waterman >>> def missing(n): return len(waterman.poly(n,0))==0 >>> filter(missing,range(2000)) [14, 30, 46, 56, 62, 78, 94, 110, 120, 126, 142, 158, 174, 184, 190, 206, 222, 224, 238, 248, 254, 270, 286, 302, 312, 318, 334, 350, 366, 376, 382, 398, 414, 430, 440, 446, 462, 478, 480, 494, 504, 510, 526, 542, 558, 568, 574, 590, 606, 622, 632, 638, 654, 670, 686, 696, 702, 718, 734, 736, 750, 760, 766, 782, 798, 814, 824, 830, 846, 862, 878, 888, 894, 896, 910, 926, 942, 952, 958, 974, 990, 992, 1006, 1016, 1022, 1038, 1054, 1070, 1080, 1086, 1102, 1118, 1134, 1144, 1150, 1166, 1182, 1198, 1208, 1214, 1230, 1246, 1248, 1262, 1272, 1278, 1294, 1310, 1326, 1336, 1342, 1358, 1374, 1390, 1400, 1406, 1422, 1438, 1454, 1464, 1470, 1486, 1502, 1504, 1518, 1528, 1534, 1550, 1566, 1582, 1592, 1598, 1614, 1630, 1646, 1656, 1662, 1678, 1694, 1710, 1720, 1726, 1742, 1758, 1760, 1774, 1784, 1790, 1806, 1822, 1838, 1848, 1854, 1870, 1886, 1902, 1912, 1918, 1920, 1934, 1950, 1966, 1976, 1982, 1998] These match your results through 1022 on: http://www.dsuper.net/%7Etinom/ph2000/MISSING.html so I think we're cookin' with gas here. In 'Numbers, groups, and codes' by J.F. Humphreys and M.Y.Prest (Cambridge U Press, 1989), we've got this paragraph on pg. 28 talking about Fermat's proof that "no number of the form 4k + 3 can be the sum of two squares (although he was by no means the first to discover this...)". A proof of this proposition appears on pp 29-30. Later, in the exercises, we're asked to prove that no number of the form 8n + 7 can be the sum of three squares (exercise 4, pg. 39). In the world of doubled distances^2 ((D*root(2))^2 = D^2 * 2), which is where we play the game of x+y+z=even (to get the ccp pattern), this series translates to 16n + 14, and gives the first column of your 2nd table on http://www.dsuper.net/%7Etinom/ph2000/MISSING.html But our game is more restrictive, given the x+y+z=even stipulation, so additional D^2 values are "missing", beyond simply the series generated by 16n + 14. You give a way of getting some of these: multiply 16n+14 by successive 2nd powerings (4,9,16...). However, although you state that "[t]his accounts for all missing numbers as does the first formula" I'm not persuaded this is true. Consider: 190, 206, 222, 224 -- where are they? 190 seems to be the first "hole" (a missing missing - heh) in Table 2. Seems to me that your 2nd generating method definitely picks up more missing, but I don't think it gets them all. Do you agree? Finding an expression in terms of n for ALL the "missing numbers" would be an interesting challenge I should think. We're looking for an expression which will list all numbers that cannot be expressed as the sum of 3 integers to the 2nd power, where x+y+z is even. Kirby ========================================================================= Date: Sun, 7 Jan 2001 11:30:36 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: more re "missing numbers" Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" > As a further check on my algorithm to generate the positive > (permuted or unpermuted) (x,y,z) coordinates of the Waterman > polys, in a ccp with sphere radius = root(2), ^^^^^^ diameter If it's OK with you, I'd like to post a query on geometry-research giving some of this background and asking about an expression in n for the missing numbers. Some proficient math heads hang out on that list, and might contribute positively and creatively to the discussion. Worth a shot. Whaddya say? Kirby ========================================================================= Date: Sun, 7 Jan 2001 12:05:57 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Draft of post to geometry-research In-Reply-To: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Steve, whaddya think? Worth posting to geometry-research at the Math Forum? -- Kirby ============= In 'Numbers, groups, and codes' by J.F. Humphreys and M.Y.Prest (Cambridge U Press, 1989), we've got this paragraph on pg. 28 talking about Fermat's proof that "no number of the form 4k + 3 can be the sum of two squares (although he was by no means the first to discover this...)". A proof of this proposition appears on pp 29-30. Later, in the exercises, we're asked to prove that no number of the form 8n + 7 can be the sum of three squares (exercise 4, pg. 39). This kind of exercise has relevance to sphere packing as per the following discussion... A gent named Steve Waterman has been studying polyhedra formed by all ccp spheres equidistant from a central sphere. He's been using the Pythagorean Theorem and writing D^2 (distance from the origin to the 2nd power) inside each ccp sphere. All those with the same value comprise a "Waterman polyhedron" (we might say). You can see some renderings of these (using the convex hull algorithm built in to Mathematica) at his website: http://www.dsuper.net/%7Etinom/ph2000/GEODESIC.html Now, in the course of generating his tabular data (a sort of brute force approach), Steve came upon the fact that some distance^2 values simply don't crop up. For example, there's no ccp sphere root(14) from the origin. A whole series of "missing numbers" occurs: 14, 30, 46, 56, 62, 78, 94, 110, 120, 126, 142, 158, 174, 184, 190, 206, 222, 224, 238, 248, 254, 270, 286, 302... (these are D^2 values -- we're assuming ccp sphere diameter = 1). We can model the Watermans algebraically in XYZ by rescaling to root(2) diameter ccp spheres, and stipulating that x+y+z = even number. I.e. all (x,y,z) satisfying this restriction will be the vertices of ccp spheres. Since the distance between sphere centers is now root(2), instead of 1, the 2nd power of the distances will be double those given earlier, i.e. (D*root(2))^2 = 2*D^2. So where Steve had a value of D^2 = 14, we would write 28 and so on. If we wish, we can get back to Steve's distances (D), with sphere diameter = 1, by multiplying our (x,y,z) solutions to x^2 + y^2 + z^2 = 2*D^2 by 1/root(2). The rescales the ccp back to what it was originally. I used a computer to generate (x,y,z) solutions using a streamlined (fairly efficient) "brute force" method. I work only with positive x,y,z and enforce the restriction that x>=y>=z, starting with x = floor(root(2*D^2)), y=0, z=0, then incrementing y (<=x) and z (<=y) until x^2 + y^2 + z^2 > 2*D^2, at which point I decrement x by 1 and repeat, until x**2 + y**2 < 2*D^2 (by which point we should have all solutions where x>=y>=z, x+y+z=even, x^2+y^2+z^2=2*D^2 -- if any). The rest of the vertices will fall out as permutations of (x,y,z) -- meaning you can reorder x,y,z plus change the signs of each of them. By means of this method, I was able to confirm Steve's "missing number" series through 1022 (plus generate XYZ coordinates for a large number of Waterman polyhedra). However, such an algorithm could be rendered more efficient if we simply had an expression for the "missing numbers" in terms of n. In short: what expression in terms of n, where n=1,2,3... will give numbers that CANNOT be the sum of 3 2nd powered integers (x,y,z) where x + y + z = even number? Based on the proof and exercise cited at the top, I'm thinking an answer should be possible. Coming up with it, however, is so far beyond my capabilities. Any assistance would be welcome. Kirby ========================================================================= Date: Sun, 7 Jan 2001 15:28:14 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: missing # algorithms MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_000F_01C078BE.73DDA9C0" This is a multi-part message in MIME format. ------=_NextPart_000_000F_01C078BE.73DDA9C0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable As a further check on my algorithm to generate the positive (permuted or unpermuted) (x,y,z) coordinates of the Waterman polys, in a ccp with sphere radius =3D root(2), here's a filtering designed to return only the missing roots: >>> import waterman >>> def missing(n): return len(waterman.poly(n,0))=3D=3D0 >>> filter(missing,range(2000)) [14, 30, 46, 56, 62, 78, 94, 110, 120, 126, 142, 158, 174, 184, 190, 206, 222, 224, 238, 248, 254, 270, 286, 302, 312, 318, 334, 350, 366, 376, 382, 398, 414, 430, 440, 446, 462, 478, 480, 494, 504, 510, 526, 542, 558, 568, 574, 590, 606, 622, 632, 638, 654, 670, 686, 696, 702, 718, 734, 736, 750, 760, 766, 782, 798, 814, 824, 830, 846, 862, 878, 888, 894, 896, 910, 926, 942, 952, 958, 974, 990, 992, 1006, 1016, 1022, 1038, 1054, 1070, 1080, 1086, 1102, 1118, 1134, 1144, 1150, 1166, 1182, 1198, 1208, 1214, 1230, 1246, 1248, 1262, 1272, 1278, 1294, 1310, 1326, 1336, 1342, 1358, 1374, 1390, 1400, 1406, 1422, 1438, 1454, 1464, 1470, 1486, 1502, 1504, 1518, 1528, 1534, 1550, 1566, 1582, 1592, 1598, 1614, 1630, 1646, 1656, 1662, 1678, 1694, 1710, 1720, 1726, 1742, 1758, 1760, 1774, 1784, 1790, 1806, 1822, 1838, 1848, 1854, 1870, 1886, 1902, 1912, 1918, 1920, 1934, 1950, 1966, 1976, 1982, 1998] These match your results through 1022 on: http://www.dsuper.net/%7Etinom/ph2000/MISSING.html so I think we're cookin' with gas here. agreed.=20 =20 In 'Numbers, groups, and codes' by J.F. Humphreys and M.Y.Prest (Cambridge U Press, 1989), we've got this paragraph on pg. 28 talking about Fermat's proof that "no number of the form 4k + 3 can be the sum of two squares (although he was by no means the first to discover this...)". A proof of this proposition appears on pp 29-30. Later, in the exercises, we're asked to prove that no number of the form 8n + 7 can be the sum of three squares (exercise 4, pg. 39). are you suggesting that 4k +3 and/ or 8n+ 7 may somehow be relate to missing numbers ? why is it a k and an n ? In the world of doubled distances^2 ((D*root(2))^2 =3D D^2 * 2), which is where we play the game of x+y+z=3Deven (to get the ccp pattern), this series translates to 16n + 14, and gives the first column of your 2nd table on http://www.dsuper.net/%7Etinom/ph2000/MISSING.html until it ( what did you call it...world double distance^2 ? )=20 gets the additional columns (Table 2) you will not have them all. But our game is more restrictive, given the x+y+z=3Deven stipulation, so additional D^2 values are "missing", beyond simply the series generated by 16n + 14. so, this method ( would did you call it...world double distance^2 ? ) is ineffective to get them all. You give a way of getting some of these: multiply 16n+14 by successive 2nd powerings (4,9,16...).=20 that should them all... and i give another way....as additive factors of 6 and 8...i find this=20 more of interest, mathematically. so, two different ways to get ALL missing numbers. =20 However, although you state that "[t]his accounts for all missing numbers as does the first formula" I'm not persuaded this is true. good...lets dissect this. Consider: 190, 206, 222, 224 -- where are they?=20 missing from where ? 190 seems to be the first "hole" (a missing missing - heh) in Table 2. you have to look at the whole chart in Table 2... i believe you will find them. Seems to me that your 2nd generating method definitely picks up more missing, but I don't think it gets them all. Do you agree? no, i think i am getting them all. Finding an expression in terms of n for ALL the "missing numbers" would be an interesting challenge I should think. me too. We're looking for an expression which will list all numbers that cannot be expressed as the sum of 3 integers to the 2nd power, where x+y+z is even. yes, i think that is another way to express it. steve ------=_NextPart_000_000F_01C078BE.73DDA9C0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

As a further check on my algorithm = to generate=20 the positive
(permuted or unpermuted) (x,y,z) coordinates of the=20 Waterman
polys, in a ccp with sphere radius =3D root(2), here's = a
filtering=20 designed to return only the missing roots:

>>> import=20 waterman
>>> def missing(n): return=20 len(waterman.poly(n,0))=3D=3D0

>>>=20 filter(missing,range(2000))
[14, 30, 46, 56, 62, 78, 94, 110, 120, = 126, 142,=20 158, 174, 184,
190, 206, 222, 224, 238, 248, 254, 270, 286, 302, 312, = 318,=20 334,
350, 366, 376, 382, 398, 414, 430, 440, 446, 462, 478, 480, = 494,
504,=20 510, 526, 542, 558, 568, 574, 590, 606, 622, 632, 638, 654,
670, 686, = 696,=20 702, 718, 734, 736, 750, 760, 766, 782, 798, 814,
824, 830, 846, 862, = 878,=20 888, 894, 896, 910, 926, 942, 952, 958,
974, 990, 992, 1006, 1016, = 1022,=20 1038, 1054, 1070, 1080, 1086,
1102, 1118, 1134, 1144, 1150, 1166, = 1182, 1198,=20 1208, 1214,
1230, 1246, 1248, 1262, 1272, 1278, 1294, 1310, 1326,=20 1336,
1342, 1358, 1374, 1390, 1400, 1406, 1422, 1438, 1454, = 1464,
1470,=20 1486, 1502, 1504, 1518, 1528, 1534, 1550, 1566, 1582,
1592, 1598, = 1614, 1630,=20 1646, 1656, 1662, 1678, 1694, 1710,
1720, 1726, 1742, 1758, 1760, = 1774, 1784,=20 1790, 1806, 1822,
1838, 1848, 1854, 1870, 1886, 1902, 1912, 1918, = 1920,=20 1934,
1950, 1966, 1976, 1982, 1998]

These match your results = through=20 1022 on:
http://www.dsup= er.net/%7Etinom/ph2000/MISSING.html

so=20 I think we're cookin' with gas here.

agreed. =

=

In=20 'Numbers, groups, and codes' by J.F. Humphreys and
M.Y.Prest = (Cambridge U=20 Press, 1989), we've got this paragraph
on pg. 28 talking about = Fermat's proof=20 that "no number of
the form 4k + 3 can be the sum of two squares=20 (although
he was by no means the first to discover this...)". =20 A
proof of this proposition appears on pp 29-30.

Later, in the = exercises, we're asked to prove that no number
of the form 8n + 7 can = be the=20 sum of three squares (exercise
4, pg. 39).

are you suggesting that 4k +3 and/ = or 8n+ 7=20 may somehow

be relate to missing numbers = ?

why is it a k and an n ?

In the = world of=20 doubled distances^2 ((D*root(2))^2 =3D D^2 * 2),
which is where we = play the=20 game of x+y+z=3Deven (to get the ccp
pattern), this series translates = to 16n +=20 14, and gives the
first column of your 2nd table on
http://www.ds= uper.net/%7Etinom/ph2000/MISSING.html

until it ( what did you call it...world = double=20 distance^2 ? )

gets the additional columns (Table 2) = you will not=20 have them all.

But our game is more restrictive, given the=20 x+y+z=3Deven
stipulation, so additional D^2 values are "missing",=20 beyond
simply the series generated by 16n + 14.

so, this method ( would did you call = it...world=20 double distance^2 ? )

is ineffective to get them = all.

You=20 give a way of getting some of these: multiply 16n+14
by = successive 2nd=20 powerings (4,9,16...).

that should them all...

and i give another way....as additive = factors of 6=20 and 8...i find this

more of interest, = mathematically.

so, two different ways to get ALL = missing=20 numbers.

However, although
you state that = "[t]his=20 accounts for all missing numbers as
does the first formula" I'm not = persuaded=20 this is true.

good...lets dissect this.

Consider: 190, 206, 222, 224 -- = where are=20 they?

missing from where ? 190 seems
to be the first "hole" (a missing = missing -=20 heh) in Table 2.

you have to look at the whole chart in = Table=20 2...

i believe you will find = them.

Seems to me that your 2nd = generating method=20 definitely
picks up more missing, but I don't think it gets them = all.
Do=20 you agree?

no, i think i am getting them = all.

Finding=20 an expression in terms of n for ALL the "missing
numbers" would be an = interesting challenge I should think.

me too.

We're looking for an expression = which will list=20 all numbers
that cannot be expressed as the sum of 3 integers to = the
2nd=20 power, where x+y+z is even.

yes, i think that is another way to = express=20 it.

steve

------=_NextPart_000_000F_01C078BE.73DDA9C0-- ========================================================================= Date: Sun, 7 Jan 2001 15:35:53 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: verify missing numbers MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0025_01C078BF.857E2FA0" This is a multi-part message in MIME format. ------=_NextPart_000_0025_01C078BF.857E2FA0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable If it's OK with you, I'd like to post a query on geometry-research giving some of this background and asking about an expression in n for the missing numbers. Some proficient math heads hang out on that list, and might contribute positively and creatively to the discussion. Worth a shot. Whaddya say? i think that this is really nice of you let them try out your board at their beach, hows the surf there ? i hung out at=20 their beach before, and i trust that the missing will hold up. all input is good....even if some is wrong. just ask TAE. steve ------=_NextPart_000_0025_01C078BF.857E2FA0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

If it's OK with you, I'd like to = post a query=20 on
geometry-research giving some of this background and = asking
about an=20 expression in n for the missing numbers. Some
proficient math = heads=20 hang out on that list, and might
contribute positively and creatively = to the=20 discussion.
Worth a shot. Whaddya say?

i think that this is really nice of you = let them=20 try out your

board at their beach, hows the surf = there ? i hung=20 out at

their beach before, and i trust that = the missing=20 will hold up.

all input is good....even if some is = wrong. just=20 ask TAE.

steve

------=_NextPart_000_0025_01C078BF.857E2FA0-- ========================================================================= Date: Sun, 7 Jan 2001 15:42:04 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Draft of post to geometry-research | I used a computer to generate (x,y,z) solutions using a | streamlined (fairly efficient) "brute force" method. I work | only with positive x,y,z and enforce the restriction that | x>=y>=z, starting with x = floor(root(2*D^2)), y=0, z=0, | then incrementing y (<=x) and z (<=y) until x^2 + y^2 + z^2 | > 2*D^2, at which point I decrement x by 1 and repeat, until | x**2 + y**2 < 2*D^2 (by which point we should have all | solutions where x>=y>=z, x+y+z=even, x^2+y^2+z^2=2*D^2 | -- if any). Helps to write it out this way -- I see it's not quite right. The terminal condition is not when x**2 + y**2 < 2*D^2, but when x**2 is less than 1/3rd 2*D^2. Because since x>=y>=z, if x**2 alone can't get a 3rd of the way to the target total, then adding y**2 + z**2 is going to fall short as well -- so we shouldn't bother checking any smaller values for x. x is as low as it needs to go, and we're done getting unique positive {x,y,z}s suitable for permutation. When I add this condition (mentioned in an earlier post, but not incorporated in the last draft of the algorithm), things speed up considerably. I can get poly(10000,0) in a much shorter time.[1] Also, it wasn't necessary to check whether a solution about to be added to coords was already in coords (takes time). The x>=y>=z approach plus the cut-off when x**2 falls below 1/3 of 2*D^2 is keeping duplication from happening. Kirby PS: I've downloaded qhull for Windows from http://www.geom.umn.edu/software/download/qhull.html It's not Python, but I'm hoping it'll be pretty easy to invoke it from within Python, and that I can take its output and send that to Povray for graphical rendering. If I enhance my permute() algorithm to include the negative sign possibilities, then I'll be able to feed qhull a complete list of all coordinates for a given Waterman, in whatever format it expects. Maybe I'll be rendering poly(10000) soon. Stay tuned. [1] Latest version of the algorithm (permute not shown): def poly(root,perm=1): """ List all-positive (x,y,z) coordinates of any Waterman poly -- optionally suppress permutations with 2nd argument of 0 """ rad = root*2 coords = [] for x in range(int(pow(rad,.5)),-1,-1): # descending order if x**2 < rad/3: break for y in range(x+1): if x**2 + y**2 > rad: break for z in range(y+1): if (x+y+z)%2 == 0: # check for even sum if x**2 + y**2 + z**2 > rad: break if x**2 + y**2 + z**2 == rad: coords.append((x,y,z)) if perm: return map(permute,coords) else: return coords ========================================================================= Date: Sun, 7 Jan 2001 15:54:04 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: missing # algorithms >Consider: 190, 206, 222, 224 -- where are they? >missing from where ? 190 seems >to be the first "hole" (a missing missing - heh) in Table 2. > >you have to look at the whole chart in Table 2... >i believe you will find them. > You're right, I made an error. Goofed. Chagrinned. > >no, i think i am getting them all. > I think you are too, now that I go back and look at it (and see the bugs in my own program -- I'm having a sense of deja vu...). Posting to geometry-research is probably premature, as we may already have the answer I'm looking for. I'll turn my attention to the convex hull algorithm instead (the one I downloaded). But I also have billable hours I need to put in, so it may be awhile before I manage to move Waterman polys to the front burner again. We shall see (depends how quickly I manage to solve these other problems in my in box). Kirby ========================================================================= Date: Sun, 7 Jan 2001 16:07:01 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: to work MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_000B_01C078C3.DEAFE880" This is a multi-part message in MIME format. ------=_NextPart_000_000B_01C078C3.DEAFE880 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable I'll turn my attention to the convex hull algorithm instead (the one I downloaded). this is great news....i doubt it will be easy. but since i dont know anything about code...i guessing. But I also have billable hours I need to put in, so it may be awhile before I manage to move Waterman polys to the front burner again. We shall see (depends how quickly I manage to solve these other problems in my in box). it is so nice to on the same team with you kirby. thanks again for picking up the board and trying it out after you watched me crash and burn with my board so many times. work ? you mean there is more to life than just ccp ? talk soon. steve ------=_NextPart_000_000B_01C078C3.DEAFE880 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

I'll turn my attention to the convex = hull algorithm=20 instead
(the one I downloaded).

this is great news....i doubt it will = be easy. but=20 since

i dont know anything about code...i=20 guessing.

But I also have billable hours I need to put in, so = it
may=20 be awhile before I manage to move Waterman polys to
the front burner=20 again. We shall see (depends how quickly
I manage to solve = these other=20 problems in my in box).

it is so nice to on the same team with = you=20 kirby.

thanks again for picking up the board = and trying=20 it

out after you watched me crash and burn = with

my board so many times.

work ? you mean there is more to life = than just ccp=20 ?

talk soon.

steve

------=_NextPart_000_000B_01C078C3.DEAFE880-- ========================================================================= Date: Sun, 7 Jan 2001 08:04:06 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: Draft of post to geometry-research <> Brian �Quincy! Hutchings 07-JAN-2001 8:04 r001806@pen2.ci.santa-monica.ca.us wow, great deduction, Kirby, on sums of squares! you can find the algorithm to generate all of the integral distances of the body-diagonal of a "box" (or a quadrirectangular tetrahedron, what is the same) in Serpinski's monograph _Pythagorean Triangles_. these are the ones that have xx + yy + zz = ww, all variables being integers. there's a further refinement on the sums of three squares, which I can never remember, from Hardy and Wright's book ob Numbertheory. I think one of the things that you-all are missing, which gives rise to some of the confusion re "scaling," can actually be *seen* in the pictures of the waterman packs, although they are sorta smallish! there's a technical term for the difference, which will make one slap the provberbial ice-cream cone to one's forehead (tee-hee). thus quoth: Later, in the exercises, we're asked to prove that no number of the form 8n + 7 can be the sum of three squares (exercise 4, pg. 39). >--Beyond Petroleum (tm) !! >http://www.tarpley.net/bush8.htm ========================================================================= Date: Sun, 7 Jan 2001 19:11:57 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: to work In-Reply-To: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Howdy again so soon, Steve -- Even amidst taking care of my 6 year old, merging health care data from neighborhood clinics serving the homeless and uninsured, and cleaning the bathroom, I was able to get qhull to share data with my Python programs fairly painlessly. I'm now generating Watermans at will. One thing I've noticed is Mathematica doesn't always do as good a job as qhull, or at least that's my conclusion from looking at Mathematica's Waterman 15 at: http://www.dsuper.net/%7Etinom/ph2000/ROOT15.html Are you aware of the discrepancy? You cardboard model at the bottom of: http://www.dsuper.net/%7Etinom/ph2000/GEODESIC.html shows the *real* Waterman 15, and corresponds to the graphic I'm getting using Python + Qhull + Povray: http://www.inetarena.com/%7Epdx4d/ocn/graphics/water15.gif The Mathematica rendering is sticking in some extraneous vertices that don't belong there. So, now it's time to unveil Waterman 10,000. In Python, all I have to do is enter a one line command: >>> waterman.mkwater(10000) Raw data generated Convex hull generated Vertices: 444 Faces: 638 Povray file generated and then I render in Povray (and even that part could be easily automated, as I already have a render() method). Here's the beauty: http://www.inetarena.com/%7Epdx4d/ocn/graphics/water10k.gif Far out, no? Any requests to see a specific Waterman? Kirby ========================================================================= Date: Sun, 7 Jan 2001 23:28:50 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: Urner Generator ! MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_000D_01C07901.97C87980" This is a multi-part message in MIME format. ------=_NextPart_000_000D_01C07901.97C87980 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable kirby, Even amidst taking care of my 6 year old, merging health care data from neighborhood clinics serving the homeless and uninsured, and cleaning the bathroom, I was able to get qhull to share data with my Python programs fairly painlessly. I'm now generating Watermans at will. and now....the official announcement of the Urner Generator for waterman spheres. this is magic...what a magnificent=20 visualization !=20 One thing I've noticed is Mathematica doesn't always do as good a job as qhull, or at least that's my conclusion it could be a glitch by russell towle or my typo putting=20 the wrong figure there too. from looking at Mathematica's Waterman 15 at: http://www.dsuper.net/%7Etinom/ph2000/ROOT15.html Are you aware of the discrepancy?=20 no, i had missed it. i am ready to replace all hulls that i have. do you think i should i try to fix my site now, or wait a bit ?=20 i fear my machine will bust. i would like to show more than=20 i have now. You cardboard model at the bottom of: http://www.dsuper.net/%7Etinom/ph2000/GEODESIC.html shows the *real* Waterman 15, and corresponds to the graphic I'm getting using Python + Qhull + Povray: http://www.inetarena.com/%7Epdx4d/ocn/graphics/water15.gif yow...are you kidding me ? The Mathematica rendering is sticking in some extraneous vertices that don't belong there. poof ! and with a cloud of smoke...it was gone. So, now it's time to unveil Waterman 10,000. In Python, all I have to do is enter a one line command: not possible....one line ? this is a trick..its mirrors right ? is see it, but i really dont believe it ! >>> waterman.mkwater(10000) Raw data generated Convex hull generated Vertices: 444 Faces: 638 Povray file generated and data too ! how wonderful ! the urner generator=20 ( i do not use caps a lot...not because i am lazy so much as i do not want to break my concentration every time ...at the beginning of every sentence... the end of the last thought...and more important to=20 mention ......there is no disrespect intended to those names that i have not been capped. ) it is truly amazing. am i really seeing what i am seeing ? and then I render in Povray (and even that part could be easily automated, as I already have a render() method). Here's the beauty: http://www.inetarena.com/%7Epdx4d/ocn/graphics/water10k.gif Far out, no? way way cool dude.... Any requests to see a specific Waterman? yes, i have a number that seems to follow me...117. and he twirled and flipped twice, catching the curl.... and it was perfect this time, the kind of huge wave you remember even days later, =20 and nobody had done THAT before,=20 and they laughed. steve ------=_NextPart_000_000D_01C07901.97C87980 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

kirby,

Even amidst taking care = of my 6 year=20 old, merging health
care data from neighborhood clinics serving the=20 homeless
and uninsured, and cleaning the bathroom, I was able = to
get qhull=20 to share data with my Python programs fairly
painlessly. I'm = now=20 generating Watermans at will.

and now....the official announcement of = the Urner=20 Generator

for waterman spheres. this is = magic...what a=20 magnificent

visualization !

One thing I've noticed is Mathematica = doesn't=20 always do
as good a job as qhull, or at least that's my=20 conclusion

it could be a glitch by russell towle = or my typo=20 putting

the wrong figure there = too.

from looking at Mathematica's = Waterman 15=20 at:

http://www.dsupe= r.net/%7Etinom/ph2000/ROOT15.html

Are=20 you aware of the discrepancy?

no, i had missed it. i am ready to = replace all=20 hulls that i have.

do you think i should i try to fix my = site now, or=20 wait a bit ?

i fear my machine will bust. i would = like to show=20 more than

i have now.

You cardboard model
at the bottom = of:

http://www.dsu= per.net/%7Etinom/ph2000/GEODESIC.html

shows=20 the *real* Waterman 15, and corresponds to the
graphic I'm getting = using=20 Python + Qhull + Povray:

http:= //www.inetarena.com/%7Epdx4d/ocn/graphics/water15.gif

yow...are you kidding me ?

The = Mathematica=20 rendering is sticking in some extraneous
vertices that don't belong=20 there.

poof ! and with a cloud of = smoke...it was=20 gone.

So, now it's time to unveil = Waterman=20 10,000. In Python,
all I have to do is enter a one line=20 command:

not possible....one line ? this is a = trick..its=20 mirrors right ?

is see it, but i really dont believe it = !

>>> waterman.mkwater(10000)
Raw data=20 generated
Convex hull generated
Vertices: 444 = Faces:=20 638
Povray file generated

and data too ! how wonderful = !

the urner generator

( i do not use caps a lot...not because = i am=20 lazy

so much as i do not want to break my=20 concentration

every time ...at the beginning of every = sentence...

the end of the last thought...and more = important to=20

mention ......there is no = disrespect

intended to those names that i have not = been=20 capped. )

it is truly amazing. am i really seeing = what=20 i am seeing ?

and then I render in Povray = (and even that=20 part could be
easily automated, as I already have a render()=20 method).

Here's the beauty:

http:/= /www.inetarena.com/%7Epdx4d/ocn/graphics/water10k.gif

Far=20 out, no?

way way cool dude....

Any = requests to see a=20 specific Waterman?

yes, i have a number that seems to = follow=20 me...117.

and he twirled and flipped twice, = catching the=20 curl....

and it was perfect this time, the kind = of huge=20 wave

you remember even days later, =

and nobody had done=20 THAT before,

and they laughed.

steve

------=_NextPart_000_000D_01C07901.97C87980-- ========================================================================= Date: Mon, 8 Jan 2001 00:01:18 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: multies MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_001D_01C07906.209D0560" This is a multi-part message in MIME format. ------=_NextPart_000_001D_01C07906.209D0560 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Any requests to see a specific Waterman? 312, 582, 625, 812, 942 steve ------=_NextPart_000_001D_01C07906.209D0560 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Any requests to see a specific=20 Waterman?

312, 582, 625, 812, 942

steve

------=_NextPart_000_001D_01C07906.209D0560-- ========================================================================= Date: Mon, 8 Jan 2001 00:32:12 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: multies On Mon, 8 Jan 2001 00:01:18 -0500, Steve Waterman wrote: > >Any requests to see a specific Waterman? > >312, 582, 625, 812, 942 > >steve Here's a transcript of the session: >>> map(waterman.mkwater,[312, 582, 625, 812, 942]) Missing for root 312 Raw data generated for root 582 Convex hull generated Vertices: 96 Faces: 146 Povray file generated Raw data generated for root 625 Convex hull generated Vertices: 444 Faces: 638 Povray file generated Raw data generated for root 812 Convex hull generated Vertices: 192 Faces: 194 Povray file generated Missing for root 942 [0, 1, 1, 1, 0] Check: http://www.inetarena.com/~pdx4d/ocn/graphics/water582.gif http://www.inetarena.com/~pdx4d/ocn/graphics/water625.gif http://www.inetarena.com/~pdx4d/ocn/graphics/water812.gif (only wait a few minutes, as I'm rendering/uploading now) Kirby ========================================================================= Date: Mon, 8 Jan 2001 00:34:03 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Urner Generator ! (new web page re Watermans) Steve -- I've got a new web page re your Waterman polys (note: I prefer "Waterman spheres" or "Waterman polys" to "Waterman domes" -- because they're spherical, not domical). Here it is: http://www.inetarena.com/~pdx4d/ocn/wgraphics.html I think you'll find some surprises, e.g. W6 is just a cube (am I right?). That makes sense, if you look at your vertex count at: http://www.dsuper.net/%7Etinom/ph2000/ROOT6.html "8 spheres at root 6" you say, and yet the graphic at right has way more than 8 vertices -- can't be right. And check out W11, with 24 vertices. Again, I think the graphic at: http://www.dsuper.net/%7Etinom/ph2000/ROOT11.html has more than the requisite number of vertices. Whereas what I show clear has 3 per cube corner i.e. 3*8 = 24. As per your request, I've included W117 on this new page, along with W10000. Kirby ========================================================================= Date: Mon, 8 Jan 2001 00:49:29 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: a bit more MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_002C_01C0790C.DB7DD840" This is a multi-part message in MIME format. ------=_NextPart_000_002C_01C0790C.DB7DD840 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable i forgot to add 1 to my odd plate value master... hence the missing number thing.... so it should be 313, 553, 813, 943 and the 625 was right,=20 ------=_NextPart_000_002C_01C0790C.DB7DD840 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

i forgot to add 1 to my odd plate value = master...

hence the missing number = thing....

so it should be 313, 553, 813, = 943

and the 625 was right,

------=_NextPart_000_002C_01C0790C.DB7DD840-- ========================================================================= Date: Mon, 8 Jan 2001 01:30:38 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: initial series MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_003A_01C07912.9B6F2AA0" This is a multi-part message in MIME format. ------=_NextPart_000_003A_01C07912.9B6F2AA0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable kirby, I've got a new web page re your Waterman polys (note: I prefer "Waterman spheres" or "Waterman polys" to "Waterman domes" -- because they're spherical, not domical). websters....a large hemispherical roof or ceiling so domes is not a good name. i wonder if geodesic could apply...what is the definition for geodesic in this context ? websters....the shortest line between two points that lies in a given surface yes, there is a glitch with 6, 8, and 11 i do not see a pattern as to what this could be i could maybe anticipate the 6 or the 8 as a likely place for error, as they are=20 weird/unusual/special...but with the 11 too ...? steve ------=_NextPart_000_003A_01C07912.9B6F2AA0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

kirby,

I've got a new web page re your = Waterman polys=20 (note:
I prefer "Waterman spheres" or "Waterman polys" = to
"Waterman domes"=20 -- because they're spherical, not domical).

websters....a large hemispherical roof = or=20 ceiling

so domes is not a good = name.

i wonder if geodesic could=20 apply...what

is the definition for geodesic in this = context=20 ?

websters....the shortest line between = two=20 points

that lies in a given = surface

yes,=20 there is a glitch with 6, 8, and 11

i do not see a pattern as to what this = could=20 be

i could maybe anticipate the 6 or the 8 = as a=20 likely

place for error, as=20 they are

weird/unusual/special...but with the 11 = too=20 ...?

steve

------=_NextPart_000_003A_01C07912.9B6F2AA0-- ========================================================================= Date: Sun, 7 Jan 2001 22:28:22 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Joe S Moore Subject: Re: central angles Comments: To: DomeHome-H@h19.hoflin.com MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit CrowBird, I don't know if this will be of any help, but here is the Table of Contents of _Geodesic Domes_: http://www.cruzio.com/~joemoore/Biblio/AboutBFbookTOC-GeodesicDomesDemoedAnd Explained.htm A used copy is available through Alibris: http://www.alibris.com/search/detail.cfm?chunk=25&qauth=Borin%20Van%20Loon&S =R&bid=3a4c32fac62&page=1&matches=20&qsort= And also Amazon.com: http://www.amazon.com/exec/obidos/ASIN/0906212928/sr=1-3/ref=sc_b_3/002-0955 107-7237652 Joe S Moore: joemoore@cruzio.com Buckminster Fuller Virtual Institute: http://www.cruzio.com/~joemoore/ ----- Original Message ----- From: "The DomeHome List" To: Sent: Sunday, January 07, 2001 8:57 PM Subject: Re: central angles > Date: 1/7/01 3:36 PM > From: H Crow, wcrow@telepath.com > > I was wondering if you found out any more about this book, if it was still > available. CrowBird > > The DomeHome List wrote: From: Trout mpowell@mho.net Date: Sat, 23 Dec > 2000 > Michael - this may be what you are looking for. I bought the book > earlier this > year. Geodesic domes by Borin Van Loon Tarquin Publications Chapters: > Underlying Symmetry Divisions of the sphere, Domes by truncation, Domes by > subdivision, Chord factors (paper models) Generating Domes from the > octahedron, > Generating Domes from the icosahedron. A geodesic rontundra, A faceted > hemisphere, A divided sphere, The "Bucky Ball" Web site: > http://www.tarquin-books.demon.co.uk > I checked the site but did not see this book listed, but it was > printed > first in 1994 and reprinted this year 2000. So it should still be > available. I > ordered it from the tattered cover book store for I think $14.00 It's a > great > book talks about the vortex angles of the 5 platonic solids. Trout > > > > o > ===== The DomeHome Email List > ========== Web: http://www.domegroup.org > ============= Send posts to: DomeHome-H@h19.hoflin.com > =============== To unsubscribe, write: unsubscribe DomeHome-H > ================ and send to this address: requests@h19.hoflin.com > > > ** subscribe/unsubscribe to this list (under DOG LISTS) and subscribe to > DOME at http://www.hoflin.com > > ========================================================================= Date: Mon, 8 Jan 2001 01:58:32 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: solids MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0011_01C07916.80F73560" This is a multi-part message in MIME format. ------=_NextPart_000_0011_01C07916.80F73560 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable I've got a new web page re your Waterman polys (note: I prefer "Waterman spheres" or "Waterman polys" to "Waterman domes" -- because they're spherical, not domical). websters....a large hemispherical roof or ceiling so domes is not a good name. i wonder if geodesic could apply...what is the definition for geodesic in this context ? websters....the shortest line between two points that lies in a given surface dah...like man, ah...there like totally solids...like totally man. steve ------=_NextPart_000_0011_01C07916.80F73560 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

I've got a new web page re your = Waterman polys=20 (note:
I prefer "Waterman spheres" or "Waterman polys" = to
"Waterman domes"=20 -- because they're spherical, not domical).

websters....a large hemispherical roof = or=20 ceiling

so domes is not a good = name.

i wonder if geodesic could=20 apply...what

is the definition for geodesic in this = context=20 ?

websters....the shortest line between = two=20 points

that lies in a given = surface

dah...like man, ah...there like totally solids...like totally = man.

steve

------=_NextPart_000_0011_01C07916.80F73560-- ========================================================================= Date: Sun, 7 Jan 2001 23:09:09 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Joe S Moore Subject: Re: Geodesic math books (was: central angles) Comments: To: DomeHome-H@h19.hoflin.com MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit H Crow, Try Harvest Booksearch. They don't charge you unless they find the book you want at a price that is agreeable with you; see: http://www.harvestbooks.com/Search.asp Joe S Moore: joemoore@cruzio.com Buckminster Fuller Virtual Institute: http://www.cruzio.com/~joemoore/ ----- Original Message ----- From: "The DomeHome List" To: Sent: Sunday, January 07, 2001 8:59 PM Subject: Geodesic math books (was: central angles) > H. Crow wrote: > > > I was wondering if you found out any more about this book, if it > > was still available. > > Also, look for Hugh Kenner's book, Geodesic Math. It's out of print but > you can still find a copy of it floating around. > > jmr ========================================================================= Date: Mon, 8 Jan 2001 02:40:33 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: a bit more On Mon, 8 Jan 2001 00:49:29 -0500, Steve Waterman wrote: >i forgot to add 1 to my odd plate value master... > >hence the missing number thing.... > >so it should be 313, 553, 813, 943 > >and the 625 was right, OK... >>> import waterman >>> map(waterman.mkwater,[313, 553, 813, 943]) Raw data generated for root 313 Convex hull generated Vertices: 432 Faces: 506 Edges: 936 Povray file generated Raw data generated for root 553 Convex hull generated Vertices: 576 Faces: 746 Edges: 1320 Povray file generated Raw data generated for root 813 Convex hull generated Vertices: 240 Faces: 266 Edges: 504 Povray file generated Raw data generated for root 943 Convex hull generated Vertices: 768 Faces: 962 Edges: 1728 Povray file generated [1, 1, 1, 1] All interesting. See: "More Waterman Polyhedra" http://www.inetarena.com/~pdx4d/ocn/wgraphics2.html Kirby PS: Note that I've added Edges as part of what gets listed during generation. I just went: E = V + F - 2 PPS: Qhull also does volume calcs. That could be for another time. ========================================================================= Date: Mon, 8 Jan 2001 06:33:58 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: physical ccp MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0009_01C0793C.FB69FDC0" This is a multi-part message in MIME format. ------=_NextPart_000_0009_01C0793C.FB69FDC0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable kirby, i suggest, i am only suggesting here,=20 from a broader view, ccp can be seen in either a physical or mathematical perspective. the physical exactitudes can be mathematically deduced using=20 either of two unique sets of parallel rows. knowledge of either set therefore giving replication of the physical. fuller and you both understood the physical ccp through abc methods alone. after i exposed you to my additional=20 mathematical method, you felt i had nothing new... perhaps because you knew that it could not possibly be any better than the physical that you already knew worked !=20 and i did not realize why you were not interested in this=20 additional mathematical method. only when i failed to=20 remember what bcc was, did i go back, and even then it did not click until our discussions and finally i noticed that your reference had ccp as abc....i would say almost 10 years to find what about amounts to a typo. who knew. method 1 i called it method 1 because it was directly related to xyz = coordination,=20 while abc (method 2) does not. and it is this fact, that has shown through the use of the urner generator for waterman solids.... (if thats what it ends up being called ) to be effective in "cross-coordinating" ccp with Cartesian xyz ! although i have only the fuller cosmography book, i am=20 probably safe in saying the he never depicted them as aba, perhaps, but it was irrelevant...he had a math to replicate the physical ccp...and it did all its ccp tricks, whether or=20 not you knew about this additional viably mathematical=20 scheme. so physically ccp and all of fuller and all of his concepts=20 do not change and are under no challenge from this new mathematical aba of ccp. and i would hope that someday ALL ccp references will say=20 ccp is aba and abc. assuming nothing can be found connecting ccp (aba)=20 and fuller ....would you agree here ? steve ------=_NextPart_000_0009_01C0793C.FB69FDC0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

kirby,

i suggest, i am only suggesting here, =

from a broader view, ccp can be seen in = either

a physical or mathematical perspective. = the=20 physical

exactitudes can be mathematically = deduced using=20

either of two unique=20 sets of parallel rows. knowledge

of either set therefore giving = replication of=20 the physical.

fuller and you both understood the = physical ccp=20 through

abc methods alone. after i exposed you = to my=20 additional

mathematical method, you felt i had = nothing=20 new...

perhaps because you=20 knew that it could not possibly

be any better than the physical = that you already knew worked !

and i did not realize why you were=20 not interested in this

additional mathematical method. only = when i failed=20 to

remember what bcc was, did i go back, = and even then

it did not click until = our discussions and finally i noticed

that your reference had ccp as = abc....i would=20 say almost 10

years to find what=20 about amounts to a typo. who knew.

method 1

i called it method 1 because it was = directly=20 related to xyz coordination, =

while abc (method 2) does = not.

and it is this fact, that has=20 shown

through the use of the urner = generator

for waterman solids.... (if thats what = it ends=20 up being called ) to be

effective in "cross-coordinating" ccp = with=20 Cartesian xyz !

although i have only the fuller = cosmography book, i=20 am

probably safe in saying the he never = depicted them=20 as aba,

perhaps, but it was irrelevant...he had = a math to=20 replicate

the physical ccp...and it did all its = ccp tricks, =20 whether or

not you knew about this additional = viably=20 mathematical

scheme.

so physically ccp and all of fuller and = all of his=20 concepts

do not change and are under no = challenge from this=20 new

mathematical aba of ccp.

and i would hope that someday ALL = ccp=20 references will say

ccp is aba and abc.

assuming nothing can be = found connecting =20 ccp (aba)

and fuller ....would you agree here = ?

steve

------=_NextPart_000_0009_01C0793C.FB69FDC0-- ========================================================================= Date: Mon, 8 Jan 2001 11:36:08 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: revised MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0009_01C07967.31C106A0" This is a multi-part message in MIME format. ------=_NextPart_000_0009_01C07967.31C106A0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable let me try this again....i think this is better ? but maybe not ready ...quite yet ? any feedback ? by steve waterman dec.2000 revised on jan.2000 causing some waves i have been forced to rock the bucky boat but strong as ever, it is still afloat he packed his spheres, 12 round 1 and from that thought, we have all begun unproven by newton, though greatly suspected 13 was wrong, as he had projected from the 12 a hull was made he took this shape and began his parade frequency 1 and frequency 2 the hull shapes the same, was his rule with these frequencies, i can agree but have a tweak for frequency 3 there he places spheres at root 9 but those at root 8, he elects to decline from my point of view, but mathematically occurs for spheres have mass and that deserves... a link to gravity and its attraction and what is meant by this action as a coin leaves a spinning plate root 9 spheres would eject before root 8 i too see spheres, grouped by distance but to ignore gravity, i have some resistance dissecting its roots, each a parameter returns a figure having radial diameter i have to mention one thing i dont get his unitary logic for all things are tet frequency 1 he counts 20 in all but there are but 8, and the rest fall... into a pyramid whose base is square each twice the tet volume, i so declare so we each get volumes of 20 tets while he needs but 1, i see 2 sets inverse pyramids along each axes inverse tets to fill up the cracks with radial sweeps show these sectors pyramids and tets along 14 vectors it does not matter what distance you choose the 14 vectors...you never will lose so 12 round 1, is surely a clue not just tetrahedrons come into view. ------=_NextPart_000_0009_01C07967.31C106A0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

let me try this again....i think this = is better=20 ?

but maybe not ready ...quite yet = ?

any feedback ?

by steve waterman dec.2000

revised=20 on jan.2000

&nbs= p; =20 causing some waves

i have been forced to rock the bucky boat
but strong as ever, = it is=20 still afloat
he packed his spheres, 12 round 1
and from that = thought, we=20 have all begun

unproven by newton, though greatly suspected
13 was wrong, as = he had=20 projected
from the 12 a hull was made
he took this shape and began = his=20 parade

frequency 1 and frequency 2
the hull shapes the same, was his=20 rule
with these frequencies, i can agree
but have a tweak for = frequency 3

there he places spheres at root 9
but those at root 8, he = elects to=20 decline
from my point of view, but mathematically occurs
for = spheres=20 have mass and that deserves...

a link to gravity and its attraction
and what is meant by this = action
as a coin leaves a spinning plate
root 9 spheres would = eject before=20 root 8

i too see spheres, grouped by distance
but to ignore gravity, = i have=20 some resistance
dissecting its roots, each a parameter
returns a = figure=20 having radial diameter

i have to mention one thing i dont get
his unitary logic for = all=20 things are tet
frequency 1 he counts 20 in all
but there are but = 8, and=20 the rest fall...

into a pyramid whose base is square
each twice the tet volume, = i so=20 declare
so we each get volumes of 20 tets
while he needs but = 1, i see=20 2 sets

inverse pyramids along each axes
inverse tets to fill up the = cracks=20 with
radial sweeps show these sectors
pyramids and tets along 14=20 vectors

it does not matter what distance you choose
the 14 = vectors...you never=20 will lose
so 12 round 1, is surely a clue
not just tetrahedrons = come into=20 view.

------=_NextPart_000_0009_01C07967.31C106A0-- ========================================================================= Date: Mon, 8 Jan 2001 12:21:25 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: urner generator MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0009_01C0796D.85133AC0" This is a multi-part message in MIME format. ------=_NextPart_000_0009_01C0796D.85133AC0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable kirby some thoughts on the new urner generator... kirby is now rendering at will. from a single line of input. volume data soon. standardized view. our sites linked....via ccp. i have in general, removed my depictions of waterman solids from my site and merely am linking from my alphabetical list. great, i can clean some space on my site and get rid of a whole=20 whack of jpgs and html. thanks for showing this material at your site. this is a BASE database. i use BASE here to mean whatever.... primitive/fundamental/elementary/pick your own name for it/other ? although kirby is now rendering these beauties at will, at break neck speed, we should be careful here to make sure they ALL are right. various sorts of anomalies occur in ccp. we still need to figure out the conditions under which, more than just the radial sweep distance spheres are going to be=20 required. this is why i wanted the n, n-1,n-2 version of the accumulating spheres. someone must do this. perhaps since kirby was able to extend his generator past my manual, it may be doable within your code, and related to your method rather than mine. or some other way, any way...it just eventually needs to be done. we are probably only seeing janetjulians=20 (waterman solids having only n to construct the hull) and requiring no n-1 etc. once this BASE has been done, then=20 the urner generator for waterman solids becomes the tool we really want, and not until.=20 i would be even happier, should/if/when/can any additional techniques/algorithms be found that duplicates these results using different methodologies. steve ------=_NextPart_000_0009_01C0796D.85133AC0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

kirby

some thoughts on the new urner=20 generator...

kirby is now rendering at = will.

from a single line of = input.

volume data soon.

standardized view.

our sites linked....via = ccp.

i have in general, removed my = depictions of=20 waterman solids

from my site and merely am linking from = my=20 alphabetical list.

great, i can clean some space on my = site and get=20 rid of a whole

whack of jpgs and html. thanks for = showing this=20 material

at your site.

this is a BASE database.

i use BASE here to mean=20 whatever....

primitive/fundamental/elementary/pick = your own name=20 for it/other ?

although kirby is now rendering these = beauties at=20 will,

at break neck speed, we should be=20 careful

here to make sure they ALL are = right.

various sorts of anomalies occur in=20 ccp.

we still need to figure out the=20 conditions

under which, more than just the=20 radial

sweep distance spheres are going to be=20

required. this is why i wanted the n,=20 n-1,n-2

version of the accumulating = spheres.

someone must do this. perhaps since=20 kirby

was able to extend his generator past=20 my

manual, it may be doable within your=20 code,

and related to your method rather than=20 mine.

or some other way, any way...it just = eventually=20 needs

to be done. we are probably only seeing = janetjulians

(waterman solids having only n to = construct the=20 hull)

and requiring no n-1 etc.

once this BASE has been done, then =

the urner generator for waterman=20 solids

becomes the tool we really want, and = not until.=20

i would be even happier, = should/if/when/can any=20 additional

techniques/algorithms be found that = duplicates=20 these

results using different = methodologies.

steve

------=_NextPart_000_0009_01C0796D.85133AC0-- ========================================================================= Date: Mon, 8 Jan 2001 13:14:39 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: physical ccp Steve -- OK, here's my perspective: Fuller never talking about either aba or abc in precisely those terms. He didn't call our sphere packing the ccp or fcc either, because both those acronyms have "cube" in them, and he was militating against our culture's cubic fixations. For him, the place to start was with 12-around-1 in the cuboctahedral conformation (not your only choice), and to pack outward in successive layers: 12, 42, 92, 162... 10F^2+2. Here were the numbers of vertices in the geodesic spheres, the capsomeres in a viral protein sheath and so on. Relevant to the atomic nucleus? Gosh, I couldn't tell you -- some stridently assert that it is. I remain open minded. Fuller was well aware of the square-grid and triangular-grid profiles, as is anyone who consistently studies the ccp using the cuboctahedron as a starting point. Both grids are readily apparent on the faces. He shows both of these cross-sections, e.g. when talking about "chef's hats" -- two pieces of a tetrahedron that fit together square-to-square, giving a ccp tetrahedron -- people still find that surprising and it's the basis for a popular wood-block puzzle (build a tetrahedron with just two pieces -- surprising how long it takes most people, products of a cube culture, to solve it). What I think is confusing about your take is you seem to identify ccp with abc with not-xyz. I think this is because when you stack your z-planes vertically, you're thinking this is more strictly "xyz" than when you stack hexagons or what I call triangular grids. But given both ways of layering go straight up the z axis (or can be oriented that way), I'm not sure even this gets to the heart of it. It's more that you're identifying the square grid pattern with both "aba" and "xyz" and the triangular grid pattern with "ccp" or, alternatively "abc". You put myself and Bucky in the "ccp/abc" camp, and talk about your "aba" approach as an "alternative mathematical method". That's confusing because the "Urner generator" is most definitely using XYZ coordinates to do all the work. But it's not really using "layering" (either aba OR abc). The whole idea of building outward in layers and exhaustively tabulating the distance^2 to each and every sphere is what I wanted to get away from. Instead, I start with x as high as possible, and push inward, forcing y and z to pick up the slack, but to remain in "descending sort" i.e. x>=y>=z. Once the unique solutions are found (and you can stop when x^2 by itself can't even get a 3rd of the way to D^2), the rest is handled with permutations. You could do all of the above with z>=y>=x -- any order of those three. There's also the need to limit x+y+z=even in order to disqualify non-ccp positions (i.e. solutions not at the centers of ccp spheres, where the spheres have root(2) diameter -- rescale at the end of the process if you want to get back to the familiar sphere diameter = 1, or if you want even smaller spheres so all the Watermans will fit in the same square window on screen (I do this in the final step, using only integers up to that point)). I'm not sure you've understood this x+y+z=even business yet. I think you're likely in a deep rut from having thought in the same grooves all of these years -- kinda like yer average fuddy-dud (PhD). I credit Jim Morrissett for first showing me that an aba layering of square grids _forces_ the ccp, whereas the triangular grid method easily goes off the rails into hcp or the random wilderness of more generalized Barlow packings. That's what I was chatting up with Conway in the 'Metal Clusters' thread on geometry-research some years back, and that's what I take up on http://www.teleport.com/~pdx4d/sphpack.html (mentions Jim). I credit Gerald de Jong for first showing me an algorithm similar to the "Urner generator" -- one which took advantage of the built in symmetries (i.e. didn't work too hard). He wrote it in Pascal and I don't know if I have a copy anywhere. In any case, my Python generator is of similar design. I credit you for introducing me to the whole concept of Waterman polyhedra. They follow a very simple rule, and yet offer variety and beauty. Your mathematics, on the other hand, is somewhat "stone age", reminds me of John Kurnalian's stuff -- the same algorithm worked over and over and over with reams of data building up. That tends to scare people off -- looks too obsessive, too "I'm living in my own private world" -- more like Bucky's "Numerology" pages. I'm not trying to be offensive, just alert you to what many consider a "red flag" (perhaps one of many).[1] I really really like the Waterman polys and all the math/thinking this has inspired on my end over the years. Finally getting a convex hull algorithm into the mix, even if it isn't in Python, was the latest breakthrough. At last I'm able to go that last step: from having the vertices to getting the edges and faces. That was the bottleneck, but now I'm through it, thanks to Qhull, which is really very powerful. Kirby [1] A well-known document in internet circles -- pays to score yourself every so often: http://math.ucr.edu/home/baez/crackpot.html (my score varies with my mood -- off the scale on some days, even though I'm just a curriculum writer and don't have any revolutionary scientific theories of my own to offer). ========================================================================= Date: Mon, 8 Jan 2001 13:25:15 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: urner generator >i have in general, removed my depictions of waterman solids >from my site and merely am linking from my alphabetical list. >great, i can clean some space on my site and get rid of a whole >whack of jpgs and html. thanks for showing this material >at your site. You can right click on them to download one at a time, or I'm happy to zip them up and email as an attachment or whatever. Use 'em at your site, or ask for others. It's really easy to generate them. >although kirby is now rendering these beauties at will, >at break neck speed, we should be careful >here to make sure they ALL are right. Yes, it'd be useful to have the work checked and confirmed, or errors pointed out. Some guy was checking my page on the binomial theorem earlier today and caught a small error, which I fixed. That's a page I've had on-line for years. http://www.inetarena.com/~pdx4d/ocn/binomial.html By the same token, it's good I finally got that convex hull piece working, since now we're seeing all the errors in those Mathematica images -- and I think in one or two of your paper models as well. Is it really the case that W6 is just a cube? I don't think that's what you show in that photograph of your models. Did I make an error? >various sorts of anomalies occur in ccp. >we still need to figure out the conditions >under which, more than just the radial >sweep distance spheres are going to be >required. this is why i wanted the n, n-1,n-2 >version of the accumulating spheres. How do you mean? My understanding is a Waterman Polyhedron consists exclusively of vertices at the centers of ccp spheres at sweep distance D from the origin. No other vertices are required or allowed. Did I get this wrong? That's been my understanding from the beginning. >someone must do this. perhaps since kirby >was able to extend his generator past my >manual, it may be doable within your code, >and related to your method rather than mine. > >or some other way, any way...it just eventually needs >to be done. we are probably only seeing janetjulians >(waterman solids having only n to construct the hull) >and requiring no n-1 etc. I haven't made a study of janetjulians. That's Towle's thing yes? I think my algorithm could be tweeked to generate them as well, fairly easily, but I'll postpone any such tweeking until we're confidant I've at least handled the Waterman case with integrity. >once this BASE has been done, then >the urner generator for waterman solids >becomes the tool we really want, and not until. If my algorithm is correct, along with my understanding of what a Waterman poly is (upon which the algorithm is based), then it's a good tool for generating the Watermans. >i would be even happier, should/if/when/can any additional >techniques/algorithms be found that duplicates these >results using different methodologies. > >steve Me too, me too. Kirby ========================================================================= Date: Mon, 8 Jan 2001 13:53:54 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: What's a Waterman Polyhedron? >or some other way, any way...it just eventually needs >to be done. we are probably only seeing janetjulians >(waterman solids having only n to construct the hull) >and requiring no n-1 etc. > It occurs to me that I may not really understand your definition of a Waterman Polyhedron. Perhaps I've been doing janetjulians all along. Seems that's the case, from your remarks. Sigh, how confusing. I've been exploring your website to try to find a short, succinct definition of a Waterman Poly, and haven't found it. You seemed to agree with my earlier formulations. But if your polyhedra are sometimes mixtures of root(n) and root(n-1) and maybe more roots, then that's definitely NOT what I'm depicting at my website under the heading of Waterman Polyhedra. Please run it by me again: why would I want root(n-1) vertices mixed in? What's the criterion for a "true Waterman"? Then I'll have to decide whether to (a) tweek the algorithm (b) retitle my page to JanetJulians (not so inclined) or (c) come up with my own way of describing these polys -- Fixed Radius Packing Networks or something. Here's my guess: you include (n-1) radials when the edge network made up of n and n-1 vertices does not cut deeper than any (n-2) radials. Is that it? Maybe I knew this once and forgot. Probably you should put those Mathematica images back. They're probably correct. It is I who was unclear about your definition. Apologies, back to the drawing board. In the meantime, I've changed the titles. Kirby ========================================================================= Date: Mon, 8 Jan 2001 12:14:58 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Ken G. Brown" Subject: Elser's Surfaces Comments: To: GEODESIC@UBVM.cc.buffalo.edu Comments: cc: "[synergeo]" Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" ; format="flowed" Elser's Surfaces Elser's Surface was described by physicist Veit Elser in an article titled "A cubic Archimedean screw", in Nature. It is a triply periodic surface with cubic symmetry of group 230, which has a number of screw axes and threefold axes. ^David Hoffman recently reviewed Elser's article in Mixing Materials and Mathematics. more ..... -------------------------------------------------------------------------------- -------------- Mixing Materials and Mathematics David Hoffman Mathematical Sciences Research Institute, Berkeley CA 94720 USA ``Oil and water don't mix'' says the old saw. But a variety of immiscible liquids, in the presence of a soap or some other surfactant, can self-assemble into a rich variety of regular mesophases. Characterized by their ``inter-material dividing surfaces''---where the different substances touch--- these structures also occur in microphase-separated block copolymers. The understanding of the interface is key to prediction of material properties, but at present the relationship between the curvature of the dividing surfaces and the relevant molecular and macromolecular physics is not well understood. Moreover, there is only a partial theoretical understanding of the range of possible periodic surfaces that might occur as interfaces. Here, differential geometry, the mathematics of curved surfaces and their generalizations, is playing an important role in the experimental physics of materials. ``Curved surfaces and chemical structures,'' a recent issue of the Philosophical Transactions of the Royal Society of London provides a good sample of current work. more... ========================================================================= Date: Mon, 8 Jan 2001 14:14:51 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: What's a Waterman Polyhedron? I've called them: IVM Polyhedra of Fixed Radius and mentioned at the bottom that Russell Towle calls 'em "JanetJulians". So far so good? Then I link to your page saying you've studied a related class of polys. Once I relearn what a _true_ Waterman poly is, I'll see if I can tweek the algorithm. I know you've used gold and silver spheres (for roots n and n-1 right? -- it's coming back to me). I'll try to do something similar, to more closely match your aesthetics. So, if all goes according to plan, I'll be able to add a couple more pages giving the true Waterman depictions. We'll be back on track at that point. I apologize for all this confusion and hope you haven't dumbed down your website unredeemably on my account. Those Mathematica images were probably correct. When you say "number of vertices" I think you must just be talking about the "gold" ones. I forget how the silvers come to be included, but as soon as you enlighten me, I'll plan to get to work on a tweeked version of the "Urner generator". Kirby ========================================================================= Date: Mon, 8 Jan 2001 05:30:44 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: urner generator <> Brian �Quincy! Hutchings 08-JAN-2001 5:30 r001806@pen2.ci.santa-monica.ca.us well, I say, Kowabunga, old chaps! I notice that the fever has not been abated by the coolth of the virtual ice cream cone, alas, but I have a conjecture: the "missing roots" are just that; they're missing from your algorithm, which was cued-in by Kirby's reference to sums of squares. most integers are the sum of at most 3 second-powers, if not just 2 (those of the form 4n-1, I think), but to make all of them, you need 4 second-powers, but never more. it would be surprizing f that is true, because you'd expect Steve's painfully empriical data, based upon some "Master" modelling, to have found anything that really was at root-14; eh? my own thing is not to relinquish the notion, that the IVM actually is the key framework for numbertheory -- and I *thought* that I'd found those roots "out" to root-50 or so. if I don't get any reply to this, I don't no *what* I'll do. --beyond petroleum (tm) !! http://www.tarpley.net/bush8.htm ========================================================================= Date: Mon, 8 Jan 2001 16:13:23 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: slowing the pace MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_001F_01C0798D.ECF4F500" This is a multi-part message in MIME format. ------=_NextPart_000_001F_01C0798D.ECF4F500 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable dudes, thanks for all the support. first, my computer shut down because i am on the free internet. a place called net zero ( i think ). well around the 4th of jan they sent me a message saying that they were going to cut people off after 40 hours per month and then=20 you would need to pay. last month i had a ridiculous 386 hours and feared getting cut off any second. sometime after 1, today it happened and i was not able to take any option ( that i could find/risk to keep going. so i thought, cool...i did not happen while i was in the midst of same letter, and that i got i break. so, i went upstairs to bobs apartment to walk his wonderful dog josh as i do upon occasion. bob supplied the graphic for the opening page. he has helped get me started into html, and helps me in many ways. he is the only way i got=20 connected to the internet at all. coming back from our very short walk this time, i was=20 ready to tell you why i was not answering your emails had they been sent. but bobs machine was not "on" as it usually is, and being unfamiliar with his system, i tried to use the mouse and that did not work so i came back downstairs...... to be continued.....in next email thought i would send this now. steve ------=_NextPart_000_001F_01C0798D.ECF4F500 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

dudes, thanks for all the = support.

first, my computer shut down because i = am on the=20 free

internet. a place called net zero ( i = think ). well=20 around

the 4th of jan they sent me a message = saying that=20 they were

going to cut people off after 40 hours = per month=20 and then

you would need to pay.

last month i had a ridiculous 386 hours = and feared=20 getting

cut off any second. sometime after 1, = today it=20 happened

and i was not able to take any option ( = that i=20 could find/risk

to keep going. so i thought, cool...i = did not=20 happen while i

was in the midst of same letter, and = that i got i=20 break.

so, i went upstairs to bobs apartment = to walk his=20 wonderful

dog josh as i do upon occasion. bob = supplied the=20 graphic

for the opening page. he has helped get = me started=20 into html,

and helps me in many ways. he is the only way i got

connected to the internet at = all.

coming back from our very short walk = this time, i=20 was

ready to tell you why i was not = answering your=20 emails

had they been sent. but bobs machine = was not=20 "on"

as it usually is, and being unfamiliar = with his=20 system,

i tried to use the mouse and that did = not work so=20 i

came back downstairs......

to be continued.....in next = email

thought i would send this = now.

steve

------=_NextPart_000_001F_01C0798D.ECF4F500-- ========================================================================= Date: Mon, 8 Jan 2001 15:26:16 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Chuck Kessler Subject: Fw: Help with condensation and wetting in SB house MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit ----- Original Message ----- From: "Mark and/or Jan Bigland-Pritchard" To: "Rene Dalmeijer" Cc: "crest" Sent: Sunday, January 07, 2001 3:28 PM Subject: Re: Help with condensation and wetting in SB house > Rene Dalmeijer wrote: > > > > I would like to chip in on this discussion. There is another factor in > > play which by itself is a major cause of condensation on the underside > > of metal roofing. Because the roofing is sky facing it has the ability > > to cool down very rapidly on clear nights, faster then the ambient air > > temperature. In these cases, clear sky, not too cool air, relatively > > high levels of condensation will take place. > > Very good point that I hadn't thought of. (You mean some people get > _clear_ winter nights?) As always, Rene knows what he's talking > about... > > Mark > ------------------------------------------------------------------------ > To unsubscribe from the strawbale list, send email to majordomo@crest.org > with the one of the following messages: > unsubscribe strawbale > or > unsubscribe strawbale-digest > if you are on the digest version of the list. > Please send any other list administration questions to > owner-strawbale@crest.org > > ========================================================================= Date: Mon, 8 Jan 2001 17:12:57 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: stitching the sails MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0039_01C07996.3F188240" This is a multi-part message in MIME format. ------=_NextPart_000_0039_01C07996.3F188240 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable ... so i came back downstairs, and went to the bank to take=20 out my last few dollars. since this was under 20, i had to go directly to the bank further away and could not use the machine. it was an enlightening walk, and as i went the few blocks, i was=20 aware that odd things were occurring now, and that i should be observant. so much happened on that walk, that i can not even talk about it yet. it was not me that was changing, but everything was incredible odd around me almost constantly until i returned. a sort of "event convergence". so, i figure that i must wait til bob comes home, and have him=20 stand by/do/instruct/support me in getting hooked back up. i would really like to see if more rides are being taken, or if=20 it is still a battle here i face, or just how much information i can download to you...how far will i get. the ccp is jammed packed with myriads of everything. i doubt strongly we will ever exhaust its possibilities, either in a mathematical sense or physical sense. here is my plan.... get a valid database of hulls. see if kirby can expand my 1000 aba to his 10000 aba bring you up to speed with what i have observed in ccp. mathematically share with you muses over 10 years of trying to=20 see if ccp can be applied to anything physical. show you how it might be linked to the physical constants. i knew nothing of physics at all after i had already known=20 about their being an aba in ccp. i want to replicate that=20 experience, with you here, on this site. i do not want to write a book, be famous, tour, be interviewed, or any of that. i want to tell my story and share my observations. i would rather not have to fix my existing pages as i hope it all will = change. i have tried to use the limitatations of words to express concepts... i wish to share the concept. i want to agree on the concept, and=20 show it, you can agree or not. i am not after agreement, i want to show=20 you what i did and show you what happened. i want to get the math right for ccp first...and linked to visual = displays containing all pertinent mathematical data...unit volumes and=20 conversions to fullers converted "integer'" volumes too. then i want to play this question and answer game. each statement, such as the postulates, can be discussed. i only ask that i get to pick the sequence that i show them to you in. in this way, i imagine many will be rephrased/cut/laughed at/mused over/ ignored/misunderstood/typos/wrong/suspicious/stupid/arrogant/redundant/ superfluous/etc. anyway, that is my plan. i would love to do it here rather than trying=20 to initially interest current academia or finally, if i got lucky (like that could happen ), and somehow get an article and then have them own the rights to it ? may be i am dead wrong on = this. and the 5 photos copies and send this to that, and what a waste of = time.... at least that is my take, perhaps i will change my turn if something = ever does, i can not guarantee who i will be in the future. i have really felt great having all the recent warm support. i think i can do this.....when we get the BASE.... I WOULD LIKE TO SET SAIL...and you are all more than welcome to come aboard....if you think their physics is untouchable like abc in ccp, perhaps you should stop with the math. however, so far, i feel that i am finally getting to download... it is a great relief.=20 so, i will answer all questions. we can hack out any discussion by first understanding the concept before having an opinion about it. the words are fixable...one thing mean another, if stuff has to = change this is great...that is what i want. i have many responses, muses, thought to consider. i will slow the pace a bit now, and try to answer those in sequence. i see a few breakers on the horizon.... steve ps when i check my computer...i am back online somehow did not do anything...and why i can write to you now. ------=_NextPart_000_0039_01C07996.3F188240 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

...

so i came back downstairs, and went to = the bank to=20 take

out my last few dollars. since this was = under 20, i=20 had to go

directly to the bank further away and = could not use=20 the machine.

it was an enlightening walk, and as i = went the few=20 blocks, i was

aware that odd things were occurring = now, and that=20 i should

be observant. so much happened on that = walk, that i=20 can not

even talk about it yet. it was not me = that was=20 changing,

but everything was incredible odd = around me almost=20 constantly

until i returned. a sort of "event=20 convergence".

so, i figure that i must wait til bob = comes home,=20 and have him

stand by/do/instruct/support me in = getting hooked=20 back up.

i would really like to see if more = rides are being=20 taken, or if

it is still a battle here i face, or = just how much=20 information

i can download to you...how far = will i=20 get.

the ccp is jammed packed with myriads = of=20 everything.

i doubt strongly we will ever exhaust = its=20 possibilities,

either in a mathematical sense or = physical=20 sense.

here is my plan....

get a valid database of = hulls.

see if kirby can expand my 1000 aba to = his 10000=20 aba

bring you up to speed with what i have = observed in=20 ccp.

mathematically

share with you muses over 10 years of = trying to=20

see if ccp can be applied to anything=20 physical.

show you how it might be linked to the = physical=20 constants.

i knew nothing of physics at all after = i had=20 already known

about their being an aba in ccp. i want = to=20 replicate that

experience, with you here, on this=20 site.

i do not want to write a book, be = famous, tour, be=20 interviewed,

or any of that. i want to tell my story = and share=20 my observations.

i would rather not have to fix my = existing pages as=20 i hope it all will change.

i have tried to use the limitatations = of words to=20 express concepts...

i wish to share the concept. i want to = agree on the=20 concept, and

show it, you can agree or not. i am not = after=20 agreement, i want to show

you what i did and show you what=20 happened.

i want to get the math right for ccp = first...and=20 linked to visual displays

containing all pertinent mathematical = data...unit=20 volumes and

conversions to fullers converted "integer'" volumes too.

then i want to play this question and = answer game.=20 each statement,

such as the postulates, can be=20 discussed.

i only ask that i get to pick the = sequence that i=20 show them to you in.

in this way, i imagine many will be=20 rephrased/cut/laughed at/mused over/

ignored/misunderstood/typos/wrong/suspicious/stupid/arrogant/red= undant/

superfluous/etc.

anyway, that is my plan. i would love = to do it here=20 rather than trying

to initially interest current academia = or finally,=20 if i got lucky

(like that could happen ), and = somehow get an=20 article

and then have them own the rights to it = ? may be i=20 am dead wrong on this.

and the 5 photos copies and send this = to that, and=20 what a waste of time....

at least that is my=20 take, perhaps i will change my turn if something ever does,

i can not guarantee who i will be in = the=20 future.

i have really felt great having all the = recent warm=20 support.

i think i can do this.....when we get = the=20 BASE....

I WOULD LIKE TO SET SAIL...and you are = all more=20 than welcome

to come aboard....if you think their = physics is=20 untouchable like

abc in ccp, perhaps you should stop = with the=20 math.

however, so far, i feel that i am = finally getting=20 to download...

it is a great relief.

so, i will answer all questions. we can = hack out=20 any discussion

by first understanding the concept = before having an=20 opinion about

it. the words are fixable...one thing = mean another,=20 if stuff has to change

this is great...that is what i = want.

i have many responses, muses, thought = to consider.=20 i will slow the pace

a bit now, and try to answer those in=20 sequence.

i see a few breakers on = the=20 horizon....

steve

ps when i check my computer...i am back = online=20 somehow

did not do anything...and why i can = write to you=20 now.

------=_NextPart_000_0039_01C07996.3F188240-- ========================================================================= Date: Mon, 8 Jan 2001 08:01:06 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: urner generator <> Brian �Quincy! Hutchings 08-JAN-2001 8:01 r001806@pen2.ci.santa-monica.ca.us well, it didn't take me very long to prove *that*. I'm sure, this is quite parallel to what you and Kirby were dyscussing, with him supplying some of the math that you may have used. I just did the basic "odd or even" analysis for the two classes of IVM vertices, which I'd never done, although it's in the spirit of Sierpinski's generating equations, as well. the first class only produces odd dystances, by going "n.5" units in the x direction, "m.5" units in the y direction, and z(root(2)) in the z direction; the formula groups like this: root((nn+n)+(mm+m)+(2(ll+l)+1)) even + even + odd = odd. the second class priduces both odds and evens, by going whole units in x and y directions, and ("n.5"(root(2)) in the z. (I trust, you saw that "n.5" means "n and a half" .-) it groups like this: root((nn + mm) + 2ll) (odd or even) + even = odd or even. so, if you take the small set of second-powers and of twice-a-second-power, less than or equal to 14, you get: 1,4,9 and 2,8; you have to add two of the "squares" (including 0) and one of the "double-sqauers" (including 0), and you cannot get 14, from those! congratulations, Steve, on planting my face -- thus far! --beyond petroleum (tm) !! http://www.tarpley.net/bushb.htm ========================================================================= Date: Mon, 8 Jan 2001 08:16:39 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: urner generator <> Brian �Quincy! Hutchings 08-JAN-2001 8:16 r001806@pen2.ci.santa-monica.ca.us boy, I can see where the "scaling" problem came-in, though; what Steve calls the root(2) dystance is not, if we're using consistant scales from the barycenter; the proper dystance, if I see what's going on, is root(1/2), for that packing o'6 spheres; dig? >--beyond petroleum (tm) !! >http://www.tarpley.net/bush8.htm I don't grok your question, Kirby. isn't the "hull" supposed to more-or-less "shrinwrap" around the extremeties of the figure?... the largest diameter is of the outermost vertices (the centers of the outermost balls); for a cube, the narrowest width its face-to-face, which is root(1/3) of the vertex-to-vertex dystance (i.e. the body-diagonal of the cube, being root(3) for an cube-edge of 1). I'm using "of" in the sense of "times," or as one'd say "a third of." --beyond petroleum (tm) !! http://www.tarpley.net/bush8.htm ========================================================================= Date: Mon, 8 Jan 2001 08:26:14 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: [Q-P] Reaction to the plague <> Brian �Quincy! Hutchings 08-JAN-2001 8:26 r001806@pen2.ci.santa-monica.ca.us thank you, ms.Street for your antiparanoia. there was a small piece in the times, yesterday, that deigned to even mention the *chemical* toxicity of "depleted" uranium, which is probably as much of a problem, if any -- considering the amounts occuring!... of course, there were virtually no dosages given, either in the "LD-50" tests of rats, or of the soldiers or civilians. an article from the day before contained a lot of the data that I'd never seen, regarding the rounds and the DU ("40% of the radiation of uranium ore," although I'm not sure at what phase of extraction they meant; there's no way to tell, from the text) -- but it was all couched in Euro-hysteria. it's probably just Rad Cow Dysease! thus quoth: Three Mile Island is naturally very radioactive, and many places on Earth are naturally more radioactive than the area that has been evacuated around Chernobyl). Brick buildings are more radioactive than wood buildings. Etc. --beyond petroleum (tm) !! http://www.tarpley.net/bush8.htm ========================================================================= Date: Mon, 8 Jan 2001 08:45:55 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: [Q-P] Reaction to the plague <> Brian �Quincy! Hutchings 08-JAN-2001 8:45 r001806@pen2.ci.santa-monica.ca.us this is how TV stands for TaVistock! your example (of climate change, almost always used to be synonymous with the defunct "overall" warming model of Svente Ahrrennius (1896) et al) is very common. look at the little "powerpoint slides" in most papers, showing a cartoon map with icons of glaciers melting -- they never show where glaciers are *not* receding, or even advancing; do they? I might also add the "Traffic" re-do from Masterpiece Theatre; thanks for that crucuial information. the British had gotten Sir George to railroad Lyn, in part by using the attribution, "he says, the Queen pushes drugs in front of Balmoral Castle," and hte usual BS that is all they ever put in the big media. back on climate, I just spoke with a Canadian, who couldn't beleive that I didn't think that hemp was some sort of panacea (or "economy" as Jack Herer et al go-on with); apparently, along with the Marijuana Party (which made a huge showing, in spite of only organizing about 3 weeks before the election), the Canadian government has been promoting industrial (and medical) hemp, like gangbusters (or perhaps more akin to the Bronfman Gang) for years! --beyond petroleum (tm) !! http://www.tarpley.net/bush8.htm ========================================================================= Date: Mon, 8 Jan 2001 18:59:37 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: urner generator > I don't grok your question, Kirby. > isn't the "hull" supposed to more-or-less "shrinwrap" > around the extremeties of the figure?... Not sure I know what question you mean, but yes, a convex hull is a shrink wrap, meaning if you throw Qhull a bunch of points, it'll use all those which define outermost convexity, and ignore any that fall within. So it has come flooding back to me now, while Steve has been out walking and losing his internet linkup: if you take the root(n) ccp spheres as your outermost, you're still going to pick up some root(n-1) spheres when doing the shrink wrap, i.e. these will be among those Qhull sees as relevant to the convexity. Question: will root(n-2) spheres ever show up as "outermost" as well? I'm going to tweak my algorithm to include (n-1) and (n-2) spheres. I'll color code n=gold, n-1=silver, n-2=green and start generating -- see what I get. If the greens don't show up in the final graphics, I'll start to think it's always either n's alone, or n's plus n-1's. If Steve were on-line he could probably tell me. Kirby ========================================================================= Date: Mon, 8 Jan 2001 09:25:08 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: urner generator <> Brian �Quincy! Hutchings 08-JAN-2001 9:25 r001806@pen2.ci.santa-monica.ca.us well, how about this: whatever was the root-dystance for the *center*-to-corner (of the cube), multiply it by root(1/3); if any root(n-1) vertices are beyond that, add them to the vertices of the hull, and find the minimal width of *that* shape, and do this over, again (using the new shape as the basis for the new minimal width, with its vertex-to-vertex (root(n-1)) dystance being the largest dimeter). thus quoth: i.e. these will be among those Qhull sees as relevant to the convexity. Question: will root(n-2) spheres ever show up as "outermost" as well? > --beyond petroleum (tm) !! > http://www.tarpley.net/bushb.htm ========================================================================= Date: Mon, 8 Jan 2001 19:36:58 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: touching BASE MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_002C_01C079AA.5DCA15A0" This is a multi-part message in MIME format. ------=_NextPart_000_002C_01C079AA.5DCA15A0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable kirby, you wrote OK, here's my perspective: Fuller never talking about either aba or abc in precisely those terms. He didn't call our sphere packing the ccp or fcc either, because both those acronyms have "cube" in them, and he was militating against our culture's cubic fixations. i understand his objection. For him, the place to start was with 12-around-1 in the cuboctahedral conformation=20 was does this mean ? (not your only choice),=20 the others being ? and to pack outward in successive layers: 12, 42, 92, 162... 10F^2+2. i agree here. Here were the numbers of vertices in the geodesic spheres, the capsomeres in a viral protein sheath and so on.=20 please rephrase or restate. Relevant to the atomic nucleus? =20 not in my opinion. Gosh, I couldn't tell you -- some stridently assert that it is.=20 i am not trying to show you what others think in a way, i do not care. i want to show you some tricks. I remain open minded. hey, does any body know how to wax a board ? Fuller was well aware of the square-grid and triangular-grid profiles, as is anyone who consistently studies the ccp using the cuboctahedron as a starting point. Both grids are readily apparent on the faces. He shows both of these cross-sections, e.g. when talking about "chef's hats" -- two pieces of a tetrahedron that fit together square-to-square, giving a ccp tetrahedron -- people still find that surprising and it's the basis for a popular wood-block puzzle (build a tetrahedron with just two pieces -- surprising how long it takes most people, products of a cube culture, to solve it). what others know is always of interest to me, as it helps to have a benchmark from which i can attempt to judge my position . What I think is confusing about your take is you seem to identify ccp with abc with not-xyz.=20 typo ? I think this is because when you stack your z-planes vertically, you're thinking this is more strictly "xyz" than when you stack hexagons or what I call triangular grids. =20 please define triangular grids. But given both ways of layering=20 so we agree that layering has two forms. go straight up the z axis (or can be oriented that way), I'm not sure even this gets to the heart of it.=20 the word 'it' is too vague ...please restate It's more that you're identifying the square grid pattern with both "aba" and "xyz" and the triangular grid pattern with "ccp" or, alternatively "abc". =20 i believe that too be true...we need to able to speak the same language. lets always try to focus on getting a singular word or phrase that means the same thing to both of us. i do not care what that word = is, my word, your word, buckys word, other peoples word, or we make one up. You put myself and Bucky in the "ccp/abc" camp, and talk about your "aba" approach as an "alternative mathematical method". not to be confused with an alternative physical approach. That's confusing because the "Urner generator" is most definitely using XYZ coordinates to do all the work.=20 you mean two different mathematical methods (mine and yours) that yield the same physical BASE ? But it's not really using "layering" (either aba OR abc). =20 well i guess you do have a second method then ? The whole idea of building outward in layers and exhaustively tabulating the distance^2 to each and every sphere is what I wanted to get away from.=20 and you have. Instead, I start with x as high as possible, and push inward, forcing y and z to pick up the slack, whereas i would have picked z and forced x and y. but to remain in "descending sort" i.e. x>=3Dy>=3Dz.=20 so why force on x then ? doesnt this above equation then become the defining characteristic ? =20 Once the unique solutions are found=20 my thinking here too was that we needed to find unique solutions, but now that i get what you are doing a bit better a have some better clarity on this issue. while it might appear that unique solutions should be required,=20 i should only be required to go to say n-100 for the 10000. 1/3 is WAY WAY too high. i would imagine that taking fewer than needed might nor result in a full convex hull but i am guessing ? (and you can stop when x^2 by itself can't even get a 3rd of the way to D^2), aha, this is why i wanted the n,n-1,n-2 accumulating i suggest you may only need up to n-100 and this should work say up to even maybe 10000. ? but 1/3 is WAY too much. the rest is handled with permutations. You could do all of the above with z>=3Dy>=3Dx -- any = order of those three. sounds good. There's also the need to limit x+y+z=3Deven in order to disqualify = non-ccp positions (i.e. solutions not at the centers of ccp spheres, where the spheres have root(2) diameter -- rescale at the end of the process if you want to get back to the familiar sphere diameter =3D 1, or if you = want even smaller spheres so all the Watermans will fit in the same square window on screen (I do this in the final step, using only integers up to that point)). I'm not sure you've understood this x+y+z=3Deven = business yet. I think you're likely in a deep rut from having thought in the same grooves all of these years -- kinda like yer average fuddy-dud = (PhD). you are replicating the physical, so the math works... you say potato i say patatoe...could dan qualye have said this ? I credit Jim Morrissett for first showing me that an aba layering of square grids _forces_ the ccp, whereas the triangular grid method=20 should we explore what the triangular grid method is ? if so, what is it. easily goes off the rails into hcp=20 please do not ask question that are not ccp related. or the random wilderness of more generalized Barlow packings. =20 are those ccp...you did not answer that last time if i remember right = here ? That's what I was chatting up with Conway in the 'Metal Clusters' thread on geometry-research some years back, and that's what I take up on http://www.teleport.com/~pdx4d/sphpack.html (mentions Jim). having trouble going here...no comment. I credit Gerald de Jong for first showing me an algorithm similar to the "Urner generator" -- one which took advantage of the built in symmetries (i.e. didn't work too hard). He wrote it in Pascal and I = don't know if I have a copy anywhere. In any case, my Python generator is of similar design. i guess we wont need it now... I credit you for introducing me to the whole concept of Waterman = polyhedra. They follow a very simple rule, and yet offer variety and beauty. they are of constant surprise to me...who knew. Your mathematics, on the other hand, is somewhat "stone age", reminds me of John Kurnalian's stuff -- the same algorithm worked over and over and over with reams of data building up.=20 i glad that it happened this way, if i had just got the "take a radial = sweep thing...i would not have known that there was anything *special* going = on. That tends to scare people off -- looks too obsessive, too "I'm living in my own private world" -- more = like Bucky's "Numerology" pages.=20 perhaps i do live in my own private word, thanks for the company. just alert you to what many consider a "red flag" (perhaps one of many).[1] any advice ? perhaps indeed, how do i deal with this ? what should i do ? i can not control what others think of me, and indeed, they have that right....is there something you would recommend that i could tone down ? how can this be improved ? I really really like the Waterman polys and all the math/thinking this has inspired on my end over the years.=20 =20 me too, and while it is an obsession no doubt, i have other interests and are not totally consumed by its pull Finally getting a convex hull algorithm into the mix, even if it isn't in Python, was the latest breakthrough. i have wanted to see these so much. i have dreamed of them, and could but only imagine. when i saw the 10000, it was a=20 special moment for me. not an ego moment, just to known what some of the upper r look like....even if the 10000 depiction ends=20 getting modified eventually, it was not the specifics but the=20 generalities i had longed to actually envision. i have tried every way i know, armed with the "singing frog" and got no further than about 40 of them through russell towle, and what karl (the first 100) had = already given me. what did 117 look like for example or 411, did he have the right lower figures...i really cannot say much past the empirically generated ones i have made....1-13, and 15. perhaps i should try to make a few more so we can check the lower levels ? i could use karls = stuff and it would be much easier than before for me ? At last I'm able to go that last step: from having the vertices to getting the edges and faces. That was the bottleneck, but now I'm through it, thanks to Qhull, which is really very powerful. your are of infinite help...without you, i may never have gotten to see above say 30...and then not knowing if it were right. what a thrill ! i feel connected to each new one and marvel at what new trick it may come to teach.=20 question/muse/ how can i give credit/honor/respect/ to you for all your work and not sound as if i am also being an egomaniac about MY WATERMAN spheres = ? maybe personality isnt my best suit, but the PR is hard for me to straddle...I what should i say about others who might support some of my work ? (like that could happen after 10 years+) who do new tricks....how do i do this without others thinking i am some ego freak, who either does give credit to others or when others support = him, say that the world only revolves around him ? it sounds as if i need a strategy here, and just being a cool surfer = dude, hanging at the beach and laughing and having the occasional Ride is=20 not going to be good enough then. [1] A well-known document in internet circles -- pays to score yourself every so often: http://math.ucr.edu/home/baez/crackpot.html (my score varies with my mood -- off the scale on some days, even though I'm just a curriculum writer and don't have any revolutionary scientific theories of my own to offer). i just checked this site...and i laughed...cant wait to read this all ! this should be quite funny...i have read her work on=20 dimensionless constants. so, today i close...and it has been the most amazing week of my life . thanks thanks thanks. steve ------=_NextPart_000_002C_01C079AA.5DCA15A0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

kirby,

you wrote

OK, here's my=20 perspective:

Fuller never talking about either aba or abc in=20 precisely
those terms. He didn't call our sphere packing the = ccp=20 or
fcc either, because both those acronyms have "cube" in = them,
and he was=20 militating against our culture's cubic fixations.

i understand his objection.

For = him, the=20 place to start was with 12-around-1 in the
cuboctahedral conformation =

was does this mean ?

(not your only choice),

the others being ?

and to
pack outward in successive = layers: 12,=20 42, 92, 162... 10F^2+2.

i agree here.

Here were the numbers of vertices = in the=20 geodesic spheres,
the capsomeres in a viral protein sheath and so=20 on.

please rephrase or = restate.

Relevant to the atomic = nucleus? =20

not in my opinion.

Gosh, I couldn't tell you -- = some
stridently=20 assert that it is.

i am not trying to show you what others = think

in a way, i do not care.

i want to show you some = tricks.

I remain open = minded.

hey, = does any body=20 know how to wax a board ?

Fuller was well aware of the = square-grid and=20 triangular-grid
profiles, as is anyone who consistently studies the = ccp=20 using
the cuboctahedron as a starting point. Both grids are=20 readily
apparent on the faces. He shows both of these=20 cross-sections,
e.g. when talking about "chef's hats" -- two pieces = of=20 a
tetrahedron that fit together square-to-square, giving
a ccp = tetrahedron=20 -- people still find that surprising and it's
the basis for a popular = wood-block puzzle (build a tetrahedron
with just two pieces -- = surprising how=20 long it takes most people,
products of a cube culture, to solve=20 it).

what others know is always of interest = to me, as it=20 helps to have

a benchmark from which i can = attempt to judge=20 my position .

What I think is confusing about your take is you = seem=20 to
identify ccp with abc with not-xyz.

typo ?

I think this is because
when = you stack=20 your z-planes vertically, you're thinking this
is more strictly "xyz" = than=20 when you stack hexagons or what I
call triangular grids. =

please define triangular = grids.

But given both ways of layering =

so we agree that layering has two=20 forms.

go straight up the z axis (or can be = oriented that=20 way), I'm not
sure even this gets to the heart of = it.

the word 'it' is too vague ...please=20 restate

It's more that = you're
identifying the=20 square grid pattern with both "aba" and "xyz"
and the triangular grid = pattern=20 with "ccp" or, alternatively
"abc".

i believe that too be true...we need to = able to=20 speak the same

language. lets always try to focus on = getting a=20 singular word or phrase

that means the same thing to both of = us. i do not=20 care what that word is,

my word, your word, buckys word, other = peoples=20 word, or we make one up.

You put myself and Bucky in the = "ccp/abc" camp,=20 and
talk about your "aba" approach as an "alternative=20 mathematical
method".

not to be confused with an alternative = physical=20 approach.

That's confusing because the "Urner generator" is most=20 definitely
using XYZ coordinates to do all the = work.

you mean two different mathematical = methods (mine=20 and yours)

that yield the same physical BASE ?

But it's not really
using = "layering"=20 (either aba OR abc).

well i guess you do have a second = method then=20 ?

The whole idea of building
outward = in layers and=20 exhaustively tabulating the distance^2 to each
and every sphere is = what I=20 wanted to get away from.

and you have.

Instead, I start
with x as = high as=20 possible, and push inward, forcing y and z to pick
up the = slack,

whereas i would have picked z and = forced x and=20 y.

but to remain in "descending = sort" i.e.=20 x>=3Dy>=3Dz.

so why force on x then ?

doesnt this above equation then = become the=20 defining characteristic ?

Once
the unique solutions are found=20

my thinking here too was that we needed = to find=20 unique solutions,

but now that i get what you are doing a = bit better=20 a have some

better clarity on this = issue.

while it might appear that unique = solutions should=20 be required,

i should only be required to go to say = n-100 for=20 the 10000.

1/3 is WAY WAY too high.

i would imagine that taking fewer than=20 needed

might nor result in a full convex = hull but i=20 am guessing ?

(and you can stop when x^2 by = itself
can't even=20 get a 3rd of the way to D^2),

aha, this is why i wanted the n,n-1,n-2 = accumulating

i suggest you may only need up to n-100 = and this=20 should

work say up to even maybe 10000. = ?

but 1/3 is WAY too much.

the rest is handled=20 with
permutations. You could do all of the above with = z>=3Dy>=3Dx --=20 any order
of those three.

sounds good.

There's also the need to limit = x+y+z=3Deven in=20 order to disqualify non-ccp
positions (i.e. solutions not at the = centers of=20 ccp spheres, where the
spheres have root(2) diameter -- rescale at = the end of=20 the process if
you want to get back to the familiar sphere diameter = =3D 1, or=20 if you want
even smaller spheres so all the Watermans will fit in the = same=20 square
window on screen (I do this in the final step, using only = integers=20 up
to that point)). I'm not sure you've understood this = x+y+z=3Deven=20 business
yet. I think you're likely in a deep rut from having = thought=20 in the
same grooves all of these years -- kinda like yer average = fuddy-dud=20 (PhD).

you are replicating the physical, so = the math=20 works...

you say potato

i say patatoe...could dan qualye = have said=20 this ?

I credit Jim Morrissett for first showing me that an aba = layering=20 of
square grids _forces_ the ccp, whereas the triangular grid method=20

should we explore what the = triangular grid=20 method is ?

if so, what is it.

easily goes off the=20 rails into hcp

please do not ask question that are not = ccp=20 related.

or the random wilderness of more=20 generalized
Barlow packings.

are those ccp...you did not answer that = last time=20 if i remember right here ?

That's what I was chatting up with = Conway in=20 the
'Metal Clusters' thread on geometry-research some years back, and = that's
what I take up on http://www.teleport.= com/~pdx4d/sphpack.html=20 (mentions
Jim).

having trouble going here...no = comment.

I=20 credit Gerald de Jong for first showing me an algorithm similar = to
the "Urner=20 generator" -- one which took advantage of the built in
symmetries = (i.e.=20 didn't work too hard). He wrote it in Pascal and I don't
know = if I have=20 a copy anywhere. In any case, my Python generator is of
similar = design.

i guess we wont need it now...

I = credit you=20 for introducing me to the whole concept of Waterman polyhedra.
They = follow a=20 very simple rule, and yet offer variety and beauty.

they are of constant surprise to = me...who=20 knew.

Your mathematics, on the other hand, is somewhat "stone = age",=20 reminds me
of John Kurnalian's stuff -- the same algorithm worked = over and=20 over and
over with reams of data building up.

i glad that it happened this way, if i = had just got=20 the "take a radial sweep

thing...i would not have known that = there was=20 anything *special* going on.

That tends to scare people off = --
looks=20 too obsessive, too "I'm living in my own private world" -- more = like
Bucky's=20 "Numerology" pages.

perhaps i do live in my own private = word, thanks=20 for the company.

just =20 alert
you to what many consider a "red flag" (perhaps one of=20 many).[1]

any advice ? perhaps indeed, how do i = deal with=20 this ?

what should i do ? i can not control = what others=20 think of me,

and indeed, they have that right....is = there=20 something you would

recommend that i could tone down ? = how can=20 this be improved ?

I really really like the = Waterman polys and=20 all the math/thinking this
has inspired on my end over the=20 years.

me too, and while it is an obsession no = doubt, i=20 have other interests

and are not totally consumed by its=20 pull

Finally getting a convex = hull
algorithm into the=20 mix, even if it isn't in Python, was the = latest
breakthrough.

i have wanted to see these so much. i = have dreamed=20 of them,

and could but only imagine. when i saw = the 10000,=20 it was a

special moment for me. not an ego = moment, just to=20 known

what some of the upper r look = like....even if the=20 10000 depiction ends

getting modified eventually, it was not = the=20 specifics but the

generalities i had longed to actually = envision. i=20 have tried every way

i know, armed with the "singing frog" = and got no=20 further than about

40 of them through russell towle, and = what karl=20 (the first 100) had already given

me. what did 117 look like = for example=20 or 411, did he have

the right lower figures...i really = cannot say much=20 past the empirically

generated ones i have made....1-13, and = 15. perhaps=20 i should try to

make a few more so we can check the = lower levels ?=20 i could use karls stuff

and it would be much easier than = before for me=20 ?

At last I'm able to go that last = step: =20 from having the
vertices to getting the edges and faces. That = was the=20 bottleneck, but
now I'm through it, thanks to Qhull, which is really = very=20 powerful.

your are of infinite help...without = you, i may=20 never have gotten to see

above say 30...and then not knowing if = it were=20 right. what a thrill !

i feel connected to each new one and = marvel at what=20 new trick it

may come to teach.

question/muse/

how can i give credit/honor/respect/ to = you for all=20 your work and

not sound as if i am also being an = egomaniac=20 about MY WATERMAN spheres ?

maybe personality isnt my best suit, = but the PR is=20 hard for me

to straddle...I

what should i say about others = who might=20 support some of my work ?

(like that could happen after 10=20 years+)

who do new tricks....how do i do this = without=20 others thinking i am some

ego freak, who either does give credit = to others or=20 when others support him,

say that the world only revolves around = him=20 ?

it sounds as if i need a strategy here, = and just=20 being a cool surfer dude, hanging

at the beach and laughing and having = the occasional=20 Ride is

not going to be good enough = then.

[1] A well-known document in internet = circles --=20 pays to score yourself
    every so often: http://math.ucr.edu/= home/baez/crackpot.html=20 (my
    score varies with my mood -- off the scale on = some=20 days, even though
    I'm just a curriculum writer and = don't=20 have any revolutionary
    scientific theories of my = own to=20 offer).

i just checked this site...and i = laughed...cant=20 wait to read this all !

this should be quite funny...i have = read her work=20 on

dimensionless=20 constants.

so, today i close...and it has been the = most=20 amazing

week of my life . thanks thanks=20 thanks.

steve

------=_NextPart_000_002C_01C079AA.5DCA15A0-- ========================================================================= Date: Mon, 8 Jan 2001 20:11:56 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: urner generator > well, how about this: > whatever was the root-dystance for the *center*-to-corner > (of the cube), multiply it by root(1/3); > if any root(n-1) vertices are beyond that, > add them to the vertices of the hull, and > find the minimal width of *that* shape, and > do this over, again (using the new shape > as the basis for the new minimal width, > with its vertex-to-vertex (root(n-1)) dystance > being the largest dimeter). Easier just to hand Qhull a complete inventory of n, n-1 and n-2 vertices and have it do the shrink wrap. How exactly it does this is a "black box" for now. I've got the program running. Renderings to be on-line within a few minutes. Kirby ========================================================================= Date: Mon, 8 Jan 2001 20:22:29 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: using n, n-1, n-2 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_000B_01C079B0.B9453760" This is a multi-part message in MIME format. ------=_NextPart_000_000B_01C079B0.B9453760 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable kirby, by running the n, n-1, n-2 i suggest that a new pattern will develop... and be mathematically, eventually visually definable. ( they always have in the past ) we match the root number to the n, n-1, n-2 for the lower roots i suspect we have the pattern=20 both mathematically definable and physical definable in doing visual comparative analysis by as little as root 100. steve ------=_NextPart_000_000B_01C079B0.B9453760 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

kirby,

by running the n, n-1, n-2

i suggest that a new pattern will=20 develop...

and be mathematically, eventually = visually=20 definable.

( they always have in the past = )

we match the root number to = the

n, n-1, n-2 for the lower = roots

i suspect we have the pattern =

both mathematically = definable

and physical definable

in doing visual = comparative

analysis by as little as root = 100.

steve

------=_NextPart_000_000B_01C079B0.B9453760-- ========================================================================= Date: Mon, 8 Jan 2001 21:12:36 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: coordination of terms MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0011_01C079B7.BA3CD9A0" This is a multi-part message in MIME format. ------=_NextPart_000_0011_01C079B7.BA3CD9A0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable his dukeness, number 1 Ride man, i see=20 you have been practicing a bit...have you thought about the step-over, 1/2 twister, with=20 an inverted rad curl perhaps.... . the second class priduces both odds and evens, by going whole units in x and y directions, and ("n.5"(root(2)) in the z. (I trust, you saw that "n.5" means "n and a half" .-) so, their were waxed, and the day was getting longer but it did not matter, in a way, cause they were having=20 fun, and they all were smiling as today was one of those adventurous days... and it wouldnt be long before they gave a name for that step-over thingy that number one had performed. it was beauty, it was magnificent and the pain from his plant faded, and had even started to become his badge rather than his failure,=20 and he dreamed about the big waves.... could his board stand the big water, he thought for a second and felt that he maybe should get some more tricks first, for he was not = stupid and he had heard that the currents were not at the same as on the beach. that is what i have tried to do in the bottom of the right hand corner of the SYNERGIT page...the unit cell thingy. can you see it now ? it wanted to depict what number 1 has deduced. well done. i forgot that you dont know the coordination of ccp in aba. can this graphic be depicted better...hey, now there IS a stupid = question ? steve =20 ------=_NextPart_000_0011_01C079B7.BA3CD9A0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

his dukeness, number 1 Ride man, i see=20

you have been practicing a = bit...have =20 you

thought about the step-over, 1/2 = twister, with=20

an inverted rad curl = perhaps....

.
the second = class priduces=20 both odds and evens,
by going whole units in x and y = directions, and=20 ("n.5"(root(2))
in the z. (I trust, you saw that "n.5" = means "n=20 and a half" .-)

so, their were waxed, and the day was = getting=20 longer

but it did not matter, in a way, cause = they were=20 having

fun, and they all were smiling as = today was=20 one of those

adventurous days...

and it wouldnt be long before they gave = a name for=20 that step-over

thingy that number one had performed. = it was=20 beauty, it

was magnificent and the pain from his = plant faded,=20 and had even

started to become=20 his badge rather than his failure,

and he dreamed about the = big waves....

could his board stand the big water, he = thought for=20 a second

and felt that he maybe should get some = more tricks=20 first, for he was not stupid

and he had heard that the currents were = not at the=20 same as on the beach.

that is what i have tried to do in = the =20 bottom of the right hand corner

of the SYNERGIT page...the unit cell=20 thingy.

can you see it now ?

it wanted to depict what number 1 has=20 deduced. well done.

i forgot that you dont know the = coordination of ccp=20 in aba.

can this graphic be depicted = better...hey, now=20 there IS a stupid question ?

steve

------=_NextPart_000_0011_01C079B7.BA3CD9A0-- ========================================================================= Date: Mon, 8 Jan 2001 11:30:26 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: bcc poof <> Brian �Quincy! Hutchings 08-JAN-2001 11:30 r001806@pen2.ci.santa-monica.ca.us since the root(2) set of (6) spheres (in octahedral formation) are centered on an octahedral void, they are not in the same CCPacking as the 12-around-1 (of Bucky, Kepler and the dyspicable Newton); the opposite spheres are root(2) away from each-other, on their centers, but only half of that from "the" center (the barycenter). that is to say, root(2)/2 or root(2/4) or root(1/2) (note that it is sometimes easier to deal with, if one avoids "simplifying" roots to get a rational denominator, and the same goes for complex denominators being "simplified" .-) OK, so, what does that make Steve's "packing" into?... it is readily dyscernable with the simples drawing (of the square array). --(zero bp (tm) [*]) Oil Platform 2000!... The Three Phases of Exploitation of the Protocols of the Elders of Kyoto (sik): fossilisation (sic)/ bore/gush/nadir @ http://www.tarpley.net/29crash.htm ; http://www.tarpley.net/bushb.htm (Copyr.92 by EIR, partial contents): INTRODUCTION: An American Caligula? (47K) 8 -- THE PERMIAN BASIN GANG (64K) 17 -- THE ATTEMPTED COUP D'ETAT OF MARCH 30, 1981 (87K) 18 -- IRAN-CONTRA (140K) 19 -- THE LEVERAGED BUYOUT MOB (67K) 20 -- THE PHONY WAR ON DRUGS (26K) 21 -- OMAHA (25K) 22 -- BUSH TAKES THE PRESIDENCY (112K) 23 -- THE END OF HISTORY (168K) 24 -- THE NEW WORLD ORDER (255K) 25 -- THYROID STORM (139K) EPILOG: Shag U.S. with a Spoon, Austin Powers? (0K) * In April, with the fanfare of a "beyond petroleum" campaign, bp (tm) merged with Arco (as with Amoco and Castrol, before) to become the USAs #1 dystributor of gasoline and motor-oil; in May, the price of "petrol" almost doubled. Things that make y'go, Hm; hm?... Merged with Internet Time, say, our lordships have provided a Year Zero, 2000 Cce (whereby, 1999 becometh 1bbp or some nasty thing .-) ========================================================================= Date: Mon, 8 Jan 2001 21:27:59 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: some guts MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_000D_01C079B9.E0668660" This is a multi-part message in MIME format. ------=_NextPart_000_000D_01C079B9.E0668660 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable have you seen these yet ? http://www.dsuper.net/%7Etinom/ph2000/COORDDET.html http://www.dsuper.net/%7Etinom/ph2000/COORDINA.html http://www.dsuper.net/%7Etinom/ph2000/DISTANCE.html http://www.dsuper.net/%7Etinom/ph2000/RADIAL.html http://www.dsuper.net/%7Etinom/ph2000/VIRUSES.html http://www.dsuper.net/%7Etinom/ph2000/PYRANG.html steve http://www.dsuper.net/%7Etinom/ph2000/14VECTOR.html ------=_NextPart_000_000D_01C079B9.E0668660 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

have you seen these yet ?

http://www.d= super.net/%7Etinom/ph2000/COORDDET.html

http://www.d= super.net/%7Etinom/ph2000/COORDINA.html

http://www.d= super.net/%7Etinom/ph2000/DISTANCE.html

http://www.dsu= per.net/%7Etinom/ph2000/RADIAL.html

http://www.ds= uper.net/%7Etinom/ph2000/VIRUSES.html

http://www.dsu= per.net/%7Etinom/ph2000/PYRANG.html

steve

http://www.d= super.net/%7Etinom/ph2000/14VECTOR.html

------=_NextPart_000_000D_01C079B9.E0668660-- ========================================================================= Date: Mon, 8 Jan 2001 21:48:24 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: totally coordinated ? MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_001B_01C079BC.BA2B8240" This is a multi-part message in MIME format. ------=_NextPart_000_001B_01C079BC.BA2B8240 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable i did not ( i think ) place my abc distance masters, on the site as i felt that the aba was better suited for xyz coordination and so called it method 1 and put in on my site. even though i had actually done all the abc manually to 1000 first. and only did the aba...to a few hundred i guess. the mathematics for method 2 ...the abc...has NO Cartesian=20 equivalent. i have HEXED sided masters for the abc. the abc has two versions, sphere centered and void centered. in the 2d plane, a predictable distancing scheme can be worked out. and although this results itself is not a root integer, it is ( if i = remember n + 1/3 or +2/3...have to check etc. however, since the vertical component all have n + 1/3 or +2/3 then the integer returns. in order to accomplish this, i used a "P, L ,V method which obviously=20 will need to be shown to you in detail. the aba in ccp, likewise has two versions....and every other parallel row repeats.....which means they line up as per coordination. steve ------=_NextPart_000_001B_01C079BC.BA2B8240 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

i did not ( i think ) place my = abc distance=20 masters,

on the site as i felt that the aba was = better=20 suited for

xyz coordination and so called it = method 1 and put=20 in on my site.

even though i had actually done all the = abc=20 manually to 1000 first.

and only did the aba...to a few hundred = i=20 guess.

the mathematics for method = 2 ...the abc...has NO Cartesian

equivalent. i have HEXED = sided masters=20 for the abc.

the abc has two versions, sphere = centered and void=20 centered.

in the 2d plane, a predictable = distancing scheme=20 can be worked out.

and although this results itself is not = a root=20 integer, it is ( if i remember

n + 1/3 or +2/3...have to check = etc.

however, since the vertical component = all have n +=20 1/3 or +2/3 then

the integer returns.

in order to accomplish this, i = used a "P, L ,V=20 method which obviously

will need to be shown to you in=20 detail.

the aba in ccp, likewise has two = versions....and=20 every other parallel

row repeats.....which means they line = up as per=20 coordination.

steve

------=_NextPart_000_001B_01C079BC.BA2B8240-- ========================================================================= Date: Mon, 8 Jan 2001 12:02:46 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: bcc poof <> Brian �Quincy! Hutchings 08-JAN-2001 12:02 r001806@pen2.ci.santa-monica.ca.us wow, the Waterman Projection; let me guess: it's projected onto a tetrakis octahedron. (of course, Canada is at the top of the map, and it's only available in Canadian dollars (pounds?) !-) anyway, I looked at your root(2) picture, and I don't know why I thought that it was just 6 spheres, together -- kissing. the hull is an octahedron, though. everything I say?... it means the oppposite, but we'll get through this mystaque, soon enough. I intend to find those missing numbers, but maybe *after* I sue the City etc. here's the first part of the program, though: using the "spheres-into-spaces-into-spheres" model, we investigate the various void(s) as a sort(s) of dual. as I recall, the spheres (cuboctohedra in the model) turn into octahedral voids. so, look at the array that is centered on that void (this has a lot to do with what Kirby was noting about interpenetrating IVMs; you have to consider the cuboctahedra with a vertex at the center). if that is uninspiring, we try the other void(s). --(zero bp (tm) [*]) Oil Platform 2000!... The Three Phases of Exploitation of the Protocols of the Elders of Kyoto (sik): fossilisation (sic)/ bore/gush/nadir @ http://www.tarpley.net/29crash.htm ; http://www.tarpley.net/bushb.htm (Copyr.92 by EIR, partial contents): INTRODUCTION: An American Caligula? (47K) 8 -- THE PERMIAN BASIN GANG (64K) 17 -- THE ATTEMPTED COUP D'ETAT OF MARCH 30, 1981 (87K) 18 -- IRAN-CONTRA (140K) 19 -- THE LEVERAGED BUYOUT MOB (67K) 20 -- THE PHONY WAR ON DRUGS (26K) 21 -- OMAHA (25K) 22 -- BUSH TAKES THE PRESIDENCY (112K) 23 -- THE END OF HISTORY (168K) 24 -- THE NEW WORLD ORDER (255K) 25 -- THYROID STORM (139K) EPILOG: Shag U.S. with a Spoon, Austin Powers? (0K) * In April, with the fanfare of a "beyond petroleum" campaign, bp (tm) merged with Arco (as with Amoco and Castrol, before) to become the USAs #1 dystributor of gasoline and motor-oil; in May, the price of "petrol" almost doubled. Things that make y'go, Hm; hm?... Merged with Internet Time, say, our lordships have provided a Year Zero, 2000 Cce (whereby, 1999 becometh 1bbp or some nasty thing .-) ========================================================================= Date: Mon, 8 Jan 2001 21:54:22 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: octrahedral void MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_002B_01C079BD.8F6C6780" This is a multi-part message in MIME format. ------=_NextPart_000_002B_01C079BD.8F6C6780 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable since the root(2) set of (6) spheres (in octahedral formation) are centered on an octahedral void, they are not in the same CCPacking as the 12-around-1 (of Bucky, Kepler and the dyspicable Newton); what is an octrahedral void ? steve ------=_NextPart_000_002B_01C079BD.8F6C6780 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

since the root(2) set of (6) = spheres
(in=20 octahedral formation) are centered on an octahedral void,
they = are not=20 in the same CCPacking as the 12-around-1
(of Bucky, Kepler and = the=20 dyspicable Newton);

what is an octrahedral void = ?

steve

------=_NextPart_000_002B_01C079BD.8F6C6780-- ========================================================================= Date: Mon, 8 Jan 2001 12:40:21 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: bcc poof <> Brian �Quincy! Hutchings 08-JAN-2001 12:40 r001806@pen2.ci.santa-monica.ca.us the void is the "empty" space that's surrounded by 6 spheres; it can be defined with ... wait a second; that'd be a cubical void, perhaps, but not in Bucky's terms!... I guess, an octahedral void would be between *4* spheres (it has 4 concave and 4 flat (but curved-edged) trigonal facets; heh-heh); doesn't Bucky call the ones that are between the 6 spheres, cuboctahedral spaces (6 concave tetragonal facets and 8 flat trigonal ones [the flat ones just cut-through the space, as it were, like soft cheese]). I never had much use for this stuff, before this! thus quoth: what is an octrahedral void ? sorry about dyssing the Second (British) Church of Christ, Issac, dude, but he was n a s t y ! --The Duke of Oil! http://www.tarpley.net/bush8.htm ========================================================================= Date: Mon, 8 Jan 2001 22:42:10 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: octrahedral voids IVM MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0046_01C079C4.3CBF6120" This is a multi-part message in MIME format. ------=_NextPart_000_0046_01C079C4.3CBF6120 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable wow, the Waterman Projection; let me guess: it's projected onto a tetrakis octahedron. the names again..sorry not very together here at all. if that is root 5 too, then it is. i view waterman solids volumetrically as, a combination of tets and octas.=20 for me, the voids relate to aba or abc. (of course, Canada is at the top of the map, are you suggesting canada be put elsewhere on the map...i suspect you have many of us here=20 musing now on this ....equatorial maybe ? and it's only available in Canadian dollars (pounds?) !-) although, there are over 4000 left of the 5000 paul had made over 4 years ago, he is now is the Turks and Cacaos, he called last week after not hearing from him quite a while,=20 and i asked if i could have 10 or 20 of them as i wanted to give some away. when i called in montreal later, i could not find hippolito, where the maps where, and=20 was told there was nobody on the island of montreal=20 with his last name. starting to muse here. as I recall, the spheres (cuboctohedra in the model) turn into octahedral voids. so, look at the array that is centered on that void=20 please show it to me. (this has a lot to do with what Kirby was noting about interpenetrating IVMs; you have to consider the cuboctahedra with a vertex at the center). i am still very confused here....any pictures of interpenetrating IVMs if that is uninspiring, we try the other void(s). how many are there in all...still can not get the terminology here. what are you trying to do that you need this information ? what information are you looking for here ? steve =20 ------=_NextPart_000_0046_01C079C4.3CBF6120 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

wow, the Waterman Projection; let me=20 guess:
it's projected onto a tetrakis octahedron.

the names again..sorry not very = together here at=20 all.

if that is root 5 too, then it = is.

i view waterman solids volumetrically = as, a=20 combination

of tets and octas.

for me, the voids relate to aba = or=20 abc.

(of course,
Canada is at = the top of=20 the map,

are you suggesting canada be put=20 elsewhere

on the map...i suspect you have many of = us here=20

musing now on this ....equatorial maybe = ?

and
it's only available = in Canadian=20 dollars (pounds?) !-)

although, there are over 4000 left of = the 5000 paul=20 had made

over 4 years ago, he=20 is now is the Turks and Cacaos, he called

last week after not hearing from him = quite a while,=20

and i asked if i could have 10 or 20 of = them

as i wanted to give some away. when i = called in=20 montreal later,

i could = not find hippolito, where=20 the maps where, and

was told there was nobody on the island = of=20 montreal

with his last name. starting to muse=20 here.

as I recall, the = spheres=20 (cuboctohedra in the model) turn
into octahedral voids. =20 so,
look at the array that is centered on that void =

please show it to me.

(this has a lot
to do with = what Kirby was=20 noting about interpenetrating IVMs;
you have to consider the=20 cuboctahedra with a vertex at the center).

i am still very confused here....any = pictures of=20 interpenetrating IVMs

if that is uninspiring, we try the = other=20 void(s).

how many are there in all...still can = not get the=20 terminology here.

what are you trying to do that you need = this=20 information ?

what information are you looking for = here=20 ?

steve

------=_NextPart_000_0046_01C079C4.3CBF6120-- ========================================================================= Date: Mon, 8 Jan 2001 23:20:14 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: is still a rose MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0016_01C079C9.8E106380" This is a multi-part message in MIME format. ------=_NextPart_000_0016_01C079C9.8E106380 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable brian, I guess, an octahedral void would be between *4* spheres that is my octa, as i thought kirby called it...or a 1/2 octahedron as i thought he also calls it, i myself have always called it a square = based pyramid what shall we call it ? (it has 4 concave and 4 flat (but curved-edged) trigonal facets; heh-heh);=20 i will take your word, never mused on it. doesn't Bucky call the ones that are between the 6 spheres, cuboctahedral spaces (6 concave tetragonal facets and 8 flat trigonal ones [the flat ones just cut-through the space, as it were, like soft cheese]). try kirby...i bet he knows. I never had much use for this stuff, before this! sorry about dyssing the Second (British) Church of Christ, Issac, dude, but he was n a s t y ! is that how you spell it ? another plant for me. dont worry...he is on the list, he too might want a Ride. but this dude could surf, he had a board he made from wood carved from an appletree. he did the twisty thing long before they were cool enough at the beach to even know about making up names. making up names, changes nothing, the underlying physical reality=20 remains whether you can mathematically or physically quantify it. for example, if you do not measure time does it occur ? and other such nonsensical semantic mind voyages. where to muse...where to focus...what=20 is basic...what is outgrowth of the basic....what is the sub-basic ? a sub - basic is for example....sub divide the tet into logical pieces. so, sub-divide the square based pyramid into its logical pieces too. you could mathematically, though not physically sub divide the=20 unit cell into its sub-basics...or the RD, or go up the polygon=20 food chain, and sub divide. and you could call them all special names for the left 1/2 or for inverted or if aba based but hcp and i do not care=20 about any sub-basics nor do i wish to try and remember=20 all their names and take a plant when i cannot remember=20 what a thing is technically called by society at large or a specific specialized interest group. i do not want to sound overly obsessive here, i do not have a great memory and this is not one of my better skills. i am better suited to finding mathematical and physical patterns, concepts..and not words...names are fine...but only when the mean the same thing to all parties involved. steve ------=_NextPart_000_0016_01C079C9.8E106380 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

brian,

I guess, an octahedral void = would be=20 between *4* spheres

that is my octa, as i thought kirby = called it...or=20 a 1/2 octahedron as

i thought he also calls it, i myself = have always=20 called it a square based pyramid

what shall we call it ?

(it has 4 concave and 4 flat = (but=20 curved-edged) trigonal facets;
heh-heh);

i will take your word, never mused on=20 it.

doesn't Bucky call the ones that are = between the 6=20 spheres,
cuboctahedral spaces (6 concave tetragonal facets=20 and
8 flat trigonal ones [the flat ones just cut-through the=20 space,
as it were, like soft cheese]).

try kirby...i bet he = knows.

I never had much = use for=20 this stuff, before this!

sorry about dyssing the Second = (British) Church=20 of Christ, Issac,
dude, but he was n a s t y = !

is that how you spell it ? another = plant for=20 me.

dont worry...he is on the list, he too = might want a=20 Ride.

but this dude could surf, he had a = board he made=20 from

wood carved from an appletree. he did = the twisty=20 thing

long before they were cool enough at = the beach to=20 even

know about making up = names.

making up names,

changes nothing, the underlying = physical reality=20

remains whether you can mathematically = or=20 physically

quantify it. for example, if you = do not=20 measure time

does it occur ? and other such = nonsensical=20 semantic

mind voyages. where to muse...where to = focus...what=20

is basic...what is outgrowth of the = basic....what=20 is the sub-basic ?

a sub - basic is for example....sub = divide the tet=20 into logical pieces.

so, sub-divide the square based pyramid = into its=20 logical pieces too.

you could mathematically, though not = physically sub=20 divide the

unit cell into its sub-basics...or the = RD, or go up=20 the polygon

food chain, and sub = divide.

and you could call them all special = names for=20 the

left 1/2 or for inverted or if aba = based but hcp=20 and i do not care

about any sub-basics nor do i wish to = try and=20 remember

all their names and take a plant when i = cannot=20 remember

what a thing is technically called by = society at=20 large or

a specific specialized interest group. = i do not=20 want to sound

overly obsessive here, i do not have a = great memory=20 and this

is not one of my better skills. i am = better suited=20 to finding

mathematical and physical patterns, = concepts..and=20 not

words...names are fine...but only when = the mean the=20 same

thing to all parties = involved.

steve

------=_NextPart_000_0016_01C079C9.8E106380-- ========================================================================= Date: Mon, 8 Jan 2001 22:01:10 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Lee Bonnifield Subject: Re: urner generator MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit [Kirby] So it has come flooding back to me now, while Steve has been out walking and losing his internet linkup: if you take the root(n) ccp spheres as your outermost, you're still going to pick up some root(n-1) spheres when doing the shrink wrap, i.e. these will be among those Qhull sees as relevant to the convexity. Question: will root(n-2) spheres ever show up as "outermost" as well? [Lee] I think you need to draw edges and faces considering only the root(n) spheres, and then find the center of the largest face. That point will be the deepest possible on a convex surface, so if its depth is root(n-m) then you never need to look deeper than n-m. ========================================================================= Date: Mon, 8 Jan 2001 21:18:45 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: touching BASE In-Reply-To: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" >> = Kirby > = Steve = Kirby >> For him, the place to start was with 12-around-1 in the >> cuboctahedral conformation > was does this mean ? It means 12 spheres at the vertices of a cuboctahedron, around a nuclear sphere in the middle. >> (not your only choice), > the others being ? The other choice is to have the top 3 spheres line up with the bottom 3, with a hexagonal sandwich layer in the middle. It's still 12-around-1, but it's not the cuboctahedron. >> and to pack outward in successive layers: 12, 42, 92, >> 162... 10F^2+2. > i agree here. >> Here were the numbers of vertices in the geodesic spheres, >> the capsomeres in a viral protein sheath and so on. > please rephrase or restate. A geodesic sphere has 10*f^2+2 hubs if based on the f-frequency icosahedron. Many viruses have this same structure. >> What I think is confusing about your take is you seem to >> identify ccp with abc with not-xyz. > typo ? No >> I think this is because >> when you stack your z-planes vertically, you're thinking this >> is more strictly "xyz" than when you stack hexagons or what I >> call triangular grids. > please define triangular grids. I mean spheres in a layer where every sphere is surrounded by 6 others, unless on an edge. Like this: * * * * * * * * * * * * * * * (won't look so good if you're viewing in a proportionally spaced font -- but you get the idea). Have you ever looked at my http://www.teleport.com/~pdx4d/sphpack.html ? I keep mentioning it. The opening paragraphs should make this all clear. >> But given both ways of layering > so we agree that layering has two forms. In the ccp, you have triangular grid layering and square grid layering, yes. >> go straight up the z axis (or can be oriented that way), I'm not >> sure even this gets to the heart of it. > the word 'it' is too vague ...please restate "It" refers to the distinction you seem to want to make between your method and what you call the ccp method. > not to be confused with an alternative physical approach. I don't understand your whole "mathematical" versus "physical" distinction very well. Do you mean that it's easier to rescale things in the imagination, or on paper, versus building sphere packings where the spheres physically change diameter (as by inflating/deflating?). That's true, but you _could_ build physical models that demonstrated the operations I'm talking about. >> That's confusing because the "Urner generator" is most definitely >> using XYZ coordinates to do all the work. > you mean two different mathematical methods (mine and yours) > that yield the same physical BASE ? What's a BASE? >> Instead, I start with x as high as possible, and push >> inward, forcing y and z to pick up the slack, > whereas i would have picked z and forced x and y. x,y or z it doesn't matter. >> but to remain in "descending sort" i.e. x>=y>=z. > so why force on x then ? It's just that one of the three needs to start high and ratchet downward, while the others see what they can do to hit the root distance. But since (3,2,1) is the same as (2,3,1) and (1,2,3) and (3,1,2) when it comes to distance, you don't want to end up finding them all (let alone the negative signed permutes). Just find (3,2,1) and then swap the digits around every way possible. By enforcing x>=y>=z, I'm saying I only need to find (3,2,1). > while it might appear that unique solutions should be required, > i should only be required to go to say n-100 for the 10000. > 1/3 is WAY WAY too high. Earlier, I was only computing vertices for n, not even n-1. I wasn't getting true Watermans, but what you and Russell call JanetJulians. Now I understand about picking up all vertices that would make a difference, i.e. be part of a shrink-wrapping. Anyway, the "coming down from x = root(N)" in the above algorithm shouldn't be confused with N itself coming down. Now that I have remembered what a true Waterman is, I'm wondering how many Ns I need to compute. If I just do N, N-1 and N-2, am I going to hit all the vertices in the shrink-wrap? Do you have examples where I'd need to go even deeper? > aha, this is why i wanted the n,n-1,n-2 accumulating > i suggest you may only need up to n-100 and this should > work say up to even maybe 10000. ? > but 1/3 is WAY too much. Not really. Think of a case where the root^2 = 10^2 + 9^2 + 9^2. I wouldn't want to stop before getting down to 10^2. You're confusing the x-coordinate with N itself, where N = root^2. > you are replicating the physical, so the math works... > you say potato i say patatoe...could dan qualye have > said this ? I'm explaining a recipe, how to make something, how to build a working machine. It's not what you *say*, but what you *do* (or don't do). > should we explore what the triangular grid method is ? > if so, what is it. That's starting with spheres packed hexagonally. You have triangles in your layer, versus squares. It's characteristic of 8 of the 14 faces of the cuboctahedron, as you pack out to higher and higher frequency. >> easily goes off the rails into hcp > please do not ask question that are not ccp related. Not a question... Again, if you have 12-around-1, you have 8 triangles and 6 squares. If you rotate one of those triangles, you no longer have a cuboctahedron -- and you are no longer doing ccp (but you still have all the same parallels -- you have layers packing in multiple parallel directions -- 4 triangular grid axes and 3 square grid axes. >> or the random wilderness of more generalized >> Barlow packings. > are those ccp...you did not answer that last time if > i remember right here ? The ccp is one of an infinite variety of Barlow packings with the same density. But you don't want to know about them. But the way to get to a lot of them is to layer the trianglar grids on top of each other, but randomly, so sometimes you're doing aba and sometimes you're doing abc. Obviously there's any number of permutations, given a deep enough packing. And yet that's _still_ not all the possible Barlow packings. Please don't ask me any more questions about what I mean by "square grid" versus "triangular grid" until you've read http://www.teleport.com/~pdx4d/sphpack.html > so, today i close...and it has been the most amazing > week of my life . thanks thanks thanks. S'been fun for me too. I've got some of the true Watermans on display by now, at http://www.inetarena.com/~pdx4d/ocn/wgraphics.html I'd like to see those Mathematica depictions of the higher N Watermans now, so I can compare results. I'm also comparing my "fixed radius" guys with the janetjulians at your site. Basically, I've tweeked my algorithm to put out wmN.pov or frN.pov, e.g. wm10.pov would be Waterman 10 (i.e. root(10)) and fr10.pov would be Fixed Radius 10 (i.e. janetjulian 10). The Watermans automatically have a black background, while the fixed radius ones have a white background -- to help me tell them apart (which version of the algorithm worked on them). The Waterman algorithm (behind the wm*.pov) files, computes all the vertices at N, N-1 and N-2 and tosses these to Qhull, which automatically figures out which of all these vertices actually participate in a shrink-wrapping convex hull. Do you think I need to compute deeper than N-2? It seems to me that those deeper spheres would have a hard time "poking through" if we've already got the Ns, N-1s and N-2s covered. Do they ever? How many colors did you use in your physical models? Kirby ========================================================================= Date: Tue, 9 Jan 2001 00:31:45 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: lee returns MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0037_01C079D3.8BD498C0" This is a multi-part message in MIME format. ------=_NextPart_000_0037_01C079D3.8BD498C0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable dude, beach party. grab a board, kirby has wax, brian is trying out his new double fin. i heard you were at JAC's i think it was .... are they still open any more ? didnt i hear something about that place ? just wasnt big enough to handle all the people or something? brian said something about working his wax with you,=20 are you still doing the waves behind JAC's ?=20 you should forget them dudes,=20 the wind has been blowing in good around here for days,=20 and i dont think it will let up for a little while, who knows. are you up to a few Rides ? i hear you were talking about maybe trimming some edge ? steve ------=_NextPart_000_0037_01C079D3.8BD498C0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

dude, beach party.

grab a board, kirby has wax, brian is = trying out=20 his new double fin.

i heard you were at JAC's i think it = was=20 ....

are they still open any more = ?

didnt i hear something about that place = ?

just wasnt big=20 enough to handle all the people or something?

brian said something about working his = wax with=20 you,

are you still doing=20 the waves behind JAC's ?

you should forget them dudes, =

the wind has been=20 blowing in good around here for days,

and i dont think it will let = up for a=20 little while, who knows.

are you up to a few Rides = ?

i hear you were talking about maybe = trimming some=20 edge ?

steve

------=_NextPart_000_0037_01C079D3.8BD498C0-- ========================================================================= Date: Tue, 9 Jan 2001 00:49:33 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: terms MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_004D_01C079D6.0886FB40" This is a multi-part message in MIME format. ------=_NextPart_000_004D_01C079D6.0886FB40 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable kirby, thank you for this line of questioning.=20 i too feel odd writing in this (efficient ? style ) myself but it is really getting a whole easier now...until we get through this terms part, it should remain a bit confusing to all of us. so we have a few more to go, these are just terms.... we can almost talk the same language. soon i hope. i will answer back tomorrow. ------=_NextPart_000_004D_01C079D6.0886FB40 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

kirby,

thank you for this line of questioning. =

i too feel odd writing in this = (efficient ?=20 style ) myself

but it is really getting a whole easier = now...until=20 we get through

this terms part, it should remain a bit = confusing=20 to all of us.

so we have a few more to go, these are = just=20 terms....

we can almost talk the same language. = soon i=20 hope.

i will answer back = tomorrow.

------=_NextPart_000_004D_01C079D6.0886FB40-- ========================================================================= Date: Tue, 9 Jan 2001 01:24:00 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: True Watermans at last? >Do you think I need to compute deeper than N-2? It seems to >me that those deeper spheres would have a hard time "poking >through" if we've already got the Ns, N-1s and N-2s covered. >Do they ever? How many colors did you use in your physical >models? > >Kirby Well, I'm starting to get some answers here. Check: http://www.inetarena.com/~pdx4d/ocn/wgraphics1.html Here at least we're starting to get some true Watermans, or so I suppose. I'm so far showing the 25, 53, 117, 150. On the 150, some of the N-3 spheres are participating in the hull! I go ahead and compute to N-4 now, and none of those are showing up (they'd be yellow). But maybe if I go out further they will (in which case I'll need to compute N-5 and so on). Note: Your JanetJulian 25 at http://www.dsuper.net/%7Etinom/ph2000/JJ25.html is actually Waterman 25. The corresponding fixed radius thing (JJ) is shown on http://www.inetarena.com/~pdx4d/ocn/wgraphics3.html And whereas your JJ150 is correct (or matches mine at least): http://www.dsuper.net/%7Etinom/ph2000/JJ150.html ...it's actually the corresponding Waterman minus some vertices of W149 (white), W148 (green), and W147 (blue)! Do you think this could be right? I have a lot of confidance in Qhull and my algorithm at this point. Kirby ========================================================================= Date: Tue, 9 Jan 2001 02:49:10 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: series of series MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0009_01C079E6.BDF59080" This is a multi-part message in MIME format. ------=_NextPart_000_0009_01C079E6.BDF59080 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable normally the ways things happens in ccp having aba analysis is that=20 first you generate=20 the n-1....and usually by the fifth=20 element/hit/good/acceptable/equal you can already determine the whole series. then what normally will happen, ( and so probably will this time too ) is get the first 5 n-2 series and determine it. when you get the 5 n-3 series. bingo. now you have a series of series. and usually, with that, you have them all. steve ------=_NextPart_000_0009_01C079E6.BDF59080 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

normally the ways things happens in=20 ccp

having aba analysis is that =

first you generate

the n-1....and usually by the fifth =

element/hit/good/acceptable/equal

you can already determine the whole=20 series.

then what normally will happen, ( and=20 so

probably will this time too ) is get=20 the

first 5 n-2 series and determine = it.

when you get the 5 n-3 series. = bingo.

now you have a series of = series.

and usually, with that, you have them=20 all.

steve

------=_NextPart_000_0009_01C079E6.BDF59080-- ========================================================================= Date: Tue, 9 Jan 2001 04:05:01 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: almost final terms MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0023_01C079F1.56EFA8C0" This is a multi-part message in MIME format. ------=_NextPart_000_0023_01C079F1.56EFA8C0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable >> =3D Kirby > =3D Steve =3D Kirby >> For him, the place to start was with 12-around-1 in the >> cuboctahedral conformation for me, i call it root 1. =20 It means 12 spheres at the vertices of a cuboctahedron, around a nuclear sphere in the middle .........................................................................= ....... The other choice is to have the top 3 spheres line up with the bottom 3, with a hexagonal sandwich layer in the middle. It's still 12-around-1, but it's not the cuboctahedron. isnt that what hcp is ? .........................................................................= ......... >> and to pack outward in successive layers: 12, 42, 92, >> 162... 10F^2+2. > i agree here. >> Here were the numbers of vertices in the geodesic spheres, >> the capsomeres in a viral protein sheath and so on. > please rephrase or restate. A geodesic sphere has 10*f^2+2 hubs if based on the f-frequency icosahedron.=20 interesting. thanks for the input. Many viruses have this same structure. i must disagree here. this is a physical issue, not a mathematical issue. .........................................................................= ................................ >> What I think is confusing about your take is you seem to >> identify ccp with abc with not-xyz. > typo ? No >> I think this is because >> when you stack your z-planes vertically, you're thinking this >> is more strictly "xyz" than when you stack hexagons or what I >> call triangular grids. > please define triangular grids. I mean spheres in a layer where every sphere is surrounded by 6 others, unless on an edge. Like this: * * * * * * * * * * * * * * * (won't look so good if you're viewing in a proportionally spaced font -- but you get the idea). oh...you mean abc ? .........................................................................= ......................... Have you ever looked at my http://www.teleport.com/~pdx4d/sphpack.html ? yes, i have seen it. I keep mentioning it.=20 The opening paragraphs should make this all clear. and i agree. i calculate that ratio of an inscribed sphere=20 having a unit (1) diameter divided by the RD volume=20 its your picture on my synergetics page (since ccp is replicatable by the RD). poof..there goes the fuzzy container=20 boundary. .........................................................................= ... >> But given both ways of layering > so we agree that layering has two forms. In the ccp, you have triangular grid layering and square grid layering, yes. >> go straight up the z axis (or can be oriented that way), I'm not >> sure even this gets to the heart of it. of what ? > the word 'it' is too vague ...please restate "It" refers to the distinction you seem to want to make between your method and what you call the ccp method. what are you referring to as my method ? .........................................................................= ........ > not to be confused with an alternative physical approach. I don't understand your whole "mathematical" versus "physical" distinction very well.=20 it is the first bridge to sail under. .........................................................................= ........... Do you mean that it's easier to rescale things in the imagination, or on paper, versus building sphere packings where the spheres physically change diameter (as by inflating/deflating?). great question. ccp has spheres of unit diameter one.=20 this never changes. so no inflating/deflating. that would never happen in ccp. .........................................................................= ............. i think there may be more left undone here ? .........................................................................= ........ That's true, but you _could_ build physical models that demonstrated the operations I'm talking about. why not. but i am only interested here in the mathematics of ccp. .........................................................................= ........................... >> That's confusing because the "Urner generator" is most definitely >> using XYZ coordinates to do all the work. > you mean two different mathematical methods (mine and yours) > that yield the same physical BASE ? What's a BASE? THE data BASE....ALL the spheres, all the coordinates, all the distances, all the angles, all the volumes, and then all its tricks. that is you kirby...you are BASE. you are working on aba now...will still need to do abc too ! .........................................................................= .. >> Instead, I start with x as high as possible, and push >> inward, forcing y and z to pick up the slack, > whereas i would have picked z and forced x and y. x,y or z it doesn't matter. perhaps not in a Cartesian 1 x 1 x 1 system... is ithis still the same for the aba of ccp since it is 1 x 1 x root 2 ? .........................................................................= ..... >> but to remain in "descending sort" i.e. x>=3Dy>=3Dz. > so why force on x then ? It's just that one of the three needs to start high and ratchet downward, while the others see what they can do to hit the root distance. But since (3,2,1) is the same as (2,3,1) and (1,2,3) and (3,1,2) when it comes to distance, you don't want to end up finding them all (let alone the negative signed permutes). Just find (3,2,1) and then swap the digits around every way possible. By enforcing x>=3Dy>=3Dz, I'm saying I only need to find (3,2,1). i think that may be the same issue. > while it might appear that unique solutions should be required, > i should only be required to go to say n-100 for the 10000. > 1/3 is WAY WAY too high. Earlier, I was only computing vertices for n, not even n-1. I wasn't getting true Watermans, but what you and Russell call JanetJulians. Now I understand about picking up all vertices that would make a difference, i.e. be part of a shrink-wrapping. cool, thanks for the feedback. .........................................................................= ...... Anyway, the "coming down from x =3D root(N)" in the above algorithm shouldn't be confused with N itself coming down. Now that I have remembered what a true Waterman is, I'm wondering how many Ns I need to compute. If I just do N, N-1 and N-2, am I going to hit all the vertices in the shrink-wrap? Do you have examples where I'd need to go even deeper? i think that is where we are now ? > aha, this is why i wanted the n,n-1,n-2 accumulating > i suggest you may only need up to n-100 and this should > work say up to even maybe 10000. ? > but 1/3 is WAY too much. Not really. Think of a case where the root^2 =3D 10^2 + 9^2 + 9^2.=20 the? I wouldn't want to stop before getting down to 10^2.=20 meaning reducing the z value ? You're confusing the x-coordinate with N itself, where N =3D root^2. yes i am still lost here...=20 > you are replicating the physical, so the math works... > you say potato i say patatoe...could dan qualye have > said this ? I'm explaining a recipe, how to make something, how to build a working machine. It's not what you *say*, but what you *do* (or don't do). cooking again ? > should we explore what the triangular grid method is ? > if so, what is it. That's starting with spheres packed hexagonally. You have triangles in your layer, versus squares. It's characteristic of 8 of the 14 faces of the cuboctahedron, as you pack out to higher and higher frequency. >> easily goes off the rails into hcp > please do not ask question that are not ccp related. Not a question... Again, if you have 12-around-1, you have 8 triangles and 6 squares. If you rotate one of those triangles, you no longer have a cuboctahedron -- and you are no longer doing ccp then you are the man. (but you still have all the same parallels -- you have layers packing in multiple parallel directions -- 4 triangular grid axes and 3 square grid axes. have not mused....but should on this i think, >> or the random wilderness of more generalized >> Barlow packings. > are those ccp...you did not answer that last time if > i remember right here ? The ccp is one of an infinite variety of Barlow packings with the same density. But you don't want to know about them. correct. i want to show you ccp. But the way to get to a lot of them is to layer the trianglar grids on top of each other, but randomly, so sometimes you're doing aba and sometimes you're doing abc. Obviously there's any number of permutations, given a deep enough packing. And yet that's _still_ not all the possible Barlow packings. you are the Barlow man. ko ko ki ju Please don't ask me any more questions about what I mean by "square grid" versus "triangular grid" until you've read http://www.teleport.com/~pdx4d/sphpack.html still open. > so, today i close...and it has been the most amazing > week of my life . thanks thanks thanks. S'been fun for me too. I've got some of the true Watermans on display by now, at http://www.inetarena.com/~pdx4d/ocn/wgraphics.html i must admit i cried when i saw some these. and then i laughed. I'd like to see those Mathematica depictions of the higher N Watermans now, so I can compare results. I'm also comparing my "fixed radius" guys with the janetjulians at your site. me too...cross verification is essential. we need a PERFECT BASE. Basically, I've tweaked my algorithm to put out wmN.pov or frN.pov, e.g. wm10.pov would be Waterman 10 (i.e. root(10)) and fr10.pov would be Fixed Radius 10 (i.e. janetjulian 10). looks good. The Watermans automatically have a black background,=20 i like this. while the fixed radius ones have a white background -- to help me tell them apart (which version of the algorithm worked on them). good idea. The Waterman algorithm (behind the wm*.pov) files, computes all the vertices at N, N-1 and N-2 and tosses these to Qhull, which automatically figures out which of all these vertices actually participate in a shrink-wrapping convex hull. there ARE rather tasty. Do you think I need to compute deeper than N-2? It seems to me that those deeper spheres would have a hard time "poking through" if we've already got the Ns, N-1s and N-2s covered. Do they ever? =20 yes...the higher the root, the higher the N-n can go. it might only be n-10 for 10000. i do not know here. How many colors did you use in your physical models? N and not N steve the list is shrinking. i have a need for the frequencies to have=20 each individual sphere show its actual r value. this is now directly in the critical path of a final=20 understanding of the basics of aba in ccp.... ( i think i am using this term properly ) ------=_NextPart_000_0023_01C079F1.56EFA8C0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

>> =3D Kirby
> =3D=20 Steve
=3D Kirby

>> For him, the place to = start was=20 with 12-around-1 in the
>> cuboctahedral = conformation

&nbs= p; =20 for me, i call it root 1.

It means 12 spheres at the vertices of = a=20 cuboctahedron,
around a nuclear sphere in the middle

................................................................= ................

The other choice is to have the top 3 = spheres line=20 up with
the bottom 3, with a hexagonal sandwich layer in the = middle.
It's=20 still 12-around-1, but it's not the cuboctahedron.

isnt that what hcp is=20 ?
....................................................................= ..............

>> and to pack outward in = successive=20 layers: 12, 42, 92,
>> 162... 10F^2+2.

> i agree=20 here.

>> Here were the numbers of vertices in the geodesic=20 spheres,
>> the capsomeres in a viral protein sheath and so=20 on.

> please rephrase or restate.

A geodesic sphere has = 10*f^2+2 hubs if based on the = f-frequency
icosahedron.

interesting. thanks for the = input.

Many viruses have this same=20 structure.

i must disagree here. this is a = physical=20 issue,

not a mathematical issue.

................................................................= .........................................

>>=20 What I think is confusing about your take is you seem to
>> = identify=20 ccp with abc with not-xyz.

> typo = ?

No

>> I=20 think this is because
>> when you stack your z-planes = vertically,=20 you're thinking this
>> is more strictly "xyz" than when you = stack=20 hexagons or what I
>> call triangular grids.

> please = define=20 triangular grids.

I mean spheres in a layer where every sphere=20 is
surrounded by 6 others, unless on an edge. Like=20 this:

          = =20 *
           *=20 *
          * *=20 *
         * * *=20 *
        * * * * *

(won't = look so=20 good if you're viewing in a proportionally
spaced font -- but you get = the=20 idea).

oh...you mean abc ?

................................................................= ..................................
Have=20 you ever looked at my
http://www.teleport.= com/~pdx4d/sphpack.html=20 ?

yes, i have seen it.
I keep = mentioning=20 it.

The opening paragraphs should = make
this=20 all clear.

and i agree.

i calculate that ratio of an = inscribed sphere=20

having a unit (1)=20 diameter divided by the RD volume

its your picture on my = synergetics=20 page

(since ccp is replicatable by the=20 RD).
poof..there goes the fuzzy container

boundary.
...................................................= .........................

>> But given both ways of=20 layering

> so we agree that layering has two forms.

In = the ccp,=20 you have triangular grid layering and square
grid layering,=20 yes.

>> go straight up the z axis (or can be oriented that = way),=20 I'm not
>> sure even this gets to the heart of it.

of what ?

> the word 'it' is = too vague=20 ...please restate

"It" refers to the distinction you seem to want = to make=20 between
your method and what you call the ccp method.

what are you referring to as my method=20 ?

................................................................= .................

> not to be confused with an = alternative=20 physical approach.

I don't understand your whole "mathematical"=20 versus
"physical" distinction very well.

it is the first bridge to sail = under.

................................................................= ....................

Do you mean that it's
easier = to rescale=20 things in the imagination, or on paper,
versus building sphere = packings where=20 the spheres
physically change diameter (as by=20 inflating/deflating?).

great question.

ccp has spheres of unit diameter one. =

this never changes.

so no inflating/deflating.

that would never happen in = ccp.

................................................................= ......................

i think there may be more left undone = here=20 ?

................................................................= .................
That's=20 true, but you _could_ build physical models
that demonstrated the = operations=20 I'm talking about.

why not. but i am only interested here = in the=20 mathematics of ccp.

................................................................= ....................................

>>=20 That's confusing because the "Urner generator" is most = definitely
>>=20 using XYZ coordinates to do all the work.

> you mean two = different=20 mathematical methods (mine and yours)
> that yield the same = physical BASE=20 ?

What's a BASE?

THE data BASE....ALL the spheres, all = the=20 coordinates,

all the distances, all the angles, all = the=20 volumes,

and then all its tricks. that is you = kirby...you=20 are BASE.
you are working on aba now...will still need to do abc too=20 !
....................................................................= .......

>> Instead, I start = with x as high=20 as possible, and push
>> inward, forcing y and z to pick = up the=20 slack,

> whereas i would have picked z and forced x and = y.

x,y=20 or z it doesn't matter.

perhaps not in a Cartesian 1 x 1 = x 1=20 system...

is ithis still the same for the aba of = ccp since it=20 is

1 x 1 x root 2=20 ?

................................................................= ..............
>>=20 but to remain in "descending sort" i.e. x>=3Dy>=3Dz.

> = so why force=20 on x then ?

It's just that one of the three needs to start = high
and=20 ratchet downward, while the others see what they
can do to hit the = root=20 distance. But since (3,2,1)
is the same as (2,3,1) and (1,2,3) = and=20 (3,1,2) when
it comes to distance, you don't want to end up = finding
them=20 all (let alone the negative signed permutes).
Just find (3,2,1) and = then swap=20 the digits around
every way possible. By enforcing = x>=3Dy>=3Dz, I'm=20 saying
I only need to find (3,2,1).

i think that may be the same = issue.

>=20 while it might appear that unique solutions should be required,
> = i should=20 only be required to go to say n-100 for the 10000.
> 1/3 is WAY = WAY too=20 high.

Earlier, I was only computing vertices for n, not
even=20 n-1. I wasn't getting true Watermans, but what
you and Russell = call=20 JanetJulians. Now I understand
about picking up all vertices = that would=20 make a
difference, i.e. be part of a shrink-wrapping.

cool, thanks for the=20 feedback.
............................................................= ...................

Anyway, the "coming down from x =3D = root(N)" in=20 the
above algorithm shouldn't be confused with N itself
coming=20 down.

Now that I have remembered what a true Waterman is,
I'm=20 wondering how many Ns I need to compute. If I
just do N, N-1 = and N-2,=20 am I going to hit all the
vertices in the shrink-wrap? Do you = have=20 examples
where I'd need to go even deeper?

i think that is where we are now = ?

>=20 aha, this is why i wanted the n,n-1,n-2 accumulating
> i suggest = you may=20 only need up to n-100 and this should
> work say up to even maybe = 10000.=20 ?
> but 1/3 is WAY too much.

Not really. Think of a = case=20 where the
root^2 =3D 10^2 + 9^2 + 9^2.

the?

I wouldn't want to stop
before = getting=20 down to 10^2.

meaning reducing the z value = ?

You're confusing = the
x-coordinate with N=20 itself, where N =3D root^2.

yes i am still lost here... =

> you are=20 replicating the physical, so the math works...
> you say potato i = say=20 patatoe...could dan qualye have
> said this ?

I'm = explaining a=20 recipe, how to make something, how to
build a working machine. = It's not=20 what you *say*, but
what you *do* (or don't do).

cooking again ?

> should we = explore what=20 the triangular grid method is ?
> if so, what is it.

That's = starting with spheres packed hexagonally. You
have triangles in = your=20 layer, versus squares. It's
characteristic of 8 of the 14 faces = of the=20 cuboctahedron,
as you pack out to higher and higher=20 frequency.

>> easily goes off the rails into = hcp

> please=20 do not ask question that are not ccp related.

Not a=20 question...

Again, if you have 12-around-1, you have 8 = triangles
and 6=20 squares. If you rotate one of those triangles,
you no longer = have a=20 cuboctahedron -- and you are no
longer doing ccp

then you are the man.

(but you still have all the = same
parallels=20 -- you have layers packing in multiple
parallel directions -- 4 = triangular=20 grid axes and
3 square grid axes.

have not mused....but should on this i=20 think,

>> or the random wilderness of more=20 generalized
>> Barlow packings.

> are those ccp...you = did not=20 answer that last time if
> i remember right here ?

The ccp = is one=20 of an infinite variety of Barlow packings
with the same = density. But=20 you don't want to know about
them.

correct. i want to show you = ccp.

But the way=20 to get to a lot of them is to layer the
trianglar grids on top of = each other,=20 but randomly, so
sometimes you're doing aba and sometimes you're=20 doing
abc. Obviously there's any number of permutations, = given
a=20 deep enough packing. And yet that's _still_ not all
the = possible Barlow=20 packings.

you are the Barlow man. ko ko ki = ju

Please=20 don't ask me any more questions about what I mean
by "square grid" = versus=20 "triangular grid" until you've
read http://www.teleport.= com/~pdx4d/sphpack.html

still open.

> so, today i close...and it has = been the=20 most amazing
> week of my life . thanks thanks = thanks.

S'been fun=20 for me too.

I've got some of the true Watermans on display by = now,
at=20 http://www.in= etarena.com/~pdx4d/ocn/wgraphics.html

i must admit i cried when i saw some = these. and=20 then i laughed.

I'd like to see those Mathematica depictions of=20 the
higher N Watermans now, so I can compare results. = I'm
also=20 comparing my "fixed radius" guys with the janetjulians
at your=20 site.

me too...cross verification is = essential. we need a=20 PERFECT

BASE.

Basically, I've tweaked my = algorithm=20 to put out wmN.pov
or frN.pov, e.g. wm10.pov would be Waterman 10 = (i.e.=20 root(10))
and fr10.pov would be Fixed Radius 10 (i.e. janetjulian=20 10).

looks good.

The Watermans = automatically have=20 a black background,

i like this.

while
the fixed radius ones have a = white=20 background -- to help me
tell them apart (which version of the = algorithm=20 worked on
them).

good idea.

The Waterman = algorithm (behind=20 the wm*.pov) files, computes
all the vertices at N, N-1 and N-2 and = tosses=20 these to Qhull,
which automatically figures out which of all these=20 vertices
actually participate in a shrink-wrapping convex = hull.

there ARE rather tasty.

Do = you think I=20 need to compute deeper than N-2? It seems to
me that those = deeper=20 spheres would have a hard time "poking
through" if we've already got = the Ns,=20 N-1s and N-2s covered.
Do they ever?

yes...the higher the root, the higher = the N-n can=20 go.

it might only be n-10 for 10000. i do = not know=20 here.

How many colors did you use in your=20 physical
models? N and not N

steve

the list is shrinking.

i have a need for the frequencies to = have=20

each individual sphere show its actual = r=20 value.

this is now directly in the critical = path of a=20 final

understanding of the basics of aba in=20 ccp....

( i think i am using this term properly = )

------=_NextPart_000_0023_01C079F1.56EFA8C0-- ========================================================================= Date: Tue, 9 Jan 2001 10:05:11 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: gathering sailors MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0024_01C07A23.A71B4480" This is a multi-part message in MIME format. ------=_NextPart_000_0024_01C07A23.A71B4480 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable lee, nice board...what's it called ? steve ------=_NextPart_000_0024_01C07A23.A71B4480 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

lee,

nice board...what's it called = ?

steve

------=_NextPart_000_0024_01C07A23.A71B4480-- ========================================================================= Date: Tue, 9 Jan 2001 10:52:34 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: the goal MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0013_01C07A2A.46202220" This is a multi-part message in MIME format. ------=_NextPart_000_0013_01C07A2A.46202220 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable ANNOUNCEMENT.... Captain Windswept is gathering crew. many positions available.... the ccp will be setting sail very soon. the captain would like to thank the wonderful ship builders...it is coming along most nicely. now that the first double row of cannons is almost properly set up, work should begin in affixing the triple rows on the port side. we may never need them, but to feel secure on this voyage, we should be getting them tested to make sure those fire just as well as the double row. as the ship gets prepared to launch, we need some additional maps. the sea beyond the breakers is different then here at 2d island. the winds are huge, and all who have=20 taken this adventure before, were lost at sea. they never found 3 light island. the myth of 3 light island was famous and well known to all nobody knew exactly where is was. many sailors told stories of its existence, some even said they had seen it, or had maps, but nobody could find it. but captain windswept had his own map, and BASE was using his compass and adding some numbers to the to it. the voyage must pick up some passengers=20 along the way, and cannot get to 3 light island without them.=20 will can depart shortly after BASE has finished with the frequency map notations. the waters will be rough, the winds may change our course but our focus should be clear...get to 3 light=20 island. steve =20 ------=_NextPart_000_0013_01C07A2A.46202220 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

ANNOUNCEMENT....

Captain Windswept is gathering = crew.

many positions = available....

the ccp will be setting sail very = soon.

the captain would like to thank = the

wonderful ship builders...it is coming=20 along

most nicely.

now that the first double row of = cannons is=20 almost

properly set up, work should = begin in=20 affixing

the triple rows on the port = side.

we may never need them, but to feel=20 secure

on this voyage, we should be getting=20 them

tested to make sure those fire just as=20 well

as the double row.

as the ship gets prepared to = launch,

we need some additional = maps.

the sea beyond the breakers is=20 different

then here at 2d island.

the winds are huge, and all who have =

taken this adventure before, were lost = at=20 sea.

they never found 3 light = island.

the myth of 3 light island was = famous

and well known to all

nobody knew exactly where is = was.

many sailors told stories of its=20 existence,

some even said they had seen = it,

or had maps, but nobody could find = it.

but captain windswept had his own = map,

and BASE was using his compass = and

adding some numbers to the to = it.

the voyage must pick up some passengers =

along the way, and cannot get to 3 = light=20 island

without them.

will can depart shortly after BASE has=20 finished

with the frequency map notations. the=20 waters

will be rough, the winds may change our = course

but our focus should be clear...get to = 3 light=20

island.

steve

------=_NextPart_000_0013_01C07A2A.46202220-- ========================================================================= Date: Tue, 9 Jan 2001 08:18:45 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: bcc poof In-Reply-To: <200101081930.f08JUQ701524@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable At 11:30 AM 01/08/2001 -0800, you wrote: ><> Brian =BFQuincy! Hutchings 08-JAN-2001 11:30 > r001806@pen2.ci.santa-monica.ca.us > > since the root(2) set of (6) spheres > (in octahedral formation) are centered on an octahedral void, > they are not in the same CCPacking as the 12-around-1 No, not true. The root(2) spheres are CCP spheres. The rule here is we don't even consider not-CCP positions, whether doing fixed-radius or true Watermans. Kirby ========================================================================= Date: Tue, 9 Jan 2001 08:23:19 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: totally coordinated ? In-Reply-To: Mime-Version: 1.0 Content-Type: text/enriched; charset="us-ascii" Arialthe mathematics for method 2 Arial...the abc...has NO Cartesian equivalent. i have HEXED sided masters for the abc. <<<<<<<< This is confusing terminology. You can have X,Y,Z i.e. Cartesian coordinates for sphere centers no matter what your orientation in XYZ. Rotating your packing in space changes the coordinates, but not the fact that you have them. Kirby ========================================================================= Date: Tue, 9 Jan 2001 08:28:02 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: urner generator In-Reply-To: <011401c079f2$371d7da0$7385fea9@pentiums133> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" >[Lee] >I think you need to draw edges and faces considering only the root(n) >spheres, and then find the center of the largest face. That point will >be the deepest possible on a convex surface, so if its depth is >root(n-m) then you never need to look deeper than n-m. > Yes, this is the kind of thought process I was going through as well. Fortunately, Qhull is doing all this figuring. I'm just through several distances into the mix and seeing what it comes up with as a final "shrink wrap". The vertices are color coded as to distance, so I can tell from the resulting graphic what range of distances ended up being used. http://www.inetarena.com/~pdx4d/ocn/wgraphics.html http://www.inetarena.com/~pdx4d/ocn/wgraphics1.html show my results so far. Kirby ========================================================================= Date: Tue, 9 Jan 2001 11:51:22 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: the mathematical grid MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_001F_01C07A32.7CE4D960" This is a multi-part message in MIME format. ------=_NextPart_000_001F_01C07A32.7CE4D960 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable the mathematics for method 2 ...the abc...has NO Cartesian equivalent. i have HEXED sided masters for the abc. <<<< This is confusing terminology.=20 agreed. You can have X,Y,Z i.e. Cartesian coordinates for sphere centers no matter what your orientation in XYZ. i would disagree here, but i may not understand what you are getting at here. .........................................................................= . Rotating your packing in space changes the coordinates,=20 (fixed point space) good work BASE, this is our first destination. ...................................................................... but not the fact that you have them. physical (ccp) ................................................................ by them, do you mean coordinates or spheres ? and in so doing, will they remain ccp ? steve ------=_NextPart_000_001F_01C07A32.7CE4D960 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

the mathematics for method = 2 ...the = abc...has=20 NO Cartesian
equivalent. i have HEXED sided masters for the = abc.

<<<<

This is = confusing=20 terminology.

agreed.

You can
have X,Y,Z i.e. Cartesian = coordinates=20 for
sphere centers no matter what your
orientation in = XYZ.

i would disagree here, but i may = not=20 understand

what you are getting at = here.

................................................................= ..........

Rotating your packing
in space = changes the=20 coordinates,

(fixed point space)

good work BASE,

this is our first=20 destination.

................................................................= ......

but not the fact that you have = them.

physical (ccp)

................................................................=

by them, do you mean = coordinates

or spheres ?

and in so doing, will they remain ccp=20 ?

steve

------=_NextPart_000_001F_01C07A32.7CE4D960-- ========================================================================= Date: Tue, 9 Jan 2001 09:04:27 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: almost final terms In-Reply-To: Mime-Version: 1.0 Content-Type: text/enriched; charset="us-ascii" Arial A geodesic sphere has 10*f^2+2 hubs if based on the f-frequency icosahedron. Arialinteresting. thanks for the input. Arial Many viruses have this same structure. Ariali must disagree here. this is a physical issue, not a mathematical issue. <<<<<<<< It has been verified in the lab: By taking F as the number of between-capsomere intervals, and using 10F2+2 on capsid "shell frequencies" of 1,2,3,4,5 and 6, we obtain corresponding counts of 12, 42, 92, 162, 252 and 812 capsomeres. "All of these numbers are in fact found in actual viruses, 12 for certain bacteriophages, 42 for wart viruses, 92 for reovirus, 162 for herpesvirus, 252 for adenovirus and 812 for a virus attacking crane-flies (Tipula or daddy-long-legs)" - The Natural History of Viruses by C.H. Andrews (W.W. Norton R Co., 1967). When it comes to physical evidence, I think it's for your speculations on: Arial0000,0000,fefehttp://www.dsuper.net/%7Etinom/ph2000/VIRUSES.html that this is lacking. Arialoh...you mean abc ? <<<<<<<< Please don't identify a single layer of spheres with what we finally end up doing with multiple layers. The whole point of the triangular layers packing is we are not forced to go abc with it. You say that's all you care about (abc) but people who actually study crystals and other natural structures need to care about not-abc as well. Arialwhat are you referring to as my method ? <<<<<<<< I don't really know. You're the one who keeps bringing it up. Exhaustive tabulations? Arialgreat question. ccp has spheres of unit diameter one. this never changes. <<<<<<<< Says who? The unit all depends on your ruler, your unit of measure. You say one, but some guy comes along and has a different measuring rod and says something else. Potato/potatoe. >>>> Arialso no inflating/deflating. that would never happen in ccp. <<<<<<<< You can make this rule in your own mind, but don't expect others to follow it. ArialTHE data BASE....ALL the spheres, all the coordinates, all the distances, all the angles, all the volumes, and then all its tricks. that is you kirby...you are BASE. you are working on aba now...will still need to do abc too ! <<<<<<<< I have no plans to rotate and compute everything all over again. Arialperhaps not in a Cartesian 1 x 1 x 1 system... is ithis still the same for the aba of ccp since it is 1 x 1 x root 2 ? <<<<<<<< Arial Again, if you have 12-around-1, you have 8 triangles and 6 squares. If you rotate one of those triangles, you no longer have a cuboctahedron -- and you are no longer doing ccp then you are the man. Arial (but you still have all the same parallels -- you have layers packing in multiple parallel directions -- 4 triangular grid axes and 3 square grid axes. <<<<<<<< Actually, you no longer have the square grids if it ain't ccp. I slipped. I'd like you to understand the algorithm I'm using better, and will explain again, relating it more closely to your thinking, when I get the time. Right now, I have to turn back to the reams of medical data which need collating, tallying, and converging. Brought home a zip disk from the cube farm yesterday -- "cube farm" is a place with pictures of heart valves on the wall, on floor LL of a large hospital. But just for fun, I'll do Waterman 383 and 447, along with the corresponding "janetjulians" (ivm polys of fixed radius). Both are "missing number + 1" shapes, and so I expect the Watermans will draw on at least (n-2) spheres. We shall see: Check: Watermans: http://www.inetarena.com/~pdx4d/ocn/wgraphics1.html Fixed Radius: http://www.inetarena.com/~pdx4d/ocn/wgraphics3.html in a few minutes. No more posts to Geodesic until I've crunched through all this medical data. Deadlines. Kirby ========================================================================= Date: Tue, 9 Jan 2001 12:00:15 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: frequencies MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0035_01C07A33.BA6B7860" This is a multi-part message in MIME format. ------=_NextPart_000_0035_01C07A33.BA6B7860 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable BASE, any news of the frequency charts. we MUST have soon. perhaps the port cannons can be polished later during our trip ? we cant leave without them. they are most essential to even have before we leave the beach. they must be studied before leaving shore. steve ------=_NextPart_000_0035_01C07A33.BA6B7860 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

BASE,

any news of the frequency = charts.

we MUST have soon.

perhaps the port cannons can be=20 polished

later during our trip ?

we cant leave without = them.

they are most essential to even = have before=20 we leave

the beach. they must be studied = before

leaving shore.

steve

------=_NextPart_000_0035_01C07A33.BA6B7860-- ========================================================================= Date: Tue, 9 Jan 2001 12:15:39 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: medical staff ? MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_004D_01C07A35.E11B6C20" This is a multi-part message in MIME format. ------=_NextPart_000_004D_01C07A35.E11B6C20 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable is there a doctor aboard ? then i guess the Doctor will be staying here at 2d island ? he has a lot of friends to comfort him here on the island. i afraid they do believe that 3 light island exists. but lets us all remember, the ccp would still be in dry-dock without him. he is still welcome aboard, for she is a vast and wondrous vessel, and there is plenty of room aboard. but for him, it is a more treacherous=20 journey, and he has his own obligations still at 2d island....has he been invited ? has karl been alerted that the ccp is sailing soon ? granted, we could stay and change 2d island to add condos there, but what is the use, if you want to get to 3 light island...why buy a condo ? steve ------=_NextPart_000_004D_01C07A35.E11B6C20 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

is there a doctor aboard ?

then i guess the Doctor will be staying = here

at 2d island ? he has a lot of friends = to=20 comfort

him here on the island. i afraid they = do=20 believe

that 3 light island = exists.

but lets us all remember, the ccp = would=20 still

be in dry-dock without him. he is still = welcome

aboard, for she is a vast and wondrous=20 vessel,

and there is plenty of room = aboard.

but for him, it is a more treacherous =

journey, and he has his own obligations = still

at 2d island....has he been invited = ?

has karl been alerted that the ccp is = sailing soon=20 ?

granted, we could stay and change 2d = island=20 to

add condos there, but what is the use, = if=20 you

want to get to 3 light island...why buy = a condo=20 ?

steve

------=_NextPart_000_004D_01C07A35.E11B6C20-- ========================================================================= Date: Tue, 9 Jan 2001 12:42:45 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: distance calc for frequencies MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_000D_01C07A39.AA7CBD00" This is a multi-part message in MIME format. ------=_NextPart_000_000D_01C07A39.AA7CBD00 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable kirby, perhaps to help affix root values to the spheres involved for frequencies,=20 you could first realign the frequency depiction to be aba rather than abc ? and use the n, n-1 technique ? steve ------=_NextPart_000_000D_01C07A39.AA7CBD00 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

kirby,

perhaps to help affix root = values

to the spheres involved for = frequencies,=20

you could first

realign the frequency = depiction

to be aba rather than abc = ?

and use the n, n-1 technique = ?

steve

------=_NextPart_000_000D_01C07A39.AA7CBD00-- ========================================================================= Date: Tue, 9 Jan 2001 15:08:28 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: still some terms MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0014_01C07A4E.05940B80" This is a multi-part message in MIME format. ------=_NextPart_000_0014_01C07A4E.05940B80 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable kirby, Many viruses have this same structure. i must disagree here. this is a physical issue, not a mathematical issue. <<<< It has been verified in the lab: are there any pictures i could see...empirical evidence ? this is not a challenge here. i, would like to become more informed about this....poof ! By taking F as the number of between-capsomere intervals, and using 10F2+2 on capsid "shell frequencies" of 1,2,3,4,5 and 6, we obtain corresponding counts of 12, 42, 92, 162, 252 and 812 capsomeres. "All of these numbers are in fact found in actual viruses,=20 in what sense are they found...f, or v, or e or other ? 12 for certain bacteriophages, 42 for wart viruses, 92 for reovirus, 162 for herpesvirus, 252 for adenovirus and 812 for a virus attacking crane-flies (Tipula or daddy-long-legs)" - The Natural History of Viruses by C.H. Andrews (W.W. Norton R Co., 1967). When it comes to physical evidence, I think it's for your speculations on: http://www.dsuper.net/%7Etinom/ph2000/VIRUSES.html that this is lacking. you may well be right. i am still interested in this though. .........................................................................= ................. oh...you mean abc ? <<<< Please don't identify a single layer of spheres with what we finally end up doing with multiple layers. definitely agree. can you find my/your original statement. this seems to be out of context to me.=20 i think there is something missing from the top of this=20 discussion .........................................................................= .... The whole point of the triangular layers packing is we are not forced to go abc with it.=20 good ...i think we can rely on the validity of the urner generator now. as long as we have aba ( we do ) or abc ( we do not yet )...we have the whole ccp thing. the other merely serves as a cross check. i am quite prepared to leave without it altogether it will be a MAJOR pain in the ass to do the abc. .........................................................................= ............ You say that's all you care about (abc) all i care about is ccp...which includes both abc and aba. ( the aba of hcp is also ignored by a ccp analysis even though it too has its aba component.) .........................................................................= .......................... but people who actually study crystals and other natural structures need to care about not-abc as well. yes indeed, they need to smarten up and add aba to ccp as i have been suggesting for a bit now. are we together on this issue ? .........................................................................= .......... Exhaustive tabulations? not really, they have all been done for some time. it is however, a bit draining to wade through all this dual linguistics. we have almost settled all the terms. but i am having a great time.=20 are you ok with the story so far ? would you want me to drop it and just do the science and math ? i find it helps me...but if it is in the way .... is there consensus on this "story " issue from you and your maties ? some feedback s.v.p. it may not seem like it, but i can be flexible. .........................................................................= ... great question. ccp has spheres of unit diameter one. this never changes. <<<< Says who? The unit all depends on your ruler, your unit of measure.=20 i would not agree. unit by definition means 1. You say one, but some guy comes along and has a different measuring rod and says something else. Potato/potatoe. unity can only be one, by definition. ( math vs physical...first voyage) this one is going to be difficult and take some time. there will be much bickering here coming up i would suspect. >>>> so no inflating/deflating. that would never happen in ccp. <<<< You can make this rule in your own mind, but don't expect others to follow it. they had better or we have no ccp BASE left to work from. though it can certainly happen FROM ccp. i was only trying to say, that if you modify the ccp in any way, it is no longer the ccp. so, inflate/deflate/stretch/squeeze/elongate....all are fine as modifications to the BASE. what i was trying to get at,=20 is that the ccp itself is inalterable. if that BASE is changed, that is not good at all ! but, feel free to modify the BASE to get other mathematical=20 variations from the BASE. but the BASE itself cannot be altered, either it is ccp or not ccp. .........................................................................= ............... THE data BASE....will still need to do abc too ! <<<< I have no plans to rotate and compute everything all over again. surprise, i am SO happy to hear this....we only need the urner generator to do the aba, and with it, we get=20 the entire ccp. ..................................................................... i'd like you to understand the algorithm I'm using better, and will explain again, relating it more closely to your thinking, when I get the time. so would i, thanks for keeping me in the loop. Right now, I have to turn back to the reams of medical data which need collating, tallying, and converging. Brought home a zip disk from the cube farm yesterday -- "cube farm" is a place with pictures of heart valves on the wall, on floor LL of a large hospital. But just for fun, I'll do Waterman 383 and 447, nice. along with the corresponding "janetjulians" (ivm polys of fixed radius). do we need these jj at all ?=20 please do not do them on my account. i could handle it, if these suddenly went missing. ...................................................................... steve ps i have checked out websters and your term polyhedra seems appropriate and my solids term is not=20 specific enough...poof ! yes, they are solids...but your term confines them to=20 only those with plane faces. ------=_NextPart_000_0014_01C07A4E.05940B80 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

kirby,

Many=20 viruses have this same = structure.

i=20 must disagree here. this is a physical issue,
not a mathematical = issue.

<<<<

It has = been=20 verified in the lab:

are there any pictures i could = see...empirical=20 evidence ?

this is not a challenge here. i, would = like=20 to become more

informed about this....poof !

By = taking F as=20 the number of between-capsomere intervals,
and using 10F2+2 on capsid = "shell=20 frequencies" of 1,2,3,4,5
and 6, we obtain corresponding counts of = 12, 42,=20 92, 162,
252 and 812 capsomeres. "All of these numbers are in = fact
found=20 in actual viruses,

in what sense are they found...f, or v, = or e or=20 other ?

12 for certain bacteriophages,
42 = for wart=20 viruses, 92 for reovirus, 162 for herpesvirus,
252 for adenovirus and = 812 for=20 a virus attacking crane-flies
(Tipula or daddy-long-legs)" - The = Natural=20 History of Viruses
by C.H. Andrews (W.W. Norton R Co., = 1967).

When it comes to physical evidence, I = think it's=20 for your
speculations on:

http://www.dsuper.net/%7Etinom/ph2000/VIRUSES.ht= ml

that=20 this is lacking.

you may well be right. i am still = interested in=20 this=20 though.

........................................................= ..................................

oh...you mean abc = ?

<<<<

Please don't identify a single layer of = spheres=20 with what
we finally end up doing with multiple layers.

definitely agree. can you find my/your original statement.

this seems to be out of context to me.

i think there is something missing from the top of this

discussion

....................................................................= .........

The whole
point of the triangular layers packing is we are not=20 forced
to go abc with it.

good ...i think we can rely on the validity of the urner

generator now. as long as we have aba ( we do )

or abc ( we do not yet )...we have the whole ccp thing.

the other merely serves as a cross check.

i am quite prepared to leave without it altogether

it will be a MAJOR pain in the ass to do the abc.

....................................................................= .................

You say that's all you care about (abc)

all i care about is ccp...which includes both abc and = aba.

( the aba of hcp is also ignored by a ccp analysis even though = it=20 too

has its aba component.)

....................................................................= ...............................
but=20 people who actually study crystals and other natural
structures need = to care=20 about not-abc as well.

yes indeed, they need to smarten up and add aba to ccp

as i have been suggesting for a bit now.

are we together on this issue ?

....................................................................= ...............

Exhaustive tabulations?

not really, they have all been done for some time.

it is however, a bit draining to wade through all

this dual linguistics. we have almost settled

all the terms.

but i am having a great time.

are you ok with the story so far ?

would you want me to drop it and just do

the science and math ?

i find it helps me...but if it is in the way ....

is there consensus on this "story " issue from you

and your maties ?

some feedback s.v.p.

it may not seem like it, but i can be flexible.

....................................................................= ........

great question.
ccp has = spheres=20 of unit diameter one.
this never = changes.

<<<<

Says who? The unit all depends on your = ruler,=20 your
unit of measure.

i would not agree. unit by definition means 1.

You say one, but some guy comes along
and has a different = measuring rod=20 and says something
else. Potato/potatoe.

unity can only be one, by definition.

( math vs physical...first voyage)

this one is going to be difficult and take some time.

there will be much bickering here coming up i would=20 suspect.

>>>>

so no=20 inflating/deflating.
that would never happen in = ccp.

<<<<

You can make this rule in your own mind, = but=20 don't
expect others to follow it.

they had better or we have no ccp BASE left to work from.

though it can certainly happen FROM ccp.

i was only trying to say, that if you modify the ccp

in any way, it is no longer the ccp.

so, inflate/deflate/stretch/squeeze/elongate....all are fine

as modifications to the BASE. what i was trying to get at, =

is that the ccp itself is inalterable. if that BASE is = changed,

that is not good at all !

but, feel free to modify the BASE to get other mathematical

variations from the BASE. but the BASE itself cannot be = altered,

either it is ccp or not ccp.

....................................................................= ....................

= THE data=20 BASE....will still need to do abc too !

<<<<

I have no plans to rotate and compute = everything=20 all
over again.

surprise, i am SO happy to hear this....we only need

the urner generator to do the aba, and with it, we get

the entire ccp.

....................................................................= .

i'd like you to understand the algorithm I'm using
better, and = will=20 explain again, relating it more
closely to your thinking, when I get = the=20 time.

so would i, thanks for keeping me in the loop.

Right now, I = have to=20 turn back to the reams of
medical data which need collating, = tallying,=20 and
converging. Brought home a zip disk from the
cube farm = yesterday --=20 "cube farm" is a place
with pictures of heart valves on the = wall,
on floor=20 LL of a large hospital.

But just for fun, I'll do Waterman 383 = and=20 447,

nice.

along with the corresponding "janetjulians"
(ivm polys of = fixed=20 radius).

do we need these jj at all ?

please do not do them on my account.

i could handle it, if these suddenly went missing.

....................................................................= ..

steve

ps i have checked out websters and your term polyhedra

seems appropriate and my solids term is not

specific enough...poof !

yes, they are solids...but your term confines them to

only those with plane faces.

------=_NextPart_000_0014_01C07A4E.05940B80-- ========================================================================= Date: Tue, 9 Jan 2001 05:41:15 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: distance calc for frequencies <> Brian �Quincy! Hutchings 09-JAN-2001 5:41 r001806@pen2.ci.santa-monica.ca.us I don't know what you meant by "frequency," Steve. it seems that the Bucky freqs are just those that add a ball to each of the "12 vectors" --that is to both ends of the six vectors going through the pairs of opposite balls of the 12 (around one; dig?)-- which will give root("square") dystances, thus being also *integral* dystances (obviously, by inspection .-) since we've been using the "descartesian" (or Fermatian) coordinates, the "aba" slicing is the only way t'go, with the proviso that one of the directions (say, z) will have to count by octahedral diagonals (of length root(2) -- which second-powers to 2, as Kirby has also shown). "abc" coordination'd requre Eisenstein numbers, I guess. Kirby, I already acknowledged my mystaque about the root(2) layer. I'm pretty sure, though, that the centers on the octahedral voids of the IVM (between 6 spheres, and actually shaped as convex cuboctahedra in Bucky's terms, as well as being the spaces of the "spheres-into-spaces" mechanical model) just give another IVM. so, this leaves the other voids to configure, if need be, and perhaps using the 3-way grid, 4 ways; eh? Steve, you are a Subject of the Queen; don't *ever* question the majexty o'Newton, if you want to keep your headboard! --The Duke of Oil! http://www.tarpley.net/bush8.htm ========================================================================= Date: Tue, 9 Jan 2001 13:00:43 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Dick Fischbeck Subject: cook MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii While making supper the other day I was cutting potatoes and I noticed that by making tangential slices while omni-rotating the potato, I get a spheric suspiciously similar in shape(without the concave or convex faces) to a bubble that is surrounded by other bubbles. I think in bubblology the average bubble in a mass of other bubbles has 14 faces. I love to find geodesic geometry in nature. And it reinforces my investigation into the self-adjusting-strut vertexion. ========================================================================= Date: Tue, 9 Jan 2001 17:04:14 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: 12 vectors MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_000D_01C07A5E.3209EE40" This is a multi-part message in MIME format. ------=_NextPart_000_000D_01C07A5E.3209EE40 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable brian, I don't know what you meant by "frequency," Steve. it seems that the Bucky freqs are just those that add a ball to each of the "12 vectors" yes, i am using the fuller term. while root values are distance determined frequency values are just those that add a ball to each of the "12 vectors. eventually, i want to show the correlation between these, roots and frequencies. i am not in any way challenging the mathematics of Fuller frequencies. they are fine, correct, valuable, interesting, viable and mathematically proper. Steve, you are a Subject of the Queen; don't *ever* question the majexty o'Newton, if you want to keep your headboard! why not ? is he so absolutely untouchable ? i have no intention of going after o'newton, just after two of his concepts. bailing out ? the life boats are ready. when you feel i have lost my mind, no, let me rephrase that, you may jump ship when you want, you are not obligated to=20 hear my take on anything. i would hope you will at least stay to watch me face plant. but i do understand how ridiculous a challenge=20 to newtons ideas is. i just want my chance to expose my line of logic. you gentleman may all subject me to this same picky technique, should you choose, that you have just been=20 subjected to. it is scheduled to be a working and pleasure cruise. surely i will not be able to put forth any sort of logical moderation to newtons ideas. however, i would like to make the attempt. steve ------=_NextPart_000_000D_01C07A5E.3209EE40 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

brian,

I don't know what you meant by = "frequency,"=20 Steve.
it seems that the Bucky freqs are just=20 those
that add a ball to each of the "12 vectors"

yes, i am using the fuller = term.

while root values are distance=20 determined

frequency values are just = those
that=20 add a ball to each of the "12 vectors.

eventually, i want to show the=20 correlation

between these, roots and = frequencies.

i am not in any way challenging the=20 mathematics

of Fuller frequencies. they are fine, = correct,=20 valuable,

interesting, viable and mathematically=20 proper.

Steve, you are a Subject of the = Queen;

don't *ever* question the majexty = o'Newton,=20 if
you want to keep your headboard!

why not ? is he so absolutely = untouchable=20 ?

i have no intention of going after=20 o'newton,

just after two of his = concepts.

bailing out ? the life boats are=20 ready.

when you feel i have lost my = mind,

no, let me rephrase that, you may jump=20 ship

when you want, you are not obligated to =

hear my take on anything. i would = hope

you will at least stay to watch me face = plant.

but i do understand how ridiculous a = challenge=20

to newtons ideas is. i just want my = chance=20 to

expose my line of logic. you gentleman=20 may

all subject me to this same picky=20 technique,

should you choose, that you have just = been=20

subjected to.

it is scheduled to be a working and = pleasure=20 cruise.

surely i will not be able to put forth = any sort=20 of

logical moderation to newtons = ideas.

however, i would=20 like to make the attempt.

steve

------=_NextPart_000_000D_01C07A5E.3209EE40-- ========================================================================= Date: Tue, 9 Jan 2001 18:51:33 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Lee Bonnifield Subject: waterman poly 25 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit Kirby - I'm surprised that WP 25 has no (n-1) white spheres, just orange (n=25) and green (n-2). Please show us WP 23 and 24. ========================================================================= Date: Tue, 9 Jan 2001 18:07:01 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: waterman poly 25 In-Reply-To: <004b01c07a97$6474cb00$7385fea9@pentiums133> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 06:51 PM 01/09/2001 -0500, you wrote: >Kirby - >I'm surprised that WP 25 has no (n-1) white spheres, just orange (n=25) >and green (n-2). Please show us WP 23 and 24. > That's an excellent question and I think this animated GIF gives some insight. It's about 180K, hope not too onerous. http://www.inetarena.com/~pdx4d/ocn/graphics/wm24to25.gif [Note: on my Netscape, the transition from W24 to W25 and back is fairly peppy -- it's a dissolve animation -- whereas on my Internet Explorer, it's way slow, even when fully downloaded] Explanation: the W24's N spheres (= the W25's N-1) spheres would appear in the middle of rings surrounded by W25's N spheres. So they don't appear. The tent is already "too high" in those regions for the N-1s to poke through. But the W24 has lots of N-1 spheres, and these correspond to the W25's N-2 spheres, which _do_ appear (i.e. are the same). Anyway, watch the animated GIF if you would and tell me if you find it enlightening. Kirby ========================================================================= Date: Tue, 9 Jan 2001 21:43:12 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: another trick MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_005C_01C07A85.2AB1AC60" This is a multi-part message in MIME format. ------=_NextPart_000_005C_01C07A85.2AB1AC60 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable kirby, so no inflating/deflating. that would never happen in ccp. <<<< You can make this rule in your own mind, but don't expect others to follow it. they had better or we have no ccp BASE left to work from. though it can certainly happen FROM ccp. i was only trying to say, that if you modify the ccp in any way, it is no longer the ccp. so, inflate/deflate/stretch/squeeze/elongate....all are fine as modifications to the BASE. what i was trying to get at,=20 is that the ccp itself is inalterable. if that BASE is changed, that is not good at all ! but, feel free to modify the BASE to get other mathematical=20 variations from the BASE. but the BASE itself cannot be altered, either it is ccp or not ccp. way to plow through the cross lingo dude. we are finally starting to talk the same language a bit. great stuff. =20 what is the name of this thing process/technique ( root 25 - root 24 ) steve ------=_NextPart_000_005C_01C07A85.2AB1AC60 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

kirby,

so no inflating/deflating.
that = would never=20 happen in ccp.

<<<<

You can make this rule in your own mind, = but=20 don't
expect others to follow it.

they had better or we have no ccp BASE left to work from.

though it can certainly happen FROM ccp.

i was only trying to say, that if you modify the ccp

in any way, it is no longer the ccp.

so, inflate/deflate/stretch/squeeze/elongate....all are fine

as modifications to the BASE. what i was trying to get at, =

is that the ccp itself is inalterable. if that BASE is = changed,

that is not good at all !

but, feel free to modify the BASE to get other mathematical

variations from the BASE. but the BASE itself cannot be = altered,

either it is ccp or not ccp.

&n= bsp;=20 way to plow through the cross lingo dude.

we are = finally=20 starting to talk the same language a bit.

= great=20 stuff.

what is the name of this thing process/technique

( root 25 - root 24 )

steve

------=_NextPart_000_005C_01C07A85.2AB1AC60-- ========================================================================= Date: Tue, 9 Jan 2001 14:01:11 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: distance calc for frequencies <> Brian �Quincy! Hutchings 09-JAN-2001 14:01 r001806@pen2.ci.santa-monica.ca.us oops. <> Brian ?Quincy! Hutchings 09-JAN-2001 8:35 r001806@pen2.ci.santa-monica.ca.us http://www.inetarena.com/~pdx4d/ocn/wgraphics1.html neat; it seems that all of the facets are "archimedean;" did you see any that were'nt in that limited class? back to the dystances (was, also: 12vectors). it seems clear that the whole answer of classifying the roots of Bucky's frequencies of cuboctohedral clumps o'balls, is that they are just the roots of "square" numbers; dig? although each facet will have many different roots, they are all in the same facets, so the "hull" is the same, cuboctahedral. are your root(second-power) shapes, cuboctahedral?... shouldn't they be, so. one more word about Newton; ***hole! thus quoth: eventually, i want to show the correlation between these, roots and frequencies. --The Duke of Oil! http://www.tarpley.net --f09GZ9506749.979058109/pen2.ci.santa-monica.ca.us-- ========================================================================= Date: Tue, 9 Jan 2001 14:02:58 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: [Q-P] Clinton farewell <> Brian �Quincy! Hutchings 09-JAN-2001 14:02 r001806@pen2.ci.santa-monica.ca.us why do you think that Gore'd have done any better (as hard as it is to ask) ??... I have one factor for you to consider before you answer: HR-4961, the Voting Rights Clarification Act of 2000 (Rep.Mel Watt (D, Congressional Black Caucus)). if you think that I have some sort of brief for the Confederate soldier, Ashcroft, note this. looking at Saturday's NYT, we see that Condoleeza Rice, the appointee for the NSC (as before, a the Russia Desk), is demanding that the trade post be downgraded, not just kept out of the Cabinet, so that she can have more control of it. please remember, this is a part of the 'WAND' Corp. cabal that was on the G2Kcmte., along witht he new Treasury guy. if you look at *any* of their literature, you'll see that they are frank ideologs for radical ("liberal") free trade, or what they refer to as classical economics ("buy cheap; sell dear"). in particular, look at their Fall freebie/digest, "Transcendental Destination," which commits the weird act of putting the idea of the "noosphere" to Tielhard de Chardin -- with a phonetic pronounciation -- without mentioning that the idea was Vernadsky's (a whole, 'nother outlook, I'd say). there is one paragraph in this thing that is honest, about how NGOs are totally unaccountable (not elected etc.); then, they continue asserting their wonderfulness, for WAND's own purposes: noopolitik! --beyond petroleum (tm) !! http://www.tarpley.net/bush8.htm ========================================================================= Date: Tue, 9 Jan 2001 14:06:55 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: The Waterman Projection is Great for ... <> Brian �Quincy! Hutchings 09-JAN-2001 14:06 r001806@pen2.ci.santa-monica.ca.us on the wayside, Steve; is there any particular benefit to your projection of the globe, navigationally? (this is also a criticism (or misapplication) of the Fuller one, in that it's basically useless for that stuff -- without some espcial tricks, anyway! --The Duke of Oil! http://www.tarpley.net/bush8.htm ========================================================================= Date: Tue, 9 Jan 2001 21:47:33 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: distance calc for frequencies In-Reply-To: <200101092201.f09M1B908297@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" > they are all in the same facets, so the "hull" is the same, > cuboctahedral. are your root(second-power) shapes, > cuboctahedral?... shouldn't they be, so. Have you checked the web page Brian??? http://www.inetarena.com/~pdx4d/ocn/wgraphics.html clearly not usually cuboctahedral (I thought you were already versed up to this point in the conversation, am a little surprised at the backsliding -- maybe I just don't get your question). The thing about the cuboctahedron is it picks up the 12 in a cuboctahedral subset of the ccp, but there are others the same distance that the cubocta hasn't yet reached. As a radar sweepout, the cubocta leaves a lot of unexplored ccp spheres in the bigger circumsphere of root N (or N frequency). It'll get to them eventually, at higher frequencies, but the Watermans connect all those dots now, not when the cubocta grows out to 'em. So Watermans pick out *all* the ccp spheres that are root N away -- but then we're _still_ not done (I had to re- remember), because in shrink wrapping this convex hull you're going to find N-1, N-2, N-3 (more?) spheres poking through the skin of the Waterman "tent". Hence the color coding of vertices, and Lee's useful question about the W24, W25. > one more word about Newton; > ***hole! > Steve -- Don't get the idea we're all cohorts or one big happy family on GEODESIC. Brian here has a long list of goodies and badies (Newton a baddy) that's unique to a certain literature he savors, but which the rest of us mostly neglect, or at the very least don't bother to memorize. I don't try to keep straight who Brian thinks the goodies are -- not my department. Kirby ========================================================================= Date: Wed, 10 Jan 2001 00:54:32 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: New web page linking to Waterman Method I In-Reply-To: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Steve -- OK, I've done my best to communicate the basic setup used by the "Urner generator" method at: http://www.inetarena.com/~pdx4d/ocn/wmalgorithm.html and to relate this to your preferred Method I. Both of us are showing abababa... stacking along the Z axis, but my sphere grid is rotated 45 degrees relative to yours. Plus I shrink my XYZ measuring apparatus, meaning my CCP spheres seem relatively larger (to XYZ, not to each other). That's what allows me to look for any/all x^2 + y^2 + z^2 = 2*D^2 with no thoughts about "even vs. odd" Z-planes. That all goes away, to be replaced by the stipulation that x + y + z must be evenly divisble by 2 -- which as far as I'm concerned, is an improvement. So, just give me a 2*D^2, and I'll find all the (x,y,z) values which solve it, keeping x>=y>=z and permuting order and signage to get the full circumsphere of values. That's what goes on in my poly(), permute() and negperm() methods: http://www.inetarena.com/~pdx4d/ocn/python/waterman.html#poly http://www.inetarena.com/~pdx4d/ocn/python/waterman.html#permute http://www.inetarena.com/~pdx4d/ocn/python/waterman.html#negperm My 2*D^2 values are double yours, for same same reason that my intersphere distances are multiples of root(2) instead of 1. That's just how I scale my XYZ, even if I consider the CCP spheres to be "really" unit diameter. If I compensate for these differences at the end of the computation, I can get back to the BASE values you're used to. It's easy enough to translate back and forth, by rescaling by 1/root(2) and rotating 45 degrees. I hope you don't have too much trouble thinking in this way. Certainly your BASE is calibrated based on certain assumptions, and it won't be useful to compare output from my algorithm with yours if I don't do the rescale and rotation. But you shouldn't confuse mere numeric values with the PATTERN that is the CCP. As long as the spheres pack together that way, abababa along some axes, abcabcabc along others, in the ways we've described, it's a CCP packing. This is not up for debate as that's how scientists use the term, and it belongs to them, not to you and I. The numbers are all secondary and nature does CCPs at many different scales, from oranges to cannon balls to fullerenes to individual atoms in some crystals. Given all these different sizes (scales), it's clearly the PATTERN which defines the CCP, not the numbers in your BASE table. However, given the pattern is always similar, there's always a way to rotate and rescale such that your BASE table matches up with whatever physical example (discounting the inevitable aberrations with a physical example will always introduce e.g. oranges aren't perfect spheres -- and even on a computer we have the limitations of floating point registers to think about). This translation to your BASE table is what I accomplish with my listbase() method. I rotate by 45 degrees and divide by root(2). Simple. Perhaps in your terminology you'd say the "physical CCP" can be any size, but the "mathematical CCP" will always match up with your BASE tables. That's a true enough I suppose. Is that how you'd put it? Or Bucky might say: the physical IVM can be any frequency, but the metaphysical IVM always has the same angles, and angles define shape irrespective of size. That's true enough too. The angle/frequency distinction (or shape/size distinction) is at the heart of synergetics. Kirby ========================================================================= Date: Wed, 10 Jan 2001 08:16:34 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: frequencies MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0065_01C07ADD.A5D2F180" This is a multi-part message in MIME format. ------=_NextPart_000_0065_01C07ADD.A5D2F180 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable brian, back to the dystances (was, also: 12vectors). it seems clear that the whole answer of classifying the roots of Bucky's frequencies of cuboctohedral clumps o'balls, is that they are just the roots of "square" numbers; dig? wonderful...number 1. although each facet will have many different roots, dig it man. they are all in the same facets,=20 so the "hull" is the same, cuboctahedral. =20 i am hip to this jive too. ! are your root(second-power) shapes, cuboctahedral?... shouldn't they be, so. here on 2d island...yes. out at sea...no. not when you take a radial sweep. look at the=20 figures you guys are now making. one more word about Newton; ***hole! perhaps true, i do not know. but regardless, we need the dude to help us to eventually get to 3 light=20 island, so we may have to temporarily put up with his attitudes. in fact, the whole voyage is off unless he comes with us, some please be nice to him. thus quoth: eventually, i want to show the correlation between these, roots and frequencies. i felt that i did not do an adequate job yet for this explanation, i am very pleased that number one has helped me bridge this gap. i have found the mathematical analysis of ccp to be hypnotic. it seems that almost anyway you dissect it...bingo...some other little doo-dad ? poops out and makes you muse further. i totally understand and all those that wish=20 to stay at 2d island. i respect those people and their choice to be at 2d island. it is a most fascinating place. it has great comforts and rewards and none=20 of the perils of the sea. bucky lived there too on 2d island. where mathematics is perfect, and mass is ignored. but as soon as you step on board and we set sail, the rules change....and those of rules that worked on 2d island, do not necessarily work anymore. thanks for bridge here number one. steve =20 ------=_NextPart_000_0065_01C07ADD.A5D2F180 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

brian,

back to the dystances (was, also:=20 12vectors).
      it seems clear that the = whole=20 answer of classifying the roots
   of Bucky's frequencies = of=20 cuboctohedral clumps o'balls,
   is that they are just the = roots of=20 "square" numbers; dig?

wonderful...number 1.

= although each=20 facet will have many different roots,

dig it man.

they are all in the = same facets,=20

so the "hull" is the same, = cuboctahedral. =20

i am hip to this jive too. = !

are=20 your root(second-power) shapes,
cuboctahedral?... =20 shouldn't they be, so.

here on 2d island...yes.

out at sea...no.

not when you take a radial sweep. = look at=20 the

figures you guys are now=20 making.

one more word about Newton;
=20 ***hole!

perhaps true, i do not know. but=20 regardless,

we need the dude to help us to = eventually get=20 to 3 light

island, so we may have to=20 temporarily

put up with his attitudes. in fact, the = whole=20 voyage is off

unless he comes with us, some please be = nice to=20 him.

   thus quoth:
   eventually, i want = to show=20 the correlation
    between these, roots and=20 frequencies.

i felt that i did not do an adequate = job=20 yet

for this explanation, i am = very pleased=20 that number

one has helped me bridge this = gap.

i have found the mathematical analysis=20 of

ccp to be hypnotic. it seems that = almost=20 anyway

you dissect it...bingo...some other = little doo-dad=20 ?

poops out and makes you muse = further.

i totally understand and all those that = wish=20

to stay at 2d=20 island. i respect those people and their choice

to be at 2d island. it is a most = fascinating=20 place.

it has great comforts and rewards and = none=20

of the perils of the sea.

bucky lived there too on 2d island.=20 where

mathematics is perfect, and mass is=20 ignored.

but as soon as you step on board and=20 we

set sail, the rules change....and those = of

rules that worked on

2d island, do not necessarily work=20 anymore.

thanks for bridge here number = one.

steve

------=_NextPart_000_0065_01C07ADD.A5D2F180-- ========================================================================= Date: Wed, 10 Jan 2001 08:28:56 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: maps MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_007B_01C07ADF.60712F60" This is a multi-part message in MIME format. ------=_NextPart_000_007B_01C07ADF.60712F60 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable brian, on the wayside, Steve; is there any particular benefit to your projection of the globe, navigationally? none that i am aware of. (this is also a criticism (or misapplication) of the Fuller one,=20 (map projection ?) in that it's basically useless for that stuff -- i think i can agree here. without some espcial tricks, anyway! although i have not mused on this.... since the map was in fact ccp based (from root 5), i would suspect something may be possible=20 here. maybe not.=20 perhaps when we go to sea, we may see then ...perhaps not. captain windswept, while having his ultimate mission to arrive at the beach of 3 light island, must be aware that it may not be a straight=20 line to get there. he must pay attention to daily winds. steve =20 ------=_NextPart_000_007B_01C07ADF.60712F60 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

brian,

on the wayside, = Steve;
is=20 there any particular benefit to your projection
of the globe,=20 navigationally?

none that i am aware = of.

(this is also=20 a criticism (or misapplication)
of the Fuller one, =

(map projection ?)

in that
it's basically useless = for that=20 stuff --

i think i can agree here.

without some espcial tricks,=20 anyway!

although i have not mused on = this....

since the map was in fact ccp based = (from root=20 5),

i would suspect something may be = possible=20

here. maybe not.

perhaps when we go to sea, we may see then

...perhaps not.

captain windswept, while = having his ultimate=20 mission

to arrive at the beach of 3 light=20 island,

must be aware that it may not be a = straight=20

line to get there. he must pay = attention=20 to

daily winds.

steve

------=_NextPart_000_007B_01C07ADF.60712F60-- ========================================================================= Date: Wed, 10 Jan 2001 08:45:16 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: scrapping off barnicles MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0085_01C07AE1.A886A300" This is a multi-part message in MIME format. ------=_NextPart_000_0085_01C07AE1.A886A300 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable kirby, > they are all in the same facets, so the "hull" is the same, > cuboctahedral. are your root(second-power) shapes, > cuboctahedral?... shouldn't they be, so. Have you checked the web page Brian??? http://www.inetarena.com/~pdx4d/ocn/wgraphics.html clearly not usually cuboctahedral (I thought you were already versed up to this point in the conversation, am a little surprised at the backsliding -- maybe I just don't get your question). The thing about the cuboctahedron is it picks up the 12 in a cuboctahedral subset of the ccp, but there are others the same distance that the cubocta hasn't yet reached. great for 2d island. As a radar sweepout, the cubocta leaves a lot of unexplored ccp spheres in the bigger circumsphere of root N (or N frequency). It'll get to them eventually, at higher frequencies, but the Watermans connect all those dots now, not when the cubocta grows out to 'em. avast, ye maties...theres the rub. this is important at sea but of no consequence, here at 2d island. So Watermans pick out *all* the ccp spheres that are root N away -- but then we're _still_ not done (I had to re- remember), because in shrink wrapping this convex hull you're going to find N-1, N-2, N-3 (more?) spheres poking through the skin of the Waterman "tent". Hence the color coding of vertices, and Lee's useful question about the W24, W25. > one more word about Newton; > ***hole! > Steve -- Don't get the idea we're all cohorts or one big happy family on GEODESIC. Brian here has a long list of goodies and badies (Newton a baddy) that's unique to a certain literature he savors, but which the rest of us mostly neglect, or at the very least don't bother to memorize. thanks for the background here BASE. he is well informed on newton, excellent...i look forward to his face plant... newtons that is...not number ones, and not captain windswept this time either. doesnt it seem odd that i am not pushing ccp being aba elsewhere. and that i want to take this ridiculous journey, when i could stay quite nicely here in 2d island ? I don't try to keep straight who Brian thinks the goodies are -- not my department. right on BASE, that is number 1's department. i suspect we may find out along the way, should he decide to go. steve Kirby ------=_NextPart_000_0085_01C07AE1.A886A300 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

kirby,

>   they are all in the = same facets,=20 so the "hull" is the same,
>   cuboctahedral. are = your=20 root(second-power) shapes,
>   cuboctahedral?... = shouldn't=20 they be, so.

Have you checked the web page Brian???
http://www.in= etarena.com/~pdx4d/ocn/wgraphics.html

clearly=20 not usually cuboctahedral (I thought you were already
versed up to = this point=20 in the conversation, am a little
surprised at the backsliding -- = maybe I just=20 don't get your
question).

The thing about the cuboctahedron is = it=20 picks up the 12 in
a cuboctahedral subset of the ccp, but there are=20 others
the same distance that the cubocta hasn't yet = reached.

great for 2d island.

As a radar = sweepout,=20 the cubocta leaves a lot of unexplored
ccp spheres in the bigger = circumsphere=20 of root N (or N
frequency). It'll get to them eventually, at=20 higher
frequencies, but the Watermans connect all those dots
now, = not when=20 the cubocta grows out to 'em.

avast, ye maties...theres the rub. this = is=20 important at sea

but of no consequence, here at 2d = island.

So=20 Watermans pick out *all* the ccp spheres that are root
N away -- but = then=20 we're _still_ not done (I had to re-
remember), because in shrink = wrapping=20 this convex hull
you're going to find N-1, N-2, N-3 (more?) spheres=20 poking
through the skin of the Waterman "tent". Hence = the
color=20 coding of vertices, and Lee's useful question
about the W24,=20 W25.

> one more word about = Newton;
> =20 ***hole!
>

Steve --

Don't get the idea we're all = cohorts or=20 one big happy
family on GEODESIC. Brian here has a long list of = goodies
and badies (Newton a baddy) that's unique to a = certain
literature=20 he savors, but which the rest of us mostly
neglect, or at the very = least=20 don't bother to memorize.

thanks for the background here BASE. he = is well=20 informed

on newton, excellent...i look forward = to his face=20 plant...

newtons that is...not number ones, and = not captain=20 windswept

this time either.

doesnt it seem odd that i am not = pushing ccp=20 being

aba elsewhere. and that i want to take = this=20 ridiculous

journey, when i could stay quite nicely = here in 2d=20 island ?

I don't try to keep straight = who Brian=20 thinks the goodies
are -- not my department.

right on BASE, that is number 1's = department. i=20 suspect

we may find out along the way, should = he decide to=20 go.

steve

Kirby

------=_NextPart_000_0085_01C07AE1.A886A300-- ========================================================================= Date: Wed, 10 Jan 2001 09:57:52 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: ccp = ccp MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_00C2_01C07AEB.CC336F40" This is a multi-part message in MIME format. ------=_NextPart_000_00C2_01C07AEB.CC336F40 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable message from BASE... OK, I've done my best to communicate the basic setup used by the "Urner generator" method at: http://www.inetarena.com/~pdx4d/ocn/wmalgorithm.html and to relate this to your preferred Method I. thus quoth... CCP spheres have diameter root(2) in this coordinate system end quote method 1 uses diameter 1 in its coordinate system. both return the ccp. Both of us are showing abababa... stacking along the Z axis, but my sphere grid is rotated 45 degrees relative to yours. Plus I shrink my XYZ measuring apparatus, meaning my CCP spheres seem relatively larger (to XYZ, not to each other). That's what allows me to look for any/all x^2 + y^2 + z^2 =3D 2*D^2 with no thoughts about "even vs. odd" Z-planes. That all goes away, to be replaced by the stipulation that x + y + z must be evenly divisible by 2 -- which as far as I'm concerned, is an improvement. So, just give me a 2*D^2, and I'll find all the (x,y,z) values which solve it, keeping x>=3Dy>=3Dz and permuting order and signage to get the full circumsphere of values. That's what goes on in my poly(), permute() and negperm() methods: http://www.inetarena.com/~pdx4d/ocn/python/waterman.html#poly http://www.inetarena.com/~pdx4d/ocn/python/waterman.html#permute http://www.inetarena.com/~pdx4d/ocn/python/waterman.html#negperm My 2*D^2 values are double yours, for same reason that my intersphere distances are multiples of root(2) instead of 1. That's just how I scale my XYZ, even if I consider the CCP spheres to be "really" unit diameter. If I compensate for these differences at the end of the computation, I can get back to the BASE values you're used to. It's easy enough to translate back and forth, by rescaling by 1/root(2) and rotating 45 degrees. I hope you don't have too much trouble thinking in this way. we only need a perfect BASE,=20 no matter how we get there or what we call it. i do not need, nor desire to comprehend your method or terms here....i only need to know the cannons will fire. Certainly your BASE is calibrated based on certain assumptions, and it won't be useful to compare output from my algorithm with yours if I don't do the rescale and rotation.=20 ccp =3D ccp no matter what procedure you have mathematically devised to decode its structure.. But you shouldn't confuse mere numeric values with the PATTERN that is the CCP. i wish i had said that. nice statement. As long as the spheres pack together that way, abababa = along some axes, abcabcabc along others, in the ways we've described, it's a CCP packing. =20 clarity it its own reward. This is not up for debate as that's how scientists use the term, and it belongs to them, not to you and I. i dig. The numbers are all secondary and nature does CCPs at many different scales, from oranges to cannon balls to fullerenes to individual atoms in some crystals. yes indeed. Given all these different sizes (scales), it's clearly the PATTERN which defines the CCP, not the numbers in your BASE table. =20 yes, yes, yes, yes, yes. However, given the pattern is always similar,=20 you mean, always exactly the same here ? there's always a way to rotate and rescale such that your BASE table matches up with whatever physical example yes on 2d island. (discounting the inevitable aberrations with a physical example will always introduce e.g. oranges aren't perfect spheres -- and even on a computer we have the limitations of floating point registers to think about). out at sea. the BASE is mathematical and therefore exact. the sea is physical and therefore never exact. This translation to your BASE table is what I accomplish with my listbase() method. I rotate by 45 degrees and divide by root(2). Simple. Perhaps in your terminology you'd say the "physical CCP" can be any size, exactly, yes. but the "mathematical CCP" will always match up with your BASE tables. =20 again, exactly yes. which by definition ALWAYS have unit diameters. That's a true enough I suppose. Is that how you'd put it? mathematically ccp by definition has unit ( 1 ) diameter spheres. remembering that the BASE is untouchable, but mods=20 ( sphere size, replaced by tets, squares, mickey mouse ears, or pictures of corn ...are all fine to replace the ccp with to obtain another base, while keeping our BASE=20 in tact. Or Bucky might say: the physical IVM can be any frequency, but the metaphysical IVM always has the same angles, and angles define shape irrespective of size. That's true enough too. The angle/frequency distinction (or shape/size distinction) is at the heart of synergetics. i am not well versed in the nuances of synergetics. i suspect it resides on 2d island. the captain lived there for 10 years. he wasnt a captain then, and he has always respected all that there was on 2d island.=20 he loved his home and the island and all those who reside there.=20 but he dreamed of the sea. and he built rafts and had a few=20 adventures. he longed to go to Cou, and right into Newtons point in the center of the vast sea and dock there for a while.=20 he was gathering some crew now hopefully. the ccp is a mighty ship and may yet win a few battles of her own. steve well done BASE, GREAT documentation. it is nice to get this documentation done now, before the tide goes out, as we may need this even at sea, particularly if you decide=20 to remain here on 2d island. i hope you do come along,=20 but do understand the pull that 2d island can have. ------=_NextPart_000_00C2_01C07AEB.CC336F40 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

message from BASE...

OK, I've = done my best=20 to communicate the basic setup used
by the "Urner generator" method=20 at:

http://www.= inetarena.com/~pdx4d/ocn/wmalgorithm.html

and=20 to relate this to your preferred Method I.

thus quoth...

CCP spheres have diameter root(2) in = this=20 coordinate system

end quote

&nbs= p; =20 method 1 uses diameter 1

&nbs= p; =20 in its coordinate system.

&nbs= p; =20 both return the ccp.

Both of us are showing abababa... = stacking along=20 the Z axis,
but my sphere grid is rotated 45 degrees relative to=20 yours.
Plus I shrink my XYZ measuring apparatus, meaning my = CCP
spheres=20 seem relatively larger (to XYZ, not to each other).
That's what = allows me to=20 look for any/all

x^2 + y^2 + z^2 =3D 2*D^2

with no = thoughts=20 about "even vs. odd" Z-planes. That all
goes away, to be = replaced by=20 the stipulation that
x + y + z must be evenly divisible by 2 -- which = as far=20 as
I'm concerned, is an improvement.

So, just give me a 2*D^2, = and=20 I'll find all the (x,y,z) values
which solve it, keeping = x>=3Dy>=3Dz and=20 permuting order and
signage to get the full circumsphere of = values. =20 That's
what goes on in my poly(), permute() and negperm() = methods:

ht= tp://www.inetarena.com/~pdx4d/ocn/python/waterman.html#poly
http://www.inetarena.com/~pdx4d/ocn/python/waterman.html#permute
= http://www.inetarena.com/~pdx4d/ocn/python/waterman.html#negperm
=
My=20 2*D^2 values are double yours, for same reason that
my intersphere = distances=20 are multiples of root(2) instead
of 1. That's just how I scale = my XYZ,=20 even if I consider
the CCP spheres to be "really" unit = diameter.

If I=20 compensate for these differences at the end of the
computation, I can = get=20 back to the BASE values you're used
to. It's easy enough to = translate=20 back and forth, by
rescaling by 1/root(2) and rotating 45 = degrees.

I=20 hope you don't have too much trouble thinking in this way.

&nbs= p; =20 we only need a perfect BASE,

&nbs= p; =20 no matter how we get there

&nbs= p; = ; =20 or what we call it.

&nbs= p; =20 i do not need, nor desire to

&nbs= p; = ; =20 comprehend your method

&nbs= p; =20 or terms here....i only need

&nbs= p; =20 to know the cannons will fire.

Certainly your BASE is calibrated = based on=20 certain assumptions,
and it won't be useful to compare output from my = algorithm
with yours if I don't do the rescale and=20 rotation.

ccp =3D ccp no matter = what=20 procedure you have mathematically

devised to decode its = structure..

But you shouldn't confuse mere = numeric values=20 with the PATTERN that
is the CCP.

&nbs= p; = ; =20 i wish i had said that. nice statement.

&nbs= p; =20 As long as the spheres pack together that way, abababa along
some = axes,=20 abcabcabc along others, in the ways we've described,
it's a CCP=20 packing.

clarity it its own reward.

This is not up for debate as that's=20 how
scientists use the term, and it belongs to them, not to = you
and=20 I.

i dig.

The numbers are all = secondary and=20 nature does CCPs at many
different scales, from oranges to cannon = balls to=20 fullerenes
to individual atoms in some crystals.

yes indeed.

Given all these = different sizes=20 (scales), it's clearly the
PATTERN which defines the CCP, not the = numbers in=20 your BASE
table.

yes, yes, yes, yes, yes.

However, given the pattern is always = similar,=20

you mean, always exactly the same here=20 ?

there's
always a way to rotate and = rescale such=20 that your BASE table
matches up with whatever physical = example

yes on 2d island.

(discounting the
inevitable = aberrations=20 with a physical example will always
introduce e.g. oranges aren't = perfect=20 spheres -- and even
on a computer we have the limitations of floating = point
registers to think about).

out at sea.

the BASE is mathematical and therefore=20 exact.

the sea is physical and therefore never = exact.

This translation to your BASE table = is what I=20 accomplish with
my listbase() method. I rotate by 45 degrees = and divide=20 by
root(2). Simple.

Perhaps in your terminology you'd = say the=20 "physical CCP"
can be any size,

exactly, yes.

but the "mathematical CCP" will=20 always
match up with your BASE tables.

again, exactly yes.

which by definition ALWAYS have unit=20 diameters.

That's a true enough I suppose. = Is that how=20 you'd put it?

mathematically ccp by definition has = unit ( 1 )=20 diameter

spheres.

remembering that the BASE is = untouchable, but mods=20

( sphere size, replaced by tets, = squares, mickey=20 mouse

ears, or pictures of corn ...are all = fine to=20 replace the

ccp with to obtain another base, while = keeping our=20 BASE

in tact.

Or Bucky might = say: the=20 physical IVM can be any frequency,
but the metaphysical IVM always = has the=20 same angles, and
angles define shape irrespective of size. = That's=20 true
enough too. The angle/frequency distinction (or=20 shape/size
distinction) is at the heart of synergetics.

i am not well versed in the nuances of=20 synergetics.

i suspect it resides on 2d = island.

the captain lived there for 10 = years. he wasnt=20 a captain then,

and he has always respected all that = there was on=20 2d island.

he loved his home and the island and all those who reside there.

but he dreamed of the sea. and he = built rafts=20 and had a few

adventures. he longed to go to Cou, and = right into=20 Newtons point

in the center of the vast sea and dock = there for a=20 while.

he was gathering some crew now = hopefully. the ccp=20 is a mighty

ship and may yet win a few battles of = her=20 own.

steve

well done BASE, GREAT = documentation. it=20 is nice to get

this documentation done now, before the = tide goes=20 out,

as we may need this even at sea, = particularly if=20 you decide

to remain here on 2d=20 island. i hope you do come along, =

but do understand the pull that 2d island can have.

------=_NextPart_000_00C2_01C07AEB.CC336F40-- ========================================================================= Date: Wed, 10 Jan 2001 10:45:04 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: jj MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0134_01C07AF2.640509E0" This is a multi-part message in MIME format. ------=_NextPart_000_0134_01C07AF2.640509E0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable crew,=20 the captain believes that the showing of jj may be counter-productive to the understanding of ccp, especially since you link to jj first, before going to waterman polyhedra. and the while the captain is generally an easy sort of man, he thinks that jj should walk the plank, or at least be maroon on jj island. but the captain has a bit of a grudge here,=20 and may be blinded by his own feelings, and have put logic aside for revenge. what say yee maties...walk the plank ? to jj island ? should he stay aboard ? steve ------=_NextPart_000_0134_01C07AF2.640509E0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

crew,

the captain believes that the showing = of=20 jj

may be counter-productive to the=20 understanding

of ccp, especially since you link = to jj=20 first,

before going to waterman = polyhedra.

and the while the captain is generally = an=20 easy

sort of man, he thinks that jj should = walk=20 the

plank, or at least be maroon on jj=20 island.

but the captain has a bit of a grudge = here,=20

and may be blinded by his own=20 feelings,

and have put logic aside for = revenge.

what say yee maties...walk the plank = ?

to jj island ? should he stay = aboard=20 ?

steve

------=_NextPart_000_0134_01C07AF2.640509E0-- ========================================================================= Date: Wed, 10 Jan 2001 08:31:09 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Dexter Graphic Subject: I think it's time for me to go MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit In spite of Bucky's personal dedication and lifelong research/development/educational efforts, most people have rejected the idea of making the world work for everyone. It's a spiritual matter, a personal choice between serving self-interest or the Universal Family. I believe Jay Hanson is right, we will soon be running out of oil and the current greed-based economic system will collapse, the established world order will come crashing down. Humankind will reap what they have sown. To prepare for this scenario which will soon unfold, I will be curtailing my on-line activities and focusing on physical preparations. It may be wise to leave the country; the higher you are the further you will fall. "Sin was bewitching and adventurous in the committing, but now must the harvest of the naked and unromantic facts be faced." "And finally, man reaps the harvest of his own iniquitous persistence in rebellion against the righteous rule of heaven on earth." (The Urantia Book) Best of luck, Dexter Graphic Links: http://dieoff.com/synopsis.htm http://www.egroups.com/group/dieoff http://www.egroups.com/group/energyresources http://www.urantia.org/papers/index.html ========================================================================= Date: Wed, 10 Jan 2001 08:51:03 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: ccp = ccp In-Reply-To: Mime-Version: 1.0 Content-Type: text/enriched; charset="us-ascii" Arial we only need a perfect BASE, no matter how we get there or what we call it. i do not need, nor desire to comprehend your method or terms here....i only need to know the cannons will fire. <<<<<<<< I think it'd be more important for you to understand this alternate method, so you can trust the numbers you get if you, or anyone else, decides to print out more exhaustive tabulations by using it. When it comes to generating W150 and higher, I don't think you have a way of doing that (see below). >>>> Arialccp = ccp no matter what procedure you have mathematically devised to decode its structure.. <<<<<<<< CCP is the PATTERN of spheres. The diameter you assign the spheres depends on the measuring stick. You count Z planes as 1,2,3... even though those are multiples of root(2), ergo you too have more than one yardstick in the mix. Arialthere's always a way to rotate and rescale such that your BASE table matches up with whatever physical example Arialyes on 2d island. <<<<<<<< I don't understand "2d island". The coordinates I'm generating are (x,y,z), meaning "3d". Arialmathematically ccp by definition has unit ( 1 ) diameter spheres. <<<<<<<< I also use "unit radius" in my calcs a lot, meaning diameter = 2. Again, deciding whether "unit" is a radius, or a diameter, is up to the user -- has no impact on the PATTERN we call CCP. You just have to label the BASE tables accordingly, and multiply all the numbers in them by a constant to go between these options (easy on a spreadsheet). Arialremembering that the BASE is untouchable, but mods ( sphere size, replaced by tets, squares, mickey mouse ears, or pictures of corn ...are all fine to replace the ccp with to obtain another base, while keeping our BASE in tact. <<<<<<<< The BASE is untouchable only because you say that it is. If someone else comes along and does all the calcs with radius = 1, diameter =2, I'm not going to say, "that's not the CCP", just "that's just multiplying Steve's BASE cells by 2 -- no problem". Arial Or Bucky might say: the physical IVM can be any frequency, but the metaphysical IVM always has the same angles, and angles define shape irrespective of size. That's true enough too. The angle/frequency distinction (or shape/size distinction) is at the heart of synergetics. Ariali am not well versed in the nuances of synergetics. i suspect it resides on 2d island. <<<<<<<< So far, your use of "2d island" is unclear over here. Arialwell done BASE, GREAT documentation. it is nice to get this documentation done now, before the tide goes out, as we may need this even at sea, particularly if you decide to remain here on 2d island. i hope you do come along, but do understand the pull that 2d island can have. <<<<<<<< I have no idea what "2d island" means. Here's a question: even if we have an exhaustive BASE table, I don't see how you manage to decide if a given sphere participates in the shrink-wrap out there in "high numbers ville". It's sometimes extremely subtle whether a given sphere is "just outside" of the plane defined by its closest neighbors or "just inside" (in which case it doesn't qualify, as the hull would no longer be convex). Just having the tables doesn't answer this question. You can solve the problem by visual inspection out to a certain distance, but I think out around 150 you have to resort to mathematical techniques that are quite sophisticated, and which for the time being I'm leaving entirely to Qhull. If there's a ship in this picture, and if the "3d sea" is the depths of the CCP ocean, vs. what we can easily manually navigate ("2d island"), then it's Qhull. I so far trust Qhull to get the right answers, in large part because I'm feeding it a diet of 100% integers. But I certainly wouldn't have the same faith in you or I, left alone with the BASE, but without Qhull. I think we'd drown. Kirby ========================================================================= Date: Wed, 10 Jan 2001 08:59:30 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: jj In-Reply-To: Mime-Version: 1.0 Content-Type: text/enriched; charset="us-ascii" At 10:45 AM 01/10/2001 -0500, you wrote: >>>> Arialcrew, Arialthe captain believes that the showing of jj may be counter-productive to the understanding of ccp, especially since you link to jj first, before going to waterman polyhedra. <<<<<<<< That's no longer the case. As soon as I refigured the true Watermans, I bumped up the web page numbers. wgraphics.html and wgraphics1.html are watermans. wgraphics2.html and wgraphics3.html are fixed radius. My Resources page (cp4e.html) goes directly to the Watermans. If I do an expository page on Watermans, which describes the algorithm and ideas using more words than pictures, I'll probably swap that in as wgraphics.html and rename the current wgraphics.html to wgraphics0.html. >>> Arialto jj island ? should he stay aboard ? Arialsteve <<<<<<<< I'm perhaps partly responsible for the JJs, as I was the one who first introduced Towle to "Watermans" and I may have committed the same error then as I did this time: I talked about all spheres at distance N w/o mentioning that a shrink-wrap would pick up additional spheres at N-1, N-2 etc. So he started doing the renderings in Mathematica. Then it came out what "true Watermans" were (deja vu!). Maybe this is how it went -- at this point, I'm no longer sure (we could ask Russell). However, whenever you compute a Waterman, you're getting the corresponding "jj" (fixed radius poly) for free. It uses all the same information, is basically a "connect the dots" using the gold spheres only. It's an easier concept to impart in some ways, and I think a useful stepping stone to the true Watermans. Since I've already done the work and posted the pages, I'm not inclined to take them down. They're correct, so far as they go. Plus I want to acknowledge Towle for his contributions to this scenario. It's thanks to him that we have any renderings of the higher watermans (which you seem to have taken down from your website, or delinked, meaning I can't find them to compare with mine). Kirby ========================================================================= Date: Wed, 10 Jan 2001 09:01:10 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: I think it's time for me to go In-Reply-To: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" >"Sin was bewitching and adventurous in the committing, >but now must the harvest of the naked and unromantic >facts be faced." "And finally, man reaps the harvest of >his own iniquitous persistence in rebellion against the >righteous rule of heaven on earth." (The Urantia Book) > > >Best of luck, >Dexter Graphic I'll be sure to let people know that the Urantia Book is for the weak minded who can't handle Bucky -- a bible of the "take care of number one first" survivalists who are more part of the problem than part of the solution. Good luck. Kirby ========================================================================= Date: Wed, 10 Jan 2001 09:28:34 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Mark Siegmund Subject: Re: I think it's time for me to go In-Reply-To: Mime-version: 1.0 Content-type: text/plain; charset="US-ASCII" Content-transfer-encoding: 7bit Dexter, I know how you feel about escaping--I sometimes share your feelings of hopelessness--however, who's going to "fight the good fight" if you leave? Furthermore, Bucky emphasized to human conditions that provide hope: 1. We are trial and error creatures 2. He believed in, "Emergence through Emergency"--see his book, "Nine Chains to the Moon"--the chapter on Emergence through Emergency. Mark > From: Dexter Graphic > Reply-To: List for the discussion of Buckminster Fuller's works > > Newsgroups: bit.listserv.geodesic > Date: Wed, 10 Jan 2001 08:31:09 -0800 > To: GEODESIC@LISTSERV.ACSU.BUFFALO.EDU > Subject: I think it's time for me to go > > In spite of Bucky's personal dedication and lifelong > research/development/educational efforts, most people > have rejected the idea of making the world work for > everyone. It's a spiritual matter, a personal choice > between serving self-interest or the Universal Family. > > I believe Jay Hanson is right, we will soon be running > out of oil and the current greed-based economic system > will collapse, the established world order will come > crashing down. Humankind will reap what they have sown. > > To prepare for this scenario which will soon unfold, I > will be curtailing my on-line activities and focusing > on physical preparations. It may be wise to leave the > country; the higher you are the further you will fall. > > "Sin was bewitching and adventurous in the committing, > but now must the harvest of the naked and unromantic > facts be faced." "And finally, man reaps the harvest of > his own iniquitous persistence in rebellion against the > righteous rule of heaven on earth." (The Urantia Book) > > > Best of luck, > Dexter Graphic > > > Links: > http://dieoff.com/synopsis.htm > http://www.egroups.com/group/dieoff > http://www.egroups.com/group/energyresources > http://www.urantia.org/papers/index.html > ========================================================================= Date: Wed, 10 Jan 2001 09:45:34 PST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: 'Bill' 'Eagleton' Subject: Re: [I think its time for me to go] Comments: cc: dextergraphic@PRODIGY.NET Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: quoted-printable Dexter Graphic wrote: >I believe ... the established world order will come crashing down. >To prepare ... I will be focusing on physical preparations. > the higher you are the further you will fall. Best of luck, Dexter Graphic *So... does this imply a geodesic portable tent? BTW... the bible suggests one head for the hills. w/o Bucky, we may not have the sown geodesic tent, to reap. Geodesics are more than mere jewels, they can also be survival. [I think its time for me to go] Then go... geodesic. The other choice... "And now it's time to say goodbye to all the boys and girls. Mic-key Mouse!" :>) BillSF9c cc: dextergraphic@PRODIGY.NET ____________________________________________________________________ Get your own FREE, personal Netscape WebMail account today at http://home= =2Enetscape.com/webmail ========================================================================= Date: Wed, 10 Jan 2001 09:46:05 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Dick Fischbeck Subject: Re: distance calc for frequencies MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii --- Brian Hutchings wrote: > <> Brian �Quincy! Hutchings > 09-JAN-2001 14:01 > r001806@pen2.ci.santa-monica.ca.us > > oops. > > <> Brian ?Quincy! Hutchings > 09-JAN-2001 8:35 > > r001806@pen2.ci.santa-monica.ca.us > > > http://www.inetarena.com/~pdx4d/ocn/wgraphics1.html > > neat; it seems that all of the facets are > "archimedean;" > did you see any that were'nt in that limited > class? > What are these shapes for? Is there a practical application, Steve? Where are we going with this stacking? Dick ========================================================================= Date: Wed, 10 Jan 2001 09:58:45 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Dick Fischbeck Subject: Re: I think it's time for me to go MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii > I believe Jay Hanson is right, we will soon be > running > out of oil and the current greed-based economic > system > will collapse, the established world order will come > crashing down. Humankind will reap what they have > sown. > Nature(gOd, if perferred) only allows what does not contradict her laws. She is not testing us in a moral sense. Wealth is life support, and it can only increase(with a couple of exceptions). > To prepare for this scenario which will soon ========================================================================= Date: Wed, 10 Jan 2001 10:14:07 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: distance calc for frequencies In-Reply-To: <20010110174605.17865.qmail@web4405.mail.yahoo.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" >What are these shapes for? Is there a practical >application, Steve? Where are we going with this >stacking? Dick > My own view is the Waterman Polys likely have no practical applications, other than to stimulate student interest in the CCP, which _is_ critical to grok. But that's not a stroke against them: they're beautiful lures, and we'll hook some mighty fine Cosmic Fish by usin' em. Kirby ========================================================================= Date: Wed, 10 Jan 2001 10:11:49 PST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: 'Bill' 'Eagleton' Subject: Re: [Re: waterman poly 25] Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: quoted-printable >It's about 180K, hope not too onerous. >http://www.inetarena.com/~pdx4d/ocn/graphics/wm24to25.gif >[Note: on my Netscape, the transition from W24 to W25 and back is fairly peppy -- Anyway, watch the animated GIF if you would a= nd tell me if you find it enlightening. Kirby *I use Netscape for eMail and I realy liked it. I will try IE also tho just to watch it slower... Nope. Ran them side by side and they kept pace exactly! If you meant download, I cannot say, as I have a fast download ability. Netscape 6.0 is to be avoided as it is largely still buggy yet. Are previous Netscapes are still downloadable and 4.75 is fine. Thx, cool gif. BillSF9c ____________________________________________________________________ Get your own FREE, personal Netscape WebMail account today at http://home= =2Enetscape.com/webmail ========================================================================= Date: Wed, 10 Jan 2001 13:17:29 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: 2d = no mass involved. MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_01BB_01C07B07.AEFBD0E0" This is a multi-part message in MIME format. ------=_NextPart_000_01BB_01C07B07.AEFBD0E0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable we only need a perfect BASE, no matter how we get there or what we call it. i do not need, nor desire to comprehend your method or terms here....i only need to know the cannons will fire. <<<< I think it'd be more important for you to understand this alternate method, so you can trust the numbers you get if you, or anyone else, decides to print out more exhaustive tabulations by using it. i trust my numbers our to 1022, i trust over that it can be mathematically discerned over time to replicate to endless root values. i trust that the urner generator will work perfectly over time, even if it does not now. eventually it can be cross checked=20 with the abc method to also replicate the ccp. more importantly, than even having it work, is your faith that it can eventually be accomplished, by you and/or others i only need to know from BASE if they believe eventually=20 they can get it to be perfect. (w i p ) ....................................................................... When it comes to generating W150 and higher, I don't think you have a way of doing that (see below). >>>> ccp =3D ccp no matter what procedure you have mathematically devised to decode its structure.. <<<< CCP is the PATTERN of spheres. yes. The diameter you assign the spheres depends on the measuring stick.=20 BASE, as i see it, can only have unit spheres by MATHEMATICAL = definition. YES, you could change all the diameters to other than unit 1, and it would still return a ccp PATTERN. this is however, a base FROM BASE....SO,=20 all manner of manipulation is fine. so, in my mind, BASE by definition must be unitary ( 1 ). FROM BASE, i see as base, and may or may not replicate the ccp. .........................................................................= ......................... You count Z planes as 1,2,3... even though those are multiples of root(2), ergo you too have more than one yardstick in the mix. yes, any technique that decodes ccp is viable, so long as the mathematical technique replicates the ccp. you needed to learn my jargon to design the urner generator. i only need to know that you belief you can replicate the=20 ccp eventually with some method, the method is totally irrelevant as to its particulars to me...not much of a=20 programmer . i KNOW it can be done mathematically... since i have had that experience. i used my mathematical method(s) to return the ccp, i suspect there are many different=20 ways to mathematically generate the ccp. i do not need to know how you do it, and fear i will just=20 get lost in stuff i already do not comprehend. .........................................................................= ............................ there's always a way to rotate and rescale such that your BASE table matches up with whatever physical example yes on 2d island. <<<< I don't understand "2d island".=20 by 2d island i mean where the mathematics of 2d always works. ( NO MASS involved) The coordinates I'm generating are (x,y,z), meaning "3d". yes, the mathematical/physical is most confusing. i have a plan, how to possible resolve this with the frequency data.=20 mathematically BASE by definition has unit ( 1 ) diameter spheres. <<<< I also use "unit radius" in my calcs a lot, meaning diameter =3D 2. Again, deciding whether "unit" is a radius, or a diameter, is up to the user --=20 anyway you can mathematically replicate the ccp is fine. potato/potatoe has no impact on the PATTERN we call CCP. that is all that is required then. You just have to label the BASE tables accordingly, and multiply all the numbers in them by a constant to go between these options (easy on a spreadsheet). however you do it is fine, i could only do it empirically. use whatever method(s) you can....but in the end, you want the BASE ccp....and it by definition has unit 1. if your program needed to multiply, say 6/7 to the eighth power, to do this i do not care. so long as it returns the valid BASE. .........................................................................= ........................... remembering that the BASE is untouchable, but mods ( sphere size, replaced by tets, squares, mickey mouse ears, or pictures of corn ...are all fine to replace the ccp with to obtain another base, while keeping our BASE in tact. <<<< The BASE is untouchable only because you say that it is. If someone else comes along and does all the calcs with radius =3D 1, diameter =3D2, I'm not going to say, "that's not the CCP", neither am i, it is ccp...just not BASE..which is unitary one diameter.=20 just "that's just multiplying Steve's BASE cells by 2 -- no problem". i have no problem here either,=20 if the ccp PATTERN has unit 1 diameter...then it is BASE. IF THE CCP PATTERN is NOT diameter 1, then it is base. base here, meaning ANY variation of BASE.=20 FROM BASE...you get base(s)....which by definition CANNOT have unit diameters this time. .........................................................................= ................ Or Bucky might say: the physical IVM can be any frequency, but the metaphysical IVM always has the same angles, and angles define shape irrespective of size. That's true enough too. The angle/frequency distinction (or shape/size distinction) is at the heart of synergetics. i am not well versed in the nuances of synergetics. i suspect it resides on 2d island. <<<< So far, your use of "2d island" is unclear over here. 2d island is where all mathematics works all the time, as there is no "physical" component of MASS. frequency 3...works fine on 2d island, but when the physical component of mass and gravitational attraction is added, frequency 3, will not work at sea. since frequency 3 contains root 9 spheres and ignores=20 root 8, i will have a problem with that at sea. at sea,=20 the root 9, cannot gravitationally adhere to this agglomeration prior to all the root 8 spheres. physically, out in the sea....it is my contention, that=20 ALL root 8 would adhere prior to any root 9. in this physical sense, frequency 3 does not equate to the sea but only here at 2d island. perhaps the most confusing thing here, is trying to wrap=20 your brain around why xyz...3d is not physical. yes it is physical on 2d island, in the sense the it has 3 dimensions, however, i see that as a mathematical entity as no mass is involved. physical (at sea contains mass) mathematical ( 2d island 2d/3d geometric no mass) ( the sea....is where the physical component of mass gets added confusing to say the least. this may take me a bit to express what i am after here....hang in, it is definitely difficult. =20 .........................................................................= .................. well done BASE, GREAT documentation. it is nice to get this documentation done now, before the tide goes out, as we may need this even at sea, particularly if you decide to remain here on 2d island. i hope you do come along, but do understand the pull that 2d island can have. <<<< I have no idea what "2d island" means. mathematically, no mass involved. .........................................................................= ........... Here's a question: even if we have an exhaustive BASE table, I don't see how you manage to decide if a given sphere participates in the shrink-wrap out there in "high numbers ville".=20 either do i, i suggest=20 thus quoth by running the n, n-1, n-2 i suggest that a new pattern will develop... and be mathematically, eventually visually definable. ( they always have in the past ) we match the root number to the n, n-1, n-2 for the lower roots i suspect we have the pattern=20 both mathematically definable and physical definable in doing visual comparative analysis by as little as root 100. [ apparently this may be a lo estimate ] and perhaps normally the ways things happens in ccp having aba analysis is that=20 =20 first you generate=20 the n-1....and usually by the fifth=20 element/hit/good/acceptable/equal you can already determine the whole series. then what normally will happen, ( and so probably will this time too ) is get the first 5 n-2 series and determine it. when you get the 5 n-3 series. bingo. now you have a series of series. and usually, with that, you have them all. .........................................................................= ... It's sometimes extremely subtle whether a given sphere is "just outside" of the plane defined by its closest neighbors or "just inside" (in which case it doesn't qualify, as the hull would no longer be convex). Just having the tables doesn't answer this question. You can solve the problem by visual inspection out to a certain distance, but I think out around 150 you have to resort to mathematical techniques that are quite sophisticated, and which for the time being I'm leaving entirely to Qhull. yes, i think so too, give me the raw data 1-100, i would like to crack at it. If there's a ship in this picture, and if the "3d sea" is the depths of the CCP ocean, vs. what we can easily manually navigate ("2d island"), then it's Qhull.=20 you the BASE, i doubt i can help much=20 anymore.... I so far trust Qhull to get the right answers, in large part because I'm feeding it a diet of 100% integers. sounds like a good strategy. But I certainly wouldn't have the same faith in you or I, left alone with the BASE, but without Qhull.=20 i have faith in you Kirby. we have years to get the BASE right if we need to.=20 you guys have done more work, got more results, understanding, muses, feedback, depictions, ideas, scrunched into 2 weeks, than i did in over 10 years on my own. I think we'd drown. i almost did, thanks for the lifeline !! steve ------=_NextPart_000_01BB_01C07B07.AEFBD0E0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

we only need a = perfect=20 BASE,
no matter how we get there
or what we call it.
i do not = need,=20 nor desire to
comprehend your method
or terms here....i only = need
to=20 know the cannons will = fire.

<<<<

I think it'd be more important for you to=20 understand
this alternate method, so you can trust the numbers
you = get if=20 you, or anyone else, decides to print out
more exhaustive tabulations = by=20 using it.

i trust my numbers our to 1022, i trust over that it can

be mathematically discerned over time to replicate

to endless root values.

i trust that the urner generator will work perfectly over = time,

even if it does not now. eventually it can be cross checked =

with the abc method to also replicate the ccp.

more importantly, than even having it work, is your faith

that it can eventually be accomplished, by you and/or

others

i only need to know from BASE if they believe eventually

they can get it to be perfect. (w i p )

....................................................................= ...

When it comes to generating W150 and higher, I = don't
think you=20 have a way of doing that (see below).

>>>>

ccp =3D ccp no = matter what=20 procedure you have mathematically
devised to decode its = structure..

<<<<

CCP is the PATTERN of spheres.

yes.

The diameter you assign
the spheres depends on the = measuring=20 stick.

BASE, as i see it, can only have unit spheres by MATHEMATICAL=20 definition.

YES, you could change all the diameters to other than unit 1,

and it would still return a ccp PATTERN.

this is however, a base FROM BASE....SO,

all manner of manipulation is fine.

so, in my mind, BASE by definition must be unitary ( 1 ).

FROM BASE, i see as base, and may or may not replicate the = ccp.

....................................................................= ..............................

You count
Z planes as 1,2,3... even though those are multiples=20 of
root(2), ergo you too have more than one yardstick in
the = mix.

yes, any technique that decodes ccp is viable, so long

as the mathematical technique replicates the ccp.

you needed to learn my jargon to design the urner = generator.

i only need to know that you belief you can replicate the

ccp eventually with some method, the method is totally

irrelevant as to its particulars to me...not much of a

programmer . i KNOW it can be done mathematically...

since i have had that experience. i used my = mathematical

method(s) to return the ccp, i suspect there are many different =

ways to mathematically generate the ccp.

i do not need to know how you do it, and fear i will just

get lost in stuff i already do not comprehend.

................................................................= .....................................

there's
always a way = to=20 rotate and rescale such that your BASE table
matches up with = whatever=20 physical example

yes=20 on 2d island.

<<<<

I don't understand "2d island".

by 2d island i mean where the mathematics of

2d always works. ( NO MASS involved)

The coordinates
I'm generating are (x,y,z), meaning "3d".

yes, the mathematical/physical is most confusing.

i have a plan, how to possible resolve this with the

frequency data.

mathematically BASE by=20 definition has unit ( 1 )=20 = diameter
spheres.

<<<<
=
I=20 also use "unit radius" in my calcs a lot,
meaning diameter =3D 2. = Again,=20 deciding whether
"unit" is a radius, or a diameter, is up to = the
user --=20

anyway you can mathematically replicate the ccp is fine.

potato/potatoe

has no impact on the PATTERN we call
CCP.

that is all that is required then.

You just have to label the BASE tables
accordingly, and = multiply=20 all the numbers in
them by a constant to go between these = options
(easy on=20 a spreadsheet).

however you do it is fine, i could only do it empirically.

use whatever method(s) you can....but in the end, you want

the BASE ccp....and it by definition has unit 1.

if your program needed to multiply, say 6/7 to the eighth = power,

to do this i do not care. so long as it returns the valid = BASE.

................................................................= ....................................

remembering that = the BASE=20 is untouchable, but mods
( sphere size, replaced by tets, squares, = mickey=20 mouse
ears, or pictures of corn ...are all fine to replace = the
ccp with=20 to obtain another base, while keeping our BASE
in = tact.

<<<<

The BASE is untouchable only because you=20 say
that it is. If someone else comes along and does
all the calcs = with=20 radius =3D 1, diameter =3D2,
I'm not going to say, "that's not the = CCP",

neither am i, it is ccp...just not BASE..which

is unitary one diameter.

just "that's just multiplying Steve's BASE
cells by 2 -- no=20 problem".

i have no problem here either,

if the ccp PATTERN has unit 1 diameter...then it is BASE.

IF THE CCP PATTERN is NOT diameter 1, then it is base.

base here, meaning ANY variation of BASE.

FROM BASE...you get base(s)....which by definition CANNOT

have unit diameters this time.

....................................................................= .....................

Or Bucky might say: = the=20 physical IVM can be any frequency,
but the metaphysical IVM always = has the=20 same angles, and
angles define shape irrespective of size. That's=20 true
enough too. The angle/frequency distinction (or=20 shape/size
distinction) is at the heart of = synergetics.

i=20 am not well versed in the nuances of synergetics.
i suspect it = resides on=20 2d island.

<<<<

So far, your use of "2d island" is unclear=20 over
here.

2d island is where all mathematics works all the time,

as there is no "physical" component of MASS.

frequency 3...works fine on 2d island,

but when the physical component of mass and = gravitational

attraction is added, frequency 3, will not work at sea.

since frequency 3 contains root 9 spheres and ignores

root 8, i will have a problem with that at sea. at sea, =

the root 9, cannot gravitationally adhere to this = agglomeration

prior to all the root 8 spheres.

physically, out in the sea....it is my contention, that

ALL root 8 would adhere prior to any root 9.

in this physical sense, frequency 3 does not equate to the

sea but only here at 2d island.

perhaps the most confusing thing here, is trying to wrap

your brain around why xyz...3d is not physical.

yes it is physical on 2d island, in the sense the it has 3=20 dimensions,

however, i see that as a mathematical entity as no mass is=20 involved.

physical (at sea contains mass)

mathematical ( 2d island =20 2d/3d geometric no mass)

( the sea....is where the physical component

of mass gets added

confusing to say the least. this may take me a bit

to express what i am after here....hang in, it is definitely

difficult.

....................................................................= .......................

well = done BASE, GREAT documentation. it is nice to get
this documentation = done=20 now, before the tide goes out,
as we may need this even at sea, = particularly=20 if you decide
to remain here on 2d island. i hope you do come = along,
but=20 do understand the pull that 2d island can=20 have.

<<<<

I have no idea what "2d island" = means.

mathematically, no mass=20 involved.
............................................................= ........................

Here's a question: even if we have an exhaustive
BASE table, = I don't=20 see how you manage to decide
if a given sphere participates in the=20 shrink-wrap
out there in "high numbers ville".

either do i, i suggest

thus quoth

by running the n, n-1, n-2

i suggest that a new pattern will=20 develop...

and be mathematically, eventually = visually=20 definable.

( they always have in the past = )

we match the root number to = the

n, n-1, n-2 for the lower = roots

i suspect we have the pattern =

both mathematically = definable

and physical definable

in doing visual = comparative

analysis by as little as root = 100.

[ apparently this may be a lo estimate ]

and perhaps

normally the ways things happens in=20 ccp

having aba analysis is that =

first you generate

the n-1....and usually by the fifth =

element/hit/good/acceptable/equal

you can already determine the whole=20 series.

then what normally will happen, ( and=20 so

probably will this time too ) is get=20 the

first 5 n-2 series and determine = it.

when you get the 5 n-3 series. = bingo.

now you have a series of = series.

and usually, with that, you have them=20 all.

....................................................................= ........

It's sometimes
extremely subtle whether a given sphere is=20 "just
outside" of the plane defined by its closest neighbors
or = "just=20 inside" (in which case it doesn't qualify,
as the hull would no = longer be=20 convex).

Just having the tables doesn't answer this = question.
You can=20 solve the problem by visual inspection out
to a certain distance, but = I think=20 out around 150
you have to resort to mathematical techniques = that
are=20 quite sophisticated, and which for the time
being I'm leaving = entirely to=20 Qhull.

yes, i think so too, give me the raw data 1-100,

i would like to crack at it.

If there's a ship in this = picture, and=20 if the "3d
sea" is the depths of the CCP ocean, vs. what we
can = easily=20 manually navigate ("2d island"), then
it's Qhull.

you the BASE, i doubt i can help much

anymore....

I so far trust Qhull to get the right
answers, in large part = because I'm=20 feeding it a
diet of 100% integers.

sounds like a good strategy.

But I certainly wouldn't
have the same faith in you or I, = left=20 alone with
the BASE, but without Qhull.

i have faith in you Kirby. we have years to get the

BASE right if we need to.

you guys have done more work, got more results, = understanding,

muses, feedback, depictions, ideas, scrunched into 2 weeks,

than i did in over 10 years on my own.

I think we'd drown.

i almost did, thanks for the lifeline !!

steve

------=_NextPart_000_01BB_01C07B07.AEFBD0E0-- ========================================================================= Date: Wed, 10 Jan 2001 13:48:42 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Stephen O'Shaughnessy Subject: Re: I think it's time for me to go MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" If the end is near/here, what's to prepare for? End or no, why do something different. I once heard someone ask, 'if you knew you only had one week (month/year) to live what would you do with the time?' Question 2 was, 'Why aren't you doing that now?' Steve O P.S. My dad was diagnosed with terminal cancer on Dec. 22. He was given 2 wk. to 2 months. The end is near. Besides the obvious (hospice has moved a bed in on the ground floor, and people are coming to see him vs him going to see them, he's sick an unable to function normally) little has really changed. > -----Original Message----- > From: Dick Fischbeck [mailto:dick_fischbeck@YAHOO.COM] > Sent: Wednesday, January 10, 2001 12:59 PM > To: GEODESIC@LISTSERV.ACSU.BUFFALO.EDU > Subject: Re: I think it's time for me to go > > > > I believe Jay Hanson is right, we will soon be > > running > > out of oil and the current greed-based economic > > system > > will collapse, the established world order will come > > crashing down. Humankind will reap what they have > > sown. > > > Nature(gOd, if perferred) only allows what does not > contradict her laws. She is not testing us in a moral > sense. Wealth is life support, and it can only > increase(with a couple of exceptions). > > To prepare for this scenario which will soon > ========================================================================= Date: Wed, 10 Jan 2001 13:58:37 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Lee Bonnifield Subject: Re: waterman poly 25 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit [Lee] I'm surprised that WP 25 has no (n-1) white spheres, just orange (n=25) and green (n-2). Please show us WP 23 and 24. [Kirby] http://www.inetarena.com/~pdx4d/ocn/graphics/wm24to25.gif Anyway, watch the animated GIF if you would and tell me if you find it enlightening. [Lee] Yes, thanks, that answers my question. The downloaded GIF cycles in 10 seconds on this old P133, IE 5, so it is easy enough to see the swarm of 25s that come up around each of the 24s. I look forward to the full length movie! But actually for the 23 -24 -25 sequence, static pictures would be easier for me to figure out. I know W1 - W15 were all drawn after scaling to be the same size diagram, so the whites in W6 are (on screen) slightly closer together than the oranges in W5, right? I can't tell with W24to25, is it getting bigger on screen? If M is the next generation with only 6 new spheres, then I bet M+1 will surround those 6 like 25 surrounds 24. So M+1 will draw in orange and green, like W25. But I don't bet a billion dollars. ========================================================================= Date: Wed, 10 Jan 2001 14:13:34 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: jj stays MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_020B_01C07B0F.84C988A0" This is a multi-part message in MIME format. ------=_NextPart_000_020B_01C07B0F.84C988A0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable to jj island ? should he stay aboard ? steve <<<< I'm perhaps partly responsible for the JJs, as I was the one who first introduced Towle to "Watermans"=20 thanks...had you not, i would not be writing now ! and I may have committed the same error then as I did this time: I talked about all spheres at distance N w/o mentioning that a shrink-wrap would pick up additional spheres at N-1, N-2 etc. So he started doing the renderings in Mathematica. Then it came out what "true Watermans" were (deja vu!). Maybe this is how it went -- at this point, I'm no longer sure (we could ask Russell). i suspect that is how it might have gone too. However, whenever you compute a Waterman, you're getting the corresponding "jj" (fixed radius poly) for free. It uses all the same information, is basically a "connect the dots" using the gold spheres only. yup. It's an easier concept to impart in some ways, and I think a useful stepping stone to the true Watermans. Since I've already done the work and posted the pages, I'm not inclined to take them down. They're correct, so far as they go. and that really is the issue here. Plus I want to acknowledge Towle for his contributions to this scenario. It's thanks to him that we have any renderings of the higher watermans and so do i, captain is getting over his little hissy-fit. (which you seem to have taken down from your website, or delinked, meaning I can't find them to compare with mine). you are right here too, kirby.... i might have removed my html stuff from my site too....perhaps you can = tell me which ones would be of use to you and i can send the jpgs ? steve ------=_NextPart_000_020B_01C07B0F.84C988A0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

to jj island ? = should he=20 stay aboard ?

steve

<<<<
I'm=20 perhaps partly responsible for the JJs, as I was the
one who first=20 introduced Towle to "Watermans"

thanks...had you not, i would not be writing now !

and I may
have committed the same error then as I did this = time:
I=20 talked about all spheres at distance N w/o mentioning
that a = shrink-wrap=20 would pick up additional spheres at
N-1, N-2 etc. So he started = doing the=20 renderings in
Mathematica. Then it came out what "true = Watermans"
were=20 (deja vu!). Maybe this is how it went -- at this
point, I'm no = longer sure=20 (we could ask Russell).

i suspect that is how it might have gone = too.

However,=20 whenever you compute a Waterman, you're getting
the corresponding = "jj"=20 (fixed radius poly) for free. It
uses all the same information, is=20 basically a "connect the
dots" using the gold spheres only.

yup.

It's an easier concept to impart in some ways, and I=20 think
a useful stepping stone to the true Watermans. Since = I've
already=20 done the work and posted the pages, I'm not
inclined to take them = down.=20 They're correct, so far as
they go.

and that really is the issue here.

Plus I want to acknowledge Towle for his = contributions
to this=20 scenario. It's thanks to him that we have any renderings
of the = higher=20 watermans

and so do i, captain is getting over his little = hissy-fit.

(which you seem to have taken down
from your website, or = delinked, meaning I can't find them
to compare with mine).

you are right here too, kirby....

i might have removed my html stuff from my site too....perhaps = you can=20

tell me which ones would be of use to you and i can send the jpgs = ?

steve

------=_NextPart_000_020B_01C07B0F.84C988A0-- ========================================================================= Date: Wed, 10 Jan 2001 14:32:36 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: Major General Lee MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_024A_01C07B12.2D714680" This is a multi-part message in MIME format. ------=_NextPart_000_024A_01C07B12.2D714680 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Major General... =20 =20 [Lee] I'm surprised that WP 25 has no (n-1) white spheres, just orange = (n=3D25) and green (n-2). Please show us WP 23 and 24. [Kirby] http://www.inetarena.com/~pdx4d/ocn/graphics/wm24to25.gif Anyway, watch the animated GIF if you would and tell me if you find it enlightening. [Lee] Yes, thanks, that answers my question. The downloaded GIF cycles in 10 seconds on this old P133, IE 5, so it is easy enough to see the swarm of 25s that come up around each of the 24s. I look forward to the full length movie! But actually for the 23 -24 -25 sequence, static pictures would be easier for me to figure out. =20 me too for analysis, but you have to like = "motion/movement/animation"=20 I know W1 - W15 were all drawn after scaling to be the same size diagram, so the whites in W6 are (on screen) slightly closer together than the oranges in W5, right? I can't tell with W24to25, is it getting bigger on screen? =20 to really see them "right", all spheres would maintain unit continuity, but that will mean that we would need a huge magnifying glass, should we = want root 1 and root 5000 side by side. i see 1 type as visual...as they are now. and one as kind of BASE related. either are fine, both are right. If M is the next generation with only 6 new spheres, then I bet M+1 will surround those 6 like 25 surrounds 24. So M+1 will draw in orange and green, like W25. But I don't bet a billion dollars. =20 me neither, but i AM interested in base FROM BASE....ccp can be prodded in SO many ways. the data is already there in the ccp, we just have=20 to find the questions to get the answers from the BASE.=20 =20 ahoy, Major General Lee. shiver me timbers ! =20 =20 ------=_NextPart_000_024A_01C07B12.2D714680 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Major=20 General...

[Lee]
I'm surprised that WP 25 = has no=20 (n-1) white spheres, just orange (n=3D25)
and green (n-2). Please = show us WP 23=20 and 24.

[Kirby]
http:/= /www.inetarena.com/~pdx4d/ocn/graphics/wm24to25.gif

Anyway,=20 watch the animated GIF if you would and tell
me if you find it=20 enlightening.

[Lee]
Yes, thanks, that answers my question. The = downloaded GIF cycles in 10
seconds on this old P133, IE 5, so it is = easy=20 enough to see the swarm of
25s that come up around each of the 24s. I = look=20 forward to the full
length movie! But actually for the 23 -24 -25 = sequence,=20 static pictures
would be easier for me to figure out.

me = too for=20 analysis, but you have to like "motion/movement/animation"

I = know W1 -=20 W15 were all drawn after scaling to be the same size
diagram, so the = whites=20 in W6 are (on screen) slightly closer together
than the oranges in = W5, right?=20 I can't tell with W24to25, is it getting
bigger on = screen?

to really see them "right", all spheres = would=20 maintain unit continuity,

but that will mean that we would need a = huge=20 magnifying glass, should we

want root 1 and root 5000 side by = side.

i see 1 type as visual...as they are=20 now.

and one as kind of BASE = related.

either are fine, both are = right.

If M is the next generation = with only 6 new=20 spheres, then I bet M+1 will
surround those 6 like 25 surrounds 24. = So M+1=20 will draw in orange and
green, like W25. But I don't bet a billion=20 dollars.

me neither, but i AM interested in base = FROM=20 BASE....ccp can be prodded

in SO many=20 ways. the data is already there in the ccp, we just have=20

to find the questions to get the answers from the BASE.

&nbs= p; =20 ahoy, Major General Lee.

&nbs= p; = ;=20 shiver me timbers !

=20

------=_NextPart_000_024A_01C07B12.2D714680-- ========================================================================= Date: Wed, 10 Jan 2001 11:47:01 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Waterman Polys (w/ some notes to people@fluidiom) In-Reply-To: Mime-Version: 1.0 Content-Type: text/enriched; charset="us-ascii" Arial i trust that the urner generator will work perfectly over time, even if it does not now. eventually it can be cross checked with the abc method to also replicate the ccp. <<<<<<<< It needs to be audited now, and I think we can do this without the benefit of an abc cross-check. Just getting the same results by exhaustive tabulation would not constitute a "proof of concept". >>>> Arial more importantly, than even having it work, is your faith that it can eventually be accomplished, by you and/or others <<<<<<<< I'm more inclined to think I'm done. Mission accomplished. Unless someone can show me a flaw in the algorithm (or prove that Qhull is unreliable). I suppose I should do a "stress test" and really try to compute Waterman 10000 again. If there's a "hole" in my algorithm, it'll probably relate to the fact that I don't go "deep enough" to pick up all the relevant spheres. So far I'm only going down to N-4, which has been sufficient for all Watermans so far computed (at least I think so). I think the manual/tabulation methods have this same "hole". We don't have a proof that X-layers will always be sufficient, nor do we have a way to mathematically prove a sphere is part of the hull _except_ through methods like those used in Qhull, which neither Steve nor I go into at our respective websites. >>>> Arial When it comes to generating W150 and higher, I don't think you have a way of doing that (see below). >>>> ccp = ccp no matter what procedure you have mathematically devised to decode its structure.. <<<<<<<< <<<<<<<< That's true, but how does that help you? Short of building a physical model and trying to wrap it with cellophane, how can you tell whether a certain N-3 sphere is or is not a part of the convex hull? You need to do some math. >>>> Arial CCP is the PATTERN of spheres. yes. The diameter you assign the spheres depends on the measuring stick. BASE, as i see it, can only have unit spheres by MATHEMATICAL definition. <<<<<<<< As you define it, yes. You're free to define anything you like. Arial you needed to learn my jargon to design the urner generator. <<<<<<<< The "urner generator" is finished, except with regard to this matter of how many layers deep is relevant -- and so far I'm not getting any answers to that from your website. Arial i do not need to know how you do it, and fear i will just get lost in stuff i already do not comprehend. <<<<<<<< I think that'd be a good experience, as you've pretty much eaten everything on your plate. What do you plan to do next I wonder? More with the empirical constants of nature I guess. That doesn't seem a productive tack to me, but if it turns you on... ArialI don't understand "2d island". by 2d island i mean where the mathematics of 2d always works. ( NO MASS involved) <<<<<<<< I'm about to give up trying to learn your peculiar lingo. 2D = no mass whereas 3D = includes mass? So 2D is mathematical and 3D is physical yes? That's very idiosyncratic and unique to Steve Waterman. Learning French is useful because a lot of people speak French. But only Steve speaks Steve. I'm not really motivated to learn it -- just trade with you, like a merchant. What do you have that's valuable. The polyhedra are excellent and I've paid you, gladly, willingly, in the form of many hours of programming and analysis over the years. Fair exchange. A _lot_ more people will learn of your research, now that I've incorporated Waterman Polyhedra pages into my Oregon Curriculum Network website (rather heavily trafficed by the math teacher crowd). >>>> Arial The coordinates I'm generating are (x,y,z), meaning "3d". yes, the mathematical/physical is most confusing. <<<<<<<< Most confusing, yes. Arial use whatever method(s) you can....but in the end, you want the BASE ccp....and it by definition has unit 1. <<<<<<<< Mostly what I wanted was the very pretty pictures. I don't want the BASE tables. Arial i have no problem here either, if the ccp PATTERN has unit 1 diameter...then it is BASE. IF THE CCP PATTERN is NOT diameter 1, then it is base. base here, meaning ANY variation of BASE. <<<<<<<< OK, I understand. Arialfrequency 3...works fine on 2d island, but when the physical component of mass and gravitational attraction is added, frequency 3, will not work at sea. since frequency 3 contains root 9 spheres and ignores root 8, i will have a problem with that at sea. at sea, the root 9, cannot gravitationally adhere to this agglomeration prior to all the root 8 spheres. <<<<<<<< The expanding cuboctahedron is just "2D" in your language (extremely confusing, because of course it's volumetric). What Fuller does to get roundness is push those cubocta spheres to the circumsphere, except he's already jitterbugged to get the 5-fold symmetry of the icosahedron. In 5-fold world, there is no CCP: unit-spheres don't pack outwardly to the icosahedral conformation. So as I see it, the big difference between Bucky's geodesics and your work is he goes over to 5-fold world, leaving the CCP/IVM behind (it's still there as a relative). >>>> Arial physically, out in the sea....it is my contention, that ALL root 8 would adhere prior to any root 9. <<<<<<<< There's possibly some relevance to epitaxial growth studies. We could look into it. There might be some way to link Waterman polyhedra to metal clustering studies. But in the molecular world, it's less "gravity" and more chemical valancies and electromagnetic issues we need to consider, plus environmental stresses and pressures. Somehow I feel myself being pulled into a Tverse vortex. You and John Brawley should get together. Have you ever chatted? I'll CC this to people@fluidiom.com in hopes of catching his eye. Also: to Gerald: I've elaborated from memory and added my two cents re that Pascal program you did ages ago to generate vertices of a Waterman poly. Remember? The bottleneck was not having a way to go from vertices to a convex hull, and thereby to a cool graphic. Enter Qhull, a free download. The cool graphics are now available: http://www.inetarena.com/~pdx4d/ocn/wgraphics.html http://www.inetarena.com/~pdx4d/ocn/wgraphics1.html Karl: have you been tracking any of this -- a long and involved thread on GEODESIC (see January archives). Qhull does volume calcs, but I haven't taken advantage of that fact yet. >>>> Arial in this physical sense, frequency 3 does not equate to the sea but only here at 2d island. perhaps the most confusing thing here, is trying to wrap your brain around why xyz...3d is not physical. <<<<<<<< Yeah, because I thought in your lingo that "3D" meant "mass added" (gravity in force), in which case we're talking _physical_. >>>> Arial yes it is physical on 2d island, in the sense the it has 3 dimensions, however, i see that as a mathematical entity as no mass is involved. physical (at sea contains mass) mathematical ( 2d island 2d/3d geometric no mass) <<<<<<<< The way I talk about this distinction is different, and more consistent with 'Synergetics'. Here it is: metaphysical mathematical angles 4D principles (*) ================================================ physical empirical frequencies 4D+ specialcases (**) (*) = Steve Waterman's '2d' (island) (**) = Steve Waterman's '3d' (at sea) >>>> Arial ( the sea....is where the physical component of mass gets added confusing to say the least. this may take me a bit to express what i am after here....hang in, it is definitely difficult. <<<<<<<< I think I've got it, but I don't really like it. I'll stick to my own lingo, but you can keep using yours and I'll parse. Arial I have no idea what "2d island" means. mathematically, no mass involved. .................................................................................... i suspect we have the pattern both mathematically definable and physical definable in doing visual comparative analysis by as little as root 100. <<<<<<<< "Visual comparative analysis" sounds very imprecise. I wouldn't trust it. Too stone age. Arial and usually, with that, you have them all. ............................................................................ <<<<<<<< But some don't belong in the hull and some do.... very hard to determine without the advanced math of Qhull to work for us. >>>> Arial It's sometimes extremely subtle whether a given sphere is "just outside" of the plane defined by its closest neighbors or "just inside" (in which case it doesn't qualify, as the hull would no longer be convex). Just having the tables doesn't answer this question. You can solve the problem by visual inspection out to a certain distance, but I think out around 150 you have to resort to mathematical techniques that are quite sophisticated, and which for the time being I'm leaving entirely to Qhull. yes, i think so too, give me the raw data 1-100, i would like to crack at it. <<<<<<<< I think my "raw data days" are probably over. But the software tools are all freely downloadable. >>>> Arial If there's a ship in this picture, and if the "3d sea" is the depths of the CCP ocean, vs. what we can easily manually navigate ("2d island"), then it's Qhull. you the BASE, i doubt i can help much anymore.... I so far trust Qhull to get the right answers, in large part because I'm feeding it a diet of 100% integers. sounds like a good strategy. But I certainly wouldn't have the same faith in you or I, left alone with the BASE, but without Qhull. <<<<<<<< I wouldn't -- not out to the higher numbers, like 117. I don't think there's a visually precise way to solve these things. I'd always be going back to the computer for the "right answer" -- so why kill yourself doing it manually in the first place? >>>> Arial i have faith in you Kirby. we have years to get the BASE right if we need to. <<<<<<<< I'm not going to be generating BASE numbers. Unless someone shows where my algorithm is wrong, or that Qhull is somehow unreliable, I'm going to trust that those very pretty pictures are also mathematically accurate and complete. A huge BASE wouldn't give me any more than I have already. >>>> Arial you guys have done more work, got more results, understanding, muses, feedback, depictions, ideas, scrunched into 2 weeks, than i did in over 10 years on my own. I think we'd drown. i almost did, thanks for the lifeline !! <<<<<<<< Glad you're surviving. See the movie 'Cast Away'? Kinda fun. >>>> Arial steve <<<<<<<< Kirby ========================================================================= Date: Wed, 10 Jan 2001 11:56:31 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: waterman poly 25 In-Reply-To: <001001c07b37$77b5e140$7385fea9@pentium> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" >I know W1 - W15 were all drawn after scaling to be the same size >diagram, so the whites in W6 are (on screen) slightly closer together >than the oranges in W5, right? I can't tell with W24to25, is it getting >bigger on screen? This is a good point. Yes, the final data is always divided through by 1/root, to make all the polys approximately the same size for rendering. This means they are not really "to scale" i.e. not all to the same scale. It's as if the movie camera were backing away from an expanding balloon, keeping it always about the same size on screen. >If M is the next generation with only 6 new spheres, then I bet M+1 will >surround those 6 like 25 surrounds 24. So M+1 will draw in orange and >green, like W25. But I don't bet a billion dollars. > Lots of fun investigations suggest themselves. I'm hoping that at least one or two folks will go to the trouble to download Python + Povray (since this is the combo I'm pushing throughout my Oregon Curriculum Network website). If you go that far, then it's just a little hop to grabbing Qhull as well, and then you're in a position to generate Watermans all the live long day. Steve, are you listening? A P133 should be sufficient. Kirby ========================================================================= Date: Wed, 10 Jan 2001 11:08:37 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: [Re: waterman poly 25] In-Reply-To: <20010110181149.21526.qmail@www0m.netaddress.usa.net> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" >I will try IE also tho just to watch it slower... >Nope. Ran them side by side and they kept pace exactly! Must be something with my version/platform. _All_ my anim GIFs seem sluggish in IE. >If you meant download, I cannot say, as I have a fast download ability. Me too, DSL. >Netscape 6.0 is to be avoided as it is largely still buggy yet. Hmmmmm, that's what I use, plus IE 5.5 >Are previous Netscapes are still downloadable and 4.75 is fine. >Thx, cool gif. Yeah. Kirby PS: just posted a brief blurb re the Watermans to geometry-research, inviting tourism. ========================================================================= Date: Wed, 10 Jan 2001 14:54:22 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: to hull and back MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="----=_NextPart_000_029E_01C07B15.387204E0" This is a multi-part message in MIME format. ------=_NextPart_000_029E_01C07B15.387204E0 Content-Type: multipart/alternative; boundary="----=_NextPart_001_029F_01C07B15.387B2CA0" ------=_NextPart_001_029F_01C07B15.387B2CA0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable BASE towle hulls attached 16-24, 32, 36 steve ------=_NextPart_001_029F_01C07B15.387B2CA0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

BASE

towle hulls attached

16-24, 32, 36

steve

------=_NextPart_001_029F_01C07B15.387B2CA0-- ------=_NextPart_000_029E_01C07B15.387204E0 Content-Type: image/gif; name="Hull16.gif" Content-Transfer-Encoding: base64 Content-Disposition: attachment; filename="Hull16.gif" R0lGODdhMAEwAfcAAP///+fn58bGxq2trXNzc3tzc72trZyMjGNSUoxzc0o5OYxjY3tSUnM5OTkY GHMpKWMYGHMYGFoICHsAAHMAAGMAAFoAAFIAAEIAADEAACkAACEAABgAAGMQCIxKQns5MVIQCFoQ CMZ7a4xrY61rWq1zY96Mc5RaSpR7c5RjUlpCOa2UhJyEc5xrSqWEa5xaKffOrZxrQqVrOaV7SsaM SqVzOd6UQsaEOaWEWv+tSta9nL2lhKWMa6VzMbWMQrWlhK2llHtzWt7e1oyMa4SMY3OMSoSMe8bW tYyce7W9rZS1e3OUWoStY2N7Upy1jK3ejKXOjISta2uUUozGa63OnM7expSljHuMc3OUY5TGe3ut Y5zee6W9nL3nrd731nucc/f/973GvYyllJSlnGuMe0qMa4SMjGuMjGucnFqUlBhCQkK1vUrO1jGE jDmcpUKElClCSoScpVKEnHuUpWOEnHuctRhjnEp7pSmU72uEnCmE1iFzvc7W3mt7jHucvYy13lp7 nGuUvTFrpSFShLW9xpzG9zFzvSljpYSt3muEpSFSlGNzjFJrlCFKjJyltWt7nJScrSE5c5ylvTFC hGtzlGt7zkJSnDFClFJajEpShDlKrVpjpUJKhEJSvTE5eykxe7W1va2ttYyMlJSUpb291oSEnHNz jKWl1mtrjIyMvWtrlGNjjDExWkJCezExcyEhazkxcxgQUoR7pUI5YxAASlpScxgIShgAWhAAOUIx aykYUhgAUnNrhFJCcxAAMUI5UhgAQlpKczkpUkIpY5SMnJRzrTEQSikIQoRjnHNahGNKczkYSkop Wloxa1pCY1o5Y2NCa721vZyUnIRzhHtre5R7lHNac3NSc1oxWntCe1IpUmMxY0ohSnM5a2s5Y1ox UkohQq2MpWtKY1IxSntjc4Rre8actWM5UkIYMVpKUpx7jJRzhHtaa61jhIRKY1IYMXtSY3NKWpxa c1IQKTEIGDkhKXNCUmspOSEACFIIGIxja2s5QmMhKVoQGFIACAAAACwAAAAAMAEwAQAI/wABCBxI sKDBgwgTKlzIsKHDhxAjSpxIsaLFixgzatzIsaPHjyBDihxJsqTJkyhTqlzJsqXLlzBjypxJs6bN mzhz6tzJs6fPn0CDCh1KtKjRo0iTKl3KtKnTp1CjSp2KcMCAUaPmJFpkhoBVqmDDfrSKVWuiQmjT pk0kB44aNGi+ip1L92AAslkTnVXLt69atm/aCIY7ZkCAuoib3r06Sq8fv5Aj+wXchg0bN23SoCks ILFnnouxOpZMunRkypYtr2nzBk2cAZ0/y3YpoE+ix6Zz65aMOrXqwXEHzB4uMsAcQYP+7F7OHHIi OoHX+PYN3Oph4tgpDrizB8+d5uDD8//1A72N9Om+MacRk739QgHH8eDRA0i8/fuFyEdHn7oNFfcA EgTJHXrIh8cegeCn4H36mYeeFF4E2B58dhgonyHKLaghg+WdV8YUQkg4WwADFmihdxluqCKHb7yx xRPXiViXAIl0d+J8362o44JkbAGFjHORKIiJN+qR4I5I3vdHFFs4ASRV29l444W4JWlleHVMsUUV Tz5lnCBTnnhIileWydwZW4DY5VIDShmmfDmaKSdzWGyRRYxrDkXhmyfSN+efy/2hxRZK5CkUiQTy eSKCgDaqW5ZbIGGoTzS6qeiFZDqqaWQ9bhHGpDkJSeSlBt6R6aao8rVkmiGCSlOUpBb/GWeqtPbl h5ZR4OkqS1/GOqWRtQbrF5pbfLFrS7D6eqMhVQrrLFqdSnrsSXsqO+WYz2aL1qpTfDrtSCVaG+as 2j4L6RSxfdsRjRWK+2t95cbbaa7qbkQKK5E0ou++/OqriB0AByywwIYgEu/BhdRZbL0ZBaBJJxBH LPHEFFfcySWnIizsrVtEyvBFm1gs8sgSM6JxvHl03O3HFI1C8ssiY3xytn84coXK6bLsUACWwOwz xSbPLGzNfBDC5Bb06uwQJT83HbHMQtNKNB98OKLlwkozBMrDTjsddNSbTk01H2Z07HHWCfHcdddQ g92o2GPzcXOa3qJtENNrd/2123PC/x230TjbXZAAXOfddNt8l+l33FVfnbTgAHBi+NrwJn7l4oyT bbaxkJcy+dqTWH65I5mXLrfZ0qJN+OeUi44k5qYDTrfdkrPedeiurwi76Y0HrrTntreeu4a78655 x48zvHrwtw+/YPHGn94x5x9jwnzelTsfHvTRy352vS5fD7r24nEffe+zqxvAJeJjT35z5p9/fJo5 72p9+6Bn/H5k8csvPdK6mlT48Ne1T8iCEo9o1v780j//eS91oFofAdf2iVNYMBWoeEQe9Ee+BvoP fVsYw67wNkGnZcKCKLSgLFTxiL3sz4MfnN/KJrW1EnbthCnM4SkymAcFig6GMfxf8v+epDYbmlCH SDxFKljowsQBMYjeo16XSGjEn+EwiUlEBSV66LYnBhGEVlhTDavYNExg8YwXzGAiOOgsL35RhnUT URHJ+DNUoPGOKkSgD4WVCNK98Y9UmxsAgQQ8OtYRj4hUIg/ZWCY/JCIPpphGOcphjnKYwY+AhOLR sCah5RnSZ3ZMpChX2EIz6cUUpqBGOcJhjla60pXhmIYoMhlEq6FORLX7JChFyUsU8nCP4XEkJCVJ yVca85iutCQhaOm/sqksjtkppC5fVsFeWvOCTGzOKVO5SmR685uuVIcsmXk+QWohgLPx5DRJVs1r unOHWwSmMCM5SXDa856vVCY5Y7f/SSy4J5frZOc7B5rGFiYClapkJT4XytBWihOT+xybLTsGwdkM MKACJShBU1GNhnr0o60MRzlKscyIUs2Z6RsR+zD6sklodKCy6ChIZ+rRh5r0f+gazv1YSrIrvrSX slAoTYfKUJGWIqLeG2JdLspTkfn0p4nkhVCJStWFWhKigJxokz4jwab2FKqiTAUvqkpWj8byqLRE 6RaS4JmdetWpYEUkR8tKV49eNZOCVNNS3/qyVcT1jjGtq2AbGstZvtF7d6LLHPlqsVD+NYlBHaxk G6rPWl5tC12gCxUZWzHHPjaHUp2saBkqTsN+UK1cEMsYOdvYz+ZQrKONLWXNUFL5/wnSU2BZLGsn pglZuBaFc5WtcBdq0/N57wlgoMpmdyuxdro2sMONLj6NWlvTaVWKT1Enc5v721NEVrrgxWdxTafW MEYFoNvlrmtDG9723tOovMsrNJcizfSq96+wda9+8XlXxiUVnUfRrn0hxonHBne/CLbnWRl3Xacs d8CdeOpLoZvgCtuzv/P7nlI+AWGKSZig37WwiMFZ2ECabYZJYWqHIwxW9o74xeC86ibPqRS3rpjF L80vjHcMTnWk47L+RIqAO+zZdx6Yx0hGZjiCcNmKDqW+Ny7yNSmc5CobkwdEOPF8g4LeKIN4qlYO szlQAIMlmI3GRBnAjSkmZV66WP/MYiazDphgtiAP5cEdvkQq3jlWOPvZHAmAAQx0MCiKDqWra4aY c3mZCmr8+c/lEDQMfnBZEQZFxTdedCKp/Ogwq0MHkh7CievHExuvWdN4DHGn4cwDScMgy8gD8E2G vGJUo/HNqxYzC1w951v6BMpr/vAZ+5zrP5OZ14UOoU84nGiJCRuJjS52pwPt6klfLac7UXOznY1I TktbzJGuNgx4YDal1sTUiX52ClX9bTh/Wtyv9jVOEL3tTpjx1mBuN6vhXWazWfommE50m1NIbH0/ utXw7nVKa9LlZg9ciY42+KqPDW9Kx9omtF7zwL0tcThTHN7knp5N8CxwJLK7437/Dje/490x886E 2fVWNBJxjfKUr1zSZl74SwKeaE0XvOadRvjKFW7ulaC72c6NNtCLLfSV7+BqhYIJvWPeTo4v3c8f X7nFt5DalwB72y71br6vbuybuxrWKGZJw7d9QpqTHdJmd3XOpyBrkmQ83T9/e6dVHneit4TkidbE L/T+7XDsIO6SfrqhVTL1mLdCGYT/dtPjvvUtj0QSMZ+YJ4oB+cgXO+txR3tyUVKJzEdME8koRjGK 6flOgz70yEsJzDPfC9WvvvWr5jviB03nrZrk7ivevO2tgfu9777ahO5YhEqi7cxfAhm2Lwbxi/9n wx/f1RbX60iaH/NgRJ/z1D/4//VdLWo71V0jgO+w8KPf+fDDedfjlzSsMzuS9A/4+d9XPevdb+XX 717hR1B/MYd6+ad//Cdm1BZ/gqZwpMYRs5dorVCAqjd9B1hluhd/FmdnH/GAN4Z/EkiBFYhk76aA khZy/9YRjddhBCiB4BeCVTZ5CphlaNYR3LdmEciCLeiCSAZ/JLiARcBJHFGDwYeDtrd/Ovhi/nd9 NWADTJB2GvF19rWCRGiERyhiCUiCM5ADOcCERVcR9rdbtUeEE1iFO3aB17cDNqCFW8gETnYRX8hZ 6yeG10CGMGaG/3cDaqiFN6AFDVgRHGhfHiiGOUiHIgaDu1cDeaiGPtAEDrhm3v8niKqXDGNHiPpl iHGXhYmoiEawEX+4XXEIiVRIifqVhE6Xhpmohj1wfg4hhOkViJBYDOQgihZGigmHh6eYhzyQEazI XFL4itInixVmhyuHiLeYhyuQETzHWjfoi6o3h8CIYMIIb5hYjGooHBjxhk3lir7Yfs9YibuHhtSY h9bohhDWi8woid24X5aIfLYYjlvYhxGxdpy1jMxYhOk4iohHjO6YAz2gEZ3IWJ9Yj7B4j+5FizAw jfvYjxnxj29ljgIJggQZXdEIAy6wj3k4A7o4YGEokNHnjBEpXdEIjhaphbmIEbvIVwHJkdz4kcJl fQlHAyOphiV5ESfpVdrIkcX/gI4sGV2WiJAjeYzXmF6PiJPfF4o7OVmvV5ExWY0ZgY3TlJJEGYtH KVygJ5JLmQPjaBFHl43QR5T5B5FTOVm6pwMweZXvuJC75ZBeWQweGZaipXs+GZMKiREMiVH0uJa2 t5JuOVguSZFmiYoZAXzrdJN4qZN7OVkIZ5VmiZEmyVpqiZe3d5iTtWtk+ZcymZGctZGQ+X1SKZmD RWZxeZUzaRFOSUZQuZlg6ZlklQBKaZlaCJTkyFePuZltqZplVQ6m6JpY2ZSMpZmb+X16aZtUlQK6 yZR0iZK/yYKGKZxV1QPFmQM3oIoNUZeGRJjJaYDMWVXl8Jz82DAr1VRDeZ35/9eZ2TlUxPmcc2kR NflJpymeqVmeHuWcz4kDmMlT1imebAmfQ7Wd3DmaFQGFhjSb+Bmc+rlQ5/mc/kkRpUlAd4mf37ec BcpQ8vmcQMCbLHWfDhqZEcpQ/MmdWemHLCWgGUqeG3pPB/qcH0oR1GlDvpmhX1miEsqd0CmdDLGi E+QKyuCiOFibMOpNHYqe9alLmpAL3ZAN2vAMOaqjwNmj99QCMtqdjfmU25ANVFqlR5qkSooM6sCk 3xQO7TifyCikw1ClZEqmV6qkRsml+vCkOZCgE7Ggn+MJU1qmdGqlz5B6DkqiXOpKTvqkbioRo/AK 31lClzCmdXqoVdoN2OAMeP+anO/JpF7KphWaEbOwC7YgqBMEC0WKqJyaqIvaqHjJo3u6pmyaohQh ALtwC7dgqZFQOLZzCczQqbJaporKqHhJoEzap09qqhQxDar6q7QQC63KOpo6q8ZKq4valRyppXv6 SpH6pNG5EQGgC79arcEaCXkzCbF6rNxaptuADdCgrMyYpiVKqk+anhlBDNW6rreAC7Fgo50wpJva rfRKpt8arsyop7nKpm3qEbPAruzqrnU5Cc1QrwZbp/cqrjj4qBv6rLvqEagKsAB7qYMKMfJ6sBiL sOCqsPknqjBqrjKKrhvhqxILsJaKqZ0gpxm7soe6DUjKgri6oboqo3+KEdP/WrIla6nCwLI8i6hn +n3MuqfqkJsyyqvpirM4qw09u7SH+rPYyaUjwK8i2xHUirQAawxMm7V1eqb6uqH6SLMjEbFWu65Y q7VmW6ba8A1CS7QeShK1MLZke7ZyS6biALX8ypgjEQC0ALe/egxz+7fZ0LXw+bXcCZsjoa58266A O7fdsA4wOrRsagPw6BFVC7e4sLhz6w2TyJxRy6Z4WxJiO7aXi7lyq7ley6+GWxJvy7dKS7pnW7cF CrlPKrkpobes67py67Gq2blP+rkngbhj27q4q7WNq5+E+5ypexKVi7TcMLxn2w1bmp2yK6O0uxKh kKpWW7bOq7WmK5zhoAL8/0qfLfGv2bu9Z4sN3lsCJ8Cvk8ore4u02mu+WQu7kqkOJWACMcCm0eoS JIuzwCC/Zyu4H6kOImAC+Mum4vsSywuwowvAWVu8bknABnzAT9q+LnG9ONvADsy027C56bgABTzB MgCtNEoS5CuxtDCvG7y03cuSCzDBEzyhYCoTtluywrvCS0u/BBkOLwzDBizDxWnBMNG/AHvDONyz OtyN4XC/PvzDIVsTNyuxRnzELAvBSszETUwCbOuaNdsSwMuuy0DFDxy9wGi/TTzB61u0N3HCcSvG TNvClCjBZ2zAaQyks4a9bezGS4u+oijHc2wCdVycXfwSRNy3ejy/lAjCf/88wfnbtvO2wIp7yEyr u/zXw4tswI1cnFNLE1+sqhosyVXsuDrIw5cMw5msm4McE2wcyaDcsx3sgktcyqb8nNWrE6G7qnPa yjwLx+EXy7Icw8jrE4U8xbqMsedwgGb8y8Csm76rEzWsqsRczAebxK3nx8psAkB8lbXcE18czdJc r1ZczSF8zU7smsnLE5Ubv9+cseFMeIpMznTMzHqCveq8zhg7DuxAxm9nyfAMyK65zUCxuvVszwZ7 Du0gD/HADh7cbvzcz4F8lefsE7b7vwS9sgbdDhjtDvBADgvdaeGQAv3sww8dk80cFOr6yRVdrxeN 0Syt0eRafVgc0pj8lwD/PRS6gNIp3a0rzdI8bQ/woM+dlswyzch/GdFBIQC+kNPGzNNMzdIInc9B Pc5DPdNXWdJEUQverNSdutNNzdQIzdHuJtVTbQIjvJQ1XRQBoMJafaxc3dVNrdECbGH6INZjnc3u aNREEQ1qvday2tZu3dU+/dL61dBjXc4jadVHodd8zdZ/3dhMbQ9QLWKEXdjYHJNnnRTUsNjG+g2O 3dlOndBAHV4fTdlZvMXUiNdIkdma3ana4NmujdHysNEdLVm+TNowPNLUiNhKkdarzamt/drA7dLS JdS2jcYjedlMwdu9vbXA3dwYHdiyZc3FHc8WidpLIQB7vdy/7dzODdqT/yXd003B7qjbTqHYy22m 3J3eB53Qs91Qcx3eTXzKxYjcUGEG543e6q3ecN3e9jTZ8C3ft2jdT6Ha973d+a3f8CDY4OTf/z3e nnEN922kBz7hz/3TZgXS8D3Hdp2H9D0Vyq3dFB7iTx3aShbTGe7DG66GAi4VH77aBh7iE/7Vm0vc pE0CJ3DjJ/ABD7DjD3ABFxABX5qI5B0W5u3iMH7kGb3RxwTepYzjN87jDwABPu7jFDABVn7lWG7l FADkmdjhYlHki/3iSB7i0G0O1iwCTu4BUB4CU34BWf7mcB7nV77lL2CM2UHgYT7meo7R9XAP/dDj U14Bcj7ohF7oWN4Bdf8+5HWB52st5nuu3vJgD/zg5oZe6ZZe6SAwuZ7hDJrt6I8e3PvQD4J+6aRe 6nBOAQYQIC2u1J7+6Y7tDvcgAVVu6rRe6xGQ6hISALnM6q7+2pJ+AbNe68Je6hFQwp4B5ind6r1+ 0Psw6cP+7KbeAMb+GdLQ6Mv+1n4+6tC+7ZbOAIbC6ASt7GNuD7Ee7Nx+7oROAQkAKuC+zuJO5s6O 7vJe6KjuKqu+zt3gDnsuD6FO6fP+73J+68dy799sD0gO66IO8Aof8NMOIMhe8PAu6ws/8XAu7fXy 8MVs8JD+6xTf8W/u7R9jBrsuzRrf3Pye8B6f8lq+7jqDAPgADtl9yCX/79mwLgHarvIpX+9ZMwAa sAH1kNVHPPN//evmjvMeXwENgOuq4wAaoAH4gA4jL8ZCz9P8Hu9Gr/IXwAAH0PD2rgBN3/T0AA4y /9ahfvNXT/EUAAEMYLSCUwBf3/QcUA9R78AlT+4Sf/ZH3wAJoOmQAwADsAFv3/RPH/POaw8cj/ce n/Vb3/cPEQBMH/g9Tw9AD7jd8A7+jvgLn/Zrz/gTEQAIAPlfzwFQP7zbMA9mj/nzjvR7z/kX4fag //VhT/gcnA9Fj/rorvhcz/oH8fev//U+P/kYuw20b/vzrvlsr/sU4fi9//aDz7Tg4A+1T/zDjvQH wPfIXxGev/xvvwFh/8+yzy/95571hnH9JXEA2h/4cT/3s/r94P/saZ8Ax0/+HjEAj3/+X//ysk+m lX/57Q8QEwQOJFiQYIUGBwQAYNjQ4UOIESVOpFjR4kWMGTVu5IgxgAMNIUWOJClyAz1t2VSuZNnt XQWDMWXOpFnT5s0LDAYE6NjT50+gQYUOpYig5NGjHNBtY5lt28ubUaVOnUoBQoIBRLVu5drVK8cD SMWSpAeu27Z8FKiuZcsWocKvceXOpRt0AMixeTWobdvXr8ycO+sOJlzYcMOPepFu4PvXsducWA9P ply5q1HFJDE85nyTwoUGOnlaJl3adMcBmUd2Zm3wAgSdC0/Ppl17oscAvIottO5cIeeBrLaFDx8e QIHiDLz9fmaAdTRx6NFpYx4LU/lU0LGlb+c+O7XYzddrvmYAvPt59KVxI218/TP55gOCp6dff7Lx kuEfX+Afurx82ewTcEDKChgpOarey4kBneQj8EEISxtgg5Csi8m37OIbIMAIO/TQso8242/B/wT7 8EQUTQvAwRRbdPFFGGOUcUYaa7TxRhxz1HFHHnv08UcggxRySCKLNPJIJJNUckkmm3TySSijlHJK Kqu08koss9TyyoAAADs= ------=_NextPart_000_029E_01C07B15.387204E0 Content-Type: image/gif; name="Hull36.gif" Content-Transfer-Encoding: base64 Content-Disposition: attachment; filename="Hull36.gif" R0lGODdhQAFAAfcAAP///+fn58bGxq2trXNzc2tra1JSUjk5ORgYGLWtra2lpZSMjJyMjIxzc2tS UlI5OXtSUpxjY8Z7e61ra3tKSpxaWloxMXtCQms5OTkYGEIYGFoYGGsYGFoQEFIICHMAAGMAAEoA AEIAADkAACkAANaUjGshGL2Ee4RSSoxjWnsxIYxKOb1jSqVaQtZzUoRCKefWzpx7a+fGtc6tnK2U hJRrUpxaMYxKIZyEc5RaMYRaOaVzSsa9ta2Ma8aMUqV7St6UQsaEOaWEWv+tSqVzMaWMY8a1lP/n tcate62llMa1jKWchN7OnKWcc5ylnIyclNbv54SlnFp7c1KUhFK9pXOclFrWvUqllGOUjEJzayla UkKMhJylpb3OzqW1tVprazlaWkqMjHuUnK29xoSlvWOEnEJaayFCWjljhHOcvQApSq3G3kJKUnOM pXucvYy13muUvSk5SkJrlCFKcxApQhhKewAxY7W9xpScpZzG9zlztTFjnBBCeylzziFjtRA5a2uE pWN7nDljnDlKY1JzpTF75yFSnGt7lGNzjFpznGN7pZSlxlprjJScrYyUpXuEnFJjpVpjjGNrlEJS nCk5hCExezFKvXN7rXuEvTFCpSk5lEJKhDlChIyU1jE5eyEpc+/v/1paY4SElHNzjFJSazExayEh YxgQYzkxa0pCc62lzhgIYwgAKWNahBgIUiEIe5yUtXNrjGtjhCEIaxAAQoR7nJyMxnNjnGNSjFpK ewgAGIx7rWtajIRrtSEIUntrlFpKc0IpYzEYUntzhM7G1rWtvUpCUmtae1I5Y3trhDkpQloxa2tS c2NKaykQMaWErZRznEohUr21vYR7hGtja3NjcykhKXNac2NCY3tCe1IpUkIhQmMxYykQKRgIGAgA CHM5a2s5Y3NKa62MpWtKYzkYMWNCWlIhQoRre1oxSsactZx7jJRzhIxac0IQKYRjc7V7lKVrhFIY MXtSYzkIGEoIGIxCUoxja5xKWq1SY5RaYzEACIRCSmspMWMhKQAAACwAAAAAQAFAAQAI/wABCBxI sKDBgwgTKlzIsKHDhxAjSpxIsaLFixgzatzIsaPHjyBDihxJsqTJkyhTqlzJsqXLlzBjypxJs6bN mzhz6tzJs6fPn0CDCh1KtKjRo0iTKl3KtKnTp1CjSp1KtWrCAQPwOFrkBlAbR2AdYcVqtaxZkli1 igEEKI/bt3Dj5mHLNqwjLmMDnN3L92BaR2vbyh1MuDDcrmzFhMUzVkDfx0sHAGZruLLly4Tf0AVk d+wAyKBxChDVBrPp06gNbxazZozj0LBTLjjkJrXt27jfuvnyObZvkKMZvclNvPjpN4gW6P3N3GKA BWwEG59O3fAbM19eN9/eUIABM8Ori/8fL/cNI2NcuKs3GGAYG0bk48uHW4ZNlOXrmw8YZKb2/P/z lQGGFNrlB1p7cSQSHoAMyudGFlmkZ2Bfjgxyhn8NZjifG2FoEUWBE0olwCN0yLGghijK90YZW2DR W4hOBeCIGXMkkuKNDK54xRRc4AfjUQIkooYcGOJo5HwrbnFFFSD++JOMf/xh45FUNsgiFVhI6GRP A6BhBxpFVinmf2WEQcUU922ZkwB18GHimHBmyCEVV2DRpJouBUDKHNLF6SeDHF5xppZ4tnSHcH8m qqGOVmwRRaErBVCaopQuWsYVVlQBKUpjDFLpp5ZuoemmJOHhBxygppphGoSS6pEihQj/ouqsOd7p 6kUB7FFIH2HS6qt4ZPh460Vj6FFIrL8mG58Yw2aERx/H8qrstOI10qxFsB6LLLXcGveGrdcqlKu2 hfhxYrfo2uaGsOEqVCy5hRCS7ry4tdFuQ8/Cay69/KbmyL0KZQuvvP0WbFqrAAMwLrzlnmvww4N9 m/BAAhjLcLwQZ2xYsBOPAe3FhmgsMmGHJKzIxxcrMvLKcN3VbgCJXKxtyCzX/EQX4OJZsczaqlzz yoBAAYUX7BbqMc/H0vzzyEELTbSrJyO9K6pLjyyG0EIj7CTMUh8ra9VWY511oTt3LS3YIj8hNhQ4 q3l019uinfEbXqw9dNHrRQ332XJD/9y03XjAyDXcXvetcRt2Y611c2UTvq/hEF+d+NjrvU04xpBD 7MjkQrfN3SWVhF4JJaSXbrohqBtSh8OZ06s253dvV4wltNdu++2399k6vX/D7sR2k+AuvPCc7F5w 77Av/tgjwzdvuyasG0+t5LB3nvNZAmTi/PaWyCE9vdRXz/b1ZXHC/faVfD/v6+I7jbdZzJ+//ZTq U0t3+2L/DlkAmsi/ffH1oxby8Ke8qkTCf9vLRK8COCvE4U9sntsLHhDIPe8xMFnhe2DszsI/Cm4P ehf81eY0KLanmeWAHpxfCH3FPhJSzioTTOH/VjirAbqwgEwJQPBk6DwF0jBVNiRhBP+lIgkecm8Q gfjhpzLoQvdNpRjaM2LzNIGJTkhigUoUExObCIXARUWHUnReJTpBRkwEInpZNFIousBFu+HQKPEL 4/DGSEYyXiKJaaxSGUSxgCQs4I9/fIIgm/jGoWRPjs2jRB0XecU84miPxCDGAmBAyUpWEpCBFGTd ODdEpZgPkcPbxCIXaUY0OnI8bhBFJCM5SUu68pUw4AEmFyBI9plQKXEEJe5EOcpF3vGU/0llMVbJ Slga85iUxGQBlnJIXQqPl71kJBaBmRthEnOVrUSmNmGJgyQoBYXOxF0kotnLUlLTONa8Jja3yU5X 4oAJ5ONJDMMpTnJG85fnvE061bn/znb6EwdHMML7etJBetbTntFsZD5Ns09+9tOf7FzCEY6wBKOA 06C1oyJCyWnOhVrnEcN0qDqzCVFtLmCiR/DmUOaJ0drRcaPkxKdH4/KGR3BBpA4laUmPedKJwlMo BW2pS2G6UYXOtKY3xWlOd7rNnk5UoEEpolBtp0iiIrSj50SqUnGqU6a+0qkTrehPoDhV20HTqvaU qSO1ulWuehWZYJ2oSnkCxrLW7qxotadRs2jTtm61q2+9JEpR+lOeSNWutMNrXjl6RiVC0q9/Dawx 4/rUgcakmYi1xDgXS1S1BvCxkI2sZGHZhMGiVKw5+WRmNctZtO5VeqANrWhH68rS/5pWrjnJZWY3 21qiYrV1sZXtbGlbSdvetrA2qcRqaafR3qLVs3ILrnCHS1wYGPe2UK3JAJZLu5c617XTXFkqpytc wI72ured60wumlnvfteqZgREeB/WUPL61bySRe9tFUCToK62qu+1aiRa0QpZwCIWCB7FIQ4RCLqY Uln1te99q2tJ/ZoWuTBh6WoVG+BeAmLAtgixLWShihKb+MS1SPCCD1EGutQQEKMYBTqokVQJyxa/ gbWwabMLE/ZmlsMd7gQmBrwLEYt4F7U4sZKXrGQEx0LBC3bwkbpyCBmjQx1YzvI40DGNkNq4rTh+ K0Bvm97LRpG7QH7vgH9h5DaPmP/JcI7zklOM4BW3mDLiobKVx5HlPvsZy+uYRo2/LNIwe3XMZDYt f1+i29XytsMDboWbJ/1mOVv60kt2MpQPQZf5ukUzZdjzn0dNanVseRqELjSFK4noRBM2niJRLXcf 7dwPS5rSlEYypnfNayYfuM4LbjAgQj0MdKyj1MhOtjq4POhUS3LVlGy1qyvbku1yt3a0XuyQW1Fk XHubxL0Ot7iVXAs+K/vcyj61s4sJbWlPO6UtOSx3m8vZNXv73iIG97j3vetkmBvdAE82l71sY0Mz 1d3vXnRK/Ltc9xI10viOeIh1ze+KxzkZAc/4udeBjgV82eA7Rfi0MWwSDTccrbb/lrjKQ/wLWFj8 5SaGxZU1TnNlD9y+IC+pRN+NXct6xMf/hem2u73ylesb5vyuxbFrzvRkc9zj5YU2DCjL8yL0ACWY vXaaO2HvonvdFhRH+rjL3fSy27zLoc05RKnuaiT8YAhDoMFJGr1cDkP863i3RcvFLm5/m/3vTkdH s0VajCRAm+3H/QEQ4D4EIPDAJLLW+iJTnvfKV5rv/Qa85pN9aoIvddWIH2wRgsB4xvvA5xjJ+rXH OXTLuz7smI+zzDdPe6cL2q2gf7fbS8/7H5BE3te2BClawWbXG1/vLo89nJVe++Yju/P8VHs7Ec8E xfP++lcXiXKDTztP5OL44L+8//JR/G/nm3/UgW629NnJ9tFf//1DeJFHTL5cTdyiF98P/+uTPH4T +/38AEhq6sZuFMYDSmBauwd/7yd/HQEJ3Ec7qdALvYALRKd/ebd3/YdxAbiBpcZs68dOxlV9i6eA CwgSoPCAluAJEiiB+WeBlXd0fDd7HDiDAugAOHCDOIhJPOBVtuV+JAh/DLgR1hZ89reCEngMLlh5 sId0zEeDTvhnDSADUjiFVEgDOHiFOMAAmERaCfiDQAgSdJdZEWiEE1iBSVh0GMiE5feEbBiFVPiG cBiHMoCFOEAAOTCCXviFHwF8q6WCZMiCZ5h3MFhx/8eGhrhscpiIijiFMZCHP/+YfT9HhPf3h0cY iF+3hPumgYd4iOiwiJ4IhzNAeo6ogJDYEdvHXWNIib3AC2ZoiRGXhuMmg5t4iONAA594izLwdqNI iiBxin2oikbYgq6ocoPIa004i5uIA7joiTSAh7uIfR+henZVhMAogbdQfMMocZiIaWSHjLPohsuY iDvwjLzoEUO4WqlYjavYitmIa7CIaYXojYcIjuEIh81IjvBXikLIXX6ojisojO14b8V4cfLojZ1Y j3E4jvj4fvqoEXw4VdToj9aIjQF5b8mAabJYkJt4kAhZhc64kIzXkBnxkEKVjhKJfxX5iskXZ8eo kZu4DjPQkVSokCDJeyKJEZH/N1X9eJL/mJL4NpAl1o0uiYzKKJMy0Ig1CY0e4YsQOYk8uYLX6JMW CWfxOJSbSI8ISZNJGZIfwZQl+ZR/CJBS2WbvqAqaaJXIiJXhiJRbWXpCYI6ZtZNguYJIOJaUdnQZ iZbfaJRa2ZZDQARwOY1OOZcrSIF2SWkXqQotqZezyJH1yJZ+CXeA2RFhSE8mSZiAeJhu1nJCyZjI 6JjLGIqRWXqTyREkGU5yiZl0qZlkaQxr6JmzWJRrOZqk6RGnqUsRqZpGaJia+QvHwAzQcA2wqZGy iYuiSZuSuZRldZm6mZlSuQvHcAzQ8AzUyQzDWZBq6YmQSZuluRFeiZrNqYpR/1mR0HkMyUCd6PkM 0LB017mXoSmKyPmXHcFw4ZSb4WmErNiOrWCe6dmfzzBz7bmR4aiL8SmfHHGOBsWc9+mcZ+ibzOCf EFoNAdqYy3iPBWqg+9hSqbmgUEmR4eeg0wmhETqhm1iLuNiXyNmdI9lS9smh+MmOeQedwCmiNPoM wkmih1icimihF6qiGHGbYaSgLsqgMRqd51mjNWqdOGqI2ZmQF1p6QWgRQIdIGzqkHVp5+3mkSIqk 67mkbfiJPPqkUVoR3ylHLWqlwfh1+/mgW9qm1AmgXjqDoCmHKFqgY0oRZRqkaKqOYumOv+mmgEqd EhqnNDincLidYpqh4Lmn1f84nrgmoyEaqIA6qITKgSaqiHVqp4qKm4PJqJTYp2BnpJI6qjZaqTSo o2+IqImqEfSnp56qjnUpYqJKqqSqpKa6gU0qhZkan0GAeg4BpClkCsAwrMRarMCAC69qmGtKq8yq nux5q+eXq6rao6bpTJ+QDdiardqKreCgDd76reAaruL6rchQruZ6ruWqDGzarM0Kp9DqfE16nE9a ejdJETnJQ5mACtu6r/zar/76r/uaDlrKrqRKqe/qfIZ6lPN6feqFEXlKQZSwDAA7sRRbsdkKDtgQ qQQbqAZ7sLUHk6AInwvbeLDWEPSZQqUADha7sizbr9zQDBsrqTfqsc6HqtP/Sq2bKkOZEAwt27M+ m63moLExm6Q0a346Kq8jOwRvKYSn8An9k0IR+7NS27MvO7Rb2qVFW3tYSaBJG3cH6gqvMAuucAoP izspO7Vo27ICa7U16q5Z+3f0GKZJe6cTMQBg+wp4+wpj67Q9xLNp+7crCw7NILRsK6hvS3uOuasX 2qsHygp5+7hhO7aVcGa0QwncALiYu7LcMLCF+wwde7hlx5FyO7K+d6C6ALmo+wqrcAqm0D+ooLKZ G7sUCw5B27nUObOg+3dFqbgXWq8UMQD/kLrCOwvOILvGW7FV27m2mrtmp4yjO7INixHAOwvCm7ra cLzYO7HmwLkx67bMS3NR/8i7BQoEJesQwHu31Zu3rpC97Puvglu43vu9GdcANzuvPiq9/0AL6fu4 vtC+/tuvazu0nyu/GYcO4lugvvu7/+C4+4u30fC/ELytGEu4tDrABAxw99C11yd3HQG8p9vAr3C9 ETzC2Jq87Lq8F5xxB6ypHfwPwdvA60vCMpwNtdusKJzC6DYOIqvB94u//7AKDSwMMzzDJkyr8YvD pZbBGlx6pdvC/4C+1fvAQzzDAUyqR4zEo7bC8ZnACpy/+zsLlzvFMzzBBYvFObzDGky3FREALszA 1RvDYjzEmzuqFmzGfqbESwx35AsSLvwN+yvEcTzFtEvBNHrDdvxnWpyiIf9xAC68v1IcyFNcxEhq yIecZevwkRrMxRVhAC4MxMMbxpAsxlWMpFdsxymQx6UXvRuxAC4MxZALx6Esxu+7paVsxomMnGps EcC7wNULyLEcyKM8opX8Z5eMyskZEmzMy8L7yL8cx2QsonVsysYMd0sbEi78wqgLxs0cy5KMnpR8 yLdMm5psEYyMza+8zc1cw+n5zWaMDtMMd7l8EZz8xKnry+gcyt1cyylcA+/MuCLByl6MuiJ8z788 yvp8wUTwzj18oG2MuqsAuwT9y88czTjszu88zs7hwh/MvxF9z3NM0fv8zkOgyh5xzahrzx0t0eYQ CsOcZQk9zXtMEuVMvY//O9Apvc3cwA4tjcfGvNAdMc9Q/NA3TdDgoNOVHM60Wc0jAdD6m7f9O9QE HQ6vmcI6LNIcjBYNnbcoDdXNnA6HzNPGHM8Zkcx+nLc2zdXbTA52jNSj6c8lYdJ4K9RoTdDigMVV /c5NXBLl7MlPPdf3XNRIDNaojNEZAdR4u9V+/cvcMNWgOw46INIjjRK73NRnndjNLNUEPA448NIw Xb4+7LiwbNnobA7yuw44cAJovMQ+zcf/4Md9Ldr3rNa5uw4nUAKnLNKErREmzcywvc2Afbi0XQIl wM9WrRJAXdm9LdFGXbTvUNvCzdaRGdMoMc+skNwdjdk0ew/Cvd2cbcx5/30Su+wN1n3djB2n2r3d JYDaxa0Su/wN493Rsn2r45AC6C3ct93ZLHHNoPze6FzXpqrZ9S3cxD3N340S1yze/P3Xy+2lph3g z73eKzHP/wDRCd7M4PCsJBrcDl4C3Z3H0m3c11wOFX7P2J3hzu3g6k3gLrHLLjzi90zaJNrcG27f Ik3SJsHi/7ANLo7O8X2d5z3jw93PvmrNB77j6OyaPg7k2w3dbanU+X3N/7DfRg7J5tAO8/AOjDnf Ss7d72zjJyHh/9ANU/7L2gAPZj4P84Dh3gjgW57eqZ20bt0SYD7hYx7L82DmZh4P81ANam6IDd7m tv3OTs4SOP4PIl7nVP+O54qu5+9Q3huo4YA+4Kjs5SeRzNfs3ogeyGWu6Jxu5QdNe5AO6EyelKuN EgB9zcid6SR855ze6nve584n44DO5cac2yOBAFCO4Ko+xebQ6r4OD4zu6H/347Pu5tMs1iYhAFAe 5bs+xZv+675u5VjefMRe7Pedx6UO4iHe7FPM6tD+62j+6elG38WO3pK+xLZOEpbuwhTO7RHc698e 769edmxe7kt+7DdBAFCu4+5Ows8e798e7DT35/ZO69ieE7jex/0uw94O8PHu6QEX6gWf4nl81TaB 41K+8O0L7w7f8fPudCde8DSOynFuE+X8D7qu8f777x3v8HpeDYwt6yL/v93n3rUWfxPKfs3trvLZ 2/At3/HSfsczH+CjvpAln+/bzvP+y/E/3/Thrg7VPvQcjso3jxMBkPD/oPQr3/Rcj+fxYAEhL/UU 37VHjxOnzu9a3/Ndz/UQIAEREPYzf+1dO+g6Uc6YnvbYy/RrD/BtLwFuD/cFX/ML++E8kfPMjvfH y/J7D+197/d/L/UlUPTkSPc7Mc9ijvjH6/OL3+rtMAGO7/hvL/UdPvieHROWvvOY/7d6v/mLrg+f //mhL/JjP7KUzxMAfeipn7mKz/pm3viv7/exb+9yT/pFget3n/uYq/ms7/u/D/yAv+WC/6S1zyUu jPbIr/q8r+j34PnN///6wT/rkj+KhC8UjJzy14+2u7/3nd/9zf/9bT760o8UyZzx5/+zyt/18eD6 7N/+zw8QJQQOLHEiyBCECRUuZNjQYUIgAgBMpFjR4kWMGTVu5IiRwL9y2USOJFnS5EmUKVWuZNnS 5UuYIs3Bo1nT5k2cNyFI4NnT50+fEU4QJEo0xUOkSZH+6NjU6VOoFhH8AxfT6lWsWbVi1ZbT61d4 O4GOHSu06NkaStWuHZIk6lu4cQEs+Ldt6128efW2nAfWL817E8gO/mn2LMEdbBU7ZCrX8eONB77t pVzZMtaZf7/Gi0DYc0/Dh0sQWVxaoVvIqVUDEPBP22XYsWWP7Ko5Z/88fZ91Swhd1KBp041XD3dM wNts5Mn19rWtc/fu3gSPAi+Nmvj1twGoKufePWbm5jTFPtcdXWBa6oqFY2f/dEFI7/Hln6wdPjD5 5+YTp2drvf3/jhCYb0ACmbONM/zIi440/tRaD0AIMxLALgIr7A68v3BLEL/QfmtQKf8iFNGiUCw0 Mbn6/hpvw/yGKmG6D5EiYkQaLwqAmxNzjM1AsFZkscUS0IvxIRpqNJIiaarSccm9MPTqvh8TFGq/ IRsKIoAjs0ySSS7vSvG23KLcMAIGq2SoyCyzRKdLNrPiEScfxXxuhTLNTOjKNNNcs00+X3LSpjjl 1A0FF2ywcyE088z/Eps+G13py5oCFdSzClhwIYdD78RS0SwDEMdRUE96Ex4oJ91tghZccGGFTBFK lNMjbwx1Vplu0tDUU1NVtQUgMsUT1jS3pBXULyXFdawVVFW2zipfBfZIYYdt1EBjj/2JH2WXPfTX Z/WU1tHMSrV2sEqzVdVQO4XoltM9v22zq3YEG5ewCCw191I7I1qXU0bdbdOcMOclC9V7VWXVTHX3 VdRTf9lMR2DCki3YBV6r1FfhhXFseElu8KEAYmQn1nbIhDFWNNqNTUwnn3w+BrmnckV2gdn0Ljb5 ZCVTrrBjlluWF+KYZUa3QSB4uBnYdnUecOWe87Hn53EJlvncD4s+//rZpJX2juemnYb6WImnXpVo o69+tl+tvWO6a6/HDVvsg6mz2uxnA8Am57SR45rtfPip4FhCxc6WZrbmprvbUF7LG7m1+c4Hn78n DVrwmYEz/PBuB+gG78Ur29vxxyMXU2rKqS7tcsy7DcAaxTuvrHHQH3f5R9JLL/T0slNXOAADNnd9 r89jZ3n2Dd+2Pe61UNd93wW+af33rWAXfngWsbU9W+SVUn75fQVAwHfoswp+epYv+Pqzya+vXK3t ud83AMk0Dt8q6cln+ennald//aTad1/hj8Bnfi8Zn/3ud76x6G9/Q3uI//6nsAH84xvyG+BK6mfA +3XGM8bb3+2Q4v/AB+5uKgKsIEoKiEGWQS5iHbxX9hYCwhBizAASpGAJSXJBFKZQdD9JHwtdCJHc xTB1EQSJDUsCDn7kMHYqLIy9WGguwsFQiCbzHg2NKBIcKjGFxFNg6VqwghWowAQm6EAIOnCDgwBx iv/j3T+KaEMkanF6s+PgvVgAxheM0QQh4CMIPvBHQAISBGcMghTXeDS6WLGCWZRjzz72NjCuQI8e 6GMgLXlJTIJgAIeM4QCm8sbwxbGRwuOHBsjIxxBgUpWrxCQHJMLJGMLPjRMMHyPleIENeMCPrORl L/8IgU3BUogzdCMJ8ybKUfYMH/0ooy+dyUsQMECYnCSiIvNmS/v/XcAfunxmN1fJgQRME5YB+Egx j5lEOeIDl6n0ZjsxiYFgipOTsrRmyrDJN374owO7dGc/BdkAeQZUAAdwI4U2hsxs5pKf/mQoOAP6 UNYQ1Buck9Y9l9lMhmb0jyEAJkQ9uoCpGFRaCOWbNrmpUYaCYAMN2KRHXToRkE70WxdU5wbYiVJ/ hgADDHjlS306kY+IFFQkzec+cepPEHC0pT9lKkXIKdNQrQ2XJz1qO0GAgQb0tKlbdSoBhNomcFyA mTetqjc5yoB4clWtFBGAMSjKJG3UY6FldaZKWbpWvGpEAL1zRzm08bwKgeMcZKWrL3WK1rwmliMD cAAJREACEuzD/x3u2MZftyaPuRZ2lSqFwFIV+9nFNlYEoyUtZCXrjr/WUC9xzaxmL3nVrIJWtlBh rGNJe9vRjgCy9JjsX9/qEsES1rWXVGpaZ3vcptQWt8u9LWRJMFm/auO3I+EGZoerSrt6FrnbhUoA FvAA2zJXvKWF7GQrqzjWXjeQScXqAIzLXfh297vhHW99SzsC9W50A53Vanz96xjvgte+9R2BcKua VAjc9b8LJk6A6Ttg0hZWp519L4MtrBpyamAEEBYBflGa1P0yQLsXJjF7BEAADRPYnUmdcGcH0N8S xxhCJ04xbknQ2vXyEQMQcDGMZfxjI9F4w49dKIt33GMgJ1lhJy7OwAiOPIAXK1nKU6Zyla18ZSxn Wctb5nKXvfxlMIdZzGMmc5nNfGY0p1nNDA4IADs= ------=_NextPart_000_029E_01C07B15.387204E0 Content-Type: image/gif; name="Hull18.gif" Content-Transfer-Encoding: base64 Content-Disposition: attachment; filename="Hull18.gif" R0lGODdhMAEwAfcAAP///+fn58bGxq2trYyMjFJSUmNSUlI5OZxjY4RSUntCQms5OTkYGGspKWMY GFoICHsAAGsAAFIAADEAACkAABgAAAgAAJRaUmMQAN6Me8Z7a5Rza+etnK17a3tKOa1rUrWMe5Ra QnspCOfWzsa1rb2cjJx7a3trY5RSMZRCGK1aKa2UhJRSKa1SGNZjGKVKEL1SENa1nPfOrVJKQr2c e62Ma6V7Uq2lnIyEe8aMSt6UQsaEOWtKIf+tSqVzMZyMc6WMY62llMata2NaQqWce97Ga/fec6WU Sr2tWqWllGNjMXN7QoSMc2t7Uoyce3uMa4SlY73GtXOMY4Sta4zGa2uMWnOUY5zee4y1e6W9nMbO xnOEc4yljHOce2OEa3N7e5SlpYSUlIScnK3W1kJSUpS9vb3393ulpTFjY1KlrUKlrUq9xjGMlEqM lEKMlFLO3lqUnDGElBhCSghrjAh7pQiMvSFzlBCc1lKEnBBjnJylrWuEnCmE1s7W3nucvYy13mOE pUprjFJ7pUJzpSlzvSFjpTGU97W9xlJaY5zG9zFjnBhSlHOUvSlShCFjtRhKjEJjnBA5hGuMznuc 50pjnFprlGN7tRgpWgAhewAYWlJaczlKhAAIIRgpa2tzlDE5WjlSvSExczFKrQgQMQAYhAAYezFC lBAppVJajDlCexAYSgAQczE5eykxe+/v962tvVJSWpSUpYSElHt7jKWlvTk5QqWl1mtrjHt7pYyM vRgYIVJShEpKewAAGAAACDkxa1pShAgAKb211lJKa5yMxjkpY0Ixa5SMpXtzjFpCjBgQKSEAYxAA MQgAGIx7rSEIUhgAQmtahFpKc1JCa2tKnCEAUkIxWjkhWpRzrTEQSikIQnNahGNKc3NjeyEQKUoh UmtKa2M5Y3tCe1IpUpRrjEohQoRae62MpXNaa617nIRre3NKYzkQKcactWM5UkIYMa1jhJxac1oY MTEIGJyEjIwpSnNCUnspQkIIGGMhMYRaY3tKUjEACMZ7hK1rcwAAACwAAAAAMAEwAQAI/wABCBxI sKDBgwgTKlzIsKHDhxAjSpxIsaLFixgzatzIsaPHjyBDihxJsqTJkyhTqlzJsqXLlzBjypxJs6bN mzhz6tzJs6fPn0CDCh1KtKjRo0iTKl3KtKnTpxUHBIBKtSpNAQPOwBk0Z46dN2nEDLBKtmxIrLHg wOla545bt3TWvJn7hg0csWbz6m0YYMAAtXbmtH1LmHAcuojn2hUjYK/jsn61cqVTuLLlOYkzz13D RgyYxo9DIz0T6NKlPKhTq0ZdqLXr160bVcLjRo1mzZw9TxXN26crQIaCCx9OvHhxPowSKf8DiLbt 24nVtBG7u7f1q4OMa98unJAf5eDBM/+nLRc6Yul4r6tv+aoQ9/fFCf0JTz+8n+ZsyptXfHfs+v8k VcIHfAQGN8h89SVoH3767bcYaABGmFEAgQxYIHyDKKhhgvfhkd9+m3X2mYQkSjRAIxfCx4cgG7ao YIcfgpibVCXWmJAY7qXIHXIu9qghjA1Chx6NNtYYgCaO6MgdIcn56OSPgLTBBohzDVlkhAGEYqGS xsn35JctNicllXX1d6V1r1yyJZfEFYIgmHBuKOaUVNo14pl7fREJm9plGOefPe6BCBpwsBHjbbnd iSdVAfySJJ/E8eEnoJQquEcffRwihhhmlKEVHFI+l9mM1S2qlAChEAJppE1W6mp4l2L/KisBYpRh xq1mjHHGp24cWuV0RJpa1CuZrLkqk68mq1yssjar6Rm4Rnurp2KoZShdVgob1C57rjqcl8q+ymyz 5PYRhhhjSKvurbuqFepi/mmbUwCXPOLtcG6G6+of45Zbrh61rivwrbp+KgcZBEAor0xpPnqvIZPq C+gfevhrsbPnpjvwxp2e8QUYpS7MkieYGLtqxBLHSfHFLDcLsK0cc3xGyCKfFMAuJT9syIopU7py y0BjqimnMQ/sRc0qBdBJtw/z2POfPwcttbnoFq3uGFwgfRKxi+hcSCOe7AHI03BGPfXUAENrNa5l bKE1Sbtk4jCkhChCSSW52KL3LWF//0e2i35UfPbgsma8thlh3PA2SAGkkvOqhUAiySSV6G255bnc ssceb/5t3yGEhy7ry2t7EcXiHQnQyeNs1k3JJJNIcsvltF+OS9hje56IH6CL7num5xY9RhUKo26R GKswrSQfdk8OuyW41C497XyL/TTvv2ePKa0wD1yGFTQbH9EupMydYuSWwK6+JXlP7z71m/udLPba 1//sxmFMEb74DCmNifkEcp36Boi39xmwdrnAXefiBIje1e+BVNOYurrgBP5F5BWrYB2BmEcJ5w0w dpU7oAildzvrwalfEHwg6aQ1hilU0IIN8QQpImGy7aDvgwOURPRGyMPpVU9+LkJhCv8heAjDsY0K WYOhQsinvCXZDYcfhF4Pp+i+zIltgfQR4hCHuELEUeF0SjSI0sqnokJ0EIofLCAV1+i+EuYOVluM o7+GdqsufDGMBFEdJlTFnRuiMYchZKMg3/fDRGhRjnLk3hT0h0cAvIIUGiSOAP/4QR0O8pIHzAUs HIjITrrsC1RgpBJl2ETh8CFyHqTk+naIyVZODxmy8KQsRxcFHFzBCkokn72KUwhFpE+VOFSjK4dJ O2QII5az7KQeojCCETzhCi803hjNN0lgBpOY2CymMGghuGRucZnNbGYVoGk8PfJxZ6i0JhQlEchs ZtOYwpiFN7/JzHCOIApQuOPbHvn/uF7+Up04lKI7BwrPY86TiDewZziTQAUo7M9UpNzZEwGKRvYN 9KIF5eZBtXeIhCo0nEy4gigXRr5F+JGiUBTmRbM5C2G4VBjH4ORGB9fRjypUCuSUl9JW0YrXoRSN 7FzpSlv6UoPOlHA1tak98XkFxQlLdacwRSp/mkNWCtWdRC0qMo86NQIo9aM3oAIVilekR3YCFKBA BVUDatWrsrSoLtUoV4Pm1a9+1JYjLZInVnFWtLJirQRsn1sHmtWixnSuLaurXT/6zCecaRelaAVa J+vTtbZzsFiF60u3ithyKXaxHx1nEkuktEyIYrKT3cRaZYdZoRYWrpzt7PZA+1V8/+pTQqrrK2rR Kop/AlSgrb3oaw0rU8R+lrYfZWhe14NBye4WtZBAqUWDO1TNFlWesu0DOJH71ZDiEkCeyIRznztZ qQJUpdTNrHU3K9vtcverOI3mdeJ2WvLuVq3ADGp6Xbvel8qVq+59r1JtC8beKE239kXtX1Vpyf3y t78uPexRAyxgpYZ1rL1R3XgTfF9KAtfBwoUwe2ea1AovFq8PJQuxTMFh+6oWjegFcTZvIWKtbrTE Jl7sM+Wrl/DWt8XP7W1KZXxVGtc4rt2cJY5zvNhxOlUvmkAwkJ/7YvWxlshCNfKRYVpcOS6ZyXYl cF7oteEpP9e8z2srlt2p5S3HFv+RxwXzYpWb4qUI4BIsNjOHozuJ6a55pW0+8n/hLGcBhxQLKjat nlv81xj/ecZbJm4n41xo0OI0C1XxxCUWDWRRWEPNj4Z0pF+K3ThSutKLZaoWoIKIMnOavKwghjOi EY3ZhZrNo7bxFk+N6jmL1Sn0+vGrE7wLYhjb2LS+hWBvjclAR3rQ9eN1r08sUqZo4RfCHjZ5RYGM Y3ubGMioNaiZ3UNnR1rC9aPwtLm7Y6WkSdtATsW35y3rZC+b3CM0d6TfLDp1rxu5Yj7KF1wN7+cC g94IB7e48Z3vXGuW34Pz978BDoXlBgUV2S74mZ2R8I7P+ha2ZrgPHQ5XaEe8nhP/zzFDHTsUV3wi 4xrfLS86TvNj21vk2iT5dX335ZQL+Jmj/YkANhFzIEej5kg3drhvMe5QF1TnLoV4y3rucwFL4bY9 eQXBi47aViT968aeda0Z/nSom3zqHq06mPFpcZzMAuZcR22xwU53Ytzc6VCHK7qBRnW1C5ihPMaJ J+LeYm7X/fAKZ/qfy553qXvW76i25ZNxkgrCMxrxmK93re9NXcY3nq6Q7/UTMIwTAcDd8mide+Yz v/SmC9XzZk+yv6QdegGzvc4t2QPqE2wKjq/+9/UGeXBhD/W9k4v2tbc9FAIvk63vXt7Ajz6yN+9W 4kMd4shP/t+hUOCZDGD3CT64//THn3jXY9L613+89tf9BIfWBBXgJ2/vyU9/zYecmOjX+d4lvn4w S+G7MhEAeRZ/qDVz9XeAdkd9rpR/Oldq/Nd/TIZPzMcSsUCAz3V0CJiBrXd+eSdisfSAEMhkScB9 MkF0FjhZsZaBKhh2d0dFDKhztEAAKBeC64YDbZcSpneCk6V6K9iDG9hDw9WBtDALyIAM6qAOM0iD 0/YELOcSuqeDoGB4PTiFx/Zx9/c+QZhrs0CER0gP7fCFX6gOSjhx+BR0K+F8qJeCVLiGNqeA05OF ELaFRXiEYFiHdogDY/hvUVAF3ZcS3weFoCB+bDiISrdwtQOHpEaERqgOdtiIjv94DmmXh6iWBODD EvAHhfNHiJrIgmNnOcN1DIpIh444iqQIiZK4hBM4EgIIiNC3ia44fco2C6A4h+pwDqR4i7jYDvSQ hKfof5NnEhUIiIL4isQ4DLWYi8iIjHjYi5W2h2Q1Eiaog15HjNRIDN2QjNiYi8vIjGs3BJVoEjkI hQZYja/IiNl4jo8YidxYYT/wA0jgNiYxeFAoheS4ichgi+iYj3W4i+toYj8gAz9gBEvQhyGBhpan hvWoideojwz5hfzYj9xFADIwkUdgBEqAexgRjFDIgwk5iObYkAy5jRC5WDcQAxMpAxVZBE1AEpeo g/TYkWwYDSA5kyI5kjYVBSX/cJIyAARGYARFcAIisYpQ2IowyYYLOZMMaYo2qVT/qJM82ZNIEC8e 8YRQOIxFOYXO4IVI2ZAPuZT21JQ6WQM92ZNCgJETEY0nmIlXSYUyuZUgWZNLWZI6OZEBOZZGQAQf EY46SJRr2YNH6ZYh6ZXNJJdzKQMxgAR2iZceIY9QiIF92YNZCZggqZQ2iZOFeZIVOZaK2REGSXjT +Jh+KZkzSZkQCZaX+ZQ9uZkboZE6yJGgiYAfKZoM2ZXraJqnaZdH4BEteYIv+ZoHeI+ySZMQSZiX OZGoaQS5yRGucHpp6Jsr+JfBGZjcSJzFCZC42REDwJyW55rOSX6xGZ36SJp5/2iZ1XmSNFAEY5mc G6E6mOh73Vl/bQmeIEmbY2ib5ZmZyOkRozCU74mA0Cmf+iiGkmif95meHuEL2sl1Vtmf0vedAKqP cNl/1FmexmmgHeELUrZ7asmg0hefD/qWShgFNEChhXmcUpkRsLCfFjiOHCp9//mh+SieyUeeJKqT ddmTJ4oRsICgFuiYLQp8kQmjM0mftUegJHqjRpCjFwELvZChnvmj4+ehQtqQEep3Rlqj+KmkFkEA vaCi4MedUIp4Lzql+VilPjehNYqZY6mlUdELPLp7vRmmiAecZDqa6lh1IpqmxYmabEoRA9ALTQp+ CCmnmDemdYqOMkqGOamnt/+Jo6kDqF5qeQtKqHXnoIeqj0T6b1eqpzcaBAfqphrqnpR6eHR6qcJZ dZvKqZr5qb3Qma/Gl6NKd4ZqquhopoWGpoyqk5mpmhrhC4CqCqg3qbGadJZKqzF6p804orlanbvq EUwKqk86rIcnpcbKlbwoZzS6rI3KqygKqK1KeCwqrV83q9V6jgLaa6m6rE/JrTrqrcAadz4qrkgX pOWKlLYqYBKpreUplnfpEV/grb4Qd4MqrzVHrfVKpZWGq/p6knWpnhvxp97qqlMGpgSLcOR6sNmY qO+VrQtbmIeZn9jprb3wrhoXpxWLcPSKsUN6rdyVrgtbkQ6rERALqAEbc7D/erIWq7KAea925bIL y5Mx26siK7EcJqw4+23FqrMQamL52rEUCrQf4avuqnEberT0VqpKa6cCprBO65Qge6EiW7Pw9gtW S3MXm7XZmKkDtqhdW54BGbQZUQsi+63aFgrWwA3cEK9la2xJi7b5qLYf5bNOe55F8IxLOreb9mqi YAzUYAzY8Lh4q7c4a7B+i7CgJbhdW5F9ShHP6q2c8GqtwAvUQA28IAuPe7qRW7ZnW7nZeK9N27Yk qrn+Ore9MICd9gujm7vccLq8iw2pe7J9y7qIiqyDaZKwW6M8ubkTMbPemrhAZgqim7ujKw29W72/ K62UK7yzea0ce7zVmbwe/8G8gPq5hfcLySC9uTsN1bu+vpu3w7q62ouN5/qV3pumAam8JkK7tcth 0Iu+0qu+7Mu+1wulKRu/9qpQmHu89xu1tOu8uyUK5uu/0uu4AVzBA8yg2WvA0jkCXFu/hXkEvyi0 c0u+u9W/Eiy9pVvBKty+kvua8KvByWiKHezBc3kE7IoRUju3tgsKoXC+J4y+u7vCK3zBj4m1MIyU 9HADbEvDJAoEN3wRctvA5cW4P+y/1CvEWEzERfnCR5yMJ8DEeurEH9G5Iku+reDDVYy+AIzFbKzF 9Ri8XXyO5wACJgDGNfoDT2wRZDy0uJvGErzGbBzIbvyKRhzHDakOHMABdf9sx26bxxXxr/qrDH58 whQcyJYMue5LjlxsyLe4AYnMAQnsvQXwEeLrrcEQvZOMwqZ7yazMwtQIx5yMjHP8ySWgrIx8mTNA yvrbC8GgDansv0Hcyq08yCuYwbEsv5+cyLV8y5d5ALqsv8GwDMXwy9J7xcJ8zcR8gJt8zI3oycnM AcvMzDrpzAxMu9EMDWj8y4B8zdicyStYwNx8jvRQAt+cyCBgvOIsA0BZzrS7DMuQDdQ8uuvMzuyc zb9nzPGMi4hcz/aMz8y8z6w6t77gz9VAxb9cyQSd0Zjcwr+3zQn9hd7M0IqczzHAAyARxRLtz8vg y9Scwhr90hs9fvD80cj/OM8i/cmLfMs+UAMgscc0q9LLcA0BHcwwDdMGjXQe/dELfdOJnNNgbAM9 wNNjvMvQoNLoTM3WXNRafdQJB8s03c1MncyhzKg0oANRDRKQTLtVrdIArc5a/da8y9XeVshfjYs2 HdbKbMv1GwM50AM9gL/LS9VALc1uDdeGHdNJl9QJvdR4Dc56fbxQ7deAnb/6ywyD/QzpXMUYfdiG bdBeXddgGNKN7dj1awJ+LdkgUcqAGs2DLdST7NKcHdtujNCgXYeMPdoccM/HGwM7cNo+IBI5LLKs DdTVgMppTNSxLdvubGyKHc+3jdu63baR7de/HRLBbcqD7c8s7cdZndze//27n13boo3bDd21003d wL3L2e3P0+zHA+3d310L+Fjbufjc5D3SHVvWp+3XNiASyqC/E73eV53G7w3fsb0N5GAO803fpGjf 9+3UucrX++3XUt3TAL7e/tzWmm3gHC4L5pAO6YAODH6Ls3zfDA3henrep13hU027vlANGF7RaZwM 28Dh8A0OIA7iIj7ijujgJg7Ky6rfE94DnhoSPg2oa73e2/3DyG3jcI3gOZ4O5EAOPA7WP87Q4Zym vD3kqB0Sqt0LSb7erv3DBe7kL+3hUQ7i5KCVVd4OJX7l9ZzlJKri+z3Zga2/YZ7dA37CZW7mGY3j aQ7iCt7m7eDjcB7dFP9K56e9A2bpp7ts2Rie4Rvu528N6IGu44Q+3nD+zYhenELO5dUdEgFw3asd 6RRt0f672ZSe0VB+6Tm+4yP+5pvO0J1emD7A5b5NEqTOy6buz5h9wjS+6mf+4a4e5c0dv4Y+6/h9 mYq+3/09Ers+3KY+5sAs7Bpt6cWu5lTO4Jqu7N+M4jLw6bjO4iDx3y7e6xRt3P9r7QSN7dku6Av+ 1Xft7TcN4RKO6ytOEkce4Oiu4WrM7tfc6u8e5YMO2slO70B+ks0+4Sug7xeO7uwtwaoO8FiM5gMf 6LD+1d2O8MkczqaN73Xu8C4O4xC/57k78RS/wu5+8Tl+7Fk77xwv0rX/LO4gb+eOjucQL+noG+wp 38Ys7+pTTtPnMAMbUPRGf/RIn/RKv/RIvw+3DvKnrQOGyxFfnuemXtzV3vNCLPA/n+YFb8jnoA76 oA8JgAAXkAFon/Zqv/Zs3/Zuz/ZPD/U9EOoiUfU5r93+2+da/7gW3/WX/vXxSw9iT/YI0A+Gb/hn //aKv/iK/wFmLfdzXxIB8Oh378/UTg16v/cr7/dRnvFoqw7mQPYJ4A+HX/qHn/iMn/qqfwGQj94l scvSXvLpjPJ7/7hcz/kYr7NhP/YJkACm//umj/qqP/xvz/qtT+4hYe5zG/sQ7++0v/d9j/uXHvTG Kvi8X/jAn/3BT/zc/+/2xg/5yI/W0Fz5p567PF/7vbv50h/la16nR8j7pK/98v/7wt/99h8CrX/W JSEADw8QywQOJFhQ4LNk1BRyw9bQ4UOIESVOpFhxIrh0GTVu5NjRI0dz59qNJFnS5EmUKdupM6cv QYJ+MWXOpFnT5swLGXTu5NnT50+gPUP0IFrU6NEBAJQuZdrU6VOoS331olrVl0GsWK8ppDbN4lew Yb9uI/fR7FmP6FSuZdvunDp9LmHepFuXbs6gefXmHXrUb9GkUQUPhgqrqtWsiQdW46XQq1jIkb/K MofW8mW1bdvSg+sSgV3QoWkm2Fva9E4ff1UHJtya8IDDVaEpVpxNof8xybl1P8R42ffZbppPsoyb wJ9o5Mn7kT7dPG9q1Ud9uKZOeGrs2bQTF6OGe/d3yL1/j+9Ijlzbty1fKmevnLlz+D2hRy86vfr9 p4axa0+MMNk28AK0iCzyCgRJJJM4K+6z9hp0Lz4IddJgB/qMCgI/DJkiILZesuMPK9sYEnBEiCgz 8ESNQlLQpeMcdJG99yJ07oIKi7IhQxwBCOC6qoL5MCvGHiNxSPFQJI+cddY5oMUXm4RRxvhorHGH AHLEsZbYfPwRK22EHFJAbow8Mkl94IFnLifTRA4vKJuTssILrczwiyy3zMqbL0ckUEzLkFynTDPN RFNNQutis03T+qL/rwY5cRQgtmbsxAoaEfPczUQ+zfIT0EADHbRQUGk6FNG9FFUthyobzVCZw66S tCBoxBknnEotDS9Tj8whs1NeBQ31V1FJPc1Uv3SIQlUc9aPK1VcXC0ccaK0JB0BbwQoT1xTXsSee Xrs9E1hw+xlV2KDm+4tRZDOEDbFmCRoHWnjBkVaWainCNFNdt/V230/DJXRccn8y9yhU08WRxw7b HehdeBsOx5pp6K2XN3y15XZfjPv1N02AA5ZPNWMNTvYwD9tluGGUH/bS1iINzPdijGPWeOMmO/YY NdXQFRnDDWVTWKBvUBYa3llrHXLPAtGxOGamPaUZVJtvfpPgVHfG/29Hn3/OZmiuoZ2V2hHv/U1p e5o22+mn/705qKmLCtnqDLGkSkuFt+66a3mnFbBltMg++29f004TAQ3WBqptonSGG7+ee6G7Xbvv vlveiHfj+yO/Add8ZsGfNPwnYnu4cfEMH53752Uil1xylSVDGnNtNZc98M5fjPHznYjVQQDScWSV KtRjXX14r2kNS+yN/Cx7duY5rx2523HPgNgVeseRzl6YbVd44rv/2iK+N2V+fNqfbzB63E0d3XoM 19W+We677z5vsB+6NiPxydffefNBQ//z+eyOfQfLXvDkd8B4QUxi2CBQ/vT3QP71z1DS+xhRqjfA DOmnZK+qxrMQ+P9BlW0DHLt6YAnLJ8HkRO1m0FkfBvGzrg2+6mQf/GA5OGXCEuqDSShMIQV38gEd 9ECALsQQ1mIoqRnS8IDjwGET7cHD9qgwYFKKExExhCVmoC6JSvReE3H4RCgqR4rkolELrXifDT2u WUHjIgKZ6MUSgjGMa/KhTi5ApTOWznGoU10bu7c8OJJPjnMMzRiFFYIq5hE/ylDjq/rox+EBMpDM GyQh7WJIUp1AkdfrBR8heUBJTlJ2lbTkXerYgapt8j4CeN+rtPFJ+YVSlIAjZSltgkkoXSCVqrxP KyUVP1hKTpazPFstbRks6XmANbzETwEMGMxIEnN2xjxmTP4XMBT//ICZOBrAEbcETGhybZjSZBo1 q3lNYaHAjNu8jzd/BM5wCm2c5MSYOY+JzjZpIAUsYGeOBtAMd/Jni/FsmDvoSctq0gWfMtJAC1Sw y37eZwC+aEYWZUjQrhn0oMVM6E0WCqGGwoAEEbUSLHxx0mBUw04Dxag4NLrRptnTlh+FzwdeIFKS ysmkJ6VoQAvCUoy+FKYxk2kpcWmaD8DABevMKYZ0wdOTVpQ/j2ypS4ca047eMmAhUGoImtqoADwV qihVaWKo2lKhXtVbRbXkUfWCAhe44KFfbRQrx8pTgGblrEFVK1GzWhO3BgWuLngBROmqrrtCVaoF 2StB39jXtf4V/5lQ0sBgcXpYVREgsWNN6UBeWVWUPRayvWIrIQPbk4bG1QXaxCyydrpZvM4Gni0V 7Wg7Vdo5nnYnqY0rU1ubo9fCNqrNAG1obdst3IZRtxn4QAtUy8/fpiuswoWqBSrADg+CtrbHhUdy oajbpKp2rtGVrlipW4EJpJcf7wBHVbd7XO/y8LThjetlyZsuu1I3vfudAAXmUQ6Mvte28ZUg4eKD AqXWd6T3FdlEhWsB/kb4utmFpYBHS+D+0bQng1WtbxksJ83CFr0RJvF62wvLefYVw+bT8E44HFev fthqwR0rBUh84/7+95MpVuuKn9difao2ruOV8c5ofNJ/4FjJE/+YcBt5fFUf107DvFVtYYsMt+mO dcRLVrKJafjkoUa5czRtrpBdYN8r7yzLPLUxl7nsXwCDkru3laxMxkhfIbM2zXBzMJLd/Of0Npl4 YIapmAUnRTx3eM+96zOEAf1oLwtzzoEydNpUyFUzuwC6iybdFk665UcDGs53I/RGK/20qL1YvIbl tMhgkeRQxzrQ2B1aWuFb55jYTNUKbjX7DiBrYKuXvQWdtJlOTTOABTnTaO714gJAgF8HW9ajtmqx j72xcVHZzB5uttUEsAVQSxvQ1z1AsbuLa3Gh1rmZdkGMu03EARygzeJ+NAMWcMPR7gPdh7Ipu+XK 6ndbLwBbYAD/vR8tj3vk49621Teu2ZRoIVs54JsUgAHmbXAl46Me9Ui4O2A21IbXGS8QVy2zJ57H Z0cb4ziexz02Xo985MPjIMc1cxDs79WevJ/fDvfK1evyl8N8AaUuYcj/SppdC5nbOldkvC/uc37k I+gvl8fQyWn0rCog6c9l+lcHXnCf71fqU6f6wkWJ9VIiIAENcIAEIiABEbyA3UTuelMr/nSDa5zs L0+42b2Idh6qne1uh0DhDQ+BCDwg7iVfcN0Pm/Kw633vfJf5xx8I+Nr5IwELaADhD//5z0cAA3Fv vONb+22wG5wfQJ/8y2M+88ubT/Oc9zzobW97CWzB9B92uurH/976oL9ef5gHVgIU0PkI3F75to+A A+ix+ys/O/XS/j3wg151ovOK+GoyfgMeIIHlhx/0EVgA76C/6Ir3PNTysP7kq47vpm3fQYL/vvjt /3kJbADg5y8ytKUt+fabur6Dv32RP+QQvLZLvvtbQMRzPv47OdQDtpYLwMkbQKYxQLrQvMFTQAZk QPIzvwdkut4LtdWjwNbrOMvrFAyUidlDvg58wcLLv/0LwXeTPhKsPhMku9dLQflrwdqDwQ5svuej wQdMv0fDwRzUQasLFMDrvgfgQCCEwQ8kQioEAGjDuxsDwCR0P6trOCcEvygMQ8TTvyosQx0hODfT wi2cvHdggP/6E0M4dL4ZNEP+GwCLW7ISXMO9y4cnhEM4JL9lokNB1BECmL4Iizo9vL4+9MMwjIAN AMFBjMSl4DkcQ0ITlAcwZMQolENJ7MSnuEISY78cvIe208QoBERPTEWo+LoIU8MKdAAoNEUPfERV rMWosMN5m8DW48NYlMX740RbDMZVLMSf2zt5WERfXEBUFEZmFAyeQ0Sqy8RkvL/8g8RmvEaogDaE K8VpFD8JcIB9oIdAxEZyXEV62AdY7MbxA0dxLEd3vJoB2IAF+EE/fLt92IABmMN33MfBEIBz5MYX tEd81Ed+LMjqiMd9oMfQk4AF2Id8NEiIXBwBGAB0BL+3a8gwAbDGiNxI0slIjvxIkAxJkRxJkixJ kzxJlExJlVxJlmxJl3xJmIxJmZxJmqzJBwwIADs= ------=_NextPart_000_029E_01C07B15.387204E0 Content-Type: image/gif; name="Hull19.gif" Content-Transfer-Encoding: base64 Content-Disposition: attachment; filename="Hull19.gif" R0lGODdhMAEwAfcAAP///+fn58bGxq2trYx7e4xzc3tSUpxjY4RSUpxaWoRKSntCQmspKWMYGFoI CHsAAGsAAFIAAEIAAJRrY4xjWpRza+etnIRKOc6cjIxKMWMhCK2Ec+fWzsa1rYQxCJSEe5xjQq1a KYxCGKVKGK2UhJxzWpRSKa1SGNZjGL1SEJyEc4xCEJRKEJRSGMa9tZSMhK2Ma6VzQpxjKa2lnKV7 St6UQsaEOb17MaWEWv+tSqVzMYRzWpyMa6WEQq2llMalUqWUWqWce97Ga4yEY4R7Uvfec6WUSr2t WqWca5yUSqWllJSUWpyljGN7QoSMe4yce2NzUnuMa1JjQoSlY73GtXutWoSta4zGa2uMWs7expSl jHuca5zee2N7WlJ7QmOUUvf/93uMe2OEa3OchIy9rXuclL3GxqWtrZylpYyUlIylpWuEhK3W1pS9 vb3393ulpXucpVqMnAhrjAh7pQiMvSFzlBCc1nOlvWO954ycpXulvUJ7nDlznFqEpcbO1nOMpXuc vYy13iFShJzG9wA5e2uEpWN7nFprhFpznGuMzhAxc3uc52N7tVJrrUJalHuEnFJjlFJjnFJrvTlK hBgxhDFChBgpawghe3N7nDlSvTFKrRgpcwgQMQAYhK213oyUvTlKnDFClCk5jClCtRgpexgxpRAh cwgYawAYlIyUxjlCexghWgAQcyEpYykxeyEpa+fn962tvVJSWnt7jKWlvTk5Qlpaa1JSYzk5ShgY IVJShEpKexgYKQgIIQAAGAAACHNrrTkxc3tznGNahL211nNrjJyMxiEYOUIxa5SMpXNjlFpKe1pC jDkpWox7rVI5e3trlGtahFpKc2tKnDEhSlpCe3tzhGtae0oxYwgAEBgIIYyEjHtre2NCY2M5Y3tC e1IpUkIhQjkYOSkQKXM5a5RrjFoxUlIpSoRae62MpVohSnNaa3tjc617nIRre8actZx7jHNSY4wp SnspQmshOVohMYRja4RaY3tSWloIGHM5QsZ7hK1rc5RSWnMxOQAAACwAAAAAMAEwAQAI/wABCBxI sKDBgwgTKlzIsKHDhxAjSpxIsaLFixgzatzIsaPHjyBDihxJsqTJkyhTqlzJsqXLlzBjypxJs6bN mzhz6tzJs6fPn0CDCh1KtKjRo0iTKl3KtKnTp1CjSp1KtarVnAEGaN3KlWueOGAPyYqTx8zVs2gH av0TZ4+ct3DfzrFDt65dO3Te8uHTpxCgQYD/vDkTIK3hpVkHgHUr567jx3nl7O37F7Dly4PguGmj RsDhzz4Tg60jZ+7j03QjT/aLubVrQGzcuGGj5gzo2zEFDPgaRy5q1Kr5snZNvPigP7KTv0FTGLfz knfwmP59Ojhl49izZ06enLPn5+A7wv+KQ/2u9eHa02eHzT05m8HNw8unCEvQ7/OV1evXj7w99zZo fDffgA15Qohd+O2n4IKWaeYfd7TZRuCEB0WiiGTC5cfghgyy92B7y8VH4YCwgHJJJIFwqOKKx334 oHcjzudHKa4ksggiLObIoIMutvceYTE650knrixiZCIa6qgkdh726B+AAgaZFiSdNGLklTguqSV2 /Tn5YIRSnhUAKZcwcuWVSG6pJnE8evlgiGFOFUspp9h45pWRrKnnZU26+WJncT71CZF3FtrHnoh2 6eeHPwa6FJWOFFponojqGUgbi3q5XJSOBjUmK1ZKamileuoRW6ZO0jZAp0HNeYmdot7/yUiKpKqp KKo9wsnqTpgQCWusdxpSq5qX4uonjLvaFACVRQIr6qzDbmmqsX42mqxMY1bpLLBZRrvkrdQ6udy1 L8XSSZnbApumt0oWG+6iYZDLUq+b/JqupN2ym+O077rJhhPyorQsKs3eq26S+qoIbr8flkFFwCUJ QEonkRq8bb4Jq+guw06KkQXEIpl7SagWb3toxizyy7GLbHQhIsgb6XKuvSXHSinKKy68MndkYPEy zBYFoArBNNcc68k4c7jxzg+O8QTQGUncSSVGWwxt0hyqzLR/WDwNdUVpdKJt1RYLizWHOm/NxhcP fy2RLqigS7bVtJ694NJbc1fGFW27/91QAJagUu/cNZttd3qFFILJ4rJokUYab7yBad5ujFHFz34b FMvEBRNu8bqHYwZI4ovPMgsxqKO+DQess+7CCy88XkbkHLNhhRWYZy5Q2GN7XjPGSZOOiem0pG68 8au3rvzysDsOueS4knHFFrofBPfIvlcNOrujLz786ceHH37yy5dv/uuxpzH7G6e6OAYXXlcPgNCo 1Jk92cCvGYjwxIvv///kM58AB8iBGbzAebObXHKwwAUtyE9iBLsf4ZC2JP7NIhn/y6AGiRFAAnqQ gOiT3RqqwDfdmWtqEiTczTjUvdKBb4Mw1GAHP0jDDyrhClfgFMyU0QlQpdBzFNTO/v8U973ixfCI MZxhDZcoQCdwAXdQC8D1ivbDkl2NOBbEIBK3uEUlMvGLymMgFEE2JsFRsYolM9zoiGg6LrrxjRwE oxzPNwX4gSwWrCAUGj2XCEgcon9wDOQbvTjHL87gClxAQ8B4R7I9Vi0Sw4CGMaIhyEoOspCYbJ0T c0iu6zXSkVaDRDSMQUpSFsOSqDwiITO5xCg8MXdBAhwqKHFGUIqqj8NwRil36QwtpvKX/lslK2vI wPgFyg+kQMUoqGbLe0FSkruM5iSBSc3xDTOTLqhCIh11QlFkIhS1bCYjRCnNcpqymuiM4zUxecMS hglunQhFJuZZsWbeCZe6NKc5e5n/TmoKc50fdOIYRxSASdRPE/OcZ+fs+Ux9OpSUwjBiP1H5T4B6 kIHUGxEsJmaKhHq0nqAc5ygfSlJjnHKiFLUoJl1QRwdOyFys8KZHE8rMPeKzpDjlJ0orWVGVDvCQ 7pwPJlDRCYTONKGaMFMVG4rTphoDGhLd6SV9WkiBwvIwAYgEKkxh1KPSNIUidapYSUlJqcKxp1QV oCsz+pyNEsmrRwWn72461rq+0KxdTCsmGehS3MypEzKF60xBajSm1vWwOsUrEtGq1/KxNKif+cRB BetVudYsrIfNbCnLqlhVNraQNxyoYSLRiY5SFq6EdRZdNctak3bWs5+doxPZipYS/wH2tIKtqbMM 29rWJva1GXxBbAvpyr5eZUbxxC1lIwEszPb2uRCNKnDFJ9zhyvGxfavKkE7RVeV6VbdogkQuoUve Up50uv6rrnXBeMjLWYVKm/DuaZN6Jt6Wl7y/Ra/x1LveL4aWKgGQREzli9tIOfe+CDZGRPUbPv72 l4muNKZTYEGn7hIYrq4Yb4I3TFYGH8/BD14iAz/2lCGZ9sKn1QWHV0zKuzIYxCGm4WPB4JRUvBXF 84UmizcMVQ+jDsYxtuEVrNAUSdwWx6dVxY5ZzNkXB1mOTpRwUcbEXSTjVsVLXvF59QvkJ3swCpAl CuBObGXBhiKfWd5wfoHbZS8PkP+l7p2yJQJbZsEqOc0rXjCX3czeK2Bhyq2QZ51PO1I8c3jLbOYz GG9o3J/EYhUWHvRRXWFoFq9ZsW1WtFrDzJMBtELSV640i/WcaE1/EQui3UksXAHqHIuaxYjGtKm/ yFLa6iQZkW71TCn9aha7GK+ZnnX5GN1pXYe61yvu8WuDLezlOYHTNVGGsSl7ZmQzudTNbmWqaRIA QU/bq3e2tpaXnW0m1jonyfi2YLEsbg5feqLMLnfrsqnIm+hC3V7ldbtX3GSpxlverFNCFXQIEwHk Wt272PeOYw1vgEN42y95BL6PqgkdK1zNvtzpvx3Oga7VZBIT3/XFd0xqlG7c4Sz/rXdMBhDymbJ7 5Ic268kdLnCCr0TaLZ9nxWFu6YwD03TWsIY7CMDxLzoB4inpds7nGW6ec1jZlQS60N3xjqpbnbFF j4KUVZLupWfi5U7fcL9jSAugu+PsVk+72tMxg6IvMeUvuffSqx12X28wGWZ3BzzUzve+vwMeLnB7 DV3ghauOxOBeT3jde348vAf97Onwu+QlD3jB01AJUGiJxL1e6MVzOBqzeLw7Ij/50pee6Jb/oNZZ AvKl69vzHL6G6WdP+3fM3OFQyK5JWO51sMMewVSvvfD9zvbUe3AHTTC8R+Se853/XuzDj37fK298 AfJACFIQmLdb/vrn31f20g+//9XdUX3rF+EIYjhJ15fue+8/1xl7F7/8UV9+5fGgCEVIgu5D0vqc 09395QV+8id/t9dsL4B/RbAEyocRiLd0TQeA0MUNAziAxVd/rHOACDgEJLF5S9d5ENhb8DeBA0h9 9YeB+CcETDASrOZ6HxiAIjiB5GeBJniCLhASvMd+LUheEviCA0h/1TeD+BcEIcF8Led8Odha0EB6 PEiAJYiACGgEIKF0LHiEvSWASyh+FWh8QFgEUPgR65dz7UeFY7WDVyh/JGh5W1gEq+IR/ddy/yeG h5WEZTiBPih4LnAEToh/a8gRDZhzDwiHY2WFcyh+deh2RpCHReADHpEKXvd1gP+oWcE3iPKXhYJ3 iHkohB1hC17XfY/oVNEgiSJIiUVniU4IBB5RC9s3cYrXiYEIiiJ4hhxHik/oEdmwCs1ncayYU/Hn ij1oebJ4gjZXEdnQCznHiblIUoLIi4RYiYiohh2RDb6Qit8WhseoT2SojJPYdqPYjIq4EQEAjbY4 cUZYjSQVgtg4gaJYbr8YhBwxAL7gC8Q4cX9IjvqUjOcYfrCYbfeHiKa4Ee74jtKoa9RIj9F0jfc4 fxy3j3nYhRrxj74Qjt/2hgRpTnJ4kCKIdSGmkE54BAvoEGnwjvCIb6s4kfVokS+YjrOmkU64hxgh CyAZjermgSQpTQZpkuKXj6b/ppIIOAMb4ZIgCZG6ZowzWUoVaZMTiJOKppPsqBE++Y7xaGwDOZP2 aJThV4iappRFgAQbwQsvCZO6No5DGU2RSJUTiJHDhZUMiRHQ+JJAKWlCGZafSJYnqY2z9gHNeH4d yRBrCZJPCWpRSZJTKZfSh5RPloZ6qBF7CZIBiWQSGZakZI6C+YqBZ2qG6YwM2JXv2JZlNo+OGZiR KX1WWZh3WQSYeBEO+ZKc0Goy6ZjGUJOfyYSaVpmlaRGnCZLZcHAX9pZDCZmviY506WaVmZYVEQCY +Y6vIGkjyZqk5Jm9GX2E2V/BiZjFmZp1BpbK6ZrNKX4xCJyjaZkXgQvFeZt1/6abM1mU2SmCoQmd 3cmSFdGUXXmcZQYMyhlNzHme0VeAFrWOCDibYFOcvkCdSOYK0jCfu4Sd9hl+KNlf+rmUpumf4oli moAM08AMuOiY5nmgRzmZQbagXJgR3+if8ElgofAM01CiyECgxlCfGDp82xljHCqcwuifAKpcmhAM zFCiOLoMBDqWK4qeT8ahQhCMEFELDoqbMzWiOJqkz4BmcNmjZYifrMSh3mkR7vmeymWjSZqlA8qa KuqkwpegnyWl3XgRHymjpxUKEpqlaqqjYcmbXiqZISal/EkRtfmSD+pVWKqmaloNTDqRXfqmwpee erUE3dmPF/GhIOpVEaqnjP86DVs6kwYKqMvYX1iJfzBKEYnZlTOqUCTaqHpKoTPpppLqm5TanUGa EURapEiVpp7KqCcKmKNahunADrBTq1D6QZV6mC3pn8Y5T0jaqp7KpgQZqbEqfe5gAciarBZQAcza rM7qrB8QrdI6rdJqq7VKBN1ZBDyJEWUqozV6o8DqqUtKkBdarANYAMqaruq6ruzarshqAj/QnXM6 EXVqp50arq36qNX4p+Y6exXgrgAbsOtaATlQA/F6l1qJEYjqn/eKr8FKj8Tar7V3rAJbsQJLAzlQ sAeLiJc6EZnalazqsI3Kp9VYrhIrff9qsSrbrjqQsRrbjByJqrzqC9QgssD/qq+dyK8nS3wbsLI+ m64E67Ivi4jsSRFV2pXHYLOtCqq5yKM7G30U+7NSi7FCO7ROuK1kOrPZoLSt+qqdGJdPK34pK7U/ 27JVW7A9cIkZUa+2ybWtKqyAqLNhm3bwgAFk+7NBe7YZm7YImLCH+rEvGbJum6XjCoiiOre0h653 67NUq7d7O4sZAbggKbiDm6Q4e4Ryi7hVN7aLa7Fm67iP26Eyy6tJW7mMCrdHGLGay3d127kqWwKg W7V8W7QTcbQvWbqmu6d9+oGHu7qTp7iuW7ExELuyO6UVwbbvuLW5q6eXC4GZq7mcG7zuigE2QLyy O68Sgby+oLzLm6XMoAxU/6i6vjt+0luxsGu9VbsN0smrlNu9XvuBJju+fge85euuw4u+LmsDebkQ kvuOzdC9eoq67ve8iBu99auu1Iu/LosDPTmzuAvAOMq0ECi+8hu1B8yu56vAOTCmu8qrvADBatq8 sBe/8st3BnzBynq/Cqy//qi1ILym3ucM13AN6MAOJWx66dCzKLyuCazBDNzCvJoN4PrCJVq4dSfD NNwOStwONnzDkmfBO6ysGazAHBy5M9u+ECzC7YbE6LDEXlwO5eDEfnfCUazC+MvCHNG/vvC/RBzB 4HtxXOzFcqzE6KCEYlx1rRvF6drDCvzDHGG7IPnAbfy+yBbHc3zI7VDHd/9sdfSrx8g6xfhbxRkB yE7ZxlkqwHhmyIi8yU28yGS8w597xvvrENrLvZY8oRW6Y5q8yazMxIucx46MrBtQAxqcAzDwEdrr Cw1ryVqMYKvcyq0MxnfcyI4MyehLu1bMvqecpJhcXr8MzNBcDrtYwp+MwqGMvjoQEmpcs8tcxLv7 fjPcxdA8znOsyCUMxY48y7V8yyBByb4gyKfcy3X1zORcz+2wDjdczRdszNaLzJM8s73QzW4MguFs zwZ9yJ28ujkcy8p6zdabzTbowgJtoppFzwd90MLsu+isx+qswewMErm8y8vczA5l0Rd90tLsu/p8 wPxMvP68vv6JxW0swQ//ZdInfdOJbMdPu9AMjawOTbwQLRJqDM/LLM82jdNIjc87mw7uYA/3gAA6 zNB5q8AkQBLuTNQjXU5HjdRc7cqxenb38NQHsA9kvQ/8ENWO3Lj4WwNCypQSPdHeXEpb3dV0ndAH ytTscA/4gABl3dd9fdYM/dOxSwMlUcpwbblzTdeKndHNCQ/uENYIMNZ+Pdl+Ddh6PNX4W9UkIQAz 6wsyPdPYYA6KPdrkbM5y6Q55/dT8QNmszdqWvcNqjb5sbRJcqcxwjQ3e8A3kwA6k3dutbNr3yNRO vdetXdzG/doXLNigS9gmwQ0OPNHPAA7fMN3f4A3l4NvYjdDY6NiQLdnG//3dx43W5YvZ6KvZhT2z H7zMzIAN5EDd1G3d2R3fS2zXJ4naeo0Aqw3e+q3fB2C3Bxzb1jvbJ9G/pkzEuO3eCO4N8i3fjG2G TS3W+x3hEr4P/X3Ayu24zH0SlCzEbRzdCP7h39ANCx7fwD2xj63aE57iE17h0kve1mveu3fFL7ze 7Q3iCL7bI57dJd53wn3fKv7jP87irmvGst3WH9G/bAzAB27jIE4O4pzjva3UasfdEA7kVg7kQn63 fIy/fowSqVqcWM21Hs7kTA7fUN7bNmzfe53fV97mVp7lUtvSsSvJJdGtmJnepkvjZL7non3mpE3c bh7ogU4BnUvk1ovGSf8nuQXOtUu+53uu4H5O1/Eg6JQ+6FpevT7cErVdnCLtsGPu6KAu4pGO1OjA 5pV+6j9O6HFeyxvcEs4d01yr56A+6zg+6ig9Aaie60Cu6j5r6MSL6CrB2f7JzSLb6LM+62Zu6waN D7re7CrO6xa75ejb5SshuWGup59+7Nqe7Mo+zpPu7OAu4dAusHIOunSOEoAc0OEq69re7t/Q590O zaUe7vS+3xOgsr4eu8C+Emy76Nie2+4e8NUd78BcDrhe7wgf3hUr7dZL7SwhuZ0eweBQ4wIf8KJO 8IjM7Am/8a2N3O1a7o577inx5SDbqMZe8e5e6xgvx9/O8S4/2R6/rhf/rrdB/RJ2/pLErqTSjfI8 z+0rP+8vH/R/Ld7p2tEK/NEvsbC3670Tz/NOX93XvfLtYPBCX/VlHfPJCvJ6+9IjH55JevJPX/GQ vvIab/VWj/UWMPNnW/Mw8epdqbzZHvZOP/bx3vJmb/VwbgFGj79IX3D+2QxNL/dyr/LKDvR3b/Zw rvVny/UqsekvqQ2CH/m6zdvKTvWHf/hZrvZVy/YxcbTZ8AvjIPmC7/NnXvaXf/csvvfo2/crh5m/ 8Po7L/pPT/ojbvenj/p2q/hVy/jV3pWvD/uyH/Z0n+OGf/uYjwGaL7QZXhNV+g+/nw0UH/wof/Ej bvnGf/r3QMsaDOM0/2Hnn//7vwD90s/zhC/fpn/9d88PI9ACmF7kOLGw3w/+oT/+KO/ktY/+ty8C KIACKQAQMmrkIFjQYEEaABQuZNjQ4UOIESUurOXL4i+MGTGO+9bR40eQIUWOJFnSo7dy7VSuZNnS 5UuY6Pjto1nT5k2cOXXu5NnT50+gOzOgIEr0hIyDSXOQmNjU6VOI3Cz60lgVnEmsWbWONAfT61eY 5SYEJVvW7Fm0OxOkKNq2hQ2lBGsIgFrXrkQBU/9V1Xh161/AJL2BJQwWX1rEiRUrXtvWcQqkShPe pVxZIS9f2fhqzEYu8GfQ37oVJt0y3mLUqVXr5DfC8WsULG4kZWrZdv9dqZo3Z+wc2rdWcuxKl5a5 2vhxxSJgw07RYqBcurelNx1AdbdGjr+1l0Q5nLBY5OHFBx26fPmIyJOnr4+o+3rG7Nvlg+zu3evh 8fn131Rg3n/sG2pjb8CGbtnrvYzCmW9Bj7qy76XT9pMwv8b+M8+EAAjUcKEBELSKQQYHe5Cl4iY0 8bjWLDQvhAw3dFEWDzXyDMT5RhuxHfBO1DG1FFWEjUUXgwQAxhh/6Y3G7YK7Eb8dm0ysPB8dK6FF ITcMIJcif9EGSfnq8y5CJ8M864IoXyuhyiqvzDI+Ln3zkrQSxZQTqArLJOpMNKvsMEsF2/xNRNJy nHNQnnq0MwUV8sz/c88i/fIzNEAJY5JQSm8ytMwUOlBUUXay/GXGRz9TkjAwKzWVJigx1XRTRYmM 8chQAxvVqzhPrTTVKENYlVVFa8lyy1g/e7MlQW2ltM5cqeQ1TzWLZDPYrYZdaVJjBz2ALTuBXJbV ZmPsE9q/Il2p1GrnvNRHDLddltEYHQVXKxtXqrVcOZWzE0911/UU1HexmrVYesXEVUV8813WVQ9h 7dckctBRidqAnUTWwhQKNvjgXxfWCiVyI25y4v8yvfhiLJ3VOCtzZvI4zHND3nVkdbv18NuTQyJH HXr0WTlMe30UGeaLA/DU3Zq/uZkeeZLWeWcdB/YvhOiAvphdD/nV//jopLOWpx6Vmd6vv2SlBprq 9xR+F2uttfana6/FA3lFZcW+GGEEgT0b57TzlsefftoWr2XzppRbbLrfe/ZRtPXOe56+/TYO8OUs HnxkmRGkuc3EFdd7HgUcX83pyCcfvPL3iAYxc801X9pzxchUMQUlRJ9cAE+9QRL11FNfnXW03n7t Z9lHZ+dABM3WDvfcc+ea97Mgf+zl4CffpuSyFzwH6eSzT3tt5slyvi1doxcfgOkRPPyzc+rRfv3t G+/eJ9Ad03Z88Qfw9TpxfEufff61Zvz9nsQPfHGjX/QEcL/NmC4r++tfA5PGOQDqxHdtAQEBCyi+ A+7GdlthoAM9KP+P3UVwH9eykOQuWMAAdKoqxhNJBz/4wRC+73t3OmENG5LCFZrEhS984fLedwAE aMA15qmYDY3IkACUbyMj2SEPecg9xwGRAQ2IAAQe8AAIOMAD2GoL8I74RfKVLH8faaITnci3nfED Af6gohWv+EY4QgACHiiKF8EIxm34yi9lNKMZ/1ctNfqDAVWEYyEN+cYIaGAF0LvjHQ8YDvX1UZKL 61ylELCAQbrxkJs0ZAPgYcFGOvIF+pjHJE2ZtRjq6JIMcEAEOPlKQ0LAHwMIZS0jIoBRlvKUkkxl fqTYSlgGs5AQKEDUbHnMh+BSH7vsow/FI8U2ClOaV4SAJ0GJTGz/csgekWTmB6GomkBmcprjxKI/ jJlNdEZkANvspgfRmJhwEpKc5IxAAa6ZTnw2ZJ3cbOf6/liWVTpAk/McZzXhkU+E1iUN+MBeP7MH QZ8E1JUEpSgEDHDOhGZ0IgFYaEMdqrucQHOiFCVpA+ypUZTahaMM/ShIRTpQkhJUlgdNaU3vEoBc tjRt86iHBGAa04pe1KZDrYwydenQeeTjp0AlqDWJ+lTLGLWb9FAqU4EqS1pCVau2wSU/zUgPgVo1 psTE6FbNepd9OrEe8hTrPA16z7PGFSpp7R9PR9pWcsqyrHLla2UGwNKHVhWv86wnXPt62Lqs1KNp o+pSB/tKgyJWkLIEUqzWwOrYx8YyAgYo5mQ9q6GVrhWzmcXiZgswAMN+VrWWCcAACmAAtj4WAhHw hwEGsNfV5tZKroXtaKUZgQYYAB641W1x0dRaA/gjtpANLjyyalzowkwAA0hubGfLWdRGV7uimy52 U7td8IZXvOMlb3nNe170ple962Vve937XvjGV77zpW997Xtf/BIoIAA7 ------=_NextPart_000_029E_01C07B15.387204E0 Content-Type: image/gif; name="Hull20.gif" Content-Transfer-Encoding: base64 Content-Disposition: attachment; filename="Hull20.gif" R0lGODdhMAEwAfcAAP///+fn58bGxq2trYyMjHNzc1paWjk5OYx7e2NSUko5OXtSUsZ7e4RSUntC QjkYGGMYGHsAAGsAAFIAADEAACkAABgAAFoIAIxaUrWEe8Z7a5Rza+etnN6Mc5RaSnMhCM6cjK1r UmM5KbWMe3spCOfWzsa1rZx7a5RSMZRCGIQxCK1aKZxzWq1SGNZjGKVKEL1SEIxCEJRSIZRKEPfO ra2Ma6VzQq2lnKV7St6UQsaEOaVrKaWEWv+tSta9nL2lhKWMa6VzMYRrQox7QqWce97Ga/fec6WU SqWca7WtWpyUSqWllHNzY3N7QoSUSoSMc2t7UsbWtYyce7W9rXuMa4SlY73GtXutWr3npYSta4zG a63OnJSljJTGe5zee6XejGuUWqW9nGN7WlJ7Qt731mOUUnOUa/f/93Oce4y9rXuclIScnFpra2uE hK3W1pS9vb3393ulpUpra2ucnFqUlEqUlDFjYzGMjEK1vUrO1jmcpRBSWiFSWlqMnAhrjAh7pQiM vQBCWiFzlBCc1oSUnBhrlIycpXulvVpzhDlznJylrSmE1iFzvc7W3oSMlHOMpXucvYy13jl7vSlj nDGU97W9xpzG91JznClShGuEpWN7nEJjnGuMznuc50pjnFprlGN7tTlKhDlCY3N7nEJSlDlSvTFK rWNrlEJSnDFClBghWjE5hCkxe7W1vVJSWoSElHt7jKWlvTk5QnNzjKWl1mtrjHt7pYyMvRgYIVpa hDExcwAAGAAAEAAACDkxcxgQQkpCa7211ko5ewgAIZyMxjEhWhAAOUIxa5SMpVpCjBgAShAAMVI5 eyEAWlJCa2tKnGNSe3tzhEoxY5RzrYRjnHNahGNKc2NKa0oxUntje2NCY3tCe1IpUmMxYzkYOSkQ KXM5a5RrjGM5Wq2MpXtac3NSa4Rje1ohSq17nIRre3NKY8actZx7jK1jhIRKY1ohOUoYKYwpSnNC UnspQmshOTkIGIxrc1IxOWMhMVoYKYRaY2s5QntKUjEACFIIEAAAACwAAAAAMAEwAQAI/wABCBxI sKDBgwgTKlzIsKHDhxAjSpxIsaLFixgzatzIsaPHjyBDihxJsqTJkyhTqlzJsqXLlzBjypxJs6bN mzhz6tzJs6fPn0CDCh1KtKjRo0iTKl3KtKnTp1CjSp1KtarVpgMGPOqTKBAdQwOuih2LMevWRH78 DFq71k+et3e+hiVLt67AAGa5pmXLt2+ht4DhfhVgt7BTvAP69BHk50/fx5D/7METuDKeO3MMETbM 2SdixYwdQx699o+fQokSZcoUKVKbOHPo1Lmjp/Lby5k3d97tUsAAQ4rTiiYd+XTq1ZEsKV+uPBOc 58/dwJZ9545lzJp5aw/pG3iftICIj/82jVo1a+bo01t6BL19+zhx6NCpDhh39u34I2b1Dl588fLI qSeggJG84d6B7sEX22x44DZAAPlFOFBeaKnl32PkHXfegBx26ByCIB74xnR18GHHHA9KWBiFe13Y V4bmJdfhjDQqx16IOCIo3RxysOFKiipC9dliLbrIFowB1qjkkgXm6CSOcRgSJFJDhmYkX0huuOSW XK735JcgFjAlUL4h0gcfgaSl5ppsttkYgFp2KaeccYBpJ3RvWDFmT5UsQsmfgAYq6KB/MjKJJ5fM qeiiykHixp13tqHnnjll4iehmAq6yKGcdNIJJ5AwKmqXN0IKZhsQUlpTAJdk6uqfk2z/AoqntHaS 6Ki4KlmnqV+6IUaqqsYUgCSvYrqpJ7Um20kmuTbboaO8fvmGmMHCVAkjxQ4a66zKJnurs+CmV2q0 OaIhRbUuxXFptpQYimy38GoS7rzM7UpujmJMii5KAWTCLiXHdgrvwKDISG+40N6Loxtg6LsvScOy u+3AFNMq78HzjqswgmmYAezDIV1b7LEVl+xpwRjPa+/GCKJBBcgiKbIuphObbPO3KTebMMsIgnEu zB75m6m7NhftKag5g6sxz9C5UYbDQF8UwCTGxiqw0UbjnDSuKzMNXRplfBw1RZUQOygjsmKt9tGh bp3rzl5Dh0YWYo8Nkcyacrr23ra6/93s0l67kcXPdkckNKA18803s36P2mTc7b2hxQ2FPzQ1oEQr rnnfjY96yKOQQ6eGFlBXfpAAxG66ydWba35x54wC7rUZdJueUJ9oc9v67ijDvujjocMh+Mu2G1QL Jp6wvvvur/s+5+fBP5eGFlwUT5Amui+v/adtOz+n7EyjQbr1AqCyyvboe6q191sCHzwYV9QddSum lGJK9um3jjT7ckIfvRtXMIPpRlG/UpTifPnT3vr4N6BIrGYUo4BFAdYQPThMj3BAC8ApDMjBVCgv gZpjHAPRA4lMQDCCyAiGClfoCEesAXSQQ4MXKJdBVHDwhqQA4fIW2DkHmjCCsIjFCv+HSMRYKKIR iiBE13gGBi3oZl+tSMUNb+hBHe5OhG57IBBTSMQuejEYyKhEI8boQhiyTHK12xcyCjhFDubQipvr Hb1KeEJYwOKLeMxjMF4xxj4m0UA8U4MXiFetDbZxigiEo+ua5UMI2lGIeoykHh3Rxz5WwoU8k2H1 VBWAUBzykO9SJN/k2CUt2pGLkkylJI1YyUq6EJDkEtz49tQKG36yjYkU5d6a9yxT3lGVwAwmGMXY SksSgoLkml78xrTGWx7yfrrk2/7Q00ggQlKY2BQmH4vZyjJGS4YCDJIhnXnIUESTb4nSIgqzyc52 qpCS3GxlEpf4JTN4AYPbCUAuyHn/yyqeU22i+KU7B+pOVsazmN60kyxL15ny8dOZb/ynzTjxiVoQ 9KLuhMVB4/lHO03PifhhxUOdmUuJUowTtqCFRTHKUmxuc6PFrMQxwSTDNO5mACMlZ0RNCi9QpJQW s2ipUIFpUJhy85VPAsM9tbPPnN6ypDyt1SduQYuqBnWoWI1kGI16UJnSsz0A9MImORMAKTr1k9CM arI+UdW2XjWrcP2iRrm60YQiSJCzNAwyzkpStdKKE6doq1vjSlgvvpSuHCUELN1TU/mNxZN8/aQ/ o4pSwQ62sJhVYVERG89LvtA9gvNCOO0iADZGto07lahPLXvZzGJ2q5yFaUfxpIWl/9plFKft5wd1 OVXWtta1hZ1rbGEqU2TCAa8MtYpIc/vJ1PLWt4IVKHALe9jh1nUNBrKnFhw7FZwy95NQhSNgoRvd 6WZ2s9bdqEzbkAUv2PQqTf0uKKO5WvK2VbrmjSts02vUSjChtvikSlnlC15dgoKq9r1vfjMrXP52 9QYlQIAXvDAFseyVwM/EXwJ7m2AFLxiz1XVwKwlQghJTwQt5pQpkMdxGc1qRrR0u74cLi14Rj5HE JS6BFargXu4ypbQsPuRk08eJWsRYsCudcWH3a+NG4DjHOr6CbaeC2yAf0rnLq++Rq5pkJRO2wSJ2 BJShvAQAU2W5Vp4iK/J34C0j2f/LmQ2xdRVhhTFD+QkoTq5SvJtm1KKPw27mMpwxW+PY0tnOY9au j48S3z7fMLzShHGg29rlQcOVybGtBIQRDeUd9/gpA3b0FNO6ucpO+s2WDm56Nc1pO9+gtmNlyoVF jcjWafnUgk41dYfL6lbbucwUdsqKac1BUu+tzbgW7Ft1DddCb/TJvh7zibXQiB+bltgGxHLRAJ1s qzJ7ycTkKrSjPWaldmHRQKkytqm425JRtNusXfa3sypnbo6b3J3mcYCLguZ1u1Ftpoa3sue9a9nW Gd+cBnYYksJnf3MQ0gT7qcAHTvC4OnuMh0Z4q/HsBT3/pNEOz/a2ETxxilf80uH/lufBNd7qaZ/B KKEO+cNtJumSy/jkcJVzr1neak9nwSizlrkBjd2t8dqctfjF+VCru3Oe91zKsQ7KsIVeChfDK+BH v7nSsbrZezsd0cCOwlCATPUOtvvWWffw1rMKW69/HdHTrnZQ1F12kSuL22lX+9qxyke3vx3R9jx3 UPpd9zWvNe/QTfreWRoLA/xd457GAlAaXne7f8rIiGftLVC5+IHGwo7RSEc62DGOTT+e3K/2wsJ9 AvLKIxDtmc9157H5eViEfvTryL3u18GOlZ/e1xLueE9iXvmhgwLZsbdspWePx9rfnh27j3700/F7 fJ/4Cy/fSdCLb0BR5CL5vl0+//OD4XzRQ1/66Ec/AqofbSuMwb08mXrxTXEKYuSiGrUgefLFv/Xy 4z79AAiApcd+nGYFPzAEUrYFOkF23GdAq0AMEAiBp4B/Eod4/Pdt/nd+AbiBG9h7BGhnREADQFAE UkYGOUF3DZgLEbiCxDANFGiBBJeBHDiDNJh7HviBJcYONCCCRpAEWkBtOEF4xZcK08CCRjgN94d5 NidvMyaDNfiET7h+OHgDPrCDQGAERqAEXvAF6KYSlMd9oWCEYhiBSah/ycaEroUMtvd8UNiGbrgO Ush+BriDNPADRYCFTuAFklcTrVd8KjiGgEgME1gLFThpaMh2ayh64/CGjPiGA/9YfXNIhzRwBFho BHm4ejJBfNzHCoHYiRDogrWghG52iBelhtFwe4vYiKrYiDd4eiEoiZNYiSToBU/0EtsHhp6YixBY hltGithkiqi4isI4jHH4d68Ii1coi1fwXi4hf5VHf7oYjYKIf2boW76oVYmYDqk4jNzIjcXodFQI i1ZYiVjog4TUG9dWfA8ojew4iIWoddh4iorYjfRYj+vwiOBYheLIg+TYg9QDE+PUgKXwh+xYkC6I f0iXR8A4j/bYkPbYipD3A/u4g3bYj1kIUi4hhJVHhAXZkSvIi7QgXQupjQ5ZkiZJfTx3jBNJiRbp BMyIErdYfGHokTQZgYPoCvL/SJImuZM8+Y3RppIraZFYWAb7ZhJ9WHkEWZM1mQs82ZROeY+mF23h OJF0mIwWSYI0lBKaOIRFqJRKmQ1PGZYmiY+tNpVUOY5CaQRFUAa1WBIoiIteWZPToIFiWZf0CJF2 FolniZZpmQRQoBLOiJRxWZPQYJeGWY8+CWVAeZZWmZZKUJQgwYANuI6D6ZFgeZiYSYyctph7yZJp aQRN4HEdEZApWJkeeQrbmJmq6YhRmYN7uY+e+ZlN0IUZoZF1B42mWZCXuZq86YYQaZavWZWfKYt/ SRIx6Xq52ZG72ZvMWYNxqJfBKZzDiYVFgAAkcZR1l5TJmYuo2Zze6ZwlBgTR/ymOjTmcSSCaUmNW AsmR2xmNy/md8Jl+pceZ0Vme5kmbE/GWMtme0pgO8fmfAGgP+jiesBib00kEIRGY2cmfuliYAPqg 0bcBIzCgBLqDBjqcCPoRkrmJDKqL7wmh/zkOGcABJ1ChksgD00mOGeoRpMl92tmhYjiXIAqi9sAB NlqiJsqPKWoESAAStll2uAmjgPihMwqfG2CjN5qj9vmZR/ARx1l3lCmkY0ikRdqcIoqkHAACElmh S5qWTeoR2Fl2LyqlNpmaVfqdNYqlWbql4+kDSbCjRvClHLGVG9mVZGqEVHqmvXmkasoBE1qhF+ql HqGflTeTd2qE/qmn8MkOIP/Qp0lKoCi6o3K6EQpadsBwqEbooIqKpo6KpDhan3A6qRmxoc94DNhg DdBQf5hKDHm6qZnJp51KouPZpVfZlhbRonWXCszwDM4wDdNADaiqqlIqo67anIwaqzaqpaAKp3Oh ET8acqbgC8nwDLzqq9YKrKkqpK1arIaZpsi6psFZkTvarBjxpCGXCsJArdR6DNbarr+KqmNamdvK rXUJq9/6p68ZqEJJrhcRpusWrdOqrs/ADNTgrgYLr8nZnfTKm+nwrWqKr2eprxbJrxVBpw6HrgIr sNZgsBw7DQg7mPO6sE/prQ77qIzJrBpBqP6mCwGbsdS6sR3bsfBqpx6ZqCL/q5r2WrKyerLjqhGV SmupcAwum7G9GrNGWw2oSrPRyJQ3q5oNq7NqKp5USav9uKIWQarrxgotO7TrarRe66tICw1K24kh 27Q7mbNQq6wTKa4HmhG4SmymILRcm7Hs+rV2G7Zje4R0abZ1eaVQq6YZQKEFuqNWWxHP2messKtz m7HJUA12+7guGKyAqKl8a5ck+7dICrGDm6KFOxHmmmZxu7hcC7OQ+7jYKqwRWLaV25Boi7k7S56E ixH+GmQYK7pDW7SlW7qnK4FmurpO6beuq6afKolUW4mdGxEWa2UAa7tci7u5m7vYeg2+a7nB26nD y5fD2aMWobK0m67My7V1//u84lsN5hAO0yuWrVu9aiud0ymqEvGzBCat3zu34Su+umsO6BAOe3u+ JXms1euo62uhKeq+EIG1LBa087u4jWu/uXsN6PDA5tC7/GuPl/u/WKq5EluJBPwQtkBrLJvAoku6 DPy11RAOD/zA5TDBZ2vBsQqxxRunFpGOGBa6ICy6zjvCMUsN+HvCD0wOKuyQ/svCjvqpL7zBDdEK jpa4NWy7N4zDHOvAPHzCPvzD9VjBQoylOFrEFTEAh8tXNLzEolu/TnywUczD4WC+VNyN6XvF4PrC RWCrDmEMQabEYGy7YjzG1lrCZczDEZzGw/i0bNypWuqmKUqxD/EPM+wLdf/8vQuMx+4KxXt8wn3s x6poxYGMpIGbwVhoyA7RC+qZW7W7yMwrwo4MyZEsxZSsimt8yX46BIVcEa6gCsy1vKL8vU3sxHp8 ylE8xanchoDMyp0qBK9MEa6wC6DsvbVsy47sqzqsy2V8xr3chqvMyiCgAzYwnZzcEK7AC5+cUx+c zPN7xzhsys58wvobzTUIvMDcpyzQAz1wzZ+ZzQwxALwgy06FwOCcwOLMwNZQzpE8yei8gZa8zhxg A+78zp95vA5Bz8vgVN+czwlMygzczP68xykc0Bs4zZdczQeN0EKp0A1Bz70gw230xRAd0XhMzhXN w7yM0dKnzgSNpO3c0R7/XbUW0Qu80MV0fNIgfMvPq9IrzdIujX4Dvc4GTdPvfIcqetO88AvOZNI8 ncA+Xbq5HNR7DM1DvXsaHcgZkANI7c46oNRYCNINgdO90E+KG9U1vM+QS9FW/c8SjM5BHNMy/dUH HdbGaxHbnNMlLb9qvcRs/bhA/dZ8HNe9XNTAHAR2fddKrb3EzAtNPUWh/NdLLNGQW9WEHcktjdFb zcZdvdiMDcOwDNnGPHR+TdlgbNl269aZfcqbHc1zTdccMNOgDdZFYMQhDdncXAqTjdpLPNVeO9it bcZoHNCIzcqKXdt3PQQWQc+QrQoP7dtgDNwxK9zDbcb7S8mdfcUboNw0/40Bza3b/yDdtRzYHYvZ 133KAJ3KvyzbHIAD3t3RS3AROM0Lu1AM5L3IBHu/6V3RF33Y7o2lyR3fOoCfCFHfvaAMW5vfIKza HWvd/b3L0bzdQtzd8e3OPIARCN4Mv8DgqX3ZJhzhFf3aKtzesg3fF94D830Re53gyqDIHt7TprvD Iu7PWJ3Gx33JA+7dBY4Re80LxsDhMS7jdgvhNR7F6z3BME3XtB3fGe7juh3kzYDfQ/695u2r/Xzk QZ3k55vjgXzUF77iF+HcvLAMzdAMCl7lzLvfRxviWr7SJO67FM7CHH3hPV4Wuj0MZy7kam67Du6r Rv7mZRznfLvkMd3k3v/95HgO2Xp+5i/e5yFstIEu6FF849Pr5WwM5vEtzxFR37uw53wO6c0bs+hN 6Tae3WY75xZc5/EdBByx4aBO5aLusj7N2qa+0lzetLHN5CneAzXw6pDdC6CO5gs+68+wz5N+62X8 35WL6Ve8497N6RHR4sow7B1u7ALL5u2a5cpO2IROr6r+v5994a7OET8u5Xv+6NiurqRs690e1N/u qrt+6L3+6+Ye5cMe6ut+w8n+7s9c3Dfr7EIM7cot7fqh22ae77KO7c7b7/5exrlerOFevePe6h5B 5o0+7Gm+7uFb6g+/5YatpybO6ylu7x1R3xlv7et+7MxM4x+f2fFepQL/z8IEX9sGLxF7/en5juYw buwL7PAvv8cxP6MTH7wWfuE4ABLOLew7r++zbg0eH/RBbembOvIxjeIXTtYWEQBm3fRnvvCijg0u L/WZfc7FOvMWXPOLnQNwnBGywAsJ7vUbP+vYQPb9HfEgaugEffTxnfQh4QiQje47f+2QzgzcsA3i YPfpzexnivb/i/XxrfUXIQCB7/U83+fJwA3gsA2crw6Kf91Db6QBnqw6kOJsPxK4UOaW7/QMLg3d wPmwDw7k8PnDHfpWOqKjj+jK7fcisc0p3/RgL92GD/vEvw3d4Oa0b9VUD6GOX72a7t2Sj+e/v/Nz 79uZv/nFT/zHn/yE/433oj/6rO7dp08SvaDzq0/4qO362b/+ic/9b+39xtqoud/rvD8SrsD0q6/u fz386w8Q2wQOFCgO3UGECRUuZNjQ4UOICcmto1jR4kWMGTVu5LjRHgeQIUWOJFnSpEgbPVSuZNlS 5RIAMWXOpFnT5s2Yjno149nTp89fz4QOJVrU6NGiybiBI9jUqUBw5CJOpVrV6sSOWbVuzbrh5Few J0HocFl2pY4AONWuvRmgl7KfcXsWQ1rXLlFp3Z7ubRrV6l/AgMOF41rYsFZ2IMIuZszC7GMebCVP BiDLmFy5ypLd5VyUGTe+oQl2CxfY9GmH4dgdZt264kfGsb8GeWwWJv9l3DcLXMYcN2hnzkqZiia+ jRtq5MnRmRvn2nlhr7Klj8yQo7ZLtLm10xSwrHdcZb6A281b3Pw2g8rVAy733H3HxNPlg3R8vWXk 7fljevvue/zRz84TUJv1CqwKq/cStAi2+aajzT6WbtNvu2jg6s8nuv4TKhlshhPQPL8MFPEhBBVM MLoGZasOwrPSmjA/V3bx7sJmNNOwvA8/BMecEXtcaDATE0wnxenqY7EH/F7M74Be/hnGwu9+6yzA HKskzUcsD2IuSPcYJJKxB4+UUEntAsClFzRl/C684Dqs8k3jssxySy5dQ/HLsDY4UqUgyJzQLTTR dBLKn6RECkc430z/T84eS6yzMC/xBAuHPXuowc8JBwh0UzXjytAoKhNNVB1GfXT0Ua3ulHS2SgfA NNNNNx3UJxuJ4tBDUeEMsVQDgUR1q3EyWDXPSvt8dUJXYo2102YMRTRXUa/ktdfVfs0q0mFLSmnP S49FVtlYB2UzVGihlXba9ei0diNVsx1prFa9/fNMcJddxs1y80UPXQPbW1ejYN09yUgWjZVXPzPr VfYbfRtelF/lTv13HWwFDmnbI7s9WD8BFF64YX1JhVg9iddt12IO4N3T1Y1h9XhT0ECGdteRUfN1 4nXiQ3kkgiE0uGX9CngZZpnNLa1m5NT9t2KUMWaRCKCVTHboXnjB/7XoN89F2jSlrT05LBA2EHts sVkw+2yzMfDAAxFksI7FHASIWkkmqbYaa1Ef3jqwkrlUZ4Gx0UZb7bUL9yCEDhJXfHHGFQ8BBhde 2IFFHOZWMmGqccE7771R6/u5dMzRpwHSGzf9dNRPf9wF1l2YgazroLb8RUCpZnjzN2nu3KqbQRed dAaCD76B1Is3fnEUIG+ddRjcfizu2ZXUlOpevME9d6l2F6zaw0IfvQHhwxee+OPLPx2F5dOPfPKy Ko9eeup7ifn6D7XWnqquN/IeePH7Fx4D8wUQeeoj4OtcIrv3vWhqVNML/T50nPv9xV8Z2R/4/HfB 8AFQgObTQAoI+P/B5r2tB9BLoNSodzcHCkhvEYwIgiqIQRj2T4MbNJ4GWvBBHK5PJe4rIe3oNTQU ptA8BGLhVMKhjnvwL4ZLFN8MaYg6G+ZQiq9DYA/nRb3bCbE4uitiQo6oDne0w4JMJOP/npi6ELxA imuUgYus+KKOYVGLIOJRFxFiDnXII4zt4OMYy0hGJ55xcatbYw5X4MY3vmh6VJvfHENjP+3hUR72 4GMl+/jHP3pAkI0jZCFBaIJEYooA8WukI/cCQe2VI4+UtGQr/YjJGGpyk4pLnidzOKZQmpB6VzOl U1bIr3CoUh6tJGYlXwlLDMpyluizJQ5ZkMtj1Q2IvOwlQUQGTHX/gLGY22yHPfSBTCYqU5DMbCYB bQDNY2FuaJqr5l64iCU8apOb3JQHOMO5yQ6W84OHRGc6f/iyLLazKZAUkSRZOc951tOesRRkFPWp PhjIrZ/HWuTQrCdQpxBUOcI8KEIRqtCFXlAfGjijQx+6PBiAcqLequjLSonRfRVImB6lqSVBGtL+ kY+GaTyp+oCw0oMtcGgvxegv//LFYdZUqXy8KU7Dp1MBdrKnrHsmUIN6QmoK9Jp/iecel/rVpjp1 eDtV3lRZJwOrtuyfHgsiTLfxTocY9KtzrWRYxQrV8tXSrKzjZ1oPpk6AunU0R3sIR+l6WKaKNacC JOdeU+rXlsXR/3aCHYhGZ4pYzLbDrk4NZPEaa9bHQrZlLfXYRSn7MKRmVrWaVWwTy5fPvbauqqJt 2SipR1SBiuOLXl1tZjeL086azqSxnS1tWybUlzXQrd14xwOS2tvV/jakwWXccPfaV+MCTZova2s1 mTuPeIQ3H/vgLXTpyo/WZrB4PI0t616AyOxuDLBsFeh3w3vf8M4DH+Q173nTa0bUSdWxKo1v1Oar sIBq0b74ZXB+99vR/iIUvf9lAHU7IOC94rLAo41fgum34AaHOLz0eMc+IBxhYk74v+JEXlnbW9wN R420CsNt0cBxDvCKWMf4JfFzUdxKFaeXxYn7bGzRGuPoIddjNf/W143psWMoN3i8Pv5xkFs75CJf F75IjpqS69Xdhjk5ymMO8X7La14rK1acsG0v8yTK5eitVWFgntk5nkxmPDdYv/ztb5rFqkzrxja0 cI7egevFznyJOc+LDvE8SnxixPrZqbIMdGx/SugE1m5oHs6dnRn9aR2TeB+rlXRIycfeNlMV0z2c cb1M2+k7g1rWIp4yZku9UOJhOLbYXfX7bMtIWM9a2FAe75lpemt7NkDXWu61Fb1cL+WCyNPDpvaO 92xsbh4T1w4QwQUuEINUM4/AzS7hs5VF56coutrrtvaDaartPzaA2xeYQATsfe8JfECNgh43uTMt 5y9nlSDciDX/uw2+Y1FD2piwlHe3631viEdcAhcgwb57CmN//1uOfOEGPg7+cTLTYx9UXvgSR+fw iKdc5feeuApcbMtzZjyRrQYXpzsOcpzjudaWhPfJITABCaxc6EOPQMubyWuZs5qUA/d4zp2OZzNf Mng+BzrRrX71fINbiu9Nei6FdlvjNP3pYyfznu8hgp8H/eprZ3sEJlDxT3YdmuYOFzzIfvey5+Ph bed72ydOgpdfWu65BLiyLNCPHONd8QyeRz7U3nfI873lkMP44K1o6FhVgAIWEPvi8U4Pfzw+8qPn +wQeYPl+ahpcFqBA6ytgd8+TPR+hJ33t/b6PN6MemjTvheZb/9/6esTe6Xq3ffGvDgF7bFn3ufx1 uH7/fMQL3+CN37vxrS/xfbBs+Vb1Muuf//t+dF76sqaH469/fohPwB653z73nf/951dA/OPPM+hF j37jS2Af7Gi/cQHrffj7vQoIPvrLs9m7P/yzPQlYAPbrP8jCnH8IwACMvgK0NuJLQOuTAAhgB+Vz QMiaHgCUQOhLvArEr8ZDQAwcPf1rQA/MrgH4B98Twe/jvBK8L/tLQdubAAhYAA5sQUIrgBCUQQGE vQK8QRyEPAmYgAWwB+3zwVULgAJ4ACGEPwKUPr1DwSMUuiQ0sQHoQCfstQFQgCCUQQpUPOrLwrXT wQUYABb8wv+ug0IpnEIK6IeCe7oTRMOh00AebEI3dMABSIAxhD/5GzsjxEOIS8Il7MI+XEQACAAC eIAYDMABzLkDNER728I1bENG7EMBAEQZrAcSrLYLxEM1ZAdN3ERUbMRHjMQRrLYzzEJEZMJUnMXJ 6MRApMFZKz8szMAJ4EIvpEVgtAlHhMTvez1QK0T0U0M2DEZmzA9b/L4qJLNKPD89ZAc+bEZsLJNV BL9QbLRRLL5YVMRsHEcyEQAgbD061LE7VMBezERyfEdvIQAFqIBBZDBkhLxSPEV43Ec4AsIqvEe2 C0d+HMi5IYAEgIeq87teZMJfJEiHZKkBWIAFSEiVU0Z9fEg2jASaABgAdliAfSjFa8xIkRxJkixJ kzxJlExJlVxJlmxJl3xJmIxJmZxJmqxJm7xJnMxJlQwIADs= ------=_NextPart_000_029E_01C07B15.387204E0 Content-Type: image/gif; name="Hull21.gif" Content-Transfer-Encoding: base64 Content-Disposition: attachment; filename="Hull21.gif" R0lGODdhMAEwAfcAAP///+fn58bGxq2trYyMjHNzc1JSUr2trZyMjIx7e2NSUoxzc0o5OYxjY8Z7 e4RSUntCQnM5OVopKTkYGGspKXMpKWMYGHMYGFoICHsAAGsAAGMAAFIAAEIAADEAACkAACEAAFoQ CIxaUpRaUsZ7a1o5Ma1rWq1zY96Mc5RaSpR7c+fWzs69tYx7c4RSObWlnK2UhJyEc4RaOffOrZxr QpyMe72ljKWMc62Ma6V7Uq2lnKV7SsaMSqVzOd6UQsaEOaWEWv+tSta9nL2lhKVzMbWlhGNaQpSM a1JSSoyMe4SMY3OMUsbWtYyce7W9rb3GtZy1jHOMY3utWr3npYSta4zGa63OnGuMWs7expSljHOU Y5TGe5zee4y1e6XejKW9nHula9731pzOjPf/99be1pylnHuMe3OMc1qMWmOUc5Slpa3W1kpjY2uc nFqUlCFaWjGMjEK1vUrO1jmcpYTGzjmElEKElClCSkqEnHuUpUp7pZylrSmE1iFzvc7W3nucvYy1 3mOEpVp7nGuUvUJzpSlKazl7vTFrpSFjpTGU97W9xpzG9zFzvWuEpSFSlCFKjGt7nAAIGJScrTlK hGtzlHuM1jlSvTFKrQgQMYSMtUJSnDFClCk5hBAYQlJajEpShDlCexghUjE5ezlClCkxeyEpc7W1 vYSEjM7O3lJSWpSUpVpaa6Wl1mtrjHt7pYyMvRgYIWNjjFJShEpKhBgYWgAAGAAAEAAACBgQUkpC cwgAKWNahEI5Y2tjhAgAIWNae5yMxhAAOSkYUhgAUhgASox7rTEYWiEAWmtahFpKc1JCY5SMnGtS hCEAQpRzrTEQSikIQoRjnHNahGNKc3Nje1pCY1IxWkohUoR7hIRzhJR7lHtje3Nac1oxWntCe1Ip UmMxY3M5a1oxUkohQq2MpXtjc4Rre0IpOTkQKcactWM5UkIYMZx7jHtaa61jhIRKY3NKWpxaczEI GHNCUpx7hIRja2spOYRaY2s5Qq1rc5xaY3MxOWMhKVIQGFoQGAAAACwAAAAAMAEwAQAI/wABCBxI sKDBgwgTKlzIsKHDhxAjSpxIsaLFixgzatzIsaPHjyBDihxJsqTJkyhTqlzJsqXLlzBjypxJs6bN mzhz6tzJs6fPn0CDCh1KtKjRo0iTKl1KUdGpAYqYSp0qVEAeRIMWLWok6A6bNmoGBKBKtuzLAJL0 8GH0R6tbrVztvIFjp02eAQLM6t3rUUCgPokSIQL0trDbuHDkxIEDp02bAQP4Sp7MMECeQ3wCJyJk uHNhxHJCy2HsBqxYyqj3DtADWDMfPZ5jG+ZaZ45o0XPo2sWbuvdRq4g0u84qu3hhQI3w1L59e3Hj x3l9S8+JVq1wzWyNa++MXLlt5s0bq/+JPr28S7+trwc+RHi7e+7Jl4MXvRgsefP4RVrGrF445/cA xtadfPMpJt59+SV4UVrp9ZcIH4IEKGFxA35XYH3jKaghRMA5eF0fxE0oomwVFhgahghuqCJa/Hko HCPtjSgjhfFZOB+KKmo4wF8uqsfejEBuV6KJOObo23499vdfkEwKWaOJBtpnpGQMJqkehE1mCeCA cUA5Gh1r+DHlVB1aqR6IWqYZ4B+B4AFHl17SMdaYRrGYmZnqwajmnhKy6Sac86UxJ51B7dggnsL9 yOeifbb5JnNwiEEoUAEcgqiHSzKqaaN/hoYGFJP2pIghl/aH5aaojugnHFwwEapOktz/WeqLIaZq q4SA7HFGFU+8elMgs+YZ463EuperH4qAUcWgvsJUabDXETJssdSSuIcf2O5RBRXMNsuSAKRCGxgf mVZrLnfXYoutGlWA4a1LisgKLR+1nmuvW8eqq+4ZXDTx7kqByBssI/Xea2+++qp7BRdl/HtSAHqI i920Bp+LcMLYKiIFrw6TBK7EgUlbccUXY7zutt12zFG8IJM7Msnpmpwwv1qo/FHALRf8MrUly6xw vzZvBDHIiRC88709+5yxsr0GfdHHIOt5tMUxK40xu1Wk6PRDLIMs8tTmJm21umZwwe3WEuUh8Kyv gU312FZHwYW7aDsUALA5ux121XCb/5ws0HUvFEC4EmenN898920y1k0HfpAihwY72OGIKw532VWQ 4bhBmTziuSOIhC566GaWS3mqYluOMb9nby5QJZbELvvsspNi++22c+K554W0dfqtqaue8N9WuB7A JLQnr/zylrTySiuQQELx72kGL3zC2nLxheMCaML898tf4gor5LPiCiWQNEK9mtZfn/ApXHDRuNOm XAL+/bSTUv7+5LeCvu/rm1H73DczLlRhDFujhP3wx0BL6I9/EHwF+tQXwAkNkID6+lvrOhYASjTw gw+EoAhZ4T9IALCCxrkgBvWVveJx0HsfbGAIRzjC56VveijUigpXqC92ac9hpoBhDP8Z+AkaGnF/ 50tfDt+yQx7qi1/ye1f9hvjBIh7xiuWDnglR2EQn6mthXkCgrxRIxSpi8Yzlk6ASf9dFL6pLY2Z7 VQA8UcYYWhGNeCTh//TWRjeqy4cupFMAhFhHBnoij4gknw0bgcO9+XGFUHTVmEyxiULGsBWJzCT5 kkjBgyXukcJbWBSNpIoFWrKBmNSkKkkYvUZqqo+gzCAYuBDGHLnilENM5SpXyUngfTKWwvMhFVQk AFPikoG63KUyS3jCPcESmAkrGxcCmSDkHVOGyswm/xbpyhE9E5oJkxsXwqAgVVwThNpMJ/96yaRv glOW8dMcfgJQyXMycIbqzCcrpSf/I3e+s4dVoKUYy0NHe95TnwhF4gRx9ct/ElCadJuOOQ3KQE4k 9KL7Y6aQGupQAkIxC9OhJ0WJiNGSpnGCjfRnR4c3S475pqAjvd8dTUrTJDZTpSvFXkA3SJmJxlSm NA3q/mwoPZzm9H3xi+hkBvlT/M1UqFBdRTZOcVRQKkIH4gQpZTzY1PslE6pBbQU50pEOc5yCo1VV 3FVXwAIqGHB+epliV8H3VbCWVBpkzWs6yDHVtBJwrStgqxTMljKqMHWudLUrTV+BV7061qxo9SvG CBDYypYhoEotC1cR+726Kjafr9CGY0dLVr5SVbJjo2xlK5vVuBqTs8nbxCs+e1FX/4iWtLgt6ykU gVqZqXa1lV2YSw1LSNgmD5+0Tacrxprb5rIjGwToLQtZANzVtpULUihsUm5pXOYhN7nKlAZzm0te 3fIWtXugbnVXe1ku1IxMr+3u7L4LXk0ytrz4zetzo5vW9K63ulD0l1SsKV/l0be+iAxtfhecV7Oe t6OA/S9w5Tbc7RaYeU9FcCJty+AOk3W/Do2whK3r1uwqpZgXXl6GNYzH5Xr4xWR1MDRFPOLV6iCg 70UKgVNMuxWzGIvihbGQ0wFiUP62xtVNQvwEbBTu8jh5Pv6xERs75CrL2ItHRnJ1KQzXoIj0ycmL hZTR+IptVPnM+oUuD7OsZeBe1//ERIEpmGfn2TFDkMNoznOMd+s+NrfZzYPNcVB8Omc62/mILtaz oomcjchiT71/lnB7mfyTLxfa0IceoVgXzem9Xtlq/o10jbkcFDlfOnZ1PjSVO91pdmCDo6EWdY0X BueeEPrUDsx0BM3M6l6X9tNv1IGstXxdQevE0rjOta7TeFtfO5vIrw72sNs86Z5sNtnKXrYr2PHs bv/6rMKedpv5VeGbyBXb2c50or3NbnaEW9xallutbXJYdFtiEssOMrv3TWRIw3vE1x0mTq6N7ijX 9778Tjg7/P3v/94YcDU5t715cWgFJ/ziCWg4kpXMsJrU296W2MUuepFqxeL54hf/p4fGJcwCGyjB gPKUCcHRTQpg2BwYI3ceeNeN8oST490rX20NZjCDJRBWJigGeexkcfOmUwIZrRifXfXdc5QvPOhC J/oMhOBWUMWkuOi+BCWaTnZgFAMZJBfqqquO8oxjfQVD1/oMihBQSbokE0qXnSjKzneb53y2CS0z 2wefDrev/AVCkDvRjwBzl6Ai77Jjet8nTwmSS125zSZ8z3++8pYrXusv34J2SzIAyFtiE8WYvOpt fvZWlLzF49V81a/+b89/XutGn0JLZo5uUKz+9zfPuSqpLnu2017ccb890bnOBSewhPfY3gXwp+93 kgMejWsvPtsNP+zkK5/odM/c/0pMje69U//8wHh61K8oeO0XX+XDRvz3Fc940auEFJCXPPrRf/a0 i9Di7id7nCdqLDAE8/d5L9cF95d3Yrd/Dhh81lc+2xaA7nd8xGYDB3h7Rrc9J5F0IOd7DxiCNld5 rhd7FCh73Idk3peBWsd8XRYSpZd3+ieCIbgLJ3iCKShhK8iCWkd3XjB6HRGDIId6NEiD1HCDFDiA IyZ/PHh7jCcpJQF9pzYLRUiD5oCEFGiB1aUDideEyvdyXjcSUnhp0leFD2iDWJiFDFdZtueFymd0 WEASYzhn5meGDshraRiAORhYMeCG88d1BzQS+AdyM2iH1FcM3JaHFAh/WeeH8/9Hd1sgiCDXgIaI fr+giCeohHDniBnIeNTUEciWbCBYieeHh5hYgerFhJw4fy9HTh8hhOhWiKS4epRggqdYfBlXgKvI gkYXcxwBi8lGhLM4fUd4iziIgbuYgVz3gx7hZNhGhcM4faZojNpnDsnIg3RHaRoxhzxGidFIi7ZI jbJ3A9fIgkeQNR3BjSlWh9+oesUojgFIjuWYgUpgbBgxiNgmi+1YdlcIjwGoAvPIi1qlEfiIa8K4 j32Hhv7ofgAZkAcoBEugNRMRipc2igjJd++4kMVnjQ55gEUQBRoBjKemjxdpdomokRvZkZ3YMBgh koVWcyXJd5eIku4njyr5fUb/AIQO4YxTGJN8N400SXg2eZPKhwQYoY7ydQnKMHY+eXOIGJTa15BE qXxCIJEPgZTdlQvOEA3T8AtMGZMzCZWyJ5VT+XlC0AIXUZCFJgrO0JZtyZW/UIYICZRiWXUcWZaf twM6kJa4dgnS4JaA2ZZdKZfDWIt1KXt3iZdaBwRBEBkVQZFPlgyBOZmCGZfDmJGHyXbkYICKSXRD 4AONaREuyWOgQJmmKZhdmXp2SJeZiXJDWZZCwANB8AM6uRCjeWGbEA2nuZvOIA2pWYQK2ZqDR5Zl mQNBEAREcBE8GZm82Zy92ZVfuX+YKZw9R5xEiQPHiZwXgZVzVZrO+Z1wGZ3T/9eP1Ml2iUmUn5md QLCdhZab3/mebzmY0xec5dlz53mTPZCdQYADF7FjKXYJzACfAuqW8ql6rFmf+7aZxamf+8mXYOad AxqhzjCYqtl0T4mgbPeaDpme+rmXFqGWBTYKuimhJPqcv1ChYYmh1UmUQvADDBqaFXGbsAWgJVqj bembJ3qgKupt1jmP+fmijkkRMspZEGqjNioN5LmjF3ef5ciYL0qbFnFr8iWiRlqlzsANSmqfKsmh DJqcFsGdFEWjVmqkWJqlF6egARmbL3qcXloRYGpQWjmmRjoNZuqaDrkDa3qc/GkR/mlcbCmnc1qn F9ejnOikebqnFQGinOWXgP9apUkqqN1GqH7IpWuKqBQRChcWp41qo48Kqc62AOWopnl6nEFKEatQ YH+6qTZapp7abUzqh8Y5qqR6EQYQX13FqKq6qq3qbezQhauInbI6qxaRCqXQXZKZqzZKp7vabRrq hZSap20ao5hgXEWKrCRKfMvKan3IiaIarNEqpLcAW+5prZyarc4mqRkYq8GqnRcxALagqCN1rORa o+Vgrr4Gqo74rKNqqRVxC52AWNU6rxLKqvbKaa/6kC66rnqaEbcQCXM1rgJbospasJzWq374owrb oBhxC7ZQTzElphErsRTLas06f+qasaVaEalgC8X6UwEbsgOKrSOLZtvKg/r/GqwpSxErO60xRaUw W6OdOrNVhq6K160Z6wNWCRErG64jBbI/S6L1KrR6hq8siKcZm53fGqO28K4j9bJPK6AEK7VWxoOG erXs2pJb+68G5bNfS6ITK7ZVZrEHeLPrugMhubVMe05O27YR+rZwO2Ql24KyabbZya8WwbEda0+a yrcSKrN/62E1q3xWS7gLqxGISwvnlKqMS6JB+7gMhq7ASrnHCQMbAQtbWwu0AK8xhKubC7WeO2RU +3l0i7IbsbJbewzHEAypW0iL27oRGravy2CvarSim7Mqi7e4m7y6q7rMo7m+27fBC2OverKii7Qb UQDIm7zau7wMxLrPC73R//tiGhq6osumv7i1tkAM2ru+uYsLpWCrsiOv3xuhjhu+5PWaLVq++pm1 oom+wcC+AEwM7htfXju/79m59ptbxImx+hsE67kRAuC/ADzBxyDA7xs7EGvAERq1CZxfZEm9+mu4 F4G4ukDBJmzB8qvBAwq8HZxbdzm7hCvCh7u1vmDCNnwM69AN1TCiKgyfftvCLrx8CdvA2emhpUvD N2zCz+AN3gAOOszDPcybPwzEuEWOk0vEwlq76JvEFLzETMzETjwNUcyb0XCSVJxbN1C2WAyjWmwL t8DFE+zFX/zF31ANYjzGlInAZ0xW9wCaa3ycUMoR2OvGcAzAcjzHc1zHd/+Mx23JwXs8WuQgA3+M tR7hrlurvoW8vYi8yV9sDdXwl3jMwo9MDidAA5NsvkEowZmsvJzcyt4QDp4Myio8xXvMDieAAkRw yg7cF6q8yrnrysAMyzuswbRMxfRAAiiAy7oswxeBviXsyxUcDsA8zU48zM9bxo+cV8eczMp8ysxs EaZrCzUMzcfwDdN8zk38xL6rx/ZbD8jMzbl8ykYsyEhMzuaMzugcxpvryFTcANyczCmgy2x8vrdr z/h80N6gyG0ryuFLDv78zygQ0LpsvAxLyOR8yAiNzgoNs8UcvKQM0QCty/yrEUtLzseA0RmNz7Ec sR3tuR8N0hEt0iFBAJf/fNEpfdOvvNLWis0dTA+3DNMoYMqnPNIZEQAc+7/QjNI4fdDCDMWNys5i u81AHdTLLBKmi9S+HAxLvdXpbM2Ays+vK9VTLdST/M0Ygb3PnNVcvdbV7NS6Gr4N8M5TTdXeLBLu Os5qvdZ6rc9V2tIz+9BznczxPMkUvRG3gNerTAzSrNeMvdEi+7oOHdj/PNh/XNgkbQsmfc+MvdmO HaFQba4vLdmCPdEjQQBvbNCbndpMrNMC+tnLGtqi3c1/TNRCc9rQrNmqndrCLMvOydD26tOxzc0S Pcm0XbqY7MtKnduM3dS9DbdiHdzDPdslUQBYvcrJrdyb3da76detag5y/x3cMV3XJDEA1Z3J143d qa3dk8ndkArY4B3Sp0y6JZHWqwwN6H3fiMzXgOnaZure703Xf2y3JvEL5KzV+H3gdGzHbsnfOxrZ //3PZI3F1msSAjAM0GzgCJ7hCW3Hvl2nsP3gAI7F8n0S2XDhGn7iTHwO7WDGnvrhIB7hDSzgKBEA xuDLwwAOKK7h6uAO8QAP5RCOO0oPJgDiIE3Z+jvhKbEMt53jGb7j7vDk7/AOYI2hz03koy3iLcEL vozbTI7eTv7kYD4P78DgKOndVl7kWCzjK1Hhq8zlXa7cXw7mcg4PK16f/n3mV37kSVsSJW7eb47f cS7nct7jP96ad47n0f9dviPeEjTu53/u5YIe6XIe5VPujw6O5xCd6JSr5i6h5IV83o/O1eIg6aQe 5mOOki6O6eFdvkgOE1oOx/Yd6sr9DaVe609O5yx+iras6jCt6Wa76DDB5lyM4bKe2rRu67ZO6EB+ g1XO68kM42bL6TExDXBM7MXe2Mie7e5A6cuufc3u7CFutq0uEwFw3DZs7de+1seu7dke5WSecO4M 7jAN7RkL7DPh6Td84+nO2eze7+4wD3Xufocu7+GesdJOE8LAxW6+7zi97v6u7T3eDt3ObwNP8Ax8 tHv+EsJuwwvP8Cnt8A/P7tx+cexgDvdwDyVA8FNt5Apr7zZB7Tfc8R7/j9AgH/L97u7PZg4mfw8P kA8O8PMioPJAzfLBevD0Zu5xPPNcXfM27+8An+tDZg7lwPMP8PNWf/VBL/RofrXjnhP43sVKv9VM 3/T+HvETj1vkYA71QPVX3/Ztn/Vaz80m4Mf1DhQJr8Rhv9RjT/YPP/LOpfY8rw9uP/hunwJx/8++ PqpGnxMbD8DNkPcNz/eSP+mnrl873/OEn/mDb/iHD98K2/U88eoTjO6Qr9GTf/phDg887/Oa3/qb 3/mev64uzxPlTsGkX/rTvPeoH/Lz4Pq+//qwT+9ruvg80ecAfPu4D8zzsPun3/u///w/z/mdL/wM Cvo/cfcALPPJz8nL/8/8ku/80P/70n/41K+fs/8TA2Dh2b/9B9393k/24B/+rj/+cV/+x0n8PyH6 66v97A8Q3gR6m+fO4EGECRUuZNiw4TwHESVOpFjRosQHKDRu5NjR40eQHHsEIVnSZBAfAgCsZNnS 5UuYMWXOpAkzALFjOXUeuzbQ50+gQYUOJVrUqM+CDpUuZbrwwUWoUSdmDFnVakgiJ7XCqNnV61ew LrPt1Pns6Fm0adUibdrWbcOnUuVapHrVrt2sWkvuCNvX71+WwsgeM7vW8GHESd8ufht37uOIde9O BplXb0rAmTXTHDCMbGHEoUUXVczY9FLHkOdKptxaowkfekly3VzbNv9LXmSbjebdm+1p4A5Tq5bK 2jXlFLKD8L3dfPPNncF8Tx9dOvj1g8OJQzV+/G7yyyqdjwc8Vqd06ukNW8d+Xft2iyK8Hwe/lfx9 vwGMnVffPy379oB7Dz6K5JuvNRr0Yg4/Br9aZqdv/JOQtAADHJBAiQw8cLIET8KsQRC7yi2nCCc0 ESgAK2TsQgwd0HBDuzo0ibYQa5RJAM+OKfFEHglSETsWMXwRRqtkJGlBG5N8ybyeeuRRnR/daxGq IYkMaaSSPlRyS5b0I8zJJ6MELh59pryoSis/siwIGrl080HQwJQQSjFNg8hMi0ZI8yrLkHTTTV7i lLM/Outc7E48KUr/YU+r8tLyTzcFQG9Q/wo11C1EE5VoUUZBgm02SEMFoABK57z0UE0V7RQk8PwU dcsAxtmx1OksPZWpTFPldNWOknv0VS4DYOCDdcKh1Tdbb1UqV0135XWj5NoE9k8FPgBBnnGOHS1Z ZR9KdSJnn0WBBlendXMAEDzwAIR1wNH2MG67XYhZPPMxQVyOXBDPXFEDmEBdDz74YBxj30UrXnkT otfM7qxM4eEUIqggAX6nDUABgNW9dlaDh0I44YMWnrLhqyCOuAKULeBgZQ4ycNnlByrmt4APMlaX WHc7FupjkN0RuUXjSDAZZZRDYLnll5NW+mUNFpC5YnRtvhlbnYHi/xnkn+HL5wEJimZ5g6XDFjts DQ54WmZ/pQYYBHRyrlqcnh3Keq6t96GAA7DH1ntvpS8w+2y0MVb7ZmILNvibuL2F7wG78eb7ccgz uCAAwAEnoObBNZaH41IRT3xeyB6AgAIMkI789L0toLxywAf4N/O12z3W888Vjkqf0UtHfffHY2ad 9bRhB/gDbA0Hk/baQ6ZInwcoUFkD3qPfWwPff/9dcOHXRodzE5FP3mfmnecAeunL17ts69MH4PLs bS68R+8/n4ef8c23f+8N/lbfetfbt/nabHWvdvHAB/3ud0C9TW5/+wue/zLGLrepJ37Kegc+/JE3 BGZwaapbYAer5f9A9w3MeL6ZoKHmYQ8MkE+DK3SZBiIwgA7GEAADwBwIH7g56pTwR/MzHQtZuIEF 7EuGHRTA62zoPtnxRofYIaA/eujDFVoAAasb4hCFdUS1ES+AoVniad5hjwtCEYouhGEVzciSD2JR amyLoFq6+JYTplCMUASiEM94RhqqMYvvc+N14sHDOYpRilS8YyEBUEQ9Dm5jaknRUpqIwUCukIyG pGRLLpbIzEHwLI1kyBcxAMlIarCOlSRlS2iGycFpcYQoasr85BjKH0ZgiqWkJUuihkpFbm8onPyj AWHJQg48YACErGUtA0CACdQQl0hcJYAqGMZfitICCyhjMa35EgH/KCBdy1wj1QZSGk+qMJoH5IAs iXlNdFqSAMPi5hplVxAeinOc5tOABYSZTnzWRAAF2GY7hweCfjxxnuXbQASCmE+EemWdyuRmBwZ6 v2AOM6ET/co++4nLDzxUehuYZjUp+tGvLBSVHwClRvlWzlmCVKV92acRsehQk/KtnvdcaU0BMwAG XNR/GY3p2Ap6UJsGNTMBKIBLhQcCefY0AxE9p1Cd6hec6lRtMFUqR6n5VKzehqhGtZlSUdrUrIY1 MwPQ5v+SGkkNrMyeNBVrW51zzGSqi6o+TCsH1krNAdjRrXslTzaResC63nUAeeVrYSM1gAc8YGUy VWti8apXw0b2NlUDQMADItDYBzxWspvlbGc9+1nQhla0oyVtaU17WtSmVrWrZW1rXfta2MZWtrOl bW1ta8aAAAA7 ------=_NextPart_000_029E_01C07B15.387204E0 Content-Type: image/gif; name="Hull22.gif" Content-Transfer-Encoding: base64 Content-Disposition: attachment; filename="Hull22.gif" R0lGODdhMAEwAfcAAP////mpT/T78OPj4+HTyt2WRtfe1M3W4Mzaxci8tMbGxsa9s8R6fsOftMKN UcKEPsKDPb/F6b+IS7zAxbvCt7ixuLeJQrKgkLGzv7C+qa+kna5scK2NoKyem6qqqqmglqmXg6ij oqiNb6ellKeEXKd6SKZxNaW5mqN1QqF6UKBwQJ/JiZ/H9J+mm5+kqZ6ciJ5/XpyVm5yOjpuKwZuD a5uBjprYeZpuS5pmP5lfYph8jJheLJWdp5WXo5TEepShjJRtVpRhRJOHhJF7PpBxho+Bgo6OkI6N fo6AjY5sYo2x2Y2AjY1xcYx7f4xxU4tLI4qXpop7rInAbIl2fYlWT4idfYhrbYahv4aOdYaAQ4Vw eoOsbYOcuYOHjINVWoNRVIKjWoJqeIJmcoJibIJeZoJaYICnZ4CJlX+RpX+EnH9rfn9VVX9CfH6O bH5uf35oeX2Zbn04Gn0AAHybvnudsHtERnpzhnpgcnlrlnlle3ioXnimbHhrlneFcHaPY3Z3jXWL pHVoNXVjfHNVbHM2OHKUYHJ8lHGLTHF5qXFxdXFxcXFWcHFIb3E7bnBhfnA5OW+PWm8lEW8AAG6A nGxef2xYZGtLZWspKmqFo2p+nWpwlGo+Z2o8dmmIh2mHlWl3mGlwkmkzIGiMbGiKemhpjGhjh2eQ UWeOX2eOXmdcgWVaO2RBX2NBYWMzYWMzYGMbHGIcHGF8UmF6YGFMcmETCWEAAF94nV5Eal1WgFxj e1w2WVw1aFsODlhwelg0W1c2OFVVW1UsU1UlRVRrl1RdjVQdN1QPG1NQgFMHDlMAAE4uWkxGa0hJ gEclR0clRUZTm0YvYkFPqT9Riz9Khj8xaT5Svj5Dfzk5QTgzcDdJqTc+jTREhTQ9fzBAlDA1eCoW Lyk3fyIubBwkWBwcJhwPJBUbRQ4SMg4SMAcJHwcJHQAAEgAAEAAADgAADAAACgAACAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACwAAAAAMAEwAQAI/wABCBxI sKDBgwgTKlzIsKHDhxAjSpxIsaLFixgzatzIsaPHjyBDihxJsqTJkyhTqlzJsqXLlzBjypxJs6bN mzhz6tzJs6fPn0CDCh1KtKjRo0iTKl3KtKnTpyUHePAABcqVOVBcKIDKtStLqVShAMI0h4XZs2aV YMq61avbtxcVeHBRFRNZtHjzolULhYcHuIADE5RLF4pdJXoTK9aLCY1fwZCXTuVRFxPixZgzJ278 OLLnnZOhoLGrubTpzJz/fl69EmzV0ZhOy55dOjXr2x1di71Lu7dv042heBiAuzjECbvL/l7OXPYc QMKJG59u0MXl5tizm34O5QD16QOgaP8fT740lO+4B1wpz759XiVd0K+eoNy9/fZ0KMiPzOP6/f/k 9WLAfoCFB+CB7MkiHYFdKbAeghBqp0QsDHY1gX8RZrgcHX1U+BQUGGooYm+jZODhUgOgMeKKyylx in4nHuUgizT6NocpC8YolHU19khbJ1vkqKNP4vlopGyiwDHkTwMAcuSTpimxRxVL8jTBg1BmiRkd UrRQZU48ainmYqNIAeOXMxk45pqKoaKHkGi2pB6bdOo1hxRBxvlSBMPU6SdentigpJ4s9VBNNyH+ yeYoNlBJaEqaVCNpn4r+KaUNXj4a1TSSSopopX9yaaamIynwTKed2gLqn53Y8CapIGH/kA2qnW6z 6p+o2JAnrBxpMiutqd5apxJ6NMqrRgNECiyqtgpLJ5fGHmvRAKcuS6uqzi5qw6jSToRBN9YC22y2 Y17KbbcP9fBruNeSu+adusKJLkLKsiuuu2u2Gu+8Cg3Aqb3LZlMfvlmKYkO0/BpkKsDhSkOwllxo YMbBmSY8kKwMhyvww09ykQABI0ix7ZkJ+5oxuw5z7KPHBLR8xMG7zpvsyfZurDKNLLfcchsHD4ou tTQDnPLNI+asMwEJTIzwsd8GDbDNRGdo9NFIF3surOo6zfDQUSM4x8dUHx2yq/LGWa/W9n7a9YFK hBB22Dzv+6i/aJ9M6dr3tf32234c/+yongvXnbHaeLen995hJ02xnhgLbnfhhruN+NtjXz2kyY6f TDjk2R0++dsvy63jzJkHfTfnzXn++dtx+3wi0KUHvTnqvqm+euJK/11h07E7fTrtvZ1x++caiGy5 fFn37vS4wNMm/PCfj/0qgWcrHzS2zcv2PPSfxx0zdXRbjzbz2Wu2PfefQ+I3eoGLjzb25WN2PvqT K44pdY27j/YyoFgWv2Lzo9/kKkcy1mBOf1rrRhRmMAM+kCITA/tfAAU4OSzArGyBIR0C0WYNBnpw BlEoRf+aZ5c//MENTaAg91rHGthtEG2p+KAMZ5CKBybKXWqZhAnDEIYG+PCHRVDh8P/s94PP8O6F WgPHDJfYwFJ8IjbOsoshThgGHfzwiljkQAeEeLvijSwyyUOi1pjBxDLSEBSZuOGT1IKJHfYQi3CM YwNqADYuDlBk0wNM9cRIs2zgwYyAdOAnIkijOWBiinaoohwXyUgt2HF1cStEgf7FR61xA5CYZGAU UtE/NdqnhFTkACNHScoGpPCRk1Pf0rjSvko67RiZjCUDBUlI7RhSh4l8Yyl3WUohoBJxCSjW/bqS P1fKboGyTGYIR8gcKYaSl9CMJgc08Mu9Va4tT0nDuowZtA4m85serCEES5NDN0bznOj0IR2r+TYL iq4plORm0HABznp6MIRPxIshp+j/BkWm85//nAI7+dazpyhgm/IcHDLtyVAa5uIPPBQlQCdK0VMO VGdEdMoeEwowMjb0o3mgqEhFqsWLHs2LxzsKODgatBh+lKFRsOJIZ/pPHdTRpKHLI1IMxdKTXfKl DKUETYeaznWadGcwWwoxenoyWALVnm8gqlSjadGjqlJ3RTkoUxnmx6fWEw8SnapYSRnEo1btYCY6 Shq2yrCfevWbjhirXEdZUrNWbkBGiSdbrUXPt34zqnMNbByNetS4+QCDPPHAXtO2UL9mEqyCjSwW HWlWAvTNBisoykYX2ylvOjaWgpCsaH9Y1Yva7wRDGQC4OGstl342k7ocrWR9aVeR/9kAAULhKWuB pcTXZjIVspXtNCsbOikIIChL3S2wPOpbQIY0uKMlrEm9BxStKhdVXW2uGWMKXdkK1Kz2w6pO1npd VLlVu0wUandlW9qBBvOLPVlpeTvlVPQy8bnrFW1djzq27+FEsfP1VGPt+0HI5ne0Nq0sC3eS3AB7 lsAyjOuBZSvdi162iDlRbYAl1VcIyxCwEx5te9mpuJTKRLfzVaCHZWjgEI+2rPwVmX9notfrMnfF DAyti4W7RbO6U7wxsW6AXYvjGcR2x5Kt8EDjVrGZkDfA58UxcJEcXMoetcTYlIl8A1zfIuuYyuyt rBdn3BIABzi7ReYumINL2xiv0v8lDZ7vg3Gs3jULl5pm5ZmJU6LhDXe4yPi1c3RvelH16ZQlT07x gD2sZkF7t7KKk+RLaqzcOa9Ywo4O7oirOTYgn0TI8yUyjkGc6dHu16QW3DNJNsva3hZ5Bi0uNYIJ veR3omTL8+0yjjEtawrTupqKc91JUFxeNBf5yL0W7aZ/6UUMoyTO5Y3yiqecbOjCGKfwNUmfufzq HFe7u6e+KM/IDJJEl1fF3Ub2t5P862qqz9MfofRuLe3hOq+7ypAuVpNDAury/hnHgb53mGsrhSyD hNWcdXWaZSpw6LYZ1TaQdEi2Pd8b07nh6x2uWfsG74wQu7yiXjGpMe5r8JpB1Rf/gfZ1pe3hWJP8 0WYt3qE10u/r6vrSL8/vslH5MolzxNzXNfaoc57xHhfWBs7eiLxZS28IU5vo0E2wWSGB8oiYOcD/ XvGXoQ5dJQNbD+SeCMIXi+5Xq5vryjYrDCwgBWFXhOLlbTqB7Y12a5v0AgUIANuTXpGPXzfkHg54 3XnsXggE4PBZKDhGlp7wboOQ4YPvertViILDWz4LYW9IzZV783pH/sBWfiQMLE/6Q3ScIUBXrtBX LPjPD9yOeCe95QsAhn1DBNfRdrzLXc9mOybA8LKfvSkM7hAMbJjDjuc176GrccoHX/YWoJBEEHH8 shd55MsPrteHN/rnQ79DEVHE//Hlbt/dZx/m9Iu992U/hAIyxAO4V27WPbz183d353v7/fqfHwjE GsQD5RBgCnds9ndg4bY6KbB/3qcKEKEA6RBgFjdtBThhUnc7NKCA3lcALwAR7rBaqvdH3dZ6E1hy q6N+GBh8BbAAD9EO4ZB73dZoI7he+Ic0EnCC6ycCD3EN5lBenQdhdBeD3XVtb5OANuh9H/AQwMAO CLVXqxd4QDhhB6gzF1iE3qcaDQEM6hB/bEV+6GV+T0iCVGOCVCh7VsgQRqAOAbhb8wdhyveF3RV6 LZMANTiGwQcB/kcQHqAO7bBb1jd0bjhhpUWEdCh7JgARebgOHrhXEdhyYfWH+f/VZlM4iIQIEQPA DuogDqwFeGzoiCE2XGIoiYeHgxDRDuqADo3neGfHiRSmAXMIiqQniiuoDkq4WD1IYE+nivl1A64Y fLDoEFioDi3IVk0IYfWHi8wHfLtoeWV4heqAhnvFchAGg8YIXVaQjGQYEb+4h2y1hnM3jQemi9ao jFbXjFm4VX3Iet6YcchojYU4js2Yhj3FhdoljekoWtUYjofXjg24Ds1oikzFjfbVhvUoWeCIjyUw EaSoDojYUwPohwOJYHmHjwHQi7HYjMHIUYsIYV74kHKVBBIZihMxDuS4gxw1jAQmkBw5VyrwkQEA AhPxi7K4hJUEjRCGfSkpVzr/EJESuYy+SI7lmFC1aF+3eJNz5ZEsyZMNkQg+CY/GZJL2VYxEOVYr +ZF2OBF5SI7ayE3yqF2pGJVDlZMsqY/u2IwLyU0AiV4/6JVTZZQfKZaUaInkiInGFA2ONwMiqJZD ZQIsGQAkUBEJ2Y/GpA2cEAy3oInzCHl4KVVhsJcT6Zc+OYtilA3U0AhsUJlsQJiG+VlpmZg0BQSM SZEQcQ0+CYxipA27YJmoWZmYaV82yZkzpZd7eYQUAZPv+EKSSZmpmZuXWZi+tZGuOVGLyZhI6RBn 6JNZ6T6mqZvKaZmr6Vco+ZsU5ZnC+XZwSY5amDm3uZzayZy8+VStCZ0AxQHr/yiRbikRIrmU4uMN rbCd7ImahMkHHzWU4ElR97iX5RkRSumT/hg72QAN7fmfqNkIvjAL8FlPUDmfAFWQYXkRV0mOZZk5 6gmgEhqgA1qgstSVCCpN4ymRoCkRf2mR2OmfEzqiFEqgv5WhM1Wfe+mSF0Gb6kCSdROhJDqjJWqh S3SXKBpNCvqRBUB8EtGgzQiZTtOfNFqkuSmgJipD9Jij5ySejBkAB4kRlTia12kvMmqkWFqjHrSZ TApNKsqSLIoRoomefSSiWXqmqYmkfICjXVpKU7mXPaoR+YmVNHOlaHqnAWoJbVpTOsmSUZoRCsCP DpqIGmOmeHqoqKmne3pObP+5ohzxoZcIMHaKqJTaCESwqNH0piwZpxvhovu5LN1gqJQ6qmzQCIiJ qYsEloz5pxoBpDFpLdiAm6Q6q2ywCY2IqnLUqGCaG9UJorTSDcpAq8JambqAq6OkqVR5hxIxpuTI lNUQq8MarYpqrHAUnIzZlx4xp82YlcAard7KBndArXAknYwpmx0RqFT6rLL6rcJqqeJ6RbC5l1X5 EZB6DsHKrt/qCreKq9a6l9j6ES76DfiKr7b6ruQamyHhqu0wsPg6rcYaryw5ryDxoQvLsOzqsJja ryz5ryDBrHposezqrri6ox9priBRnOQYDCD7raaKqk7KmPd5roLajCq7st7/WrCL+qUf2aEecZ40 a7PfWqyLSrI7WRK0KbBA660Yi6Iva58mAaRIm7TROghtqrMcehJ/GbVS266XyqREi4/D+RHMWrFb O6z6mqOq6rQngbJkW7bCirMIqqs7ixLo+rFuG62rgKLI+pFhCxI+W7N3K6xLy5lp66cqMaeAG7iz KrLQKbcSGaYn0aCJq7ikyriuubf4yKkpkZBaS7mkCreJWbgfyaoo8Yud67mjKrSc6bj4CLkoUZzk gLrDOrhECbE86qNRYYltK7ukSrV4qbGj6xIiubu8W6ld65UHu6stoZTssK7FS6ln65W2K5GauxJX ObnPi6igy5HAK5GkuxKk/4i92XuoeUuUyVuyMIGFzTC+tEq7uMgBYTAG04uPEtsSZ3i67IunlsuJ 8DsGZPAFOcAADDC/4cixcsIO+Ju/d7q/Mdi//xvAAhzBG7Ch+Giywhu7Cvy5+7p8DgzAEfzBH/wF T1q/LpEIxJvBeLq9g9fBEAzCLhzBInytM6EA7oDCs+q+GKcDYUAGD/zCPuzCMYywM/EOzmvDeOq7 JKfDZFAGX7ABP/zELxzEyUoTwCC+RnymDCxrSszETgzFXvzCQSDDNOEBVnzFWdqypbbFTfzFbPzD YbyXfdsazmDGo6rCIabGXdzGeuzDb9yWN7EIdDyq5TthYSAGZOAFa7zHiv/8xH18tTZRAUUcyGeK w3NVyIf8BYucyV+MA3CME5AsyYgarpFlyYisyabMxgTsijErE2oAyoeaxTNFyph8yrSMyizJszPR yq58p3b8T7Jcy8Csx6kMinEcE6ywy7y8wbvUwbMczM7cxsM8iKtMEwPACMiMppScRfHbw8/czXos xeGIyzWhAJF8zSSKxHHEwt68zooMzslYvTvxyeZspJarzux8z+38ka7LE0gwz1jaCJXgvx6MzwS9 yO7sit/bE7rszzTazAX90HtMBZmLuzxxzAw9ow4N0RrtxY28i/vMJNZ80SOa0Rtd0mAcjgkNFAPg CiI9oSRt0jAtwB0tifD/PBTy3NLt+dIxbdIzPYjiDBQxgNP/qdM7vdHRfIIOoKw+sdBCvZxEXdQQ fdQKmIJNAchN7dRQXdRSvX8/nVohfdW5+dRZTdBb7X1J/RQrDdZhPdYwPcGgSNVQcdNqzQZizdbr fNBF2NVHIddgXdd23c14jdRKbRRM3dd/vdGBPdUq+BaF3dR+fdjBnNhcXSBffdWPDdm13NMYeNaU rdaXjdmnrNn7B9eBwdct/dmgvcg58AWh8ABjaMCAYdoXjdqp7cWrfQmvkAySIAdyIAmRsNUkHBiN Pdu1fcq3ndu7zdvKvdy0sAN9+nwWDBnD7c+0XdvHrdvLnd3azdu18ASu//18sB0ZFn3axW3bX4Db 2L3d6q3evr0DshfckVHNOF3dUL0BX0AIl5De673f/E0LTxCR0f0Z5Eze5W3f+J0MtcDfCr7gyl0L ceAE1CHbyEzfBW3g+Z3gDJ7hDA4LMjDYgNHPxM3WFo7gGl7iCy4Jj1DMqzHdrkzhwDziGG7iMr7f tcAEFD0d423OLq7JX1AHl8ALMT7jQr7dksDhHt5ClT3hD93jP54MQ/7k610Lj3Dj+5HWOs7OTM4L Tg7lXL7dycAERx7h5UzHOw7CWb7lXZ7my13kMqApQX3NO54DPq7lal7n2V0La0DlS8LiV0zb153c dh7ocgALYN4tVt3iX//854K+6L39CG0uM0lO5j6s6IzO6Hiu55pi5ZLczJRe6ZVu5BZDEBKOwr+A 3oDu6ZWO4ireLaM+vo0gDMiA6rLO3TYe6grB58XbCMUQ5LO+6Gwe5uiC657bCrve654u5Zhu6wIx AGqwntnbCsZw6sYe6F8O7LY+ADGwCGO+tcEQ7dPu6xyu7BihAEtQxjYL69++6Jcu7hyR7c4OtK8e 6+ke6IRu7ey+EAOwBDk+sLrO6/PO5Sj+6PcuEh7Q7Pja7/9e5+s+8NoWA6yw7XcK7f6e8EMO6gyv EgqgBuaOpdAu7RQv5Kp+8TCR7RA/orDu8R8v4zWe7CJfEuS+8f+J7inUP+SSkAyObu8tT/CL8O4S qutoPvMlbvNr4AEsn/Nyou8lX5kID/QZngywsAYysOpGP84Gv5wSz/QKXgvJAPVSP/U6ge0Pn5od j/XsvfVMMBxeb1DlzgYnT/ZrLvREn/Zw4QFMsAbJ8PMp7/RQX/Ry/xRTsQaPQOLTXgtPH/V9Lx9S UfewoN8Kb/Zof/g6IhdrYPd4X+I1/whDj/OQTx0eIAOAz/jqDfd8v/lVIheKv+V6b/ikz/BTsfqu //qwH/uyP/u0X/u2f/u4n/u6v/u83/sxEhAAOw== ------=_NextPart_000_029E_01C07B15.387204E0 Content-Type: image/gif; name="Hull23.gif" Content-Transfer-Encoding: base64 Content-Disposition: attachment; filename="Hull23.gif" R0lGODdhMAEwAfcAAP///+fn58bGxq2trXNzc1JSUkJCQjk5ORgYGLWtra2lpdbGxr2trWNaWqWU lJSEhIx7e6WEhHNaWsaUlIRjY5xzc8Z7e4RSUns5OUohIWspKWshISkICFoQEBAAAL1aUq1SSpRK QpRCOd6tpYRKQoRCOZx7c5Rza3spEIxaSnsxGHshAIxSOZQxCL05AK0xAOfWzs69tZxCGIw5EIQx CLWlnJSEe5RrUntjUpRjQpRKGJRzWpxjOaVrOZxaIaWUhL21rZyUjJyEa62Ma5x7WqV7UmNKMZxz SoxaKZxjKYRSIa2lnKV7SqVzOd6UQsaEOaWEWv+tSqVzMb2MQoRrMZyEQrWtWpyUSrW1pZycjO/v zqWljNbWtaWle5yca5ycWkpKKefne87Oa621WpScUrW9pYSMc0pSQmtza1prWpStnIyllK3nxoyt nISllJTGrb3/3nutlJS9tb3GxnOUnHuUpWuMpZylrWuEnK21vXucvYy13pScpZzG96W93oScvWuE pRgpQlpznFJrlGN7pRA5hHOEpSlKjIyUpTlSjCFCjBhCnAA5vTlKcwgxnAAxrQAplAAhc1pjewgp hAAhe3N7lFpzxkJapQAYY2uE3lJjrQAQY0pSjCkxc4yMlHNzjDk5SlJSa0JCY2NjnCEhORgYORgY WggIUgAAcwAAYwAAUgAASgAAQgAAMQAAKQAAIQAAEAAACIR7xnNrrTkxa1pShFJKe0I5czEpWkpC a1pKpVJClGNahEo5hJyMxkIxa4x7rXtrlHtzhL2tzkpCUmtae0oxY5yEra2UvWNKcxgIIa2ctZSE nHNje4xzlFIpWr21vZyUnIyEjIR7hGNaYykhKXNac0IxQmNCY3tCe1IpUkIhQmMxYykQKQgACHM5 a5xzlHNKa1oxUoxrhGtKYzkYMYRje3Naa7WEpYx7hHtaa1ohOda9xoxze2tKUlIxOVoYKYRaY1oQ IYxja0ohKa17hJxrczkIEMaMlK1rc5xaY0oIEIwYIWsQGHsQGAAAACwAAAAAMAEwAQAI/wABCBxI sKDBgwgTKlzIsKHDhxAjSpxIsaLFixgzatzIsaPHjyBDihxJsqTJkyhTqlzJsqXLlzBjypxJs6bN mzhz6tzJs6fPn0CDCh1KtKjRoybnCEDKtKnTAAMGIEJUB5CePnsAIbqz1KnXrzYFDLgz1ZDVPmjT qkWbdWtXsHDjhozKhyogQHvW6t27ti1XuYADOxQrFZFZQHwTK+br963gx1/pTr2bd7Hly4n9DoDM GSjUwlURYx5N+jKgOnw2d14NUyxZRHevlp5Ne/Tp1Kxzi4RaN3Tl2sCDk76tWrfxiwH+CF/OvDbx 49AhzpHdvLp1zID8zInOHeGd39fDi//fuwdNgO7oASAaz769Wjtytqc/HsCQ+/vt6bBRc34+6wTK 4SdgeHvIAUd8/nU2B3gDNsicHmzAsV9/CQKGCIMOZhicHXB0iGCFcAVQh4YkNkdHhxLyB6JXCwRY 4ovAFYjigfKteNR0MOYIHIQzTmhjUdJgqOOQl504I40/BhXAekQ2WVocR6ZIYZI6JefklaPt8UaU SFKZ0xz2YSmmZTxG6aOXNQU55pqLGcnlh2jGxCSbdJJnIJdSxulSAJ/U6edeZeIJp54oCeDin4ii xSGeHZ5JaEl8XCJkonW6yeigj4IUiiWZCELppzIy2qiKmXoUgCiXZJKJJpN+umagomL/WupFCyyS iKqqeupqopaK6uisFeUBiSK4qsrqrryKeqQcCgBbES+PFFIsroQgi6iWyh7ZxpTOMhTAIIw4wum0 mXBiLaKwZvtGs916uwgjkIxLbibVnutnr9nCsW27CeVBCSOPpDqvquba6yeU+c64Lr8GCfMII4zc OjC1BteJbcIz7sswAOBCTOzEuBZcMZuLYoziwu0GUAjEjHwMMsUjs4kvxhrPmse7EIv7crEixyym J2m4EaHJHaKcaTQP5yzvzqrW6/OVnsCwBBdlZCE00fpy6+UgSQMsMNMhPw01DGTXwIUWWlR9NcZG UxlAJyx7DTa5oomtY9Rkkx0E2nyr/z10vjXbKADOLLs8N66j2H133oxnwffjfufbdoV5dO3x4eRa Qp3iGuLNONkxYPH46FWvsaWygc8HbdzhLo25qolz3vnnn5s9+u1cZGG6qJNzF4AtrLf+euaby47f HzHQ/vkPtzevRe6745k6fYSzHPDw88Zu/PHJK//53s43D/3pR/aem7DBX4898dvfh7z3tIcefvjQ I5yx1p1VYnnh6w+sffvieR/8aDe1+RlQd/aDg/kE863gXa5/89IcAAPYvQHSznYGPOAa7Dc9wKjM gcKDYPYmeB0BWlB54MtgBhGoQHYJ5mYg1JkII1g8EgLHhCdUnuNUyEMEdtAriNif9f++NkNy6cqG wdmDAnI4QPnx8IlZSIM05NIxB6qviPM6FhJro0QmWhCDT+QhF4rzFLiBsGVYBNkRt0iaLnrRgswL 4xPR8JXBnRGNaZyYFtmIGTe+0YIplKMBz+CVyt1Rhnkc2Br5qBg//rGJohPkAcloFK4d0nWJnFYj 8NAqRmJliY/MYQElGb4ymAEpAUjEHeWWyXlxoha88EUweIGHunmSLaAMZQ7BSMrbgeEotVrlFVup Kku8UhazCIYvlrlMXlSCk1vMCh4qUYkCLEGXXgxkLx/nhSUUBX2rPAQxcWXMUcjinLVgpjqXOcta yk4PgKDmJ4TBjGHYcxjTYMA1sZn/wx1uk5teIIr+VolHYpbznAiN5ToX6gtnQtNed6GmMISxjHta 9J7TYEc0KshP+Dnxn2jLwhjwV6Uq3nES4zwoQs85CmAw9KWypKUt6STNSsxTGBfNaU7TwQ52PKCj J+TlP8ngzZ8EoHpnRGQeNVELc64UoemEqVQb+sxOkiiiNqWnTre6VZ729KdAHWAcQaqFLwTUJ+AU piYyydRZPPWpCp3qVNs50wFlJZ6VmChX97rXZTigp+zQZ1gHqM1eemGkPQkiQVmZxra+9alRlatk m1nV9sBTnlrlq2b5KgzA9nSjg/XeR7eZhTBsgScmDWceL1ELtz4WrpONLTPpyhys/86zopvN7WY7 61l2pCO03hvlNrkwhi/sJBCLfWARj/natyZTttBlpkOtmpaa5hWnus1udjPaW58CV3lCleQXxOCY mgggEslF6XJr0dzXRja68KWtWi6b1Xpq97735W5vBfvd74HUC6bNySf+RVClro+57X1sXOHL4GZK QhITxS1+J4xfr3aXv/3Nmz9JWVrj4qQVkCDoI9baP2OyN8GvbWmDV7zMYjSDwjCesIW7C9oMgy6S pCyDGMh7kwGwQsREfJ1KUexeFq8YGM5ABnZjzGTN+rW7ngWrjWEQ3jCSIcA2EcWPVYu9IRP5tQs2 MnR5gQxkHMO+TU6zTnkLZcBK2f/GY5UkgMlgkwCsYhOrNNzhvPzlx6pYzPBtRpmR4QwJq/nQw2Bz mwO7zykXFophCAMlYeKJVOD5jOrFHFOd2uf2hhnQkw3GMQatZESbWr+LZocDONrf0YaxtGHoQk1M kQr0xhCTL3Nsp1H8aVDLlcykLrWp1YzqVP92ylI7mySvTOeZCEAVqSBw+kgMNl3vOsHv9fVkBR3s Mw87zTNOtXeRXeUMfiHSk27JJ1KhihCnL8ggY61rr81rbcsW2MEmtKG/LWNx9/bNGX50BgEc65mw IhVbDp44mYZgeqP4ufaebDHyPegl8xu/T/Y3YDFs4w33MNKIhckAUoFwB+p5YA3/dziKsx1xqXKb 4sK++H0VrXGNsvq7rs4gcSNd1JeIguSXjpu0XpZylde75b+G+aC9LXPt0rzmAO9vucN37jCcdU+r ADrrDFwsExt9139GulQnrvQyF7rp2615d6P+3TirkOAhb0mlSW5riMVrYHz+OpFZLvZ1IrnsFUe7 boutdo4H/NWRDkPPWUJrkkt7mOTkBKf13ule9126gCe1xQXP1XCrXdU3B27OSymGSF99Jc8mebtZ JrGuS57y9Ob75Zn58swznfOd/3x3jz1l4WbwymHgMUvWTfKE63nTsHe45Wcv6syT+sW432rGdR9l ZFNZ2QNP/GlZcvDiQ2zoxmpt//IdDvHZLxTfzi/z5qNvz6dTf9yO/nikPaySkZPc0iG09vivLXvz 1z79t8d+7fd+F9ZoHadCOhZpwpcSP3d/m3B38rZ/Rrd8l4d+6Wd2+xZ9hEeANWZjo3c7wIdlKGFn 95cKmHAJRSeBYOdS5rdQZHeBzyeAGEWAUMZ2wDV1fFN1YUB/JzF39xcIJ6aCRtd/s/d/MBhz7Od5 NAh/cJZ9ClheJNF4xUcKQqh3FNh3FniEZoZm0aeENGh4/SVwfANrkSZrJ5F6qqcKuMALVahyYdeC zPSCWjhoZxd907eEnrVqyPaBfBOCzWYSxFd8qEALt9CGygeHfpdkcxhs69d07v+HhzaHbL53Ozoo aSfRfeymCoOoC7ZgiNd2hWKXhYuIhGj3iJBog6E1dQRXhiZhf4K4iYXoiX1GhJdnhKMYgE23gZD4 VdYnhmQYBn84Eg2YClmHCpvIibL4ZaCIdM03ivlWh2ini7sIht/lcXyzc4mXbh1BgiS3CsZ4jL0w b8n4WuWHiA3ljDDXiN/mhbsYiVP2gSFodSThg8VojLSgC/jYiePYXLTYd7aIjqTIb+zYjqg4WFW2 imEQdyAhhd5ojKqwC/ioC7swefu4UsvYcqIIkFvYdHfYjmtnfW4XUonHcyKBhqzwjaiwChGJj7FY kSv1hogohxpJatD4babokYz/1ou3k4CJd3oeEYgNaYwquZIT6ZIr1Y9i948zqY5qdpM4SY2hlXPx qJAd0X0niZJDuZItaZQXGXEZOZPqd3HSiJOfFXqhNYkIqXggYX+qoIlYuZIRqY8uiZRIJ5NgSZMZ SGxkKW4FGVa8lJY8yBENeJVvCZe6sJX72JX29nd3CXPQN2wDuZdMeHhjOJLBB4UYQYJtiZJCaZj5 6JLliIhf2ZgBCW6SmWpQGVobFo8iuBFzR5iFaZjhWJF02XJKSZq42GQdeZq91YEZ9lGVuIMeQWv1 yJlZaZhymYyKqW3NSJowV5NN5pS8yXs2hkFpuYAZkXpBaZyeiY+zmYyhCYej/+mcyPCYaSadvNmX QBVHvxhp26cR61ac3NmdyJiMtRlxt0mepUlhY8mbPZWag7U32Jh4gXkRB7ed89mdRSmLy+lr46mf ucmf/ulvAApU8hOclpgRIwebnJmS9MmSsgiTcGiX+vmMeVlhE+pvvtlfU5OWBZcRP4egCaqgFKmC Depr+Vmi+3lfkZmik9lfD9CewJgRdsahHXqc3YmYNmqOmKejmceUurWbPvqRyNYApWeZ2ggRnrCZ HRqbH5qcEnif9kaiTtptXIhf6OmjFdpRMXAFlvmiFmEKRnqkHxqRSjp+NwpojFmmZQedTjelGqeH NtYETmAFlhmMEyEAq+CWXf/6jadQp3EphOHZgg/Kpzu6Wf0JqD1FncBFBFEQBU4wBpa5eBLxCXPa oaYAqd4pjsknptqWo5Z6qXyVqZr6o0BVA07wqVEwBVdqehbhCqnQqJyZqqpan/uXp2LWnLGqdBG6 WT1aq7aKTTHwBLr6qbyaeFT5EAMgo41KrKr6ncknopS6rM7np84KrRRqgB3VBNWqq1UwkqT6EKAQ rMKKkt6qqmCqd66Ko+TqfFAqfX+FruK2orrkqe3qrj05EQHQCvU6rMWKjwsKe8hqZJXar7KaU2mK ruoZVLl6sLrqpglJUgrhCQ3rsA97mK3KpHFoseV6oluVsRrLT9PqsdVaqO7/KRGhULL2erISyYaU N7EstqcsW3bmqVm0KrA5qUvsSrM1a6gFyhDSQK86e6/FeqfXNqnmV7FD+68WdbRIK6h/ZLBMW628 ip0N4WM6a4xUW6z5yn8q22JDC4BnmntIW3ME+0UdO7ZkKwbv6RAD4Appiwprq6pWW3lvK7Rx26cu a1HPWre86EUxMAV667FN8LQKEQCxELiDi69Gh7Wzp7WJy7VS6rhttrFkUwSTS7NUgJkKEQvc2qWb C6ng6rZvC6uJG3h7BbOOu6YwIASpy7Q/EBGxwLBTy7Mr2bbK+LbKeruA16wDSLpqd7eMg6u/S7ND EBEFAAtpG7uyy6pfJq5Z/8u8MGiu9uS10ButoCO51euxWYoQ2cuo9cq9kFq4nva2vmC74huWW2W+ 54uKqLu+7Iu9sHCqJmu8EFujR8ekoJu/+9m45/uf6ko2vgvAAQwRAwALr1C8Bmynu7avoEamDAxz EerADwx6tZO3FKyrUiARFxwLUius97jBEOuzyauyiBvCgAedo1vCbdaBkZvCB7vCESEAsAALr4uS MSzDKPtlnluBOHyEm6e7PCxl/wvE1coEExELsAC4DZvESoy8b+XBgAbCT5yOFiXFU9y7Vnyw1ysR Wpy5XazEETm7zQW0R6aIZSy3M8jDuscANoDCaxwFbRwRCFDE8NulXvzFKP8Gvp+bx0dYh/wLrQyQ DpScDhDQDpiMySdwAkgQyO0avBKRvbBAvDAsx3PsvZBlv/jryPpLwh45yZWcDpmMyRWwyZtcDyOQ y7q8yyNQD4AcyO2bEKKsvfWayIpcvyq7vKzcvPXkyuIWy5Y8y7Vsy7jMy9Z8zdi8A57crsGMEJ5Q xC5czKYckREbxva7wMvsDMwQsMYWy5c8y7a8ydg8z/Rcz7y8tNscBU8gsgpxwUVMwMc4zkusYKq8 zFpIDJT8zpkczydgzw790BC9y76cz58qxCxcxBgszgItkQjcxFho0ADYDNZgDe4wDxF90iid0tpM 0VFg0RGBueCs0Rt9p2L/LGZkDNLNINLjgA7ooA74gA8mndJCPdTYjM/5DAUVocVFfMTGbMr5ascN dsMg7QwifQ48fdXgYA8/DdRE3dVEPdEsPchujNFcjMgbzcEr5dGhCNLPN9LgcNVw3dNbjQ/1EAFe fdcnvdJhXRHDTMxmfdafCVX2e9P5S9XWYNVxHddZPdd0bdd4/dj1LAUs/andLMwYDQuH/I1Nbcrg CtUMJtX5ewxV/daJXdo+zdj4UAETANmsbc0nMNmUzdeXTcqcudlOzVIsqMBlLNLWsNOl/dvoMA71 gNo/rdqtfdwjcASwHQWVjRD+XMQZ/NeArQuzWdNGtsplatiIDdzcHQ/E/73VFIDcrS3Zk+3SF43R 4Tyj092Jnh1fo5a4on3YpM3d9H3a3/3TQS3ed/3asG3eQ3zZA0yn003OuXDOcZvTvU3fCo7VWn3f W53f+k3Uyg3bWGwRSl3EZf2NSDrduaBMKovdM6ndCz7iV23fDo7fEd7V5D3ZYp3Flw3HXgrYvfAM 2fAN4pAMHj6ulhrf1jDfJD7iwn3ic13XKS7U/A3bLS4RhXzZCLrhAm0M35ANUi7lNo7j5kfYGong vv3jXI4O3i3kQ+7YRR7REw7boCzbs63e4zzjU97mU17lOR5xoK2R8b3dXd7lJg7mxb3aY/7QE0Ct y93cCUEAAO7XnbnRu/8A5W6+6G9+43EOaujsfLy95Xd+54ut54xt3H1uz3oN24KOEEQM4PDr5Bvc C9zA6Kje5nDua1iefiJe6bBe4phO3OG96fVc5pO9zxhx4f8c4xuc6FGe6sLe6FYetHi8iHXu47EO 60E+66gN4bbOy3++3C2dEX2d0RrO2ac+7Nyu6o7eYJFeZlq+7OQO13nu7A8e7dfc6eWtoQCe3h4q w8De7fTu5qsOXdj96uW+78E93OhO3NCu7rg+2UidmbxuxNle6tte7wzv7cUuV8pMccnO7xTP01/+ 76hN5Oqey9NO7UlOEQcA4GVN6nU67w1/8vb+7VI1nuNe8S5/7hi/1Rr/r+7sPtmfrhCE/uIJf7Km jvI+z+j3vlC2qO8u7/KXHvPErenRPvAs7d8VEeqX7ZYk75m78AzB/vNYn/IPf45Lx9vKXvQvj/QO rvR9DtbL/fFJDeDEO/Vw+QsLn/Vwr/XKNHEtD/Z2z9PNLvbfXeubXvMsffMLce3EzPYQS+Nxf/io buPXYOd33/gXr/ffHfARbtTtzhHf/OLB+qh16vaI3/mJbw6NH/pyDfknLvnIbfZIvo0Hf5LcW/We //qMzg1fL/r8fvSkf9+m39p+T9GAzxBLjtEZHLucD/vE3+bkMPu0T+4wf/uMPfP6TflN/xE5j96C S/WGX/zYL+XYkPwV/5/3zH/fzn/cqM/iH/HcGL0Kazv82b/+28/9+77835/pfI7cu5/Pvd8QB+8K 98rm6w8Q2QQOJFjQ4EGEAr+ZQ9fQ4UOIESVOpFixojp8GTVu5NjR48ePFSaMIFnS5EmUKU82idLS 5UuYMWXClALA5k2cOXXuzFkA1k+gpnQNNfYt4VGkSZUuRbjQ4lOoUaPGA1nV6lWNIlVu5WqynpOZ YcXGHMLT7FmdnoACLaWr1zOmceXOXUoOnFS8eaNixNrX78Z5XQWrPDLW8NgBaBWfDRBrLaxSRelO plzZrl7MmR2Cs/fXs9/Ag0WTlHLYdMyai1XvRPBYWWXYseNi01w7L//fz7mthh7d9cRp4C7LriZ+ k4Br2cmVIyRn27nFcfV0TwdZL0LvroWDA09cvPiAx7GWjx/v9Pl5iFSpr+9oHfvW0ttNp/Ze3DFQ 8eT1y/42Dv1/3NgTMCN7RnrvpN/kM224+ojzCT+j9pOQssv+c46zATPMSKsDS9JOwbGcEKDB4tRa S5sJU6RLHAudC1BDATnsMD4QxWKCxOIaO1FFHmdrUbPoYISRt/d2qNGwH3AsrjWgUOzxyaTC+RGz F4UUkMjePjxSJhGVdHCtbqAUMyHzptzLSiuxHGyCJ7YM60YvVwMPqDDHtLMgbu4y8ykM0YTRvd6M dHOmJONc7T5Y6rz/c9FsKtyToir9FBBQ0bQc1KUuDVXtgLUY9ZSbRykKUlIhCxSNzUtjglPTxUyE JT9PF6Ut1IgiJTVGA7sSNNWXCmVVMQHwi9VTKWl1aNRbhZRxK0tTzfRXxZiEhZthFy2TVvWSTbMr VHl1aVVo0XoQFiertdPRR23VdkA1TdrV2yh8DfesOck1d1F0p+xzXTTbJYkleKN4dt6z7tvmXllD VZffSa9D6auAowCXYLM4TRThhM1ElmErKS3pXW/lpZgnExXFWMxrLcyWYzRNNQlgeAceeadgLz7Z zv5+XJjlAWWEOOCJZ2bt1ZvvzPfCzngmlUOQeRVZaJ18grVoMVkE/1DpZEOD2VuZoc4JvKmphnLW 5zbG2s95foYXCq/RcqxcsaFs7rmdzx6wHiMijmKJts/iFO64e0yZSrvRrCeeeC64QJ8cIn4igL7N Og7wwHnMubaVC6fu8MQXt+DzzxsPmO3IeQq2nMrHPFqqujUHyZ7OPQd99s9p9Jbv0nmKxeTUewQV s31dvwp2xS/Ih3bkZ7c91cdz56kA3nvnkWy8Wi+ceMWPT3575Ud3nqcBXpNezGKlMlt4xIvXnnv2 u4cX9+9zamx8lBmSKnO701e8ff6T1wcsbzUvfjo5AP3ElKcznY1zxetfA7d3Ae8NUCcEiJABe7Q6 iARvXQuUnQM9mP88CL5PgjoRAOUsOCHqTcR6k9KfPj74QvaFkFcCHCFOwnHCsVXkfBqCXedcCEMg si8Fa6shCU2IQ/0MziEr9Av2jBdEKPJPdLyCXxGNU0EkTkiJTKyKE9cXRTCyb4qXoqEVb2IALGZx P/nS4F/098QwxrF/YxwU6cyIkwB4Q40qQhcX3yhHQHqQjm6q4h1tIo3o7XE8ZGtjR/4YSEh6sAcz hJwhc3IA1ClSQnOLFAcvEElQvnB5W7KjJW8SgH8cUZOxWcioOPjDUMbyg6OsURlNechUrjKJ7/Ch LH0JRFqCqJC3tEkBvJFGXcrmk79k5gvz0aY6EnMnAUDAMZO5nGX/NlOb/ZPhlmwpTZsM4B+JvOZk srlNdD7wUsMEZzHHWU5lplOeIIxmO6eJgH8cDJ6VOec859lNEH3TnuH8Ry73aU5/JtQCQ9wSOwdq EwIUFJkHVUo/FbrNQW6nlA/VCT6tSdG4WPSizcwocATKUZsIoKB6BClTRDrSX5b0NA5FKUHf2dKK wjSdPKjRRmuqE3H+I5M4PcpLdRrLYB7mpD+9SVBVSdRsGPWooEyqYWjK1KYW9Kk4lepUIVlVsfgU qzuJ6EehWpCuehWQYJ3JUseKkwL8w6xnFUha1RpGgM70raqJKzm5eldf5vUwYt3r825K16gCNpT5 uAA92AoTtxa2/yf5RGxiFRtHxpKABBgIgQhe4AIaJAGAVpUscQ5g0LPa9bLby+xmQ/AB2H7Asy6g rQta4ANohoWwpeUJNf8xUYqqdrWfu4BmORtb5H5ABZ+tbW1fMINgRpa38qsmcPcp3LsqjgQlwEBy vavc5oa3tjTwwWhbctXp3pOlRMUuTLXL3e/GF7zipa9tdQDN3abXLNT0aznbO099FBe+8pUvCFBQ XwS74LlKqKR+iYPKoYL0v80MsHFBQGAMfwAELUhwglUABAfXR5xbXeWEQ1nhzV44wyvecIfr2wIT hJhEI26pieWIYgyoeMU7li2HXRzeF7CgwTIW8VzhaeMgtjbHPP9mcmxn++PmygDERFbSAIx8TSQ7 UMmvbXKXYftkKCvYBEOmMokQGVxQbtnLa47tcsNMWxaMqMyGgt5Bs0w77R6XzXuGrQre7AIZBGHO vyqAPv0bxfd2l8+L7vObX3ADMg86TgUgMQ7/m2hGZxq2Bn6zCuQsaWgVwLpZtGuFB6xpVLcYyi0Q NKgJRo1RW3p7ONYxqm2tahcHOdKuZlUAqoFl0NHa1sNOrgh87OIP83pmAbhGMt9hYWJHu9jM7TCM lQ21AFQ6dd/Qhjw2UAJph9vJ1E6wkK/ttQDcEInfWEc/+PFuf2hA3NJ2c4cDfe6+pfuE3Gj3u/39 7n7Uet6M9nP/h18wZnxHDhrWiPXJuAEPf/xb4vzoh6IHvuiCl/vTCY+cAKSh7VhpA+ITJzk/NCDw izMZBBl/cas5Hr9oWINaN+t2yW3Oj2+nvMu4pu+jd/3y3AVAGti4F7flcXOkx1vnPOa5eD0N9DsO QOaeYre7kX51inN56fINwbHFy2qom1LoRB9T1bF+dn74w+Jbn3Z9dR12aUp95ip6uNXRjvYNoHzp YA5vsuHezrE3nDIPj/jdDU9xcLP9Axggd22t/XeOCqAZc09Otwt/+MPHW+/iZnlzzQ35mgYgGtgQ PFJqjnnU+3sDWh9452l7b9CPVfKUZwq7O5B63Ptb6fNeuXgP//7z2KNU9KRfitlzf/x35z3cTXdB nIM/Xck/te7Ipz7A155qr9vW5c9Pb8zTSPjqh//dJ7d115vrc+4T2eMosrz43Y/zxDOa709P/5wH QIB40KMDHbD7+4+/ez4Ds8erP14TgPsrAHrggHvYv8vzP8PrB9brMsajrbcjwJczQAIoAATwAA7g gH3gPwfEOrVbs4zzOwuEvAEYgAKIq5VSQAYMwYlTPiYruIM7QQtMwRUsKB3swA+8PQfMORYrOOez QSIMJxVkQR2Uqw58QeoDwALjMNgrQimUnxSUhhU8rSTkwf3DPQh8wt+bQjBUjRQ8Qg0sKA7kgP3r v6STN+/qOlr6C0M4rA8DPMACOK0OXEAfLDkZ/LIV2L44/EMvCYAxXMEG0EK764fEwwAcAD5AbERD GUMCkID8y4AL2DhHvERMzERN3ERO7ERP/ERQDEVRHEVSLEVTPMURCggAOw== ------=_NextPart_000_029E_01C07B15.387204E0 Content-Type: image/gif; name="Hull24.gif" Content-Transfer-Encoding: base64 Content-Disposition: attachment; filename="Hull24.gif" R0lGODdhMAEwAfcAAP///+fn58bGxq2trXNzc1JSUjk5ORgYGFpSUqWUlIxjY9aUlL1aWpxKSns5 OWMYGFIQEHsAAGMAAEoAADEAACEAABgAAK17c4RCObWEe96Me8Z7a7WUjJRza5RSQtZzWoxKOeet nM6cjK1rUmMhCJRrWnspCMa1rYxCIWtKOa1KGK1aKcZaGN5jGJRCEJyEc9a1nJRSIffOraWMc5xz SqVzQmtjWkpCOd6UQsaEOf+tSr2lhKVzMa2ce8a1jIRzQvfntf/ee8atWqWUUt7Ga9bOnJycjISU a2t7UkpjMb3Gta3OlGN7UpSljFprUpTGe2uUWmuEY3uta1JjUnOce2OEa4yclFqEe0qUhFKEe2PG tWuclHPeztbn573OzkpSUpSlpYScnGuEhK3W1pS9vb3393OcnFqcnGPGxjFzc1LW3jmMlEKlrUq9 xlqUnMbv90p7hFqMnAhrlGO95xB7rRCMxhCc3hhrlIycpTlSYyE5SjlznBhjnBBShAhCcwBrxgBa rQBSnM7W3nucvTGE1jGU9wBChAApUpzG9zFzvSFanBhSlFpznAAxhJyltVpjcyE5Y1JjhGuMzjlS hDlanAA5rQAxlHuc50pjnFprlGN7tUJSe1pztQA5xjlKhDFChDlSvTFKrXN7pSk5lCkxeyEpczE5 lIyMlISElHt7jEpKWqWl1oyMvWNjjFpahHNzrRgYKTExexgYWgAAcwAAWgAASgAAEAAACIR7xlpS hFJKe62lziEQYykQhBgIUr211ikYWikQcxgISnNjnBAAOZSMpSEAYxgASggAGCEYMVI5e0oxc4x7 pXNjjFpKc1JCa2tKnDkhWmNCjEoxaykQSmNSc5RzrYRjnK2UvXNahGNKa6WErWNCY2M5Y3tCe1Ip UjkYOSkQKRAAEHM5a5RrjHNSa617nMactYx7hK1jhLV7lKVrhHNKWloYMda9xr2lrYwpSoRrc3NC UmsxQsaMnGMpOYRCUloYKVIQIYRaY61aazEACGMpMUIIEEoIEAAAACwAAAAAMAEwAQAI/wABCBxI sKDBgwgTKlzIsKHDhxAjSpxIsaLFixgzatzIsaPHjyBDihxJsqTJkyhTqlzJsqXLlzBjypxJs6bN mzhz6tzJs6fPn0CDCh1KtKjRo0iTKl3KtKnTpw8HDDATp6rVq1izWp0zx8ybAQGgih1bUSrVPXLk 2FnLtq3bt3DlqJnLZg0WM2akhiXLd6yAAWDioFULt7Dhw3fmKl6spq4bM3ik9p0s9G/gOGnrHN7M ufAaxqBBr1nzOPIAyqhngpkjR3Pn17DZpr0DB82aNqFzi16DF8wAAamDlwxg5pDr2MjjyrmzB5Mo UYiiDxpThgweM26wjNbNfW6b0b2BC/8fj1HApECBjieHTWd58+fR48uPbqaM/fv28eA5k30Nm+66 pbGFeOQV+BAekwDyR3rrbdYec3s8t8p8FFK4Chn4ZYjfGPq54cZouAG4BhdaDGjgiQgFgMcif7Ro SB98xCjjjDGmZeONN9YBoYQV9ugjIqJoKKSQ1mH34W2icaFkiQSiaKAAZgTSYiCG8FHIlVhmqeWW WBJCCSeaTPjjmD7iMeSZZ1rHn3afYaHkkiY6OZ55Cv5hyCKEcKnnnopgosklgDJC5qAUTofmoYde 5+abJMYp52QrKhjIIorsaamWiVCCCaCcXiLJIISGGl2QiJZ6phlnaMEok4+ORZwhfwD/UmWel15K SJ+SdKorJqKGeqGpwBJpxqJwNtlqUgJkIuWdidRaa59/6irtJdD1OiipwWaL37CqFnssUgMkKKuV zlqa6abTphumtYOaqe279pGxxRlvsvptUCqyyGy5e96KSa7pBnyJoOyO+Su88I4xbL2O3qsTcegZ Uim/eipCSbQCC7xuwT9iizC8+9HbqLEOz2SeIXfSSrGWXqKb8csDczymux8jrPCi9pYcE4L7rrwl tDAH7SmoMvdoaM01o6pqzjqrRJwfs/qMqaZCVx1z0dGt8txzqRAQBtJIk4HqyE2jBOUhizQrdZea Amx11dWKqvXWqaRSzC94543KKWFg/wi2zdwyXfZHA+Thx8RrXwn024zz+uPcXNud9+SU/1KMAIII EAbNf78rb6oND64RHnrgmfiV5zKuOqcEIwK5KHXfXfnss6ciyO2CoBIGdZ2/e7Pgok8UAAGHIL62 v26vrvomsEtO+/PQ/4IK7rc7snnvIJ9xRujBOyTAI32ovPbiyiuvySPRpw+9I45Qj7vuvGMfrNgC ktw9Qo4wonbiqZfvfyasaIX6Bji7y7kPd9bjnPxMZYYsXMF+9xNIACahiApa8IIYvGCWkOc//0ki E6tYhQAJSEK9HdB98Fvg/K4wBQh27xGEiKEMZ0hDGloQEhjroPIkIYoQrqIZJQyi9P9O6D7r+U2F pRqDGL7gwrKtqIZQjKKXkqdD1Wmihz4EohBJyD4iuk8AKURiqazThQgG4BBSTKMMKVHF/7HChyHU 4hYJaEAvFrFvYjQVGO43CjypMYqJcFkbVQdCOMZxjiWcnh0PCMbd5fFQBAieKBrxR0ByYpCrk0Qr DJlFRCZykUQ04iOHNAYlDG4XlfBjJWdICSpiUmhX5GQnPUnALoLyhJr72igzFJmmBWARlFwlK19p xTfK8pC0JKDtbulFvh1xl1XYi8My0QlVrjKQxGQcAI85y2QOUJHMJGIud2mfKUjzWHjoRDCFmYhL ZrNqH+QmHFPhzVq2L5x2dOYox+D/hHsFwBLVFCYhEuHKdwqMh/KcZz3piDl82lFzClwgGSJ5rEmo U6CtNCgssZjQENJzod906C3DqEIqNKFVouhEQCuJTY0GTRPG7KhHQUpAcIrUjglEIhNM6SQBVOKi LHWnS1+2TZn68KM0TZ8tbwpKAoghDFDVz9/GwIRzkueXKrWmFBORw6GmK55GVWhS1VdHpi7yFF1I a1qtYAWobg4PzwQWGZiAImoCVY0Z9epBORrWmY5VfTY1azPVSljCeoGtbtVPXIVEBSoYCJVZVWOm 9JqxWPbVh6yQ3V/TF1jBMnIAhQ2taA/b1qjiIX722elVAXpXS1JWYEW9bAhHuFml/97Ts0QcgBdE y9vedmEAiIWqGJjQxLFYNLJbFeprpVVI2fqQtrWNXllxe0C0+va6vfVCFaBg1b6kU6XrhGJel6sr sDr3udENKXWJaF3suletVgDCERyLGp+qdKXiJe+0LHte9KbXtuvFJWjf+974yveklBnFfcM7w5bq t1Mw7a8hofvf5003wLfTLYHda+AiQIGnfLErcmnYzgfrKrYSnm2F1bdMDFOvvRvurRGAQOMlSKG7 ToEseKFIUBN3qrkp9u+Ko9fZAP8lxr6dMY3lKwWyYPW+Wp2ijwGlySBzUo5Dft5SXSwIR+wWyaE1 8JLlS1+oHHfHDRakiflr5W5m2f/CDeWyIGAM5rWOmcZFkEJxi/JdKDdYuWuOaZvd/GbaFTnAdAaz mMc8ACgIwin2XXCDC0peFA8amYWG3qGpe+Q6p1XJdwbCErjbFAXfF7/jNbF5Lw1HLGd6dlt2sZc9 3QVQh/oIS2BKSk8dzMlO2VN8ZTWhX125C2M40QQeQBFCPWYo5DopOvZziX/NZmEPm9iU2zR1kc1h Zo/ZwyAuypMlzdVfX+IVgrb2tbE9OW17ttMxXrS3l/AEpIgYyqnWryYy0YpNqpuTSGV3AePMZQ3H 29t3PkKT+Xxq8AJ6uR9shTH9/W+xCpx2LZYzt5OM8IQ/Wyj/bHgnPmHiTGSCr6L/SHfFA35xyqVi b7d18cZHO4COf/vDQzH1fS0xilB0daj7pjgchV5xv7a8cqkQwF/QcQouwxu78rb5EqoalF0vOBSg AAXJvRpxlT+36IZk+dHxlnSlKx3mGDY41G0e6iYs3CeRBm/Wsz4KSg/S5MGWJdGLLvaxl93sSh8A 0xFdYLbfGsE8GXclSDH3uU/inUEP695XPnakA/7yYDwFwc06c7Xa2vBAAHdPRMzzxs9964Ps+mUn r+7MVt7lmMd8MQYv2Kfz9vOgLwLVdaLjRmDd9HNXc/nwfl7WW5vCr/977C+/t83jU+2iVTboQ72E KDwMoJVoBPBNj3rlYYLfKTa+/7CRX3nlL//ys2/6TWce9dwbIQl7xIlFKzGK7Zve56uLvJXFz2ry +/38AJh5zgdKG9d+NlcERuADQDAEP7BnK5FSlmAK9gd8j2c1H2Rp4Qd2z+UIrzc55heAskd7zDRr ooV7HYeACkhjQ0AESIBjLuFTvjeBwFd3QvN9ebd/Gqg1juBq5QeCPth8zMRtJuhtCXhnQxAERBAP NBEAo6B9Mrh9wict+qdu/NdmreAIu7ALfddyH+iDy5d+t5RoXlBzbGcEPcBsRxgEQhB/MREJ9feE 29d95WVyXtd/YNcKWZiFjqBZPeiFfgiEXmR7BjhmZohwaRgEQ+CCKSEAEgiH2/+Hf7tycjkoQhXH Cs2Qh3nIg1zoh5woAGAYSl9mZwhXiB13iEGABDGBCo44gag3hZNYhf0lCsyAiZi4hezWhZ0YgIDo PjBmgKRoc6YYBD0AE56wivY3CvuGgTkIi84lClhIi3m4h8mXi9RYDKcQc7fTXrj3i2wXjEPwEgNg jMfoDHWogSl3fM8IjXnIDBz4f9RIjQOwi51mawNwhtO3gEGQj/p4Gi2RCeK4fZ6AC8PAjON3fOqo jrb4arj4jl5ojfekW2JWj8t2j/ioj/nIjyvBhP8IfLqACx7pCuX4bwRpVJZ4kOoojUe3kAzphfGo eacQXxJJkUsWjMLYEsWwkab/RwoeuZMDOYmzdWmsMIsmqY7smJIreZRKZ4030AMTKZMqaJH5OIws EQk42XgBuZM7mQs3SIWDJgqoMJQmmZBvppJI6YMDQAA3kIJOSWMzAJWIyBIC8HtVCQq5gJVY+Qqu sIxt5oxgOZRiOWRkWZbnJ3gJgA4vAANq6ZRtCZXfuBKqOJegEAt2OZlaeYf7l459qY6o0I63KJi5 iA4J4A4JAAMcAAM70JQyuZgWSQQO6BHFCJlXOZl3CZIVN5KyFECZ2ZeaWGiB6Zlmhw7o4A7CGZzu MAMyMANrCQSqaZEYeRLhCJmhMAyyKZs9yZX9FZS5mZl/+V+96ZmzJ5zDCZ4v/yADx7mWy6mPRqAS /gib09metFmQ5yWL2ZmZKEls3YmUs/cO4Bmewjme5ImcqemWNYkSGgmZHdme01mdl2abPsSX85mZ uwmYvrl8gqef++kOxNmf5CkDiBmgbtmYJ3GTkDkKr4CgCFqZg8agIoSZDwqW21lb9wmPoHmhwvkO HLCf/kmeHXqP55mPIGoSrzmXsWmi04mXKSpbeNii2VmfvDmhgDejNMqf4FmaGyoDp8mjAsqaJxGX kEmXREqkKJqBYVWSSjqfRZlpMeqHwBml4DmaNGqcVQqguScEAtqcI/GYc6mTX0qkeBmSMkWQ2Fmm D/qiY5WmIPidbAqeGYqjVf/6n/dIk0FgpyLBeOy5p186DFtpVMzolYLaokwqoYKZn4napjAQpTka p9MHqVJJEs85l9FpqXvap87FjFfYqUp6pllmqLFXoaO6n4vKqI3KoYlZigI6AyZBlZApmbBqqQoq eX9qq4JKqCClq4BHmL3qq4l6qlW6o8AooD8aEgU6lwe6rJbqCpmqdwmFm9AarWO5klB6rYqaqFQa rFaKmt4GqUKgiBshonNJouS6rEaqqfIUqOtappuZq++4pvCKraMKp/Qqp4YooJFKEkFalUP6r5Ya pvJkfPJZsJ0aoX9lqIi6sOBpo72qrY0KsWgosZLaEVwKmXWJseQqqxt7TA7/6rGdKq3JFKOiSrIM O6oom7LEKqCrChJ4WpV6KrP/iqk1y0m1irO2+qkwypLoYKE+S6rXGrTbOqxjBqlBYKyT2qUXq7Sw SrNO67RQW7AgS1OBaa1Xe6G/yqZaW6VXurLeKhJK0KWvSrYy26xfh1mXmLYFq7OIRJbv+rZYe63z Sq8bWrdGKLHf2hHrOZfKyrdKa64T1qBCKbjrKrWFen4Ki7hwS7IOy7iOGmpeO7EgYQByiZNja7kz m5d/e7Ocu664ulldOLKi+7PwOrdC+7gsGxK1UAr9WqKwy7couklPW7seS7hCZH49u7v7abIk67u/ O5MSO6AfUQu0IKTHC7t9/9pvzJu2njutZser0kujcXuyphus3FqRRAsSAUALtNC64qgHuZC/+ru/ /Nu//qsLABzAAjzABEzA0QAL2dAMCjy+Hnu7SZV0bpu+F0q91du+weq4qRu5GjEAszALxPuPobAM 0/AKJFzCJnzCKJzCKrzCLFwNz5ANxYAN2JANNFzDCbzADDyfzktCqXC4Esy7C2u9FzyRGQwSHDwL 3SuOpqAM0AANz8DCUBzFUpzCzmAN1bANzZANMrzFXCzDNlzDCvyVOQyNOww9dZMK8WADVvvD++mm b1u6Fny6PcqcH3EKHVy/xhgL0tDE0KAMwzDFgBzIKCwN12DF23DI1YAKXf+8yIxcDF9Mw2HMvAeL SMVwxvEQD+eQyZkcD2ysvqILx3FcnnO8jx+hCx3swY4YwnzMxyMsyK4MyNVgDYZ8yNtgDTDMyLic yzLsyI8cydC6trVTN5dcDJpczMW8vumLzL0bysE6A6MclaV8ykksg0u8yqv8xK+czStcxbJ8Dc1A y4ecxbo8zuS8y498wyzqotJlyZhszO7szsosuvHMvsy8rTaQvdrLEdMgzfZresuwx9bMx36szQRt woQsy7J8xeB8yLdczg790KjQywqczkzqCOxMzO+c0e9cDKHJxvNMz/W8oc/8lh5RC6eMyttnCtMQ 0AGNzQWtzcOQDQid0Av/Tcvi/NA4ndNbHNFf3AyqIMzxQA4aPdRETQ5rvLsUjLhCzLgwQKeQu70n Pc2NRwoAzdKrLA258NLazM0zrdA1jciKrNNiPdbtTNRmTdScLMEffa2gzMypq6UcMb9R3bqqbNUs 3cpaLcgHPdOz/NWHbMsxPNaC7dBlfdaG/c5rPapJ/ckhXaWpq7obccQn/cGgUM12bdUunddSHNN8 TdN+Dc43PdiizcjZcNimvdEdLc8/vNQPi8/pyRGSLc1Zp8eXbdfSIA2aPcWx3NnW4M2fvdANPdrC jQ2FfdrGzdGi68bpy9rNjM9FmxF2fNJIrNK1Xdt4ndvbzNsI7dW/Hc5a/zzco13cxn3aRo24iZ21 jS3S+KzBFmHK0k0L0VDd1Z3Z2H3Ce63d3N3dYA3egl3a4/3fm/y2543e6c2hTn23HOHeJ10L8S3f lz3Q9Y3Cu63dfa3ftAzY/K3T4g3gpj3gGNrJxVngMvDWrekQ+yzdvtDgDm7X1x3hr8DVFJ7fFu7d Gf7QxSDUHP7fyL2wHs7WIv7YLVsRJo3ivrDil43VLk7C9x3jM+7X2RDWNa7L/p3j/13e17rYEszc KYvPQU4RQy7NwVDkRm7XEF7fnE3hCO3bTV7TthzlurzhVH7YVj6qPU7g6T3Sz20Rcr3gvdALKz3m mO3iMI7mFb7m4JzIbv++yKiA0XH+3/Os3J2s5XGKz2CbEbHdwb7Q538O6AF92/W95IQu44b+18Gd 6HDe6Icdz3Vu5429A0SQvew9EZdOC7zQ5yrO6dbc4i995oS+3aP+2aHt5qeO6me94zQK6SDe1qFc xBoR3adcC33eC7eO69ec2xPe6579636N6FG+6MTO4XMOxMn+47C+EQqO6dEu5tRuzWVe0IOO7aKu 7Rde6sM97N9+1uH+4SB+oZKu3k+tEec+C5ne57xQ1evOylrN69jezd8s78AO5fV+7zm+qFgO4v3+ n9kL1xhx4nccDNHu5wff0i997Quf7Q7/1Rgu3FMu8QCeoatewQU+0l3/HhFfPgvQ/vHTHvLt7srv XvLxfvI2/d2ibe8sb9bIXfEWL+Kunr0zDxE1P/DRnvMhT9+BDOolX+hA/9XcLthEX/RF/Q4v77PK Hsep2/QOsefo/vHAEPKdntWurPBXb/JZ79cpr9Mr7/X/HQ/58AJ8f6P7Dp5jb8Flb+l8/vG9oO5s j/A8H/ed/fNzD9pCj9Ndj/dDHQ8hcPkhIAIdsPmc3/l8//mgH/qg7/caGvNMT/jPbvi9UPCJb81U D8VWH/cy/fgWTu/jfOOUz+EdgPm83/u+//vAr/mdDwOmH7wY0QwnDfUfv+mtDw2ePsVwz/hyT/t+ HezjfPe5b9qWD/zc/9/93h8CGUD8jf3MZt8QCk7rqi/tzb/Kur7CJC/900/92w7xuTz52e/O2//9 +r//HQAQMgQOJFhw4A4iQRQuVNgDwEOIESVOjKhr1sVavTRu1BgN2keQIUWOJCny2SuUKVWmdGbN 5UuYMWXKrLbN5k2cOXXu5MnTWrZi2IQOJVqM3DmkSZUuZdrU6VOoSTuEoFrV6lWsWbVi7WDQa8Eh DBk6pFjWrKyLs3xx5Ais5Fu4I5UNW1l3WLaZefW+rNnT71/AN5tlI1o4W1TEiRU7jbfV8WPIVLt+ /RpWbEOzmSfWSruWrUZfcUXHnVZ3ZbW9qWf2DdzaNU6ghYXGW1zbNv/UqZF17w4hYgdlrzMuY9Zc HADnWbSCfdbIS9po6COl5TKNsqVq7C/xvubuenBhVMVujydfLANv9JB9Ay8ofDhZ42YF0MLIfOO0 6PlBzjUt7Vp2AK1hrTsC/aoGlaFoI2/B2hpL78GtMoCBvYHcuwy++CgaoDP7OtLvw5PqQi3A7AYs 8ESdfgpKQQZbjCo3CGO8SkIKZUDovQzN2vAiz+zz6MP8pJFmpetIxM5EFJMUDAHxXHSyKXJEkHFK q2ik0DKxhsixrGbq67AXt4DMr7SU/DOyRCXTtEnAcuJh8Uk4z3GQSjonYw9LhrTcciKL1Pqyl9DE zC/Eu85EU80T2Yz/xxxGzXkzThdhpJNKOymzMM89+eTxz2CUETQ6IV8p0tDUtkP0NUUbVZWcoyB1 McpJY32BvUsX0jNTiNBS7s9e8PsUumlGJTU1JE/lqZo2VVWW0XiadHXBOWOlcj1Lh7sV1+NmyYjX H38dbcRhVSvW2JuQLWdZdBkt51kGJZV2Smq9ujFLbCHirMcvu/U2rmfCPZJcncxNd2Bm2R0v2nep tNIrPBW6NtP5/OSVl31H69dfYgG2SWCCO3bUYNsQTnjKhcG6TIgA6t1wW14DrRiuaTDO2NhmkPX4 ZnNYBXkxd0eeslKCalVoAJW15VWjTl+GWea9TFWy5nLIwXnqZndG/0xkn38Objiise0S3z99VZok afBiOq9xvUNW6qnbdtRZq5vqOWut2+O6Xl1o4eVoD8cuCdyzY0r7LzbZdvvwR+NOyjy6pY1XIKGD 6BpXXVg+Wl+/Q7o4cMG5S/Vw0BtNXHGsG5fxcRkalrxeWcD+k+LMR9qcc75a+zx03HNuVXGpTH+3 ZNUnz7QW1790OXaQYqYdpsG3uT136Kvm/RzGfZd2YaGF35OY5fjuJWnkk18eJqdzQnZR6NNXVXrS rU/YSqGNwFYAYry/L/yQAF/eRI7V91/06c3NfXUTGoa2NIDi/QlzyNMf7frSv/9FsGBxg9UA39WV AmILgfbrG/6gMf+75T2jHOeSYAkbpTOrlc6CU5pVwwyYIwJwsDke/AgIOZcNw5lQh+wzmABXeLod uBBbrpAhoGgIDeUt7xro02ET3wYyG0jph+8SwQ/E8sIMDYAYwtib/cQWviTSThtOJKM51gWnYrgp H2vMRwmmmDAQJGQhWMxQMozhi2NwkW9fDF8DZVaNMpZxdItR4xpfQA9EIlIBC3DjGyeVARzkQAgL mUG9CEAMY2QSj3rM1xH96K8lBpKMKEwMOQqZj0SmMpWLZKQj6UQDHegAB5MMwsO2FABb+CKTu9xk Fz+zwNjZEGNjFOUod8eUU15AlctUJStb6UoZ8SCWsgyLLbdkAEz/7lKbvWTL8cInzHARs5hklJ4p 48FGZqZzmflYQDvb2UhopgeS04xlDayZowHY4hja5Ocd89hFbyIvjBjD4TgD+Y01KlOdC12nO90J z3juBpb0jGUK6vUQWCCjnxvtJR9jN9BwhdKgZCwHKhl60mY69KER5Y00KaoDOuboFLbI5kb76Ysw efCTZxLnSHe4DnWYFKUodaZDM3AelkJmnhTFgQAuCgBcIkOXNr2pp3T6R5860ZTqCOpQh1pUoyI1 qVuZKEVp8NSHFICmVN2oMGgIThIVNKs6LAdXu+pVhl7gAioN61i34lKKxnRLArCFPtnaT2CODa4B 6ulcI1hXu94V/6/pZCdf++rXq3TgpbJ0KloBAAtbaPSw2jzGc8Dor8Y61n/xAGpkhTrZhlr2spil SlnpeVbPAmCmax3tLqmBP2X8h1RyVe3/thpZycI2pbKdLWYBS0/B7gmXoZ1qb32xDPztVDUiLe7/ IIvcdRxSuctlrjuPSlvNvrSpuU1rYWtqXdPGTliM7e5jkeva8ZK3vO08r19tO03cspewhd1nbzOZ 2Iotdi+prS/uWHtfu752vJXdr0MvIMWkPnea0cUVaENrYE1aNXMKzgtxG5y740JYHfFQaH4pXGF3 Xjip6WVqZ9mr28Ly1sC//aiRuHvi3H1XxclVLlhhvAAZR/S/sf8M8I2nS10QGwPBvwouiRgMZLcJ ecgShq2Rj5xkaGo4lhzGllrdG+XSxk67MjExlhHX2iFzlcX5pYeXv4zhN9KYnuu9MUQGTOAo53Rs 89XLj93sthTHmatc9uoLMnBk2YJ5ijXY7D1za4Aci9bAvhCx0kj8kisf+mZaVjSjh/piSKtU0hYU QQ42m4A+S2S3ZwaxW/32aWuEWtQdI3Wp82vnVD/zh3qeZg5SFuuI3CLT1e3tlMUE0pm0edc3e7Ci 72vqkwI72BAdIKVfamn2EiDHOu5tmpVW5b0YetoeS7S1IzxebW97ha1+NbIl8mdAg5jHSluzrteN rl67G9sL1Wv/sPfLbdMRO5bGtrdEMJ3pKF930HsB5L+nFnB3ExmlqDa4ZRFON29TFNw3njWtNx3f fcFV3RZPF8YzPnDKdrzCHx8ZvV8K64ZLRNnLjrKz9QNXf7OcWXDO+LW7LPOZ+07hOmB4ziMi7nG/ d7Scfhm0cy10dsej6EMO72TjjfQF5KMDYyc72UtwdrSnXe1p90Db3e4BB5jA1SJ3+r3HnW8D23pf ZWNzDrEO8K3HGebL/LrMO7ABDSRe8YtnfOMd3/gNqKAFLNAwzusOkYdDvOcv09/K/94olwd+8Knk ONgdevjHp171jh+B5Fvw+hjgYOHHvvxDSm7ycqP8UyAMutCr/x14FXf91KaXbQkQv3rkq34ELHh9 81ugAleP3N4e5jmIBb175n1+YO0GvtG/Sny+liD543/88p3vfBbEwPK1fwjUox5x7HoridLWvrq6 7+vvg/+h5Of/4j3A/PNzvhJgP4l4snErsLzblyTqPZYLvfubM6LSvwXIAPHrv/6LgQA8Pw8gwInI PM0DMZ8TDb5jQIv7vfvbMpRyNP3LgBGwwAvMQOdbAdrjwIfIp7sjt9Eyt0+pBvrTPu47Qe9jqNLr uA5oQRccvw1wARhsPhawMRqECOqrvh3zFlVgovpTFQcEwtEbwmBDvSNMvshbwtdjgRN4wolwv/fb PEGRhm+4wv9lyUIg1DjCIz4v/MLVaz0xfL1KMsMCvEG8g69n6wZv6AY3FB2ii0MUZKjCKy/js0Pk M788HEA+7EA/vAVkQMDRCkGRUIZv8AZP9AZuKMQfRMQgTKeCQ7oKdETlA0AxlMFJnAgbHLdbmMVZ JAZMtCmqgw42HIdP9MRxIKH6g0NSHDgurDAKVMXV+788bAFXfMWJiEJboEVpRAZiYLZ+0ju4kIZp EMRe/MRu8DuhE8ZhXKhiLC8WREbVw8BlJENnpAg0jEZpjMdLpCpn28ZuvMdv/DwTJEX8S6dFVKlz RMfHU8c8ZMd2nAgDhMd4jEeaskZj0MFN7MR7nEhCxLpR5Ef/CBM+ZvpHdypCgXS8JFzG15PEg6TE HFtIlJzFedSmfQMJbeTFiYzJimxAjNw6bOPIBajDj1S8MBTJDSxJivizlBzKWiwwiUseboxJpQxF i5OHmrTJdFJBSNPJndSAnlzGZgTKZywsouxKavQFW5sGiVRKsvzFaSsHdpAHfWAHdtC6p1Q0jSS9 VGvEqlQ8PBRJFZhBrYyI3epKv7TEaBhLshzMfAQyckBLeUgHxVzMtWSHQ3xL/JrDI0vFutQASFzH MtxLipiuv/xLwRxMsizM4iIHtsyHxTxN1MwHtoTMUkykwjvGykw8ZRTJFthDzaQIterMv0xK0AxN 1YqH0kRN/+EcTnlgh3xgTTlrMdc0RiOMTYIUSZK8zYkQAN38S3GAyd70zZECTnbQh+H8TvAsTrd8 Swk7ReYKSOekTdiTzsw4gOr0S3HITtBkykBCy+4ET/zEz8Z8zDiUsHL0yNjcgOfESr1kz4gYgPf0 y3CQz7IERrpKy/yMUAlVTcfkRwhEpGKkyp28SpFsQgPNDARNUKIEBwZVynGwQv85TAiVUBZlUdU8 TkR8LWCjy8rkUMz8UM0oABElys8sUW8Ex9AhTeNsUSItUvHUwlUqvthMvLtUz+jE0bLQ0R1NSd70 0U9sw9zhTtMsUi4t0sYcT6hczvBbUstkRdp8UigtC/ec0v+FvE4rxUfQ4U7v7FI67dL9FD0M5SvY jM3ZVM+sTFOzCIA1ZVNpjM837Ub69Bj7nNM6bVQ6pVD+hDCTQjX0rMwBxcsCBdSgJNSFXNBD/USz JBjEdFRSLdUXtTaTKqoLaE5LVU8mzExNLY4Q5VRaJNFP9UUUzZlRLVVe5dUjDb5DciYN/UgBddXm W79Y1YxToFVp7FErLUwh3dJenVZe/VJJrbN2GlaBtNEzTdYckVJmvYUqfdNvCE5qPVdqvdMIU0Ea rUtu9UlvvaZwvQU3/dRvqId2mIfERFd+ndZTVYd1mAdGOsIReDuDdTsQAIF7cD1j/dN4LQ5BnVdD tdJvaAf/eLjYi81Xae1Xjm3U4swHeajAgx3ZhC1ZEBiBD0hZlV1ZlW0AM1VPD33YHInYcPVUBu0G i8VYnYWHeaiHeWDUjg1aIpUHeTiAkmVZpE1apUXaJnVVg5RZfJrXW7DV3uwGn91ZrL3YeqgHtRRa rw1PefjZeXCApS1bs2VZFDDW5rNNqI3aeXXWbhyHq81autVarv3ar9UHov1ZfehbB2iABjhbwVXa tFXbFkDTto0PcGXWcQXVe61byNVZjcVbftVbebCHvs1cfZgHBmAAEBhc0FXZGnhZ2nTYxM2QxeXU eu3Gx41c18XYnp2HjaXcOgXZy9Vc3HWAzsWA0AVdlzVc/9M93QwZVFqdWE+s2NdN3p3t2a6l3SK1 3QbAXenl3N3tXcFtWpiFVeGVLuLlVE/FWeUNX6zd2n11Xvzc2+iVXvXV3c71AJS13rItXGN92u2F GKkNh7kVX/2VXH01X9TcW/UN4L6l3s71XPhdWvl1Wu2t30yZVVq1gJzdXwnm39kVWsvlWwEWYPYt 4M89YKQdXbV1Ae1h4ExZVmalAArAhwleYdj12Qo+V8vF3AyeYQIuYN714JX9XWMVYRJGKwJ4YBSm gH5gYSLmWa4FWl61XRmeYSbe4AImWxxOWewVSR7uYbQSgAP4BzYNYhTeh3koYiImX1Ml2vRlYjOu 4QIG3P8o/oAEpk0SGGErtqR/0OIE/Qcu7uJ6AOMiztfyHdqwLWMzDmQnLmADxuE2FkkSeIc4vjEs nuP3rIA7DuII1mMWdmEJBeBAzuTMRWNCvuEDBmFXTeRFjjUCmGM6/stI5mIVpuQiZl4kTocL1mRZ ztxB7mQP1mHaZAEJUORRjrVGduSutIBU5uIhZmUwJt++JdolnmVZ5mRChmLrnWIx1GVe7mVkK2VT PuWFHOY79mJj1uN64AdmHme/JWRz7twO7t1DnuZdtuac+2VTXkhh5mYu3oc8/uZWXmZyDmRnNud0 Bt11XkIXeAAndGd7w+ZslkZIpuc7nmR8nuB5wOB9NuP/Wj5nTx5cUKbiB8hUg/blLM5mOmboVF7l h67kiT7jc05paBZcXF5GF6gHju7oawbpORbpVC7mkl7hejjpGa7oc1bj62XYZTQBeZBpDoRnU15o mw5ib87pCa4HQObpzLWHBkjplP7n+FVPEogHo35ChE7qpa5nh3bq8IVqqc5dq07pi0Zgra7mrj7q jzbleQ5rFB5rsk5esz5rfaDqtLbos83oaZ4At35rGvzqf5hrusbpuy5rfZ5on7bqlU7all5CFtho wn5FpLZjukbhfvjixQ7feWjscebrvj5nrF5ZaQ7Ayo7pyyZAw1bqsG7qz07eiObpx07r01bZgD4/ F7CB/9YuSaRG7KXeB7ue7brd6X0m7dI257XWbSou6t8Gyq8W7qUubuPOWuQe59tO68hOWcCGQRc4 hejeS6TebM6+bryO6kBW7uUmZPdl2cnOwDce79v8avMWYs9Gb8jNa03e7r7+59R2Pn4oaPoGSniG 7eHOb/2m23oQbQFm7/a2ZefOQ35g7QJvR4SmbpEm7gWH3NDOZP/ua0/e7TH8AQu/8Hb8ZQ0Xaevu 8A9nYgiP8Cf2btJFP99GcShFaPOugH64BwXvcNiV6AAO8dIGgfhGP3TAcUD9ZQQX6QmYACH2cSDf 2exW3xiX8ScW6gBUgQVWchzF5iYf5gp4cjKH8h6fcv+MrXK0xvJzhjsIcIEab4Eq9nJNbeQVj+Qy z3MK8IcW/2x+UO8rL224ewAImAAJiABElwAJMAElbL7gpfMcP2yGHvM8r3Qo53Mg5+9ybu8GiLtC P3RED3VRR/QJIAETiIETh3T2bGSGtnRXv/R7Ru8Gn+qqtupON4EHMPRR3/Vdl4AUkB9Vh9pSDnNK f/VX3wd8iPXZfvFadgB+yHVQ53VpD3UJkAcCD/Z4xWIEL3Zj73ZkV/a7Dm2+dvYHkIAJmHZ0F/UH iIdUx3ZNJQDh7nZ5L/N9kPLFrod+MPd03/dE/3V372EsRmFun/d5j/IfN+Z6gIBo53d0r/Zr//ft JQD2SCZ4ii9zgzfme9B1hk/3dW93iIdaARgABECAG1Dqii94TCfiecCHc9/4hvf3j3/rkB+AAiiA G7CAuT75St/zPj9uhXf5hrf2mEfxma95A8B5CzB5iud55c34hQf6UJ+AB5AHI/D4of/toi8AA5hj pF9oY//2ul35lof6RJ8AeYgHOL76oc/6rZfrpA9iMgf7NP95qDf3FJCHAbB6tVd7tgdppLcAfHB6 oJd6qn/4vT/8Pen7pNZ4aTf3s097xI/83GJ7YT53u8d7vZd8zfeskDf8zf980A990R990i990z99 1E991V991m9913992I992Z/9oQ8IADs= ------=_NextPart_000_029E_01C07B15.387204E0 Content-Type: image/jpeg; name="Hull32.jpg" Content-Transfer-Encoding: base64 Content-Disposition: attachment; filename="Hull32.jpg" /9j/4AAQSkZJRgABAgEASABIAAD/7QG4UGhvdG9zaG9wIDMuMAA4QklNA+kAAAAAAHgAAwAAAEgA SAAAAAADAAJM//T/9AMMAlgDRwUoA/wAAgAAAEgASAAAAAAC2AIoAAEAAABkAAAAAQADAwMAAAAB Jw8AAQABAAAAAAAAAAAAAAAAYAAAGQGQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA4 QklNA+0AAAAAABAASAAAAAEAAQBIAAAAAQABOEJJTQPzAAAAAAAIAAAAAAAAAAA4QklNJxAAAAAA AAoAAQAAAAAAAAACOEJJTQP1AAAAAABIAC9mZgABAGxmZgAGAAAAAAABAC9mZgABAKGZmgAGAAAA AAABADIAAAABAFoAAAAGAAAAAAABADUAAAABAC0AAAAGAAAAAAABOEJJTQP4AAAAAABwAAD///// ////////////////////////A+gAAAAA/////////////////////////////wPoAAAAAP////// //////////////////////8D6AAAAAD/////////////////////////////A+gAADhCSU0EBgAA AAAAAgAC/+4ADkFkb2JlAGSAAAAAAf/bAIQADAgICAkIDAkJDBELCgsRFQ8MDA8VGBMTFRMTGBEM DAwMDAwRDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAENCwsNDg0QDg4QFA4ODhQUDg4ODhQR DAwMDAwREQwMDAwMDBEMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwM/8AAEQgB4AKAAwEiAAIR AQMRAf/EAT8AAAEFAQEBAQEBAAAAAAAAAAMAAQIEBQYHCAkKCwEAAQUBAQEBAQEAAAAAAAAAAQAC AwQFBgcICQoLEAABBAEDAgQCBQcGCAUDDDMBAAIRAwQhEjEFQVFhEyJxgTIGFJGhsUIjJBVSwWIz NHKC0UMHJZJT8OHxY3M1FqKygyZEk1RkRcKjdDYX0lXiZfKzhMPTdePzRieUpIW0lcTU5PSltcXV 5fVWZnaGlqa2xtbm9jdHV2d3h5ent8fX5/cRAAICAQIEBAMEBQYHBwYFNQEAAhEDITESBEFRYXEi EwUygZEUobFCI8FS0fAzJGLhcoKSQ1MVY3M08SUGFqKygwcmNcLSRJNUoxdkRVU2dGXi8rOEw9N1 4/NGlKSFtJXE1OT0pbXF1eX1VmZ2hpamtsbW5vYnN0dXZ3eHl6e3x//dAAQAKP/aAAwDAQACEQMR AD8A5wgEwRqOxYSR8m/o0g4aQRPk46fN36NqYRoNPIB5/wCiz81SJcTHuJ+Ief8AMHtUXiPwF/jL 9J6U9j+JER/iw/QVLjqCT8HB3/Sf9H+ykQZmCfE7Qf8AwQpETMglw/eZuPy2exRlk/mz85/8hWkf E/aeH8P3lDwHTpEy/wCdL5of1krnBrKLRoK3lhgEaO9353uVnOH6EWf6Mh33H3f9FVPp49rQQXBo ePfvPsMo78hjsUM+kXtg+GohRkaiu/Rzsw4Z5InTiHEL7/4LYpcNhnsq4tr9exrTJezQ9pH/AJ2g Cx762E6CII8wog7bmO84+/2pCO7DLLYFdEpybXtgHaPAf3oVQDhaHcgbh/r8k5G1zm+enwSpMZA/ lAj+KICyRJokrctSYAGA+BIj8UgIlvgY+5PWDsePn93KKOzF+hBUphwPCZ3CRnaPL/XukyY5cOSJ 7EFIQe4cfDcGuP8AZYFGBoXDU8F7DPyaxRAbwNoI7NaZ/ql/5qcQDDS0E6xW4yfi93tRP2+cuLXy j/6O7Mdq1HlHg9P96f6P+PiUSBqSA4cFxcD8dn5qee5J8i54c7+yz6Kk0ngbgTqQxwef7TnfRTQ5 piHNJ1gNDnfFz0q6i/oOH/pf+jqsbGr/AK0uLT+7j4vT/wCGYlntdMuBk8Fwa8/BrAokN5cInu9h JPwa1ONg9pDWHsA074/76mgNOhawnSGuJf8A1ZP0Ur8j3s8Wv8v7iOEjQWO3DHg9PnLi9P8A4bjW MD3S0EcOeXA/1ticOgTujuHOeCY/ksKcOcDHuaeIDg9x+9ItcJOrT2Lmh7j9yNHcX40OH/pf+gLb G0q12uXH/wA3Hxf833Yf6tTmu5Id/WeGuPwa1VXZNkV1PAil3tPeAfolWPa0yQ1k/nPad0/vQql7 Rudt7HnXUHvqloT/AG2Wj8REhjhIbWY2I8Mft/wP3ndc+rJwwWuElhDmzrxqidMdvw6D32EfJp2r E/NBHBCJU5zWAAwA6NPCEw49CL6tIcybBMdhW7r5RFd9Fh4bY2fgfafyoFuttjv3nE/f7lSsD4ne 4gD2gk6Kfq2C0+4ndBI/D+CQhQRLOCSaoFM0tY54cY3Vn8un5UgW2MEGQVXeXG0EnUzKbG31PmJb 3CPCtGXWq0TvaPVZ4loJ+IQXtG4+3eRMCJ1R2OY+HfnCQfvQboDjIkeEx+RDrq2MEqyYyO42/lFg 4NktMOI09NjXAT5wlO32lw00aytxH+cSnPtEbvTaOGMf7pJ/lJ/0jRB3Vt7AFrnEn/pJ9anTzqN/ bx/93/4W616AXeuglMR/xY4//UX/AIesXabSS0cNrY4E6pFrgIINbToGBrXOOnkkBAkD0mjl7mAu J+SYANHsDQB/hHhwJP8AJSN9e3evwj6uH/wvGkVrVb/u8Xq/vS9HH/4dmUYDdQKmkwCWHcfuKQho JZtqaTG5xcHEfyUmlskshzgINpeRqR4OTt3E+zda4DncC0E+CQo1VeHCDL7P/Xf+Oo2Lux1InKMB 4cX/ADf5/wD8KU13LmGAdPUc/kDyckA50ur3OPBsdtMAfupOnd791r2jjaC0E+KZwbIFhBc0SKw0 jn+qkb69D3jjo/y/v5EADpRsdp5uKP6PzcPFH5Pn9rCxtEseQ02OIILyzTQfmwmxBuw7WfH8ik+A 2LCxrYJFbSQZP7yj07Wu1v8ArwUDsXP58evGehjKINaent+j/iNrpjT6Gx2nP5Udm4dSoc4R7Syf GA5V+mHV3x/g1HyXbMmh/g7+5NO58mnE1CJ7Efm7NQ/V48NFSwpDspvg9h++P/Iq7SZqd8T+VUsQ D7TmA/usd929RDaTbl80Pr/0WznCaD8FVsaHGt51PptIPyVzLE0H4KmYNdBH+iaPuRjsty7nyDVe NT8VV9ocSWl7tYbt3BWn/TcEB+4WPa0NaYEvcSOw/OapBuycgay/4JHZgQz2uugSPaza4fkT8hps c2uuNGAuBP8AZSaQ10Vj1LCNXB/96f6Dm7y+yz90EOA+SI6mh4mpeHzz/T/2cHWJOgs3RMRxQif0 v5rFH+aj/rsqwcXNG39HWOSH/wB6dpeRFG6J1edpSc15DX3kkA6M2g/kUS0vbLw2uoHgtIJ+7/yS Ov8AWuu8ccq/wf5mCPSRpwkX2nnhxX/X9fNZf+YvAZLWNL3zq4skD7kzhUwu3Q+3sIcEg4Hc2jax oiXEuBUgdpLKRucRq4Pn/qkNK6EdNJZO/wDNx/yk/wCvJceIE3xA1crMMMq9Mv18/wDI4/8AVY1n QCXXOae7WBzgnl1nue4srjQB41+9KPTcC7e+wg6CHQkWnSy8kx+aWD+COuu/9bYf+G5P+4W2NDY2 qB9Uj5cthj6f0f52bSznBxrLQQ2CATGsHyR+m/zbv9fFAzSXFp2hrQDADdvcKx04foXHz/vSJuPd w+aFc5kFVrtv+iwwgBkujw/itHKqBrc7+TqPks/D/pLv6v8AFaeR/MO+BQluGCHyFr4H8w3+u7+K JnfzTvgh4H8w3+u78rkTO/mnfBD9JP8Ak/oko+gz+o1Dd/SW/P8AIi0fQZ/Ub+RC/wC1I+BQ7rjs F3MLWCeSQq7ml73AuIrGjodGvzVy1pdA57n4BZtDH2MLSSGAzO3dqiBfQy/qjT/G/qtrkTWf5hAc MvWQZcP9yMf00xfY/wBlO4NGjj7T/r/nJjFQ2MYXWDuWA/kTOe0/o6Q2Do47SPyJTVQNNrrBoYJH 96JO54ttJZDL0x/q4YxdcRIAiIH1eqOEQqeT/WczOf6KtldQLrI3O1aC0hID1T6lxaGdhLh90p2M /wALa7zaN/8Ar/1aX6XIM+5tR8CEgNgI7/LjAMuL+vlJUZGzIz20yZzKMY4/9Vy8Y/pLb3WnayQ1 vJD+R/a9ykXlg9KkuLuQZaUznuH6OoO00d7QfyJEV0N1LS/kSwo2dTxV+/k9MOH/AFeNHCDwjgBs 3iwevKZ/67Of3VwwUt32Aue7+SDB+X/klFrNxN1wgDkFh189EzK2O/S27NruBJGqfc+9+1ujRoQH 8/f/AOQQ09Omn+Tx3KZn/rMi71Az9RBr9dmqGOOOP+Zw8X+I5uQ4G95bxOkaaKDPpBStAFrwONxj 70zPpJ/m8tlIOSZF0ZEi9917R7/GQiY30bPh/eo3NmCPgiYwBrPmdfwSWv8A/9DndzgDu3QdDuYA 3/Nb70ztoEe2O24Fg+4e56TWyZYPdH5j5P8AaLvanHqNP54PcAB5/wA/81Ra1qL8fVL/AKfC9JoD oQDuY+iH/pL3Jf4cVhAGoG0+Dyxv+Z9JSIft/PDRzMR/mfnKO5sn3DcOZZLv7TvopgAHANDCT2a4 l3yeUr6fkR/3HF/ipIO5G2vqEv8AG/WShD/Dh+rXkhoDiQ06QWhoM9hChjgiuDy0kIkEzDXAnQ7X bz/an6KjSP0tjON0OHxQO3/o3/dudzsayQlp6rBrh/8AUfpXqE7mfuu0+fuTWg7fMflU6gDcR+82 QPNp/wDMlO2skbh8wg1RsQyyGgvD2jR7Q4ITDtta/wDdIJ+EiUZsnHqPeslh+XH/AEQmfU0NJHdB W4WyW7ch/gdfvUK2kkCJ3SD9yPe0PFT+7mwT5hMGhhb5GSUldGuQYg8p3DkJst4pe7SSToPjqq1u RaHTpHgiASiUwDq2QHObLdxHg10NH8nVOHOI2ne4futaNvw3fnNQaXCxgLtpIJ+n7QPn+cigFwID RYByGP2sCd4a/S/yhH/1Y7GKQljhOhqBKyI/9LJP/wBUr+x0iWu11Y1paPm9MCAdrdpJ/MrcRP8A WenlxG39IfAMI2j+TvSLyPaSXeNbWf8ARJQrrX1/9iS/l/mmYS6XfXhv8f1MP+d+r/8AOhcfut3D +TW4O+bpT+9v7zfBoaHOPmXoe5nDvTnjawET5b04hujYZP5tb/cUQT0O37p/9V/99/1NBA6jf96O /wDhZpf8/wBuf+2Y+wQHba/IsO+PNKGtEjZXPMOO9E97WxD6wewIc5xUSdo3Sax+9Y2XEpVW4qvD h/8ASko/+olWTsSRLtLjv/wmE+L/ANuFe5smCydS7eHOPwagXtl5EO9zZl/MhGETI9PzfYCCT4ta hWxua5uo1BfMydD9E/RSB/l/6JFqc/C8EjWsTE3R/u/5SXH/AIP/AI2qoF9I01HHy0T1zDvkpUaG FN7dTGhIKTisnasUGwNhHdsfcpt1Yhjbtb4hxH3+5JTOyZaR4hJncHxTW/QTt+mUlL1Payw7jAP5 US5mrXDvOo50Ve1skx5QitfsNbXH2jT4EhAjqGXFkogHuwEiSAWAaussZqZPkotDOWbHdzY8FomU Sut9ljWMDr7edrX+0a+au39GzqqfWyDI5NbXNPy/dcmSzYoyEZTjGR2Ej/33pdyWWEPmkI8XjEcX +DH9bL/qk8eJz2hu4bQLXjUuDyAD804mRJfa8alocC1M5wLQLHhjCZ2bOwPknYx1oittYa7sAQ8g HyUgrYedej8vV/jZV524jttxfrDH6TlwR/wOX/8ADFzu9ouLnHkVhoKi7bAFpbW067Awgq3R0jqd xLcXCsG7TfJBI/tKGfi53RcukZlVlZsbuZ6pmYMaf1U3JOok1x+BM/V5ylwSl/0GDJzOPFG+IX0j j9qM/wDBjD3oYf8A0qxbh5Zq3ik1UnUuAeCQP5UITQ4t/RNLGk+6zf4f1lsftv1sMMBd6skOGm3b 2j87cq+P0DqGaz7UGsNTp2NcSCTP8kfRVfl+ZnMmM4CBHWJ/9B9Ef7jFDnbP6yPDCR0NymP8KPHD 3Jf1sjnt3T+jFjnEwXuAIgfuqPTWnfczu0T9xhabvq91YaOoaGD81jon/vqFh9K6jjZT3WY7mscI /ejy9u5WSfT/AC/6LFzs4SOMxlGRBN8PCTrtxS4v6rX6eQLHN7zr/r8kfOEGp3g9v5VGrEvoynl1 T2tOoJaQNC7up9Q0qDuIMoH5mkP5s+Dq4X8xHxVamRnZAHemfmD/AOZKxgGa3DwKAwD9qEH8+pw/ Fii6ybZ2xnxDbv1o+SpCfQonwcPuKuv1x/kqlTC7ErjVzXP/ABceEAaGvdWQan+7+1q7d10HjT+K De1xsfLnNYBJ2x4K8/Dyaneo+stZ+8s/NbUHl74OkgF0EnThPhOMtYyEh4S9P+FwcSeTNZo9bsaR E5f4Ilwx4mIJMNrBYyNXOYNfuTNNYLW07Hv7uc0hJvqPgkOrrA02vmU7XWENZVvazu5wBUlGxofD SXF+j/NRnwcEf67rAxINEV+kOKHBE+v+fyY45J5Z/wCqgxitkOdtssnTa8hSc10F9xc0TIYHA/gm 3srlrPfZOpc37/5SRbWwudaWOeR9GDz8v/IpulV6dN9YjHH+/L5sk15skE8RJ+XTJLNMXHTFjlww wY/67L9NbM7q644gE/8AkkwJdDKhDeC4s5+5MG+pDrNja40AdCcepYGiprmMGkh3b5p2p/eN/wB6 WSf93/NY1lACvTER/wBnHBjPq+aUpcWfMx3VV7QzY986kghOWtZL7C175kAPIKcuNYcyr1C6dSQH JO2VkutcHPcNA5ibQH7o4fCIxY/8eX6ya+yTfqPH2M5Z8w/6lCEcOL1NXN9R7wXggOaS0Tu8FY6U 3dQ8d9I+9yBkFznse7bq0wGiOCPFWej/AM0/5flcnSNxuyb1suBzQrm5igKqNR+WPDDb1IMQRlO/ q/xWnk/zDvgVQq/pjv6v8Vfyf5h3wKEtwww+QoMD+js/rO/K5Sz/AOad8FHA/o1f9Z35XKWf/NO+ CH6Sf8n9E1QhrR/ICF/2pHwKMzgf1QoUgOzWg8Efxah3X9h4tm1np0F5+k4E/KFj0tsewVt0HJId HPkt/MZ6kVjTf7fvCxbvUpsdje3dPu0ka6/6+xCMhR4iRfQby/q+pvcnCX3gcEQeGEvVK+GHy+uX Aou9IelVuc49w4FIN9IerbvLjpwCoxVQ0zsdYPj/AOZJMq3n1bQ3aeIcpNbA04x8sL/V4R3lwx+Z 0aiIkkkY5H15DH9dzUv3cfuT+RQa+077DDW/vM5CZz22H0qtgaeDBGqkXWWkCtrg0aEteCpPd6Lf TZ6m7sYBQoUTrw/p5CJcWT+rDjkmyJRFD3P8nhjKAx4B/nMntRn6v02M10N9oaXnR215T11OANtm 6RxDgdP9f5SZrWt/S3O+lyHM7qH8+6f0cN+LZCV0RoL/AMniHBH/AA58PEmrEqka/wAtzEhllxf6 rFx+3/cZH1Mh8e9tZ8hH8E9lmwCquZ4Ms/1/6lJ72t/RUhvu7tfCdjBj1mx7Xbu4Dgf/ACKI4iSB Kz/lcvr9P9WCwmERGUogRH8xy/6sSmf85k9U5OQdST5p6/pJNHscfh+VExmgvTnlybJPdmeFLF/m /i7RQfo0/BFxv5pnz/KUlP8A/9Hm/Y4cscB3PsAP9X85S2ujRhc3vtftZ8kznCZc5mvewS8f2Ui1 pO4sZJ/Oc7n+qxRaa9/5f7b/AJ70pvTeul3+Hq5b/wAb/wDC15MamwNA7iGj/wAk1NvBEB7XNPYt 2s+bk8OHuLXiOHudJH9hIuPJc7+tYPb/AGW/vI6/7/ENP8KUP+7ggAHajr04Zer/AAI5PV/h48iw hwgNY6PpBh2D+04/SUR7L63CO7NDIUtzXj6bLI/fG0Nn/qlC0H0y/wBoDXAyzj+Um6f71f8Ac/8A qxrc9EnETqOCQlR4v+jPg/8ASOP/AA/nT2AsvrsHBcAf7Xt/irEQPFDePUp84kfFHqiwR+8AQm9H O/S80VZOy5s8EP8A7/8AqVM1kjQSDwnbVsth3+EBbp96JjkmuDyND8kCodkJE0Rwa3/gf/OkgN0f P8ilt99rO7myPi3/AHolYaWb/EapKGzl53vurM8NE/H85VrhpKs5EbiRqNx18ihFu5rh5KQbNeRs krYh9rmngaiRLB4lysS1xA3MsI4BG0D5qti/SGhMkgBvjz/BWS+fabfUj8zbA/tfyUj49f5fpSj/ ANDK7Pw+XFgjW8DIadP8XHPh/wDDcCtu4xta89m1ugDzcn1HtIsZGgZWd0fEpjB9rvTM8V16Sf6y fbt5aah+7W6Xn/ySVfy/lH/1L/1NtE7A/Sz/ANGMsn/Qwf8AVVb3MgF5rPZm0FxH9ZMYA5rrb8Pf Hm1PLmtkbqWd3H3En/vqW6NQY8bLRr8GJX0J+3/0KX/c4lAdQBv0Ed/Hgxzj/wA/mMizWgasa2sH h5frHi391TAcffW1897HEGB47fzlAQ4kjZa7857ht/BOG7nfQFru+x0NH8lIdK+nD+z24T/8b/8A DEk7iX+FxX/zvey4/wDx7g/2S30tQXvP7z2y0eaHe5rgD6ge4EQA2IB80Z4I0ebRP5jDIA8EO55N bg6wt7istg6H2yldb/j/AOhTj/zuNizw48UwBdxlw8I4v8XgxZPT/s/ax/6xjUYcju5BQSIeHdna hGd9GUnn1q/ox4aKBgB3iCD9/tU2aEjz/KougF48Wz9ySmTtWJmTLSe7QpDVigwQG/E/iUlLv+kE 1wlg+Kv4/SMrKIdHp1/vO/761atOJgYIkj1LB+c7X7v3UrUBbhYmF1fd61GOQwACTtZMDmHua5yt 2Z9+RS2o17HVgtedZJn8/cV0OHg9S6q/bjM21Aw612jB810GH9Sun1N3ZD322OgviA0x/Jc16q5u V9wicR6r6tmE4iROUk39S8f9SKsE52UzqVHrNLA+kkcFp2v2n+VvXeVNxmAfZemjXglv8SFewum4 WDP2WkVlwhzuXEf1ne5WpPgrGPHIRAlLbsFhyQv5OLtxS6f3YueHdVdoyqulvy/J7li/WX6o5f1g bSb8itr8cu2c8P2z7tv8j91dSQE3tT/bj1JP1WnJYoRjHyGv2vCYH+La/HJF19bmkRoS4/c6ti0D 9SMmsRj521o+i0sIA8vpuXV7h5pb/AIRwY4kkDU7qllmYiJ2GzyDvqv9YavoZdTx8XA/9SgnpX1r rMemy0eIez/v5au0JJ5TgT2hOMAts9XhXV/WGsxZ05z+8taHf9Sg25N9emV017QexY4fwXoIAS08 EOAK4vB83HUum8uxyzxITC7oT7BbDmPAIDvIr0ayqmwRZW144hwB0+arWdH6Rd9PEpJPJDGg/wCc Ah7YTxnufteG29Jeza3ILRHdcg/qvpZtgqJNLHkVT4T9P+2vXbPqn9X3g7sRomfolzef6jguT6h/ ivrteTi5LWjtvBafIOLfUa7+tsUeXDY4dwd1HJI7knzcJ/VcjMxmjGqtsIEWuALmz/J2N9vtWN67 t723NBLZ2h4mDP0V0n2bK6FZ9iyBsFQ0cD7SP9IHafSQW/s3qOULjLCNNzdC/tqIVcY8fKjiuvpx H/FZcGXhyRkQfSdaNWOziFjXOD7jXEaNBIU6y+0NDWbK+5a9aPVcHCofvrc5zm6FlgB/g1yywHXN BIrbWD20U+HNjzAmAOu4I4ckv78/1nDB2MPMxmBUgDGtJGXBi+b+bxcWL3J/1024tBZQ18zq7Qif xakSyoy9znWEaAif9f8AOQ2ujfXRXp++16KNtJn9I57h5EKSjv0GnFUvbx/3I/q+ObYEomxXqlrw XD382kdcs/13t4/6rHV22y97Y/dLdf4OTa2gtYK2sB7EhS1ID73kCfouZomLzduY1zAweII/Kmmt j+l+iSDlyen9L1z4Irxe42h+mBKPLYPV/k+HHj93IvowllDJJGrmvTgeltfZ6hedIkOTS1hDaWMe 8j6Qd/r/ANWkKm1j1LWOL50h0/xTtelensKw4v0v0cfrktJFeq/X0keLmeY04P0836uDWyDa57XW Tw4DcI09qn0681VkATPj81HJdY6xrnhzQQ7aHf2VHD+gjuNyfGXzFwefuPNZKEY/Lpjrgj6I+n0s 22bMsmJln8VZtynvrLYABCpu/pJ/qfxRnfRSpqiRAq2WNkOZSxoAMOdqfi5PlZD31kEAaINP823+ sfyuT3/QKVC1cUqq24zLAIDm6AASCjYGy3NkH6LCY78tVD875K10j+n/ANg/lCZIaE+DLimTOIOu rrXfz1f9ZZfULdmTYG797oIgAjQBad38/X/WWXmVsbk23Oa4kEatPaP7Kbi4r9Ommsv3Y/pF1OW4 PclxjiH6MNPXP08EfU12tiLr3HwhzFFzje7aHM2t4kESE4FlzzJsYw+KezI2gMreZGhLm/7P++px I4TZMcd9f5zMevz5HRiJGY4QJZq04R+p5WP6P83hl6v0fnU57KwGVNYS7QkOj/X/AD09dIqb6tjT uHg7/cmaxlTSXurc46gEf6/9SmYx2Q/eWMLRoYJCOtj0gz/Qxjh4cY/elwxmjThlUjHF/lc0uPjz S/ch7k8XzfIoNsvfr6jaz938E9t+2K63OkaGWg/6/wCak9xH6GljhGoLXKTWihvqO9QE8jQhEXqB I/63L6tP6sf5tB4TwylAEf8Agfl/Rcv6+T+f+ZYNrqbL3MLjq3c3X/ySE4G1r7SGQ0EmCQdB4KTd 95lzztGrdzJEfL2psq9opcystLS2D7SP/MU30kAmo4x8sTXFkl/jzVP3IDJRM85jI5JjiEMMK6cO PH8zn1iWvCnifTP+vimpHtJU8Maz5qR5Zlewt3eHY9lPHEMYPKfv1Sy/5o/L8qen6LP6oQU//9Ln N4B/nQ0/1dzv7R/eT7Y/NrB8AZf/AGf5SW9xMeoyT+YwTP8AJ3/yktpGhYxvi1hl/wAlFv4/y/6p w/8Ajb0m3YE/4N/83Bx/+Pf38atgadxrcw9n7tzv81Nu2677Gedokf2WpbQz3Fjqp03g7nH+TCcO A1D3M/lWiZ/qJbeH/N/9UJ3/AK3T/OfT/wAF/wCL6/8AZK3b9d7LI/OsG0f2Wp21+puG1pDgWl7T DR/JDU24v13MtjTfYNsf2U7WkuDhWHlvDmGGj+qlv43/AIX/AKu/l/lGPLEHHKJoaEVpD/4G4f8A Eh/sU+MS/Ga48j2u+KnjGIH7pLf/ACP/AEU2JAstrPBMgeRTmv07XAd4cP8AqSmd3HGw8NE2RoGv 42kEny7pqvba9vnP36qdgDqiPEITXH1GPP57dY8R/vQ6LurJ/tvY7sdD81Xst2g0t7Eg/AHRGzHB jA/uDLR5hUnOJvc48u1Toi2PJKrA6o7Ro74T9yapstcfKAUR41HnynrksE8905hadYDZ0MB3bmFb Nhbo601j9zbqB/WVdwhz28Tr/D+CPW87QW2FgI1dYASSf3f3kb8a/l/fxf8ATdL4aQROJF0RIaXv 6euPP/6TX1jQ1VtPiIdHwSFZia6gxp1Fhd28W/upCXklmy0/nWPEfgm9NpP80LXdyx0NHkhV9L7f +g+jL/41/juldWLo/pD5f8eMsnL/APj/AP4Uu0azWywu7Pd2nv8Aykwe0nSx1ruwLfZ/aak6Adtn qAkaVsMgBOXkCHXGpvZhb7oS202rf9H/ALrFH/wzjmqro1d6A+qfp8JRhnnOP+x9rEs50wHvZYfz awNJP8pO5hiHta0fuMMOJSaTEsNTWHQPIgmEmsA1qpD44fu0kdxKVX43/en/AOrZT/5mNViP9Wj3 hj4T/jYMeP8A8dzJGshntY6mvlzgZP3IckAhrngH6VlgkQk0tY73NtseInuAfiFN7mn+dudOh2Bs fI/moXw9a+sYcP8A6S4f7uNeY+4NuInwlk4//dic/wC/mnDGjb7qR5fwU+WKNZ3McDpqePPVWqca luN62Rbskwytolzif+pTZ5YQAMjvt1t5qUCJSj1iTE/RqsPv+IBKc6WDz0/itzD6f0t+M57mPufW 3c9wJho8TsVOjK6bi5oFlYc1x9lh12H+qfaocfOY8kzACQrrIelXAd0WB0vKyWB2302H852n+a38 5a1HTcHBG53vs53O118h+ajHJsusFGIw2WO0AaCSfuW50v6l33EXdWfsbyKGGXH+u76LVZolVAbu LT9t6jd9nwanPcfDgDiXO+i1dH0v6mUUlt/U3+vaNfSafYP65+k9dHi4WLh1CrGrbUwdmjnzcfzk ZOjHugy7MKmMrYGVNFbG6Na0QAPJTEeMpjxooEuKdaALSEhR3+ATBp7qW0JJ0DGCeUi2FPQJtyVl VsYPgnBI7J/mn1KV2q1p8kpPZIgpBviUEaKg+KRb4lPEJiT4IqVsCWwcpS5Rc4jvr4JWrXuzMRqg vbPCiS8nUrL6j12rGBqxyLbuCfzWn+V+8gSB1TRc76+YpyOjCmprXZFljWsceWiHOed37vt2OXC/ sDJxKvUrywbmiQzaWiR+7Zu/74t/P6lZZYX2vNlh7n8jVUxMTP6pf6WLWbX8kcNaPGx/0WqKcRkO otcHn7GdSyazk2Mssa4ndaQXCe+56r01PLC120Vsdru8T23LvcB/2ih+HcC2xmgaRBDm+1zVg2dO rx7bq3Nlljpc0qKGIQPh+78rYwZ+DJGcRRj2+aj81f1nFOu6uitp/ltdr96doZj7TseXuHYz+RWc rDdSCceoOa7QmYIVVtddIa+xj958DOv9nap/HTT9Ij9Xi/u/q/mdbHljOHpkeGX+TEr5jNLh1939 d6I/4KRsvaX22PY0H6JCc2vtca67GhkfnCNO/ZBG98ue99bB2IMR8UX7SXkV0vHHLhH8E26G5ANd f1uX/wAc9MWwPUfljKcb/R/o3L6Rl/mJcc/8NeWVNa1grsf46JCgAOsurHiAD/r/ANUlFdNevp2P nySbQ6x5fbWACOGn/alw2QOESPSFXjx+M5cGT1J4xESlxmESTxZSeHNnqXFw4o+7h4If4KHILrHs 9rmja7aDJmNvCFhfRPkjWOabag1jmNaHAT8kLE5s/rJw234vH+XC8/8AEBXNZBw8Hy1Eni04I7+q f/TU7+kn+p/FGd9FBd/ST/U/ijO+ik1WFP8ANt/rH8rkr/oFKn+bb/WP5XJZH0CkpL3Vro4nOJ8G E/i1V6KLbrHNraXHv4DTutDpmL6OU8uMv2gacan/AMxTZkUR4M2CBM4mtL3blwm+vyMrIyqDbm2O cz2TEgrZeAchoPgT9yxM1zrMiytleocZcCoo8P6QMq2iB85/d+Wbsclx+5PgIhYIlMnh9uP7/wDO YkdjyB6VTbGlvh/q5TaW0Dc+x+5wmCO/+v8ALSArxmhxa8E86gx/31DYHWkufY8NbqJGkf8AUqaz GQ290/LH5Y4o/wDjTc4YygdxgB9c6458xk+zmPTxqYXXnc+xsM7OA4/1/lKVrxPpVtrcHeGn8Qnt yJhldjYOhJH+rU7KxUyXitx5Hb8oQAu4xlxf53L83+CPVlUTXDOcOD/McuBwa/vy9HL/AKSzaRSw WOrBe3wcVEMdfZLm2NYeNf8AySZtbr3h5rGw87TCna4Vt9Ktr2nsQf8AzpKo8NkcOGOwrXKen+T/ AEk3IT4RLj5mfzS4rjy8f0o/z8/kWtv2AVsc8OGmoBn7/ch3sDMZ7y8Oc8aS2D/5JFqArHq2PeCd DIP4/SVbNuc+tzQ8OZIgRHdHi1Epn1H5IX8n9avc/wC5Yc8SMGaOEVCEJnLm4f52VfLxez+//rGq z+ad8/yIuGOUNoiknxB/uRsQe3/XxTnml8wxXHiY/iiMEHTwQswEtaByXaIzOSgp/9PnYcQWxWQe a69CUizZE1Godiw7nymc2BD6vTaePTgu+/8AdTDY2SN1H8pwJLgoj49P3tP/AEpD/wBSYnpRrtqD +56h/wCM5Jxn/wCE51wWskgvpPG94kn5J2vmSyxr45db2/qJNdya7AY5db2/qJ4e7Xa3II/O0AH8 n+UkPD/m6/Z7cv8Ao4lSoXxeF8dR/wAb3YQ/8c5j/qaoe/Xa28jTfMAfyYTOYJIfW4u/dZ9BM5jZ iyol37tY9qbdW3QvdTH+CbMj+0ka14q/wq/H3I/9LJkVG9OC/DgEv+b7OSfp/uYcWP8Artil2y+s kbA5u0g+StZDfc0+MtPz/wByohx2B4O7Y4ESfdB096v3Q6ncNYhw+Wqad3Gyx4Z5I9jbKs7q0A+1 knQVv5Pgf/OkWg8hVMi3cbGM1Dh+RABZKQABWusNpJ7dh5IH7hA0+ifkp1mWqDvokd2kEfNPa5Nm yzf9GfBNVALgOx/L7lLlqgw+7nkfk5SUiuEW+RCnSZaGAh7xIDHjQBNkj6LvA/l0T1hwDmnbsMOc Dyf6v+ai2/h8uHPX7wI/7r+X83/tGbwXEeo1lhGjWMMEeKTmwJex1LOIYZJP8pJrTHspNY7vn3Ad +VFpq3TWbHP7POoE+KBrr1/53+PCOTI7QvYXUex+T/wrLkw4f8TJkZAho9jn0t/Oc9syUmuBMVvb Y+Pc+wHQfyUxe2ZfcLD2YR7SfNSeLYi30wzksBglHy6dv0f8ScseP/FWmv0v0v3hXH/4bihnz/8A hkMa0FzpeG32HSGmIATPZoDcwtHAZXEf2k4Y4thtHpt7uB90eX5yiw1DWkWF5/PImED49e4+b/Hh 7mX/AB1wJ14f0dPSfk/d9WLLLDg/wMfuLzDdC/HrHiDqVOu3XZTYD3L7OfvUC9jTuN/qOH0Wke2f NSeLTpc6sM5LJhIeHT90/L/hQnwYv8RGgq9j++Pn/e9GXF7ueX9/KjyHOAs93qEgat4VM3W2Mbyd pIAWtRhnJa57m+iwNhsHk87kz+khmLuLv00zpx/Vao5w4iDvp4/936nE5kRGfINvUTpw/per/Jfq /wDFZ9CxXZjXG+19VX0YaYLvv3e1WMr6tPty66sUuua8xtiXE/ydoCpYeX9jc2qYP53aP5K3x1eh 2E5wdWNsN9M/TM/nDRVM+WOIgRxGZO5vhpjjZ6vffV7o7OmdPqY6pleVt/TPGpn93fr/AOQWp5yv L/q79b+o4nUWY7hZldPeQ2xgBeagT/O1/uN/kL0yu7Hs+g9r/wCqQfyK/hmJwBojwLHLQpAZEpi5 PLeJCiWnsnlQpUz3UhKgWwkCkmuyRMQO5Udzo0UC4nsUd0AJQAngIYeR5J5cUFUuSE24p9oSLSjo rRYvgSmFzfNIgHQ8IRaQYRoUpsB4KW4IMGJJXNZH11xn5LqMANtZWYde+dpI59JrS3c3/hNyhy5o 4o8UzQUBez1Js7BByMnHxqjbe8MYO5/IP3ly+T9csjH9/p1WNjVo3NP+duesq7r37Sb9qfZvPG3g M/kbPzUzFzWPKLgT5EcKeA26/VOv25AdXTNNHB/fcP5R/NaufuyyTsYotGVm3Cqljnvcfa1oJJXW 9E+qNONGR1AC27ltPLGn+X/pXf8AgaeAZL6Ed93D6L9VcvqbxkZO6jEP5x+m/wD4pp/N/wCE/wDP i7jB6fiYFAoxaxWwcxyT+8935zlY0CRnspQAGMkl4/6zYLsDqTOo0CKsg++O1g+l/wBuNVDqWPXe 2vKadrHfTcNY8dF2vU8GvqODbiv0LxLCezxqx3+cuM6eXA29OyRte0kbT2cDBCjmKNqiSHLy8K/E s2Wga6tcNWuH7zHLJyenVl5vq3bhqWA/9Su4wWU5WPZ0zMbudR/N+O381zT/AMGsXqfSL8F+/wCn QT7bR/1Ng/NQIqjuN2zizTgSYS4JEVKtpx/deRLn3Oe31DWxvIcI+RhS9b0w1lLmOdwTEa/L2rUy 8Y3NOxwrs8xIP9ZZj6/swDXsY+z5A+XKIJ1Nm69WQ8Xf5YR4p/8ARdPDmx5QBwgUajy44N+H+cyT MMfp/wCqMmV7A59zGOdyBMf+YpbHXuaTUWMiNDH/AFSE2hz7C+2qAdfae/wlS9dpiqoWMg6xP5JT ZRAGo4YdIf5TKb/rY25jySMtJCeUAXls+zy8TH5QMeb/ALhaz023VsYHDbund5whYvNn9Yo1jGst rAeXO1JB+CDi/Ss/rFOF1qAPCOw/xXB+I195mQZSsRPFPi4peiPq9anf0k/1P4ozvooLv6Sf6n8U Z30Umoiq/M/tflUsj6BUauGf2vyqV/CSnb6P/RrP65/6lqJi/wBLt+A/KVDpH9Gs/rn8jVPEH61c fANH37lBLeToYvkxJnf0lvwKx8nZVdZZ6bi5zne4HxPxWu7+lN+BWJZUH5Fz7N7QHuII4ie2idjJ v0gGVekmvR/W9Td5QRJmZyMYD5ox4uLJxfoeiUWFdZscXWGxoGrZk/8AST25PAqtPgSR/GE1uRJD arSBwSR/36NyJW0VAk2MLjqJ/wDJfSTx1hjl/tMt/Zw8ORvS04cmaFnbDy9f4MuL3MEv7yzGNqaS X1l3IkAf9JQDbMhwea2lvBIMfkKUW5Dg4sY5o0mY/juU7dtQ2NpPuHIP8fpJUJRujHDHbSXrP6Pz QyIuUJ0CJ81P5qMKwx/TiODJg9X6SrC2oemypw3d2n+6VGmtrR6lnqMcOf8AWNyamlkepYLGEf69 huSsv3vAZY5oPlH/AFPuQJArJMAf5rH6f8Y/zS4Rkbw4zI/+KM/6w8X9WP8AuiPyrPu9R+1tpa0+ Ij/qVDO214vp72uO4SAAD84VhkU1lotYXdp/2HcqOa572B7tsF0S2PBOBMTcvVknv14I/pf5SbV5 ypctlEKhgxjTSMTlyfoH+ZxzRvb+qtd8vxRcQQxNcAMRoHePx1U8b+bHy/InPOo8k/pah/K/iFYZ 3QLgHX1jwkozOCgp/9TnPY3VrnUTyXCS5SaXGXVvDxwX2Tof5KQFjtWBt/8AwjgNP5MJniXRbUbH j9yQ0BR0RqBQ6fNEfTg48f8A4XB6SxI0TxHqLxzl/hDL7Wb/AMOyw/2ave4yWDIP7wMNH8lM4MmL a3B37lcbY8dEnGoSHudT/wAE1Oww39HcK6zMboLkNCaJ4u/yS/xhPgn/AOGzXagWAYjaJrLD/Elj 93H/AOEYv+qLSxunqGhv+jgypAvAmqxgZ++/6R8d0pNFx1ra2wf6V3J/78ouALpfSbbO7hO3yR1A vbsfXH/FlHj/APGoLdJGjUu8bxT/AMeGT2pf4XMZfc/1aWpjn+ozbO9p/Sg6Fw1borDbSMQEjU+1 VBayt4ducx7eKvzR2/qp5O4tPHIHxTSATv8Ay/l+/wCtzOfBhkEqI4470QNP3f0Zf9S/Vf5tRts3 AFxiIj4JnaOBTP0Mp3/RkcoueTbGrSW+BITkHc4D84JgYtOs7gCPyKTtHNPn+XRJSqzLFDhw07x8 ipV6Fw81GwASfn92qSl7xNZ8UzwwFh2GwRAAOviPoqbtWfJDBmppB2bSBPh+Yl/Lp/3TLy8+DNjl dVIdZR06/J61yav8La+eSzXT+Sp7rXCTc1jTxxMJMN3FO2wDmw6GfvTObtd+kq9W06ktmEdavUDr 88Qf8OEp+5/gO8eEnh0lIfKD7U5R/wCpZYYvZ/6p+sXaLf8ABVMjgP01UNtTNPQc94+lExKT21xN wdUD9FjePyJ2ODmxVYaqx+9Gp/klDQmtz0B4JS+mOcYe3/hrhYHFqI/pEe7CB/vZsU8nvS/2XoWf 6X+GseHc7PCVIPseJFwYw/RBjdCTHPB21Obe7kudyB96T2uB33sFrzo0NnQJC9SLA61xAf4WXHKX H/gINaA0T+iJe3KX/U+XzQh7f9/LJdpsn9CxjgNPU0ElEx8VllwY+uXfSe4E7QD4IbajcWsNbqmn gN7k+Iha2NjV49fp1/Fzu5KR6aX24v8Aucc4cX+E1ea5kYYERPDkkKqHzf3smbHk4Jf7OCRrWsaA BDGiAPgrnRunHqGR69o/VqTweHu/d/8AJKtjY1mfkjGq0aNbH9g0LqHPx+mYIDRDGDaxncn/AMyT ojqXFJ18S+f/AFsqsb17J0Ikt2jtt2M2bVHo/SM3qLttcNaOXuMD/wAl/wBFafVsQ59jsp5/T8kn iPD+yifVzIFL2NGgaYhQSx8RN7bsgPCAa1Z4fr9HrOO5rXOeS5zhrP5v5wa7srQ6zXMWVD8i07cP Cu6rjszK/Ux7XgFu4t+mNrTuYWfRetuz6k9CsPsZZR/xb/8A0r6qkhAcOnRaTZsvN09erafZZZWf 5LyP4q7V9Y7h9DMd/bDXf9UFbu/xfYjnF1OW9k/vsD/+pdUqFn+L7qDZ9HIqeO24uaf+psTuE9Cj Rv1/WPLP+Fqs/rAg/wDRc1W6vrFcD7qWvHi18fgWrmLfqf8AWCmdtPqAfnMe0/8ARLmv/wCiqlnT OvY30se9uvOx0f5zQWpepP1e7Z9Y8c/zlNjfMAOH/VIreudNdzaWHwc1w/76vOhndQqMFxBHY6fl RGddzG/SEjvISEpDsjhfR29RwH/RyKyfDcJ+5YmT9dcYZLsfA22isw+5x9kjtW1sb/6+5ch1DrWR b0+8VVe4tI9Ro+jPt5XK42bbVABiFBzE8hjWM8Ej+kkAPqOT9dcnHh5ZVawfSaNzSfg7c/8A6ha3 S/rJ07qeL9oqvbXBLX1WENe1w/N2/nLyfJ6ll5sWXO3EANBgAQNBwtP6ldV/ZXUrnPYHsvr27Xcb gd7H/wBlu5qh5XJmiKyy4/PWmQ4zpQ3fTD1HHeP0XqXHwYxx/FwaxTbfmOj0sN8dza5rP+p9Vc7d 9dLyD6QawDwEoDPrbkva71HOPh+arZyHsSkYCTUpRj5l6HqmH1TOwMnE9WrEbfW5gcCXOEj9/wBj f5LvYvGaMjIx7DW6WuYYI8wu+t6/kv1a0kHg6n8gXJ5nTXvy7bdu2xz3F9bxBEu3d/o+1QZfUPUF 0sMY1U+K96CS3KzM5vr3EumG7ogaDyT9BxnWZ7qHGGWtJ+Ylyu4PROsWYLsmvG/V2/SsJaBxBcBu 3P8A7Cn06jIpyzfSx1jmNIcWtLueYH0va1QYMc4y0jUemlM8o4jGNS1/SrWu71fSMpvSqyyvFZY9 2j7Q6Hkf2g//ADWrWZ9ZMY/ztNtZ8QA4fg7d/wBFciOrvaP0tYHxlp/6SKzq1BElpHwMq4Mkx0Yz y2M7ZB/haPYM650qzT1w0ns8Ob+Lm7UavKx7DFNzLP6rg7/qSuNGfiO5ft/rBTDsWzhzD+CPv9wt +6T/AESJeRe2EzK5T624JxsurqlGgsIbaB+8OH/22f8AULPb1G2l7m13W17SR7XmND8US/qmRlUP x77zZW8QQ9oJ01ad0bvanHJEhhOOYOy78pnq0ZtBDrR9Osclv54/tNWs3Nwb3egXtcXiPTeIny2v +kvO8fqww82ymxxLGWua5zeSA7bLUupdXGQ53pFxYD+jLvpfyeFR+9545eH24+39eL/GSI2PF6jq 31fdSHX4YL6Rq6vlzf6v77FgXY2PeWjIZvA4IkH8F0/1O6zb1TpzhkEuycZ2x7j+cDrW8/ykXq3Q GZG6/EAZdy6v81x/745XTESjY2I2XwySjIESMJjacTwyDyfUsTpbccejvreRp7yZ/suJWM22uuot rtO/wcJ/gtvJxASar2GWmCDo4FZdnTzjPc4BttbtW7omf3VDy+PJjkR7hnxWBKZlKUG1y/MS4448 pM8ZPFwen1S/R9WTia36U2VvseHhwO2Ph8AoYv0rP6xRHOe66suq9MagT30Q8X6Vn9YqfStCSO5v X/Ga/P394lxAR+X0x4eGI4dI/q/Qp39JP9T+KM76CC/+kn+p/FGd9BJqo6uGf2vyp7+E1XDP7X5U 9/EJKdzpH9Ff/XP5GqeH/Sb/AOx/39R6V/RHf1j+QKWEP1i8/wBX/vyglvJ0Mfy4vL9iR39KHwKx cm8m0trt26kGRAGv70LZM/age0FZPpur3vc1jjJI7HU/vJ+MTNiJ4RXqkOLSv7jc5SWOMpSmBKV1 jgeCpSl/tIyj6WNbDS0kvYSdQTp/0kOLsghxraQDqQY/GUxFl7w806dyNJ/tIj3UUAsDHtLhyD/3 6U7SQ/cwR78Xr/d/nISbw4oS0Ayc1k/dEP1UflmP1OXGqw10t2iojdpIMf8ASQ6amEF9m9hbrPl8 YSpY159R1jgR3On/AEyp23ncBVaNdDI/79CFxNZJgCA/m8Y9v/12uAnG8OMyOQ/z+Y+8Pl/R9Uc3 6LG7I3OAqtIB5kQP86NyLWDUwzYwk8Tp/wBJKml9YJcGOPIPf/OhBebL3fzQO06kfk3p1zj65gnJ L5IfrPT+9++sAxzHtYzEYMf85k/U3kP6HzRxf4yv02Q4OLGODTBIMfx3IPU2NY2trWbZkyNZVo+j QJNbmlwiQf8Av25Z2U7c5pknU/S18O6QqB4ZerLP5j1j/jQjJr8+ZT5TJOA4OXx8Mccdoz4p6/Jl yY/SzyP6NX8vyIuOIZHghZkBjGjgcfJGq+gi88hf/S2/D/ySsN+jKrgzlOHg2PyKwNGJKf/V5txo mLQ5ru9bOAn0DYbd6TOzPzh/W/ORSMkaM2tZ2eeSPE8oYOv8x6jjy88E+OoUVVqRV/1ZxJ/wsXrn /wAzG9LxXoCDw9BPHkjH/Bz/AKvH/wCO5mTPX2/otpb2sdyVHUuk0+q/u/8ANPw/NUHfZQZs3F3d jeAf3VKJbIv9NnLW9wPvSu9Lvh6cUJV/g5fRD/pq4a1IMeL9IwyY+L/DwS9zL/43iWf9nn9LuDu9 beAn/N0u9Jn5rPzh+O5TZ9piK9pb2sPJ/lKJ0cd1Jts/Od2n7kqrWqvrwzh/zsfqyf8ApNXFfpB4 uHoJ48nD/wBTzx4MP+Fx5mTPXIiraWHix3JT2s2GszO4anzQnDHmbpa/vU3gfgiOcx2OzYIa2YB5 iZ1SvYXt04uKv8D9D/ptH4ji/VDJwkUfm4OHi4v9bxfrf8CHtLWCQk3Vqc6tUa+I8EnJYn8w/JTs Es0UXj2u0kggqQ1akpiCPUkcOAKd41H3FRPDD4Etj/X4Kb/oz4JKVXqyCZI0PxQ2iWWM58B8lOvQ uEQJ/LqmbpcR+8PyJKWOx7Q61pprj27e5PySY6syyhxr7uc5JktE7w9zSWtpPx2tRCMh7YtY0VjV zRyQNfFLhN2Br3EfV9cmP+aehhkEscSZDhIBozqF/wBXBnjxZ5f4ft+4xBLXeywX2HgHj8qd7biN 17WuYNQwcyobmQRVQ4Tpv1JH5UoxGO3F7nOB/H7kOIVViv73Dj/8dj+tZOA3fDLi/wBnGeb/ABuX nwcvH/nr/TEeiamfnPGhj7lFrsZh/RF286Nd8UVjLbHsFt+1r/3fD/oreOJ02rEF1YcfcG+p+bu5 2+32qHNzOPHOMZCXEaqXBEmN/wByUeD/AKbXy83jxXC+P97HinPg/wCqyzRl7nF+60cLGfS0vscX 2O4B4AVh29zm01AussMNA5kpPeKwXHnst76v9LNLPtuQP01g/Rg/mtP/AH5ysAX/ACtxcuWWSRnK rPYcI+kYtrp3T6um4kOI3Rvus8SP++tWPn5jsy/fxW3Stvl+9/aVrrPUPWf9lqP6Nh/SEfnOH5v9 lA6ZgPzbwzisa2O8B/5JyUpX6QqEf0jsG10Xpbckm7IaDS3QNIkOP/kGoH1jxxjZuPk1t2tsb6bg BABZ9H/oP/8AA11NdbK2NrYNrGiGgeAWV9ZcU3dNtIHupIub/Z+n/wCBl6cI0KROVm2reTdg13NJ 3M0JBg/euz6fkjLwqcjvYwF39Ye14/z1w/RbRkYb6DyRIXRfVLIJouw3c0u3t+DvpD+y9v8A00yG 5CDs7yeU6i4taJJhSIXlIuAEnRVMnqNGO2bHhoPE8n+oz6TlU9XqGXLqx9kx+91v0yP5Ff0Wf2kD KlU2s7LwqmRkbSD9FrgHE/1K/wA5ZF3R6OogvOHThY51NzmNbaR/Y27f7SV3Uuk9MJdV+tZX511h nX+sVzvU/rJlZZMv9vYDRqjMydAyxxHeXpHj/B3MjJ6B03FsxaKm372FljncEOG1wXmN/THC5/pA Pa1xA8SNNq7Pp31c6t1VwseDj45/wtoIkf8AB0/Sd/aVvrH1E9Gg5WFcbH1N3Wts0Lg33O2bPb9H /B2f9uIHFKQ1STAaR6d+ryWD9X+r5GK7JqxiMdmrrTAbodYn6X9laHQuhP6jnMxK3mv0wX23bZj2 7fo+3xauo+ployem5WA/wMD4jarH1OFdT87GLQLmPBLo1LdWxP8AJ2puPDESBVLLIitKHZbH+o/T mbTkXXXOHIBDGn+zDnf+CLTxfqz0PGO6rEbuiCXFzp+T3OatMtCdWaHZiMj0YVY9FIimtlY8GNDf +pWP9Y/q/hdRxrcn0wMyphcyxuhdtG7ZZ+9u+ittJAi0WRrbyv1PtGT03JwHmYmB5OCN9UKqa7M1 hH6xW8CTzsP5v+exZ3Q/8mfWa7COjHOdW2e4ndV/0Ni0qT9g+tbmRFeawgeE/wA43/qdqjGkh9i/ oa7W9DZRTb/O1tf/AFgD+VUrugdGvM2Ydc+LRtP/AIHtWgkpVgJGxLhXfU7o9h3M9Wo9g18j/Nfu VK36jtmacx3kLGAx/aaWrqkkOEdlwySHV4K/6k9YYXOqfVaSdNrnMOv9cbVSv6D9YMYEuxrH7edm 2zjXTYV6QeVF6ZKIXDJLu+FZ2FYL3XjVrzuee4J+lKTWV7RPbmPivSfrT9V6PTs6piH03A7sikDR wJh1jP3HfnPQW9I6VmfVb1qsSkZFM73hjd5g+7c8jf3VeWGR3K+GQDpduD9R86jAtyW3gtrv9MCz sCzfz/J/SLu5DgHMIIOoI1BC86rayoenAaAdCP4rX6V1y/AcKrZtxz+b3b51/wDkVNjPCBE9ESF+ oO91PpdGe2SPTvA9tg/6l/7zVyWdW/plk5I2lpHwdr+au4quoyqRdQ4PYe4/IVR67g4+Z097b2B+ yHNPwOv/AEUckBOJrqKWiVCnj+q9VxrqwxrmWjaDuaCIJH0fcPzVgY4Ae+O5ldJ1Hp2GcYmultbm cOYNvHjt+kudqAD3RoqnLYPYPACTGSZAGJl2YP8A6R/Y/ijO+ggv/pH9j+KM76CtsSOrhn9r8qlZ 9JvxH5U1XDPn+VPZ9JvxH5UlO50r+hu/rH8gUsL+eu+Lf4pul/0L+0U+CP0tx8wPwUEt5Ohj+XF5 fsSgA3uns2QsB+266fTcGk6luvz4W+3+ef8A1f4rGc/0qyG2guHG7VOhHiviNQFSlpE3W3zN/ksh gZcIvJL0R1nHh4vml+r4v+exLqKGuYx7g74T+X2qFLLLff62rdYOsfIp2MyLXCx4Y4dt0RH9lSvs 2TX6ILTxHH4BSbjjkDDFH5IVkhf7vySk29Yk4schlz5NcuTiw5eGvTkj+tjj4v7i911oOyssfu08 /ulNTSWgm2ppPIiCfu+ioU01bS61jmxrrMfh7k11zHEBj3tHB5iPvQM/8rkOp+THxf8Ac5IpGM68 vgBAH87mEJayj6o+vBkY2vba4AVEEaGOY/qwjNFGOJ3OaXDvP5IT1MFTZ9YEO1E8flQ3HIucWAtc 0HtEfj7kgDD1yjxZp/KBGMuH/wAKkomOX9VCXt8tj+eUpzhx/wDh+Of6f6DFu+55b6xA7ToT/Z+i gdSn1a2l24tbqeO6vmaa93pNJ/O2/wC5ZlxD8psM2Ax7fmnRHB6SbyS1l/OfL0+b0tD4nM5MBnEC OGEhCFeyfX+l/N+uLLM1dW3xn+CPXowKvl/ztY/15Vhv0B8EnDQNB+0WOHYR96sfmqtTrZbPj/er LvopKf/W52xuJ9Ivc8jsE5bbG197WAaACP8AzFFFloEtoFbfzjwY7/uqu77GHbWsc4nj/WVADEfu i/8AaYOL/u8j1M4yOtTlw/7DmuD/AKOHB/3aRpyuGMaB+8eT58oe6mSRS6yyTuPae/7ycsr/AMLk Fw8Af/OlPbmkQC1gHH+vuT6J0qRr/Z5jH6fLjYbjHW4RvreblYz/AML+czf4KNzcY/zj3NP7g7H9 3hTDbdo22iukj2zzCYPdOmPuf3fHJ7n6Kg77KCXWgmw/SYOAU2wNdB4+vD/jT/T/ALkF9SNRIlKt RGsXNf4UMX+T/wBrlSNNzf5pgs/4U9/xSLiXljxFhHujjyhMGhzQ5l3o1/msnUf9JO3eAG1w+oHV 55lO1qta6axnH/Bj/Of9Um1uahGWLJ8vFRvSeKdx9XDOcv1Mpen+ZxKZqxM3R5807dHOHn+VROjg g4bJwkkTG4EJqjLE7ux8Cos0e4c6z9+qSliNHiOCHSpjVqYgb4PDgQlUZbqkpiww8a8jj4f+dJ7N LGO84+/RMZDhEaHX4FPdOyRyNQkpYuqZY6WFzzBaR20/8xTurp5tyC74c/8Af05daHt9GCXiNfLV MXU1uiyrdcdXdwSdUCBVkCu8xKMP/G/52buchOUsMBEy4o2KxyhPLwx/238xjj/USD7XYNzXtDDw fL7lHc5h2spD3DT1AND+CiW0v99pNQ7M8vLROyT+jxXw0CXbvP5J3Eb3JJ29QyZJf3MWT+bZ+AAG 4xERveOWHDD/AGnMYf53/oMK8TJy81lTR6b36uI4A7vhbX7Ox8SwFttluwah5G3d+80NCl07HOHQ bbHbr7uCezUbDw7eo5QoZpW3W1/gFGMYMrI1v9Lf/muHzUgc0zEiQveN8P8Ag8fq4W30Pppzb/td 4/V6z7Gnhzv/ACLVrdY6h9nr9Co/prBqR+a3x/rORsi+jpmIAxsBo21Vjuf9fpLm7H2XWusf7nvM kqWRERTDGJkWWPRZfa2msS55gBdhg4deHjtqZqeXu7uPiqnRemDEq9Wwfp7BqD+aP3f/ACa00Iit TuV8z+iNgxL4H5EK0C1hY8AtcC0jxBUrBGqipGIno8l0l5ws9+PYf5t5YSdJg7d39r6S3umZDcPr LbC4CiyWPcSIAdqP/BGsXG9Q65Tb1rIurAFYdtbH52z2eof621W8jrdL8NpbbutcSHV7Ygdjv/OW bzHN5IZQMcBKN/Mb/wC5ZIxsPp1/UcaqoWmxord9F0zP9Tb9JUTdn5supb9mo733fSj+RX/5JcH9 VPrJTiZVteVULdwmhzvzXDtr+8tHqX1ly8skboZ2aNGq1HMZgGqPZdHEdyaHd3rs/pPTCXs/W8rv a8zqsDqX1ky8skbvb2A0aodO6B1bqxFgb6dB/wANbo2P5DPpPXVdM+q/TOnlr3D7TkD/AAtokD+p X9BqcMZO67ijH5RZ7l5bp31e6t1aLSPRx3f4a3QEf8HV9J66zpX1X6Z04ts2/aMkf4azWD/wbPo1 rXBSOikoRYpSkTqVAAcJOAc0tcJBEEKIcJU0gbQXhfq2T076xW4TtAXOq+4w1adE4H1vczivLaQf DUb2/wDgjdqzfrIw4H1mry2aNu2WT5j9G4f+B/8ATWl9aCa7sDqlQktLXaeRD2ph0KQ9Qmgykx7X sa9plrgCD4gpypQVrDdDvJEQn8qbTLQkkjQF4761MOH13Hzm6C0NJP8AKYfTd/0PSV76yktGF1Wr mtzXT8IeifXXF9XpbcgaOx7BJ/kv/Rn/AKfpIVBHUvqpHL6RH+b/AOYqKY1/FdA7fZ9r0jHNe0Oa Za4Ag+RUll/VvK+09Hon6VI9Fw/qe1v/AIHsWmpBssIo0pOmTpBCx4Qi5FQrWnkd+UJLo7rXVMyc eyh/0LWljvg4bVy/1Sef1zpd2hIMt8x7HrqGaLlshx6b9bm2cVZJD/lYNj//AAVj0wnTyTVFB03p 2LlDM6XlNh9Nm+p40e3d7HbP8xY3U+lZfS7Ntw30uP6O1o0P/kH/APBrps4fYfrPXYNK8xu0/F3H /gjVq2VU5FTqbmh7HCHNdqClVjyZIl4PA6jkYFnq0Olp+kw8OH8pdRRn4/U8O0VGLNhD6jyCR/0m rG6z9XbcEuycSbMblzeXMH8r99n8tZFN1lbxbU4se3wSEiEyje32N69odS4Ll7qfRyrABta+HtHg CP8AyS6jHsqurd6rtp7gD8VhdWdWLmwZj27v+pVePNYzlli1Eo6aj0/4zGYmnLf/AEj+x/FGf9BB f/SP7H8UZ/0FYWI6uGfP8qlZ9JvxH5U1X0W/P8qe36Tf6w/Kkp3emf0H5u/KpYH0rv638FHpv9AH mXflUsAa3H+X/AKCW8vN0ce2L+7+xlMW2+TFhMZ6tsvqIafCQFutG66xvG5sT8Ss/qWJl9Niq1w3 ctcfzh/IKdCMTZl8salVRPFX95u8llMTLHAj3c3ogSZw4R6rkPballmPW01s3NPi2Rr/AGio0VNd +k9aCOexH3qVdeQ94fYGuH8qOPLapX37ZqNWh4nj5QnkD+cyDghHTHHgnj/u/wA23QZD9Rgl7mSf qzZBkxZv9p/PRjxKuut3BtL2meIifnPtT002MBL2MceR4z9yHTVTtLrWObGpmY/BNfbW6BXY4Dg8 wlx1+tyS13hj4/8AuMkVHFf9GwxqI0y5va+avVH9bgktfY61201EOb8yisbj1Na9wc13aZn8E9FL qxvFoLT5afHlDsfk2OdW3a4d9sR/0kqlH9ZOPHln8g4YZP7p/Vq4oZD7GKYx4Mf85IZMuHf54/ro y/xWBLbbNvquDDxv11+9V72lua1hcXbS0SVoMaa69zqhvH7sSs/eLM8vA2z2+SMYCIuX85P1fpx9 H+E5/wAWzGeGMYfzMJiG+OfFk4Zerix+v1RWyNclo8B/erPDFVu1yvgP4K0foouI16ADvcO7+Ud/ 0UDFnZ8XfwR7PopKf//Xw3NvBl9oc4f4Md/Lsme/JLDNYawD3eMd+6ZjKZjHcTb2J4Hj2UnV3N9z 7N559Md/JQjiokcVdTCcckf8LJP/AKEHqZCFiMuC/wBGOXHLBk/6nhxemMP9bla7X4oP6OkuPedf /JJOrx/8JeXny1/8mivflQZrDa+T4x37oQtxW6V1Fx89f/JJHh68I7ccJYv8XHD51seOyY8ZPU4s sOYOn+czZf5r/ASenlkaPDWdvGPuTB9rTFdO5w5sI+l/KlRNWNzZdu+H+rlNrMotAY8CuPbPO383 snDivTiv+rOOaX/O/m2M8FWfb4f9Zjny2P8AxoevPJg91AcTkNJtP0gOB+73/dSDa7BLbPRr4DD3 8/pKRfbWdgr9R45sjmdVF7qyd2U0h/ZrfD7001rdf1uKJx6/6zPH55LxZArioj08E45vT/qeVn/N w/v+vGyn3gzo4JrB3TbmuaHMENB0BUnCQjfbXyecywMJygQQYkxo76KOrFEk+oDwHBSZq2FB2gBj 6Lon4pLWVmkGYg8pM0e4ec/fqneJYoz7w6I3BJS1sCSeBrp5aqbtWFM/kFKvVkEyRoT5pKYCXVM2 uLCCBu8PzEVpur9lJFxJlxPb/pIQE12M5iYCk30jDMVxFjuSZ4hLY2DR20lWT+7jj8knT+GyuGSB HFEHjqUOLCP6+bJH9ZCMeFntsJDslm+TDGtiZK1qOgmypttvp1sBDiwHUgfmu0WDkPux3s3P3Hnk 6fetXAzuqZONbXi0C7cA0vMDb3/Rue5rdyq81PmAeHEK/f8AcEcmSXnJXM82RPhxyAEP0sfHDH/1 PG3bPWuubRUJteQ1rRouowcOjpeEQSJHuts8T/r9BZv1V6dbVXZk5QHrTsbrMfnO/wCqTdY6h9os 9Co/oazqR+c7/wAi1WoE8AMhRLm7mmrnZj8y82O0aNK2+DVq9A6XujMuHtH8009yPz/7Ko9J6a7N v90ipmtjv++D+sutaGtaGtADWiABwAEoizZZD6Rwjc7qCdJMVJuxsQJmeEKwEhwaYkEA+CI935o+ ayOs9S+zs+z0n9M8e4j81v8A5JyBKHzHIosryHtd7XtJa4HxGisUVyPce2mvy8Fp9Q6Yywm6vQ/n Dx8dq2vqZ9X+k5+S9mc11xDdzGF20cz+Ztd/0lUliMtB9rPExibkDqLpwsLCJBImbYbWB4zpt/tL 07pX1T6bghtlw+1ZA/PsHtB/4Or6P+csXovSMVv1kNVsgYu99VfYuaW+nP8AU3b12pKlww4Y2eqz JKzpooRwmLUwcJU1NErNmABlT7JjASnwRJCjqwIE6J5KeJSDYKYm3mPr3jbsTHyxzU8scfJw3j/p VqVhHUfqk1/L6QP+itX6xYv2ro2VWBLms9Rvxr/Sf99WJ9S7Rfg5WA4zoY+ftSkEB3Pq7k/aej47 z9JjfTM/yPa3/obVpdlzn1QtdWczAf8A4J+9oPOvsf8A5u2tdInRqgg7sC0nlSaI0STpyra3UsX7 ZgZGN3trc1v9aPYf89cz9Srw9mTgv0DhuAPno5deuJo/yX9b7Kvo12WGB222fpG/+fEyfdMezp/V dxx8zO6e7813qMH/AEH/APotdGubyf1H61UXcV5Xsd/aG0f+CbV0iMNq7aKnvffVSSSjJOictXkJ ESISjRIcJKROBGi5v640H0cbNZ9Kp5rdHMO97P8ANdX/ANNdQ4SPNZvXMQ5XSsmoCXbC9o/lM/SN /wCpUZFLwbDkdenL6Nh9Sq/nKtpnz/8AOmrVxbGX49WQ3i1jXj+0NyyegOGd0HKwXaurksHkfc1G +rV2/pxocffjPcwjvBO9v/VIRNL4uk8kHyXM9e6PiNe27FIpseffT+aR/pGx/Nrc6j1CvFYWth1x Gg7DzcuXzc4y573S53JKC6UtKG7z+ezqnT32WV3bqb/a/YSND+Y9v7qy7vUefcZ2zPyWp1DM3NcD rPDVn0MsyrWUt9skAvPAVWeICdxGst10OGjxFC5r22tLwRurBEiJBj3Iz/oKxn5WTaWY+QQ9uN7a SQA4MMfo9zY3N9qs153SNgbb0wOMRuF9g/D3K1rQax3curhnz/Klb9Jv9YflV3Gd05l7n302W0g/ oqw8NgTxY6NzkXNu6TcyMfCdQ8QWv9Uu1B/OY9r/APqkb8FN3p3/ACe34u/6pysdFxbMo3sYWt2u LiXGBADPim6N1m9tH2Wuqpjamj3hsuJk7nOn2q2zFy8x5dXXJefc8ANaT/KI2tUEtCR3LfxkmEZa RERw2fsQ1utxct9FD2WvydtW9kkAF3u27mtWp9aMKi3pdjrv8G5rq3dwSQ3/AKTXImJ07E6YPtWZ Y03Ae3wb/wAW36T3LB+s3XLclgbU2KGOkNPLjxuelGrF/L+l5KxiUs0DiJEhIcM/l9Uj3cKx9Da9 tVhaRxEmU1FNriLRbPnqfvmFGpvq2brKTDu4kBTstxQ01hpB/kiD+KkBB/WT4YwjpCIM8Osfl0d2 QlEezi455J+rLklHDzI4Z/N6v+/ZX25DHbWAOB4gSf8ANUaKnCTbSD3nT/qUPHx2WDd6hBHIGhCN fY9oHpWg9iNJTgTL9dk4uEawgJQyf9JbKIjXK4TDjOmXJKGXAbj8vqh/7DQ33UvG0VkFugPEfJTp qxwBbvI+JhSoqyA/fYGmed2p+RCbIyCJrfV950TQKvNlAB2hGePh1Hy/IuMjIjluWJMfmyTx5oz9 Mv5wCOX/ALhjbY59gbXdoe3EfMBUqwRmOBMkEgn71doqpLC61jgRqSZj8FUoIOVaW8GSPhKMBI3k kRc9QBKR4Y/3Zub8YlGMMeGAPDjkeKRhCPHMf18XzfMxOuW75fwVmw7ayfASqrNcl584/FWb/wCa d8CnOKjxv5pvz/KUS76KhjthjPhP36p8g+w/BJT/AP/Q58PqtG0AUt536Cf5KdjaQYoeXW/mzwPH sp5JZ6zhkCGAzWBOs8obPRs9lANbhrv8vvUAqRHySl0/Qzf4EPkx/wBST1ImRAke7DGfUf8AK8tr /nckv1ub/W4/+ps7Ksnb6llm4N12Dv8AyeygLsk/QqDW+f8Aq1JtTGO3Ms9S381unKTm5pBLiGt5 I04+ScOIdMg78BGb/Hyy+X+6xzEJUScMug9yMuW/8LwR/nP9oj34TeGFx/18SpGmt3ust2tOoZPA Ou3UpNyRxTT9w/8AIhMW4YJdY4lx1c3z78JvoI/ych5HBj+3/KLv1kTtmjLzjzeWX+D/AJFk0ZEB uOf0Q+i4xr4/9JIudSQLWetYdQ7wHhwk2l9g3VWGun81sn+0k31afbTFs6l3h5cp9SAB9QHSV+5D /qWH9391ZcCZC8Zl+lAiWDL/AOnHM/5z/Of11brLJ3s2aQ2RCQ1YlOQCDfoCYaBHPySZpLfAoefF /hjhl/iuNz2MQzmuHhkBIe0ePH+76ZrM0JCZ40ePKfuS4epHRwKTVU0yxQ7Dxa6J+KerQbT20+5J w+mJ8wPgkpk/6Mpq9C4RAn8uqcasUGQHjXkRHw/3pKXbpa4R9ITPwUW2VBvpBkP+iXjnwlSfpY08 dinF1tbnMrZu1mdTyPJK+5r/AAfcbvw2RGbhEeLijoOP2RxR9XFI/pcP7qHIoqYwFtgce/8AqFu/ Vx4OO2pg1BILR8Vj7cNg/STvjVuuh8NE+B1R2MTshuvZV85lCJOMQ4iKEQTPg/vsvxCEeMSvIZTs ylkhGAnX6WPh/ReyvysjGofS0bfViXTqNId/nqliY1mVe2mrl3fsB3c5URnZXU7WDEpIawAWHdI/ lul/7y6/6u4za8Q2vA+0PJD/ABABhrf+/pcrPLkiBlFSHUNLSFnr0dDFxqsShtNQ9reT3J7uKKEt ElbKxRKGXwPMqbiAFWuurorddaYY0SSnBaUPUM5mFjmw+57tK2+J/wDMVy1lj7HussMveZc4oubm WZl5tfoOK2eATYOFd1DKbjVad7H8hrRy8/8AfVFI2aDJjiB6jsl6b0W7q5eA70KGCDbG7U/mNG5n uRPq+x3SPrC3Ee/fscGF8RIcP3Zd+8uvxsanEoZj0N21sEAf9+P8py5X6x1nF63TktECwAz4lp1/ 6pqPDUVTNmy7XUP1H604+RHtuLQfCH/oXf8AV7l0TyZXO/WhvrYWHnM5gCfiJH/SXQY9rcnGqyG8 Wsa//OG5AI7FdqkXQmLCExBSToVy6VJqhtKm0pdUHZmkUlFykGq1YkOlrhIOhC4j6vOPTvrJZiO0 G91WveCWt/76u5AC4f6zVuwfrJXlt0bbssBHEj9G/wD89oT28ldXTr/UPrcRwzKBb5e4bv8Az62t dQuV+tB2nB6pXy0tdI8RD2Lp6rWW1tsYZa8BzT5ESEIHoqXdknSTJ61dcd9dKXUdQxM5n5zdpPnW d3/UWrsVifXDEGR0Z7wJdjubYI5j+bs/6D9yEhYKRu1PrGDk9KxeoV/SZtdI+/8A6pdDjXtycarI Z9G1jXgeG4TC53ozv2h9Wbcd2r6gQPl7gr31UyDb0oVO+ljPdX8p3t/6tRwOpHdfLbyLspJJKVjU kkkkpZRd4qRIAkmB4rN6l1XHrxrq6LA7ILHCvbqA4iGT/aTCUh5vpWU3pPWMtsbsUOdXI0Ebv0ai 3PHTbsnIqM15GoYNdpB0f/K+kuS6zkZvT8mqq1pYC3c09nEnUoeR1x+SxjWsFexoa7bOp/fduKzM 2XmhlBgRGHah+LLEdA7+R1RlzTax+/dye8/yv5SyrLX3vgH4nwWVg22HK2E+23n5a/wWlda2hoaw S92jWhXsRMog9equGtSwy24rK4saHH80HlC9WGhrAGgcQrdHT9zHPyfdbYI/qz4fylRDH1k1v0dW YP8ABSmI3WcdnTR1R1TDx6wMnCZlMtO4OdEtMe5rdzHfnfykwy/qpZ9PDuqceS0kj/z7/wB8WfYP UxnN7s94/iqYTDHzWl3CfqmTIbkAeA/3pxkfVNh/o19g+On/AJ9YsNOhXiVPRY3X+l4tgZhdPA3E ND3kTHAJ0sd3/wBItK7rOa8QwtqH8ga/e7cuOp/n6/6zfyrcvy8ehpdY8ADsNT9zVHkjroOmrc5S IlYI4jYER5s77H2OLrHF7jyXGSsnqDfVHpNcA6Q4+ICa7rfqP2Y9bi3u88/2Wqq9+Mxzi4kWO5Pu 3ap2GEZeqUoiA0PEeD7G+cGXHKPolx/PjEIjL8v78f0Uj7LqqhBDyOSRB/KhsF9lgfZVuHBkAflV aukXPO2zjjd9JXh6tVO1rwXDguUgEsp4zxjFHYRlHJcof3m3xY8AGIHHLmMhoynCeDhhk/rQ+X/m LW3U1g1mo69oACBRXRaSHEtPIGnH9ZSH2q0hxbvA1AcAAj2XiloBrIkcCI+CZpkl7k/Tihtx469J /rQZfVggMOL18xl+Y4s3Fwzj/Uyfy/rsbXMZXtru2kdplQppySRaLB8SSdEJv2eyz3A1g8QZE/cr JGNU0tbZsJ5IMmR5JRIyS4yYiENI8M5Q+X5dJ/8AoCcgOCHtRE5ZcusjPFDL6Z/P6sfzf+Oo8zNf jkMDQSRI5VHDk2Od4jX712vUvq7i9Q6JU7EaPtNdTbKbB+f7dzmu/wCO/wCrXJdIx25FxoN1eO93 BuJa0kfm7g12139ZSHJx2ST5Ho8zzGUzlQAEY6DhFcX9aV/pNejW95/lf3o2UYqPy/Km+yX4mXbj 3t221OLXD+I/ku3JsxzRXBOp4HdBhroyo+i3+qFHKIDCShjIef5toa2I3O/8iFAjdq8lzuxdx/ZY kzw5XJLf0jx3/wAV/9HHy3VtYy2xm4n2/A891X3V3t2vHosbqDMT+C0csGoXBrdxad7R8efy2LON jbf6UNgH0BBEzyq8ZWK4h/dlHhgR/XzPRctrjEhCVwP85CfHkjL/AFXLKayjjHdN35pM/PttSdj5 EF9lkhvu2iTMJAUPOzHlj+d+vH/VJHG9M73WbnjVrfEj5pwjYsQEojrinwYvs/TmzSnRo5JQlLaP MY/d5k/4Xy4sS3r5b9GVx5kf+SUfUxGH3MLn/ndxPf6RUy7OcdAGD5f9+lR+00M+jXuf3JAGv4om XWUiP62eGn/UoLI494wxxPeHKZfV/wCnGT/oLelVbFpeK2nhmgiPapBr2+3EduH55MHVMWUW/pbX bC78yRpHtSDN3txHQB9MyeeyQjrYAs/pY5fr5/1ow/yf9ZJka4TKXDHTgzQvlMVfoZMn+V4P0J/5 SanC6ob7jvB0Angn85P+f8RKQrvpixzja76IbqeVPIovx7BXkMNdoguYe24b2pbGjYO/DL1Sr97j cz4kBIY8gMJamBnj9EZf1Y4v6n76N+hB807voz4apPEhJurEnNYjSwjx1CkR7xpMyFA6FhjtBPwU rOAfAz9ySlVfRg8jRRMhwjx1+Ck3R7h80z2lztoEkxAHiDokpV30N3hqtPo/Tjf1XHryWWMpuY8j QtDtrd/J/rKHUek24NE5N1LbSNKA4us/zWt2/wDTV36vWZ3VOu15tp/R4dZbp9EAtdUyv+s/d6iH EQLBrxUNC1evdIq6VeDZNld8mp8a6RLXD6O5srnw1m4yfn3XZfXLqWMLqMEgWOZNlg52kiK2/wCb uXMsfRfZBaGkatjTQfmlRy1EbMbPQD1a/pzLeyZBPl8c5CZmCYcUj+r9P6MI/ocPodPpWWKaWsGm pJ+M+5dDhdQc0hzHQ6FSb0wZnRXZdLR6uER6gb3qd+d/1p3/AEFk42YWHU6jTVSRFDTo0zv5voGJ n1XDa4htnh2P9VXJESuMxc8OABOq18brDZ9Fx9RwHbkf10ZZowiTMiIH6RQN3VL5JJ0AXN9X6j9q t9Os/oKzp/Kd+9/5FWurdQsNHo1DaH/zjp1jw/tLDcQBKbDPDJDixy4onqujAmWvRk1j7XtprBdb YQ1rRzJXa9H6XX07GDNHXP1ueO5/dH8hiofV3pJxW/bMlsZFghjT+Y0/+jHrc3J8Y0vlK9BsNl1z v1yonFpyBzU+D8D/AOZLoeSqHXcf1+lZDIkhpcPi33N/6SesOyKh32/6paavoGn9kytH6r5Hr9Ir aeaXOrPy97P+g9ixvqRcLsPKwnayJA+PtVr6pWGrJzMJx4Ie0f1Sa3/+ilHHdB2elhNCdMSnmkKh KE24KSAoq1UmjWU6aEdRspUhcv8AXvH34uPlAGanlhjweN3/AFdS6jSVn/WDFGV0fKrAlwYbGeO5 n6Qf9SgdVOTP7R+qTXcvoH/UrT+rOR9o6RQZ1qHpny2/R/6G1Yv1LuF2JlYDjIIMA+B9qs/VG003 ZuA7Qsf6jW/9Cw/+e0wbp6PTpKO4JwdFIJLKXQsmhuRjW47vo3Mcw/Bw2oqYkAEngalOU8b9TbnU 5uRg26FwMt/lN9rlf6EfsfXM3BOgtG9g82n/AMg9Y99zcP6yXZtTmNrFhcdx5c4bnshv52/erOR1 bH+3N6oAfXr+iBAbBGz3N+l9H/hFRy85hxZBGRN3+iLZQLB8Q9knXOYf1xx81vp0VE5IGrCdNE2T n5dgP2i8UsP5jOYVoZYGIINgrBCR6O5kZ+Jj/wA5YAf3RqfwWdd1y18jFq0/fesO3PxapLG73fvP 8VnZPWXvMbp8AE05SdmWOA7nR28rNe+TlZBd/IZws+3qlVY/RNDf5R1KxzdlX/Qb7T+cVJuEXGbn lx7gcJmp3Z4YB0HF+EWl9Y7/ALdjt3EvfW7c0jsCIfCyK20mnTnTdPf85dFn9OofQbK5ZZUCWkaz /WlVcLodGTjXXuLy+smGiA3/AKn/AL8oskL1XiJE+HhGotyMUxf6gBIrGgHdzht2rXxMQsd69/uu d9zR4BDwmVi6yvbBpjb/AGp3FXlaxQ4IgfVpZZmUiyVTOx2uYbgPe0QfMf8AmKtJnAOaWngiCpCx uRU7a6CdDo74Kja7I9RzBWPaY9rfAq9Yz07C3wMKFnqybGEOkfRPiP5Sj4TI8NmPfhb/ACOWEJy4 4QycQHB7vy8SF1lVbQbGFrj2QHW12WANc6tp5P8AqUn332gs2adwASjNdRXW1z69jvAiT96aZDIa BjHHGiZTjwX/AIUXTjy2PBESOHizTJjGOIxycPF8von/AOvGQqZVJNpBIiXEfxVeMq1xAfuAMEgg D8E1jse2wFs1z9IkaflVmrGZV7w88c6QiB7suGArFE6mE9/8ErrHLQ45m8+QemOTD8pHaUP++UHX 1VS5oeR+6e33Kq+/1njdWDH7szCm77U95ax+8Du0gfkR6hfVUd4DtvAB1RPFlPCDOOOI14ojIDwe KgIYAZkYp55nQY8ksMojJ/Vl8v8A42xH2SqCRtJ11BlV9lV1sMeQDxu/gnuyvVEFggfejVtxAwPc 3b5On8iYTHLLhj7ftw9W0sXmviMnLw45+8c2S4CjDmAD+ilqrsorLWv3eG4aBB9TKulvIHkNv3oV 5qtsGx/PO6YVijGfUdws55bGicYnJIY4CQxQ9JOPJYr/AAkRyexE5sphLPk9cY5sJjISG+sE4eaa dz69p7hkQqlt1Nrw5zC0fnEHU/gpWX5jX7CNP5InT/pItR9OpxuYGtA+mIBQnxZJDEDIQj83Hj4t Y+MWTDwYYS5iQhLLP5RizSgeGf8AVn/68dP6q/WivGqb0/PMVN/mbuds/wCDs/kfuJ/rZ0fBpnqe Pcys3Hc+kn6ZP+Eo27v7a5QHafEBIunv2/15S4Rdg14PP4+VnLWfpCb7ZcHBxMlrS1u73QPD3bmo IdvfJ4PJ8f8AySGXCQe34n4KLcims7n+89mN0H3/APkU5sViwi9v+kW01rnu2MaXuP0WjU/giOpr qE5NzWPGgY33uHltaW1s/tPVN/UrHgtYRSw/mt0kfyvzn/23IEpUwT5uR0iK8X//0hZjQ25jz9F4 LXf6/wBXesZ7mbiMsQ9phrRPHitzKi3EFg/Nh/3fS/6KyMz7O27dd7nOALRrx9H+r9IOVXGdKuIH bJ/N/X/uXd5YjjI4ZknUHB/PR/un92X+UQgU3jZSPTI1Lo5HyKb7MyrVr91o+i3QSf6qfbVkjZUP TDdToNfuKXoV1+6t+60fRbpz/VUnDfq4Iz/1sTw/+F4v3otvj4bx+7PHe+CceOWv+e5j/Nz/AOgs W5z+TtHyH/U+5R+11s0ZXr3Og1U9mc/QnaPiB/1KicxrDtZX/BLi4deOeO/0s0fclL+5H9FBx8eg xYc9bw5Wfs44f7Wf6fEttx7P0t52vPLJ/wC+/SS2NfpiO2AfTMkT+6kBQ/8AS3na88smONPo/SS2 Ns9uI7ZGrjJE/uo1fSB4tfTpzM/639T+utuv0sseHT1ji5HF/U/1nD8uJ2vqn01jup+tc7e6lhe1 v8qQ3d/Z3K59bLKse1zbMdr25dQ2XwN7LKz+9+45vprBwbsnpWQM6p4c9ghzCNHNP0mkrq2dV6F1 7F+z5LhW52vp2Ha5rh+dXZ9FyYYGBvgMB+7xcf1cj4jMzzA+6M3pAEhH24/3OF5/H6Vj5GKbW59A tDS4UkkOkCdn6T00DA6T1HMrL8akvYDG4lrR8t7mrVyfqZe07sK9tjDqBZof85m5rlUd9WOtNMCk P8w9n/fnNR4h3+1pNPL6R1DFfXVfVsfa6a27mmY9p1a5236StnojGVE5GfjVmBDGv3uk9nNYE/8A zb61/wBxv+nX/wCTR6/qp1Nzd1jqqREu3OJIHf6DXN/6SXF4hTn4f7NossdmNflloDam1ksY7nc9 7jstb/J9qbNzq8lwFGLVjNaZb6Yl/wA7Fp/sjomMZzOoiyP8HSJM+Et9ZP8AtvpWCP8AJeEDZ/pr uflq9/8A060r7AlTWwPq1n5zvXyycek6vfZ9MjmQ13/V2K/mde6d0nF+w9Ga2ywaG3loPewu/wAN Z/4H/wBQsXP6x1DP0yLSa+1bfa3/ADW/S/trPclV7/Ypg+11mT61xNjnO3PJ1Jn6XKDZtFhcwlsG WnwVhtF5O5rPvgc/1kWy/Fgs9Lg66AJTA/SPAI7cQPrP9WTpYOTnPl/SDPJI8UYxlE+3D/Ww/Q9z 9F7X/F9kMssdj2Dcy+ote08H94Fc117pj+mdTvoAPptefTd5TLdVpfVK8YnU6ADDQ6I50cug+tuH W7PO9ocy5oMHxGifDdzy8GzMfUwkfSA08CULD6vbUZJMk6z491b6l0t+PudXL6T37t/rLFaxu6OC DGh1lQ81jEqBGiYAl3MzrTshzXUs9LaANrSTJA9zvd+8uj6XgelbVk5cXBg3eiOzvzd5/O2Ljsdz BtA90EETrxqtavqV7OHHXhRcrjEARHSmTIOGqO73w6njuOocw95E/wDUyjMyqH/RsbPgTH5Vw1XX bxydwVuvrtZjez7tFb4z2Y9XtmjSU1rQa3DyK5ajrGNyyx1Z8jH/AFMK07qs1Fzrw5jAXHd4D/pJ cffRVtP6qWfYeuvxiYbudX/5Fa1bm4f1r3NI9G4lrnDUe9s8/wDGNrXHM69Tb1CzJaxrC4899Btn XdtWj1Dr1ldLHNua/wBRu7aDuj+TY395UM3PShlEYY+KN/MTSRHR9JJQ3O8Fxn1S+smdlvfjtrdk VMaTtmTWQWiGuj6Dty6b7TmHjEf8zH8FdjMTAOyAAN2zJRa5IVD1uoxLcMz5vCmLerRpisafN4Kc qRDf7KG4yqu/q5/wVTfiSf8AvyYt6yeBQ3x+knCQ8fsWhukSoWPYytxf9Hj4yqvp9YI1tpb8Af8A vypdYGfj9NyMl+UyaKn2ANbrIaU0yANqec6JY/pXV7nR+hY51ZlwEwdoj95Xxl42H1V/UxYA2yQ+ qDqD/wAJ/W930F57+2rPtLzukNJDfgFcyuuHJrY1lYr2th0EncR+edyzM2XmvdBgRGHaon/pMkQC +r4PVMDMo9em5oaNHBxAIPmpP6rg18Wh/k0Eryz6p9Wbi9YYzLb6mM/c1zTryDt/8E2Lun/WnBxx GPjsZHjA/Ir0MlxBO6hinLYOv+1LLNKMW2zwJG0feo2ftfIrcwMroa4EEky4f5srE/54TXue9rCe GtHZUcj62l0wXv8AwTjlPQH8mQcqd5SjH628f9YbMrp/WrcKxxcaDAd4z7t/9tu1EZ1TLyceuggb K5IIAB1/ecq31hyPtvUTklurmtB76gf7GqOBcxgIadsgg88KjzGIHXh9Q2X4cceMgyuN1bOq7IxM 2vJrcWlh3Hz/AJP+at92dfe6KmlxOhPKxq2nMyW1UxAEuPA4W7TZ6MVubAGg8lNgB4dV5jGMjRqJ /Sr9JG3CyLNbnwP3RqVYqw6axo3c7sTqVuYfR67WNtstD2O1Ar1H+eVpUYeNQP0VYaf3uT/nFWOH RPFAf1nAx+k5l/uLfTb4v0/6P0loUdExq4NpNrvDhv3LUIUDykIi0nLI+HkgyMSm3DsxQwBj2kQ0 RrGi5fobg5l9XYtn8F165HpwFPVr6PzWuez/ADXOCGQek0tgayw8bDjMGzqjx2cz8QVdCHfQW9Te /s0OB+Z9qIFNA3EFpZRWSQ8VJJJJ7G0Oo1Q5tg78/L/zFU3Y92TWa6TD2+6JiQPpLWyqzZS4NYXu EENaJPPgsh3V68eo49dJruaSLLCTuI/NaWn6O1VOamYgiAJlLbtH+8z4Mssc4zjVwNi9UVNeRS1w dDo4bOs/FAty3vBYWAA6QdSh/abrbTsJBf2CtYzchhJeJB11PulPhKeSMMceOAqpmvcg7PL5sc4T 5rJHFLLxemHF7M+KPUD5VqxjNrD7K9h4O4E/dKFkPx7HDYS08ExpClbmBwLDX5EOKWOzFeyX6OHO 4x/clIxnWLGcZFamUTj1i2IRlivmM0cwldRjCcc44Z/y/SSU4gYQ8WE+Ecf9+UL35bbCxpkHjaNY SyDQWba7NpHDRJBQhX6RDjaAeW7dT/BOnp+rxRIAqUpY8n2rYa/r+YmCTcYQz4e3y1w/9w2MZuQy d7JB1nTch3ZbHgsNc/1tCE1ubfH6MNM8eP5VR/aV4e51lAeeDuATpWIDHjma2kZiMtGsOYxe4c2b GCdDAYfch6ot/HrxXtl07h9IOMfkhPkGrYBXbECNoJIKFT1SqxhbZSWCOOQfyKvY9pPskA+PZNnH hgIQjCRkPVOjAs2HmIZckss55IiBuGIkZB/d9X/ef4aZxdjkPDxvPAbr/nIN2TZaZsdoOG9ghudB 8Sgvta0En3GPxSjERHDGwD0tgz5+M8eUjTQGhHT93+skLj/r/wB+QbL2g6aj8qBZa55MmZUJ+/xT gGhl5snSG3738Gb7XO0PHh2/zUOe/dJJFqEk6lScEjgwmThjjwEiQN0xjKRqIMj2D//TjiQ6h1Tv zZHyKzMptLKmuubJrcWeP+v0FoYrtuQW/vj8QgZtTN9rXiWub6keY/8AOFTial0/wtY/V2McqlE3 LsfbPDP/AAS5e2rJ/mh6Yb9LQaz8CkaRT7q3brh9Funf+SomtuR/MwxjdDpElL0DjD1Gne/gCPFT 8F+v2we+eJ/52PH/AFW77tVj94x7crONy1/Qz5v3Z/pf1F/19/J2j5D/AKlSfmVtE116fIfkQTdl uB12jvw3/qkZubisENZH3BASrWOScO8s0eOUv9mqXCfRkx4sn7uPlp+zCH+3l/0GAbj3D1rXbXH8 2Y40/rJbGP8AbiO2n88yR8E36teTbZYGE6bdw7fFM80s0xrBuP0juHHzR4TXEYRMT+nH+fyf1o/u cSz3sYlwDNKMxoMUyDymGv0J/wCcjj/QmucWxjXWWP3EA6amZ8ygsnSURrXgix1rXbPdG6SY1hKz JdboKxPbkn8IQuERqDjvaJ9cpn962HmuWnzdcGSGWUN8kTHHjhD/ADfD+l+9xpaci+n+atfX/VcW /wDUq0zq/VG8Zd3ze4/9UVS/RtaNz9r41aQeVKn9LOz83+KOhIiKMj0uy5k+T5iAlI45cMd516P3 dJNv9qdTP/au/wD7cd/5JAfZZYZe4uPi4z+VM5jmNLj27DlRBsd9Gt3z0/KkYkGqN+AWw5bLMWI6 bXIxhH7ZrpiouvrZ7XB28cjSJ+KTAzJ3EzW1kSAfHxlAEE8MSDP91sR+GZ+Hjyj2sQ3n8/zfLwwj 8ymje/Y0iVP7NYCH7hLdQ2JmFFzKGN/QO/SnRpBn/wAxUfsmS/6bvvJKdqNOA5Jb3jl6I+cv3m3h 5PBA8fujGNv6RD1y/eljxfuK+0Zb/oMjzA/8kpCymoD1mfpeXaA/NNbmWVHZtEjTce8d1TyH/aP5 x3l7dPklruJynLb9ZH0Dvwx/eZcmWMfT7MYR+asM+HJL933Mn7n9V3OmXxfXazgkEfJd/wDWQC/C w8wfnNgn4iV5j0xzKa663Hb7iGhx1Ou7T976S9Nrd9s+qTXcuo/76UARYN24s64jWgs+LzboJKwM /BotynsYNgB0jiY1W9KyoFlrn+LifxTslVRW4xcmkzp5r9osEdyBqrTa2VsDGjQeKk4kvAGpPHzW 1X0zE9NrXtO+BucCef8AqUIRAGzId3CLGkzwU2yDIK2rOi1x+jtI/rAH8m1VbOj5bfo7X/Awf+kn UEU5wDwNNSoZNtopcyYJHj/erj8TJq+nU4ecSPvCDZWyxpa4aIGIQQ8+31WuMSfNW6g97TJI8ApZ OI+p276bToO0JUNveYY0mO7QXBU8mM9mTFw3q631b6nk9HyLbqHAOtYWmQD3Y5bzvrn1Q/4WPgAu aw8cNcLLiGNbIaCQCT+85WnW4Y1LmGPCD+RTY4ERF2omJJNAebru+t/VT/h3fJDd9a+rH/tRZ+Ky Tk4M/SH+af8AyKk2+qA5lD3eBaxScF9EXEdYt9/1l6kR7r3/AHlDd1/qB5tcf7SrC2x2oxrz8GFP 6twGmLfP/FlLg8FGQ/eH2JP2znPP03H5oOR1DMuqspJcTYxwjXWRCm12UQHOxntaeSYEfIojRXVL 3mXHl3/fW/yUjEBaZ6aG3lX1Q8k6E+HmrNOxrS0nngHxGivdSow7jvrO151JgwfkqVVDSQLHhgnU 6n/ogf8AflBLFKWwXwkIHWvonxKzZkgViA0zu+BlbtHTBY3da92vAGmn/SQelUYzvZS4OAEvPf8A zVscDQJ8YGArqz44iVyI06BA3AxWQdm4juSSiNqrYDsaGz4CFJztYUuydsGURHQANLJ6ZjZZJsbD +N7dD/5kqbfq5jNd/Ou2zwAAVsTKGeUwgSOyfbidSHMswX4ZNmPrXyf3h8f3lZozK727LtCOHKzq q1/T22y+r2WcxwCiQNlpgY2Yax6wLdxM7K6c8OqdvpPLDqCukwOpY+czdWYePpVnkf8Aklw9OXbj uNVw+LSrtbvcL8V5a9pnQ6goiRGhYuEHWH1gd3tzwoEarI6d9YGWRTmxXZwLOGn+t+6tho7zIPCd fULQViCuTyQaPrFYOA58/wCe1rl18LlPrEw09ZqsHD2scfkXMQlqCE3Rie0g0uot2dQfHDhP5EEK 51ZhOXWWiS4dvgqcQn4TcAwc1GssvFRTtBc4NaJJ4CaCTA1J0CtHZiVEuP6QjU+HknylTAAs97MS o6y8/SP8AuU65ZXdc20ibDoSO4/lK/n5pc46/AKgaGWEPeS4ntOiilEkea+NDdoUuDXBwlsdwFZt 6g4GGkAHgkf6tWbkZVTXPaxxZtcRtPx7cqNYteQ9pnzmUaMY8EeMSNEyg6fKGERxSOKcAT6Mg1v+ 9/6O62ObH2brK94d+cQPvRLMuiCwtLhwREflWd9rux429/PRO/OFoe97AHhpiJ/zkTI448EJ8Uyf V7kf3m1CUM8/dy4/bxwj6Panp6P3R/7DVZbXJbXJcO3h81XfY2sy+wNPPmqbLLWse9sg/vd9VWeS XH4oQxiI0A8WpzPOzyGzdfoAnSMXVZe5w9rp3dxrA+9IkvdA0aORqJKoYIc57mtEl34LUDG1jaO3 KdoFuORnEGv7PFiJ78cAJOeBPYDkprLGsGvJ4CpWXOeedAdEAD1VmzwxigBf7o/aktv02t05E9// ADFAJk6/cmSTnPyZJTNyP8FJJJJLFJ2tc47WiSVIVnZvcdrexPf+qhutJEN9rfxSN9mWGMEcUjwj sNZSbGyikTc6XfuhD+1tH0GT4F39yrEyU5mEjRN0NGaMpQjwx9PFvrT/AP/U5mz6w5BfvrYxhBkc uj/qUG7rOfc4OfZEcQAOfksw2D4otDA8zZLW9o5P3qPgiOjPGWWegJ+3hSC+2NrXu17A8/cptx8i w+6Gju6x0fgfcpimlvu2afvEz+CJ6hI5cfgAErA02/l2Zhy85eqcr70eL/n+pAMV3d4jxaJ/6vYp DGZ3cSfKP4bkSfNv9rlMDr7Yd5N0/FK2UYMY/Rvz4vz+Rb0Kh2cfv/8AIpenV4A/P/zJP7/3Xf5y g6yocvYPiAkb/l6f+kuGPEP0Y/8AT/6HEyLKuSB+I/6lIV1Ey0fcShnIpH5/+Zom+0UO03k/1uEt VcOE/ox/D/opvTB4c4Hwk/xanAuZ9CwtnnT/AM5Qw9h0btcfAPn8FNtdjzDAD5CQUK66fkkHGBQJ iP6s/wDvZrh1zbA4EOIM6zJRndQyePTA8wZKj9jy4/mj8NpH5EjjZTeanjyAdH4IxPCCInhvX0lJ yiRiTMzMdBx1k/6aSvLw9u68RafpbmnX/vqmXU5ZDK/btkzAj8Cqj5bo+NeQ6f4hCLGA7mex38kx +TakSCBEgcP6Wnqn/hfvMkMmQSOQHilqcZvhhi/uw9ceB1GYldfuc8yO+gEqvkW5ddRscS1vAERq qQdZrD98dnan/oomVk25LWMeA0VjSNQT48IcMdo3iiOkJfzn99llzZECZfrsh2llxj9QP9VwcTUB ue82WEl7ue+n9pEALSJJA0B0/wCiq2Re+pwYwAfyiFLGv9QEHQt7gx+VOI0aEJxvgBvx8f7zdL7G 2MPIqeCPkvU/qhb9p6VmYbjMtkD4heWY7RZY2pxcN0x8hP8A31eg/UHJFeaKZ0sYW/Mf7lFGJjYp qZIcJpp5B9NlhPLQfvWS20M7Eu7Lb+sdf2bIyauJsgfAncufPKllrXktgSLIbmDTa677Q6G1t/mx zJ8f7K0/Xt/e/IgY7dtDG/yRPxRE8DRbxHuz9a0/nn70vVs/fd95UE6SLLI2WHQvd95QrKq7P5xo cfEjVTSRU81cDXe9v7jyAPgVcodYydrokdkPqtJryy6PbYNw+PDkqD7WkGdPxTJhdEkbGm70zGbZ mtsd7hW1x111+iFuAACAIA7LG6W8Nyg394Fp+7d/31bKMdlpXSTSnlOQpRJEJEqrlZEDa3juUCaC UeVkAnT6LVk5F5eYCnk5E6DhULX6wDPioxZK7ZjY/dp2CgkkpFqbDsdVlVPadpDxr5TquwnRcUCQ QRyNQvQa8SnaHEl0ifJRZNw3OTOkx5NFzZ1Umgu0aCfgtFtFI4aPnr+VTAAEBNLacx1bmxuBE8Sh OGq0MxksDv3T+VUiJTTomJYNARE1dcuA8SAi3Uvq51b2ISGqSWvfj1Xs22D4O7j4LMtpyMJ+5p3V /vD/AL9+6tcGQoP10PB5CR00WHHxGx6Zd2pVkVZIh3ts8VpdP6xkYBFVs2UeB5H9QrIyOnkH1MfQ 8ln/AJFRx84j9FkDQaa8gpbbbMUhrU/TLpMfLJ77Gy6MqoW0u3NPI7g+DgsD63Vw/FuHPvaflte3 /vyzse+/FeL8V8eMfkcFZ6x1OvqOBWNuy+uwbmjgtLXNc5v/AEU8SBDFMECirMdDsG/sHMk+UiVo dRrD8O0ASQN2nPt1WVkEv6RU8fSZ3V/KzWmsbfouAPxUcNPoWbNIAG/04ivq5rWsxmeo/wDnDx5L G6hnFxOunZG6nmHeROnKxbHl7pKmA4tS0NlnvLjJR2RsA8gqyssEsHkAnS2Co7l5K5pN1nH0nflT tdZXqw6hTyKX1XO3AtLiSPCCgHfMfkSFAXrr1DPZkasUO7aZm2PhlmsnTTn4q5I2gBu2eRCy2lwG q0KL/W2zoQ3Xz5CW2pJuXdsY8nF6eEVDXiB3/vKNbdpaPhOiotxLbLdgEeLvLxK09u76KKGsqaSO f4oXS+WITrpSKqlmMwNboTz4nzQ7Lgwlo1cOfAJsi8gkA+48nw8lTc7wSA6sWbmBAcGP6kfo/wB1 d73O0J+Kgkki0SSTZUkknAJMBJQBJoCyVkVrAxvqPGg7HxRWMFWjRNh7/wDkVXy3PkMJ0aJ+9Dc0 L03r+Lajg9uHHMDilpCMv+lworrX2vlx+A7BR0CQA5TSJR8e63c1qQPpquPgm1KcmEwlLwUOsqHh b//V89Ywu1AOndWJbxuPkAielYBL/a3iAiMLW/Qrk+KjJF66eY1/5rowxSqxqO4lHh/56qWuDSWm D4lEl3ewfgoEsdBsMO8Ev0Mw0a9ihfiP8Yx/5kWav6stOvBGdf8AVJspd/oxPiVF7i1hc4bSBI29 z8kN9lskB3zQbbHMHvO8niUaPiP73D/3LHLJEaAxP9wzv7cnpQvte/6TjHh2UNUi6TMJfNHy/BrE kmyb/ver/oq+OnwS+aX4ppHgkoX/AC/9CTUWBsiIJ7rq8HJw/srHVOa0QNw/OnvuXH6otORdS7c1 yBjayQN6EeXV3cjq0Zb67HvbS3RvpRJ0+kSdqrU9Zy6/zm2g6e8kH/qgs92QLnFzz7vHhQc4N5IS EQsJI3dFnVMxky8lvg8B7f8AOTv6k141opk/SLZaT8pasr14+jI8/NMbXu+lD55nn/ySPCoTI2JD ffdhvMua6gknQgOH+d+jThsj2PbY3sGkgn+y73/9FZ7XtGgLmGZPcf5qk0nwDvNmh1/k/wDmCFM0 OZmNL4g3XAOG1zQZ0jQ/3IX2asO3MJrP/RlCF06bpjSH6EAfyvoogtgCRtnz5/tfRS1Zhlwz+YcJ 7j/vmxQ11V1byNGuBnynX91db9W8j7N1Op06NsH3Fcey74j46q3iZ1mPa19Lw1zY9rvomPu2pFGb CclSiRKh/L1PefXxgr6jWW8WsD/u9q5etu+0NjQkCfiVa6v9ZB1m+m26v7O+mltREy0lpc5zw7T6 e5DwGh2S08gSfuHt/KkGpKJiKIp1U6SSlY1k6ZJBS6SSSKkOTi1ZLNlnbUOHIWbZQ3GtNTZIbBBP Oq11Q6i2LWO8Wx9x/wDMk2WyhuwxnFmQx3YOaSfnB/Kt4rnByDMdguhY/fW1/wC8AfvCEFFlKaUk O20VtnueE61Mci4MbA57rJycjsCp5ORE66rNut7/ACAUe5XAMbbeR3P4ICckkydSUk8CkE2skrle LFLg76bh9ypooXXouO7fj1nxY0/gvPKml9rGgSXOAAHmV6BiMdXjU1v+m1jWn4gKPL0bfJjWfkEs OCcTyU6RUYLbIYvbvY5niNFmO9undaoVLMp2v3j6LvyoSSEWMZvaD4z9y0XAFuokHkKniUmTYeOA rh0bCUd0ypq2Ymm6rj93+5Vi3sVqN4Q7qGWiTo7sUSgOW/Qwq+RjV3j3aOHDgreRS+p0OGnY9kJG I0tMgCKOrmB2RhOh2rT37FW67ar27mENeOR2Vn02ObteJB5BXJdRvvb6lVZ2DeWacxr7UyRG4a+Q e3ofXE9Ooepb1XEPTtrDXDXbfT1Lnafzmvt2rEd1O2rI2STS8/R8Cfzmqh05u549QnZ3iFYyqQWg DV74a0eZVDGDDMSZSkZHr4/ooGGUocZO3fwRZV5usn80cIKSS2QK0aJNmyuA5xDWgucdABySiv6m /HoZhuobXbTO57mxYS73fpC73e3d7FqdPxG4dX2q8fpnD9Gw/mj97+ssjrVgvua4iXay7y81W5iI mBe0SugC5We77RWXuOoOn/flmBj2mDwtDLf7RW0iZ90fkKquOkEJ+GPDGzYrZsRiZQEI0bvzQl+s RCtBhd6dtP5h26cEEcFVHTug6rXwMYUsNjx738DsE4668W3cMuGPDxQMD6hrKMq4ZR+VLXV6bdT7 iJPkFWycnQgaRoP7giZdwbLWnX84/wDfVQc6T+TySARzGfeMd/0pMXOPJ5P4KCR1KSc0CpJJTrrd Y6B8z4JKWYwvMD5nsFZpbWySATHdSAZW3a1Ce9CzYpsY5wxg2DKR0u+HhCVrrHvkaAIGZS5z90gn iPJOzIe32zp+RMWlzi4pa6DWRPqkf0Wx7kJwlL0wEfRGNXP97iahAboeUgQk4e4g89/iloEevQU1 zsBqb1WJlPqmBSJSB62kjYCL/9bjt7qzB9xPnwl6lx4bHyWi26hpc0UMBn2zrp57k4vr2hj6Ky4f nREj+youI7cRA7f2ugc0dziBl1JP/cObup5Op78pnlj2ltbYceDCuZlPT2sbbT7CTDqyTp3lVTsc Ir0d9yQJP7n90fPJlBjIWPdr96f83D/0FqemfFRsYIjv4qy7Fc4zInvyhPY6nQwZ10RqteEw/rHV YQT6eIZf6kRw/wDOaxY8dtPFRgI5yWjtKgYfrAEo77er8GI4zHU/qx/jf9FHp2TF0c6JzV33HTwQ 9nmltv6VogZfKPc8flXNjeUxsPYJCpzuCNEvs7/EIgXqBfiggjQnh/q/+hMC8nkpBxHHCn6R4JH4 pelpoZ8QEvqPpurgkf0T/hfL9qzXkkCOUQtcEzQG8jXxRNrxwZSB7WUHlx1Ihe3Yo5KfT4fBWWUV lkPMO7gqL8djSBuI+UhLxOn1Wnlp/o+vwr1Ig90QYeB46qTHNn2uNZPjqFF1Tx/KHiFEk9/9qGjG Yzj80SP7wTby0atgfvM4/wA36KK210EtO8dwNf8AouVVrnN+g6PJPuaTqNjh3b/5FJMchibBp0Ks iRAIg9uFoYOfbiv31+5sQWO108isQPI1sG9v+kbz/r/WRq7NJYd4GsjQ/NqHk2Y5ozHDkFj8XtMP qOPlgBh22RJrPP8AZ/eVtcTXkNMEOg9j5/JbfT+tOBFeUdzO1nJH9b99v/TTxLoWPJy2nHjPFHs7 ScKYpe+sW1RZW4S17DIKgWuaYcCD5oggtalJFOkihiqnUmj0mP8AB0ff/uVxAzW7sZ4HI1+5A7JD mggAGJg8LcwXbsVk8tlp+RWGJI+K1umWD0H7jo0yT8QEyO6S23uDG7j8lmZWTOp57IuVkzJ4A4Cy b7i5xn5+QSkbSAxutmSToqjnFxkp3v3HyHCinAUglSt4tEfpHjX80fxUMWjed7vojgeJV1FClWdg 333xQwu3ak9h/WKsrT6BtOU+twlr6zp5gtQkSAaX44iU4xOxKTofRa8a0XWfpLWid3YE6exb0KLG 11thogJbwoCCdS6URGAqIoMuE0pt/ipaIUV1hbdqnIBEESPBKAnSCj4LDiEiJTpidEdkKJA0SkIe pSHKC+lrQ14giR4KnbiOb7q9R4dwrxEqKIOlKcsmFj9X6SLRZkMiHa2MPj++xdPdistMj2v8fH4r Oz63V49rXCCGlAgaBZliDA30Fh5KjHymuLa2PMeA0/zitbp2E+Rk5Jl7Z2sHY/vFSxD9IeRVrHP6 GPMoRxRErrUMESeEWbvo84eVqdLwGtb9syB7G/zbD3P7x/kofT+ni+x112mPWTP8oj8wI/UM4fRb o0aNA8lPI9A0QGGblusedVzvW7SwsZUdr3S55HMcNWowkjceXLnOoXm7KseNWg7W/AaJCIO+wZIk ggj8UYcds8+KYuJQvUcOFbxK/tDw0CI1efAJHU0JUG3j0FmAMr6JsLGa9wvcPaNGiO/irOReGN0M Hgf3qb3CpgaABpHgs62ze4uPAQ3VmmMQ4I/MdZG0b3EnzPEqB0EJ57qKc0SVkk6QBJgJLUmNQ6+0 MBDBy554AW5Tk9LwmBlbC8jmzaJJ8ZcWqlh3dPpxHPsYX2gkNBmD+6dIUcXMxfSuOVUHkmWACOfz dw+imnVeKHm7OP1TDyHemHFrjw14ifytVbqnSarKnXUNDLWAuLRw4d9P3liPY70W5Dfolxbp+a4e 4D/NXQ9O6gy7FY6143gbXydZGiBFahF3oXl0QNOznnVJ7A7IcxnG8hvwlFyK7C6QJB7BPO10T0+1 m5aJJNEDrr/VaxoLhuET4ITmkciIVprIHPKiGSeeEKIAAjuzVGUpSM9uwa+iUE9laLWgeCi1rT5+ SJuwNFsYwoyJka8H/9fi35V1pAa2I8OUnOzHDWQBxMAokmImAOw0TSAo9Oy+z1LFxyXABxDo7H/c mAsaJZAd37/wU9wSlKh/avhnnDQSsHeJ9UShd9pOhM/CAmboP0o18xKsJcpCwbsn+96gy/eyRwmE R/cHty/xkG6ny+5DdQHnc0aHjsrD6WO7QfEJmUZLpbSze1vcfxSMr+fQf1GbHkgdYH19RmI4eH+q Wt9ldMz+KRZX4/grZxuoASaD9yEccNMOkHuER2x69+NcTjOuUj+r7J+3iQOqBEVu93whN9nvH+9H NYYN7ZkeKj67vAJGh85MT/V+VdGHEP1UROPX3Pm4kYx5HvIDu8mEvs5aC4EGPmix6xJ+jHzS9FwM gjRLXeMOIdJ9fNHBAaTyGMv0sZ+X+7aIAT7uPJSbUfpM18NUXfUefxCi5xEenx3ASP8AWnxD+p86 YgA1DFwSP+cuWNi8hrS+6QRxHdVftTmkw1pHgdUbJc62rbGoM6KlBQHCdQOL+sd/qx555YnhkeAH 9GPy/wCCf0U7cyxpkAfDVSdl1vEPrg+IVeAmkd07pWgHgw+4SbNz78Wv+N+82A0PMVncfDgpjI0c OOxQQ4gyPkUZuQ5wDbfcP3u4SG3UrJYxI2Kx+F+hcEgywmfDupsewnX2O7EcJPocG72nezxCHM8/ f3SIYdY7/wBjZL3RLxE8WDv/AFkevIc0CYczsf8Ab+aqLXuZx7mnkHg/JEYZl1Rhx5rOoKDJDIQd N+z0PS+s5eA/djvmt306jq0/Efmv/lLp8T6x4eUz9LWAeHN8F55VYSfZ7XDms/8AfFdoyZOjtrm8 Tym0zHgzdoz/AAk+gtf0u/6LthKc9ODtarA4Ljac06BxAd2jgq7T1K+vVrzA7zKXqGxa8sZiaI1d 9+FkM5bI8Qq11btjmuBbuBGuiDj/AFhyWRuIcPND6z9Y92D6bGBr7DBd/JHIROQgWRazhaVNb7CG Vtc9x4aASfuV1lV+LV+mY6ov4a4RoJ92v9ZUunfWI0OYbS5zAfc1p2kj+SfzULqX1hfe522TVulr XGSB/XVIc1lOQROKodZXa7hHdJkXlx0PwVK18mAZA7+Kj9qFugBBOvyUVehRFrT2Ui0Um138kclR rrdY8Nb8z4LQYxtbQ1vAT0LgAAAaAcBOkkkpS0Ohu29RYP3muH4bv++rPVrpbtnUKT/Kj7wWoS2P kvxGpx/vB6s8IZYZlTDpKdQW6lFgGayVKNU8hLcEuJFFRTTCiXpAhA91wDPlIiUwMpOJCQ1RsuAE oCg2SURHhCrK0BLaEk6FBVlYABZvWAPRs863fgCtFx7LM63YyvHDObbQ5rGzHI1d/ZR0As6LJn0m z0cLD+k75q1ij1Ipadp1Lz4Nn6SFiYlrW3WHaWV/TO5uknTTduVCzIdjZwt3TWdIA4/eTBnxcVCY J29J4vta3ERjjW7odRvZQwVVDbWB7QsSx5tf8eETMyXX2HX2j8UKoS6fBWIihZa0t6DK4Wei8Uib Np2DjXsubdiZgMGuD8R/euhuyHVEBoEnx7BDotY+39M0Eu4Md0w5BxCEZVImjxfL9rrcp8P4sBz5 YSlCuKAgRx+n+rJw6sDKedor151IH/VFaeNj/Zq4dG7lzvP/AMwWnYWMrIZA7QP9izMy8NG0duVJ IEegkEjfh/JikMeIHLGMhekRkPEf7w9MGtl273bR/r/5kqr+zR31KkSSZPKiT2SaBJkST1YO8Eyk 5RSWFQBJgcorGySwGG8vd8EzWmQ0fSd+AKd/apnE6+ZSVSxPqGB7WBQc6dBoBwE7oA2j5lNwPMpK UXHbsBO2ZI7Eo2JkNq3B30TqPigJ2N3O147pGq1TGMpSEYiydgmxgZdaRJ7J33GdznR4JX5bKmhl Wp/AKiXFxJOpPJQkLocWng3MUxiiaxiUtrl/ztG1dlsdoGz4nhA9V0y0QEMlPOiWhldkrTknw8IE RfYJPVn6QJ8wVYx20PP0ju/dOipSnkjVICPFeqTlyCIjp22f/9DjgUjwoq3j19PNTnZNrxZ+YxjZ /wA5xUaWqAnTEiTt47Sl8UlKJSAKf4BLVJS6lXY6p+4fMc/goCe6RO0byPaO6S6N6NhmXc0usrdu DhqABp/VUm5b9pFgF7D2drCpG+oDfWdTqWeKTMmtw3Tsf3EaFNostx7hs5GLTYw34zi0t1spJnTu 5iqfof5P4IrLa7JDDDzy090GzG1mvju08hESMenFfdsYpRnpLIY18sh/3SzyGia4HjCH61nipMY5 jtzhAHJRPVrPdOonUy9r+qzExjoMfvj/ADnzf4N+pgKmvbukgnlOG+iC8mR3UbC7dLCY8uEN73lp a46aShcIn5fUNBLpfdPDklEniBgdTjPzCP7qn5AefAdlTfo7RWPTHiq7xteQU48W8tPENSRhVQ9W u0un91jEpfFInwS8ilos1O+g7fpBfhNPglCfTslr5I08/H+LOm59Z0PtPLVbOOx7d7HaESqEq3h7 ntcAYc3j4FDrYBkzQ9QOOZEYnuL/AJf3mDmuYYP3hMNTpoeyuekwjXw9zVWtqDdWHc0/eEda1oMO XBwknHc4Dw1iyD2vG2zRw0Dhz80bc4fT0P5rx/r7mqoDx+VGZZtEEbmHkf3IUxxle/2/xdCrI3bW WAAxo7x8wVZY5wO13PZwWUIDdzffUeR3Cs0XiIfq0/RfxB8HJA0y8QlHgn/gy3Mf/QXRD3DvPxQs s+pXLvzfDzTVvcIa/v8ARd4oiJiJDzYZRlCVH8Ni0NhmR34/6pIMB1JnwKt/Yw+SyAdNCpswoPug eICrHHIGq+q8GG9eNMKQS0E9hH3mUVrS5wa0STwmDY9oHyV/Go9Nu530z+CswjwxAYibNsqaRU2B qTyURJJOQpJJJJSkXFdtyaXeD2n8UJO07XB3gZSSDRB7F6+UtxTeadQ0C7GqpKUlOGp9hTbCmMJJ 3CE0pAkpZtB5UlBrlIkBAXa2StAU4MqLpPCdogJx2WrFykCChu5TtKb4ryF3SuM+suXcc+8tMGsN rZ5CB/35zl2GTe2pk8uP0Qub6r0t2a1+SHBlv5xdw6OEp6xa2az6I6nc04GA+17g1ziAeTyrOXSN jnnWJjz8CqdLMmh5aWOlvYCePgrGQ3IDWG0bWPktaYmP5SqjBOWQUKHVQljhiNiz/KkAmBPPdGrE N+OqA5wa0uPAQ/2lSRta108do/zloTkBpbRjuz9Sp90WtBZwCJHzKuNrqZG1oHYFQqx8ctD2tkES J1Q7q2V2etMQNG+fCMIzxQM5RhMkjUbgH+tw+p25zw5jDHjnkxY4QrhPqjPg/q8Xo4mGS9lZIZo1 vhwXFY9zy55JMqzkWmI5AmVTJlAD6OZzWU5MlXcY6A9/6zFxgKI0178p7NICY8BFg/Yx5U2NH0na gcDxKZrSTAR62tPvP0GcDxStQDEzW2fz38+Sht2N/lO/BFDS9xsd/qVEtLjKCeFDHdMUYsUC1FaY sA0uIA5KndtpbtBlx/1KsVYzmtLjo4jQKjeCbTOm3RAjUAx8W1ij7eOWTiqZ9AA+aPEjMJaJo1Tw na2TTGaoC1tJTkpgEiENatR4TICzooQnlKExCOoCvSZbv//R4xJPE8JnEiAAXE9gmJUnUP0xOgDR 56ojQ4N9xk9ydElK+abVDtvZXoAXO8BoPvKq25D7Btks8m/xSrvp5r445S2Ce7MqqO2dz/Aagf1l Wdc57tzjIKrurPZSra+NeOyIo7aqninEWRSUO2kEcHsnJ/OB1Q50hOCkxpmb3ma+R56hXmWOLQLI Dx3HdZbHuY4OaYIV2u1trfA/nDwTZMuIj6prGhwI7n7iq/oP8QiztEO48U5J7/eh6SRxatnHmnjB EeqNg9IHeYB4Ui+twInlRfLzsI2nkKHoP8k4SkNMY4oBm4Mc/VllwTl2I4a6NZ29pjXRRew2DdyR +RW3tbtAJh7RwgPOmh1CQFa8V94sc7J4eCrPpyftasRqlIRHtJ1HKGWxpwiDfysM4GJ9Z8iFSUo8 EpA0Snw4S066os9BX5SX0U6bXMdA0JQ4nVLTvylqfBQIiQdyPwbxsLm7jo4cKxj5DSAxwg/gVRFp LIPflWemsbbm1Mdq2SSP6oL/APvqbQ11vx6pz5cnFGxwxrSI+X6Ni7pV1rTbRWZ5LeAf6qzgXMJa 4Edi09iuoys8UbWNANjhOvYLPzMZ+eDa2sNtaJLm6SP5bZQEu7CY36ho5TSazvYZHdHY4EGyvg/T rVYh1bix4jxCk0lh3NOg58k+kCVaN6m5jmhrtW8CeR5O/wDJK3Vbrsfoe2vKzGmTvr+mOWePwViq 2Wgj83QHuP5Lp/6KANMoIlHhl8v6J/c/9B/edSqdxjwRT4hVMW0PcAT7gNfuVoeHfulJj4TEkFgz TIb/AFh+VaCz9fXafEgrQTxsxqSSSSUpJJJJSkkkklPWUO3UVu/ea0/eEZrJ1KrdOO7Cod/IA+72 q4oCdadeJ9IPcBQ0TFxmITpEwhYCNSxehqcykWJRlS+lmcpWTKk1sap48Ub3K07sBuRBMKO9oSDw UCdFUV3N0QbXtqZud8h4lTsuaxpc7QDlZtllmRbJ0aO3gEPyWzyGNRGs5bBYufe82WGAO/aAs/qG W6xjm1aVM0nxKPkXG532egwxv03KrntbXjtY0RLvyBKIs2foxS9EJAGyfml3PZpsnbpyUDqrv1hr P3GAfxVqoS5g8SJVHKO/KtedRuIHnHtUsNy18vyedNW6g2VFsw48D+9Z7aoME8dgttmPdYxzmQDI G53EkqrndPODV6jnB79DAGgPz+kosmsvzRixGVX1IFnb1HhWsqubjscHGAPe2fHVVcizZWGTr3+J U23OthznEt55VLJtLnz4Ix4ZyMwCABw1LwdbnZy5blo4OKMpHXiiOH0/o/3mFzyTH3/JDSJlJTOK s4e6Tx2SI0USZd8FL8ndJTNjZ9se534BGcJIqbw3T5qLCWM9Q/Tdo1EqG1u7udAmlfELlo0aOAl6 WiLW3uihiFs0YW1DSToBqndjGsjcNey0Kaw1wcRM6BRud7xA0CYZRIPqrWm9g5SUTGZhxXHjF/8A N/wmlb6gYJETyVm5DXNsJIiYIWtkP/NA+Mqpmhr6muiHjhSAx4z6ieEUx5sczhiBjA4pcWjmiZSM pweQUxKOlbtPXi2GihKSeU06omtBaAZWTS+sKKlKadUj0FqiTqeF/9Ljt7AOZ+CC7LYNGsJjx0Qn XwdB96kKmckSSmkCWmM7b23I4Y49c0Tr8oBWdl2niG/Af3qTXy0F7pMckpw1o4AVd/03fFDXFqTx XoyxjjzemEfbEdb6lM59REOIP4oXoB7tzdGlRDHngFGY9rGhrtHDkJCfHpMcMe+2qTiGPXH657V8 3p78IYDDd3cPuUHVekdsz3lWRkMjuouZ63uBiNETw7Yzck8JOueNY/8Auv8AB9TVc3uFFWvs47u/ BBtr2OjkHVICYHqDU5iGO+LEdOo19LAAlErY/dLJLvJGxsbeN79G9h4q40BohogBAlgALClry2LW gHx8UT02xGkJSkm0yCZrdiahpHbj/Uob9zddsjyRoS1ThIjYrhkN6i2m5ptO5vwMqBodMkR5q6a2 9hB8lFzIB8EhGJPESRLfwbA5okcAiOCuGjqf8ZpOABgwfxQn8wdQEd1T41bKTceW8ag8FISlI1Ri V8sUMY4hIZY7V2anol2rfuUC1zPpCArT2mvtB7qO7f7e/ijoND8zFwcWo0x/9FrE+CdrXPMDlWBX DpIBHipGANzYS1Op08FvCAQIm72l+yTFrGhoaeQiYtnoZddh+i1wn4cFD1sIA5R/QBq2GA8ceaQ1 0A0/eTlx3Akn1jaH8v0W/wBYYfteO+doeNu7wg/+Zob87IsuD2RXlUAse0cOAKFkZJyMBjHD9Jjk bnd9PaqRe9z95cTZM7u5KFaNUGi27GsuqJA0Hj9Jh/8ASarFrmGDz4qxVabTvZ7b2jUdnBSLGWsJ bpHI7tP/AJBAGl9A6hriWgOaeOfJEDj/ADjPpfnt8UE7q3wfn4KQcWu3M0RQDX7Q3KLQ1wc3Vv5v iD+6t3EGHfjvtsyBS9okVlpJcT+buBXNbgP0jR7T9NitMsloaHc/RPio8sZmNQkYS8gfp6mTSQr/ ABT/ANy6V9+L6gdUCLGxBJkGPuV6qwWVtePzh+K59rSX8+7t+K6DArBxWCYdrofMpuAkWCSfNinE jwZpJy0tMEQUysrFJJJJKUkkkkp6fozwenVSdRuH/ScrodKzegQ7CP8AJeR+DXfxWmoZUCfN08Rv HHyCpUHSSp6JpTSGQGlmtTp0yBCbtflLsm3BIapXoikZ5TFwaCSYA5KKQOSs3LyPVf6df0B38SnC XcInkERe5Pyhhdc++za3Ro4/8kq2Rdr9lxz7j9N3gFLIu9EejV7rn8nwUKqRW2Bq46ud4lN+Y+DE ARZOsz8x/d/qhepja27Gcdz4lUuqH3Vt8ASfnC0AIWTm31WZe1rgS0BvzH+9Ptbk+WvEMfU9KHAS RMA+MKo2h77CBzG4nwCjn5JY6v0ju2ul4HHwV/AsFuLZaNNwIHwEpvGADTFwccqOw1ZtAGBVAidj j8SGuKqfWEO9B23UwOPDurbf6BV8K/8AqWK7RS1vUsey4lgBGxpb9OQ7d9It9jGbnvcmA6/azyIj EGr4eA1/deKFwGI0Bu0iZ0iSSqTz+PCudTuY/LsNLQyouc5jBoA1xO1sfyWqi4yVYF1ruwc1MSy0 Plj31VCblOSm04PdFg8WDTqiNbucG9+ShtGvkEcQykuP0n8JFQXLg94A+iOPgihwLtOBwqzDtb5l EY6ECF8ZN2sq1S0PeGnQdz5LPretHDcwNLjz5+CYRqP2tzAOI7GhrKm0HVbzAjwVd7qzaTHwPmpM dX7iDPx8EEemSSDMcJsRP0/LqTJ0cssY9z5xwxEEF7qjYJ1jkqpmubtDfnCsPYw2EToOyq5lY3NI 0nSPgpBx1I0NT0amb27gBKXpF6/4zQsjeY4Q9JRrq4M+KCAna6CmiauR4juuUwCRSEpddloFR+Zc hMAkZSCWhOyakI7v/9PgzQ6JJhRN7uwAR3PYQWgyToEIY57n7kwxI0xH+9q6nGD6uYFfuAj/ABkZ see/8FYb9EfBRFDBzJQnOdJEmEgZY9Z634okIZvTj9PDqdKbCBY1znktEg90PVWav5sf690eL3Tw 1VepBgeXHGDxE+nav63/AHKJtVk8corXCobXcnXROXNHJAUXg2EFmoiChKAhrCzL7UwynKeHKBHH vfy/85Z14B0CiGHIsbpDR9L4JzRYRxEI2NWWNcT3KAlkPzA15LOYhgjA8BBlpVS4k3AgaAcBOD2T JItJdKUimQQyBCUhNwpzX6cFsPB0d5JJBYyE6ilqElWpzAVWyGmR4hFsyWs0Hud4DhB+0ud9ICPL lHUjhOxZcOb25iW9dGDDucGu1aexU3Y1fLZBHh/tRCQ5hI8NEAWvHf70vTjFS9V6iTdHFn9UKhWh jfpkwIbBkwIVRz3TpwrmTWBQXNJ1j8VRlIA/p/RhzTiDw4QQP02Qe9p3NcQfIogy7HQH+6O/dA1C eI1RIsEbDqGKMzCQINy/RLfaQ+ovr1cQWvb4/wDmSrITXua7c3QhW31tsqF1fh7gkB26DdZljxXM fMT6oefUIw4zuGjhrIVuuz1P0tcC5o97ezgqSk1zmneww5qBDFGVN22tl1e9nHn+af3XfyVUaXMJ aRxoQVbrfuHr1geF1f8AEKGRSNH16tP0T4j9z+sgD0ZJC/UN2DXFh3Dg6EeI80RjvTIA/m3/AET4 FABgweFNhAlrvon8P5SJWxLo43pusAs7fiVq12loEcdiFgVWOY7aT72cR3C0qbSWBwPPPggIjWt1 2Q3RPkXYryQ4bX+4KRqBG6s7h3HcLNZaNJMFWK8gtPgjqGOh0TcJKbba7R7+ezgk6pzdR7m+IThI FbTBJJJFTu/V5x9G1vYOB+8f7FsSsP6uH33t8Q0/du/8ktwBRT3Locvrij9VolINScUhKZxM/Cuo E6qaYtCBSCxaFJPCpZ2WGA1Vn3n6RHbySq1s5iIssM7L3E0V6/vEd/JUrrRjtge65/A8E9ljMev1 H/TP0Wqk3IY1xusPqWu4A4AS+byDCNDxS+c7D9yLZpp2S953WO1cf4JW5NVWhMu/dHKqvfk3D3H0 mILrcajwLjoC7+CNqMtNNB3knfkZFwIYPTZ49/vXPW44bmuY9wcGHT+qdf8Avy07cyyww0aeJWcK LH2PtD90n88a6f1U2WOWT0x+bevBZYJB1lR3bd1dURU2XOMMrGupgbVu9P6Ucej0bsXI1aBDRHuj 9LzX+c/6Cw8JgqsFtj/ewy13ER+d/WW1V1TI2gjLfB4/SH/ySihgyYwYyBss8jxniiKHy/utzH6T Y7GGOMQjbp6tznNIAgNMTU32/wBRB63mYmDh2+rd9r6jdW6ustMtrDhsc5h+j9EoF/Udw/S3Otga CS5cr1TLdkWWPiAdGz2HAUkYniHFYvbT5lHDMwlkABhjrj/qx/wnKtfuc53ihdkpJ0HcpFWXOJuy d5FSSQCXx4SUsxu6wN+Sna7c6B9EaBRqOxps78BMB7Se6SuixdJ8hoFIOjRD4KQKSAW3R73gduT8 FerLC12vl8FRxGNc0k6uOgHkjipwYfEppGoNAipdXR5aQhjNzMJSMOn6LYbBYTOp8ENoME7oniEK HisidTrCi02CskfIJsYi43A6RJ0bMssjGdZYm5garta/dPEd1XyWvJ11I4+CLU98nuO6gbnF0nji EBwcEfmFlEvdOSekZVGvFrWBxZB+9V4LTBVy+GmAJBUW7XNiPiFLoZUJNGcT7dmFG2pKeUR1VZdo SPxT/Z3eSIsk0bY5xAAuJFoSU6n6D5gEKYxtNTr5JDi1VKI0Gz//1ODYPcD2B1RXWsB5n4Irm+w/ BA9FzuBKiJOH0jXi1djhjzI45Ax4NKBWN47NTihnJkypDEtP5pUnOAEAEp0ZXZy/4Nhjnj4aGDf9 PhP+LbAVMHZAtEPIGgHZFdc7sAnaxrxvcNSjLhyDhhQrXalsePCePLZB9O/EbaysYx9pHmpbGfuh Cv0cI8EBA4/WdfBJyjP+rAMb14vJsF7BqSNEsazex3Gh48lTefYVPBfttIPDtPn2QGUz0qlnMcsI RsSJoW3ZTlM72mTwoOvqE+77tUWikHHinQBlMjRpntwFB2W7s2D56oUptSmkAa8Kmcm0mZj4D+9D c5zvpEmPEpUpuOyKm6TPwQLch79B7WnshQZgAkngKFxurMPYWfEaogIZSByYTeqwRryghjnmZktH 3hJxBjbqPBFfCIIvXTdsgg6gq1sYRMDVZ9T4OvB7qxvcO5Q4hCyRdtzDGU6xiXDw3KJ8P0orZJds ezsOPlqqMTqtH2mvc7V3AVCxvpvjtyEgDuTcTrHwRzHDYEBU4+menzV1YzGhTfkTxOqQMaI7/sYN ttT1CuNUfFcfU2jg9vMKv3hEpdstYfMJGiNdAvhKUJgj1S/6UW3kUtHvr4PICrgwrjGQdzgNh8VC 2oOeWtAB7HxQs7kVZoBOXlhqcZ4jEGUv5fvRYUWmp+9vHcf99Vvcxg3c49p1H7rlniWn8qs0XBpL X61v+l/5JIhrwlWi+TSWGQPif+/IQlw29x9FW2DnGeZIE1O8R+6qr2FjiEh2TIUeIbdQkYS8AAxY zVp8vBW8O0SBwHdvA+CoAn6Y5B/FGDg1weNGWaHycO6WxUDo6ym2xzfMeCBjv31gT7m6FET92M2C 2WWj80wfAqzVlFp5jyWaiNtI0dqPxTTHskEdXVHpWDT2O/BRexzDDgqddv7pkeCt1ZQjafc3uCgC Qoh0ugP25bx41n7wWroGu3fJc/0ZlTs9ha/YCCHA9lvZzhhVktIsjUgGD/FV83NYYZBCUqnIWBUm 3y0gIUTsWRMpxCH04W9Sp9bEY57JLXdocOWuWnT0LMdrY5tY+Mn8E4RO41bEs2MbzDRJQcnKpxmB 1hguMNb3JW2OlYVWt+RMcgQP/JLl/r8zCowaMnBkW1vNbjqZDxIdr+46tCdgHUX0Yjn0PBGR/rV6 XTpyMJ2M+17v5sDfBnbPH0VguysQWWOFosLT7QeT56rmcHIue7Y5xaHH3EyQiZtB2GyePonglUMU suPLITyGYl+ienkqMZyHuEXw93WtFmQ71LXbWngeSVTdztmNWXu8eUanBZTSx/ULIO0foxzx3UL+ rtY30sRgrYNJHK0IiUtIji/6K7hA9Uzw+HzZP/QUxxKqhvzrdf8ARM/iuUzbam59m126rdLC4zpz t3fyFa6jZkWt3biR+c0d5VFuNe7hhHx0/KmZIZBLg4TI/wBVuYuUw5cIySywxa6cW/8AhmUof81v V5W+vZWA4kRI/iVC2p9dJNTiCNXR3Tb7caloe0PjQEHgfcguzrjxDfh/tUkY4MMSJGXuzGunrh5J wcrzEpiWPgnjhKhIke3kET+76pIC95MkknzMrQwrzsIcDsGodGg8lDDdW9v0R6g5Mcq20tgh3Hnw n8vy50zDJuO34SZ+c52J4uVlh0BHWq7Sx+lg7NpHEu+A/vWR1K1ry5zRt3chXnY7nWOFMPaO4I0l Zea7bYWnXbI8k2OTNOf6wARjdUPTxbemTD8Sx8tg5UDDInJlMeISl6xjrj9eMfL+i0h9L4J0w51U hqSeApXCUT8k3eEp7qVQG8TwNTKSOld2N4DdtY1gSfiUx8PBO732F576lQJ1SUuRKdlfqPawcuMK ElaHR8R+Rc540bWNXeZSJoJFEhssoZU2GfMqDyRytb7NhViLSJ8XOj+LUzsDCvB9J3+adyiZ5Tvu 4j3IZuLREfBWs3Bvxfc4bq+zxx/a/dWe8p8SehY+MxN7+B2Kau0QQ7SNUzHMdYTETwo49jdWO78F SZWwuJBkDsj6/QLEterdhkxTGSdShY6L3tY4anVDdiwPb7pUrKzukagqW2xteh18EgfXImHTomUQ cWMRy6k9dP5cLT2O3RCk4ODdD8UTcGy52o7yq1129xDRtZ2CEDEg7hbzAnjlEGpdf4q9QNMg6+Sk ckAaN180EFIx3ToigaLBkycUhcX/1eUxqn2vDTqD2WzjdKc8aN0ReldMMh5gx2XX9N6c5wENA+Si hMx0nZkdfo7WfHCVSgYjGBR6DieU/YlkfRWRkdJsaNGn7l6q/ozizXVZ/WOjNY0kBOMfc39PD+1h x5Y4weAiZl+HC+U3YVrTxCruf6Q2RJC6fqeKGOOi5vKrd6roBKUo+2LhdnRMZ+9IxyAcIHF+7qhN 7uwCdgFkl4mOFD0bPBSBNQh2s+CETK7yXw+I0RkjjArDXudOE+rx1StrZtLYVW5mwxx5ov2gzoFI Rf7XjQaiE4yhL0x3O2lLI4so9eS6jvZ4mBvN1TZ+k3Rw8T+8o6KbsbY7czXyKYtcBJESlwkDVqZA OImOzEQB8FE2t1AMqGTv9OW+OsKuHHuktiB1bDnkj2cqAl30p0TNe1uvKcnfoEvP/FDMAK9Iofvn 5otiq1gDWvMOb9B/8HKx1DIyc1tfqbXbfaHAdh3O2VUpqDvp/io2tLdGn7kvHbwWzxHTW7/S/RXD RSwuf9IggDv4f5qEBoXDumGv0/lOiReA6RwPBLxRGPDYJ8/3T/VXbwCPmFeoAc0yAeFRDgSXD5jy VmolrBtMSJSMhHU6hlxxlPJGMTRN6rXuiyG6AdlVeS9xJ7aKw33yXalVn+1xjxKW/q/RPROQ/o/5 TrLv/hLcJHXUJcpcJb/3WLb++v2Sq1sbJ7poJ1SJ0S332H4qGlVuf+aXRFgc30wPKVIDY0tMbxq1 AxSHCTqeR8QjCbTu4LUNbvcnSH9z/wBBbsSDHtEa5D/rf3v7s0VtZc31RzMOCgBAgqyTvcCJLPzg g3MDHkDjsiPt6X+81OYxUeMCuLUx/wA2koebG+kTFjNa3fD81Guabq/UGjhpY3zVGS1wcNCFfFgO 3IA9rhtub/35NOjFE3of5Bp8Eg/AhEr2wa3EbT38/wA1wT5NXpv04PEeCENR8Ed0Vwmm9hWlr4f2 O1/8HLT2M81iNd9G3t9Gz/vrls0ZBNTZEmImUhfRUgN+zP02ef4JBjf3Z+aY2z2S9XyR9SzTuya0 AyBHzUi8N9x0A7ofqk6BuqI+p5rLXw0uHGug8SgQUjwRftd1L5qdG387x+C0LM/L6jX9qscS9xjc NNW+381YNtbmHY4fAngq70/I9Gp1fcuBAHJMQ6IWfzGLilx1cxp9P3W1gjHiuR9JBeo+qv1js6bV lY9rj7nNeIE6wWu/6liv5H1uyLfoBzvAk6LncHCvgv2Evs5gTAHaVYy6MjExXZVrDsZAIkTqQ0fl ViEQIjjOv7tsguNmEBQs8fC2cjrue8FxdsHl/qVidRy8rNqNbnbtZ1J5CG3LdliQNsfmp37qA18A mR7T31TicYHTXQd2Izy5DQJ4evZr1UZdIa51NjGuHtO0kET2c1HrtNlgNkew7vTPJPbdztQMzqGX fYWOJaAY2hCx6722B4YY4M6afNRQhE5RcJSo1Kg6seQlDAZTyxhceKELHq/vT/rN/IdkZLibbSAf zW6f9JU8qy+t+3edh+iRz96I/OY0kBpJBgzoguyRa5otaNgPaZVnNPAImGOfDMkagyr/AAj+6v5T BzAkJ5cIliiD6SMfF/ehH99DueTvkkjWe60K8it1Ye5waTyD4qTKqmQWNHx5Uc2gWV728t1/vCfi w5cEZyEhMkXw/wDoS3PzPL83PHjMJYwDXuaWBL+qjtysctLDLgR2H96HThssYHl5IPYCEBtFzuGH 56flVqmu/HY4kBzedoOsqKEpZpiWbHcADqBL0/8AfM+WEOWxGHLZ+HJKQ9MpQkZ/o/4CQYtbQdkt cRAdJlULN4eQ8kuB7o7s60/RAb+JSx7g+39MA4u0DiBoUMssGUwhjPBrV1UF3Lx5vBHJlzD3dLri 4sun7sv3V8W17XbmguA+kAOyyct2+0k9zqugtdspe4aQ0x9y5u0zYT5qUYfZAjxcQ322cj4nzn3q UJcAgRoTfEZ1txI+5+Kl2nuVBpJJUyIgRCLnliVNh21vd4+0fNQPKlcdrGN7xJ+aSOp8GBMNPiVB O7sPJMkglS6Lp7H43T62Vibr5s+AP53+ZtXP1M32NZ+8QFuZ+Y+q+xtJhldewjtJ7Jsuy6Hdc0us oOSHtLBMmTMg7fBAe2+prbmyGuALLG8QeNQqu51WERJHqHiUWjLvr6c6omWcNEa/vHVCvzX8RP2W 6OH1Vlv6DKj3aBx4P9dUOr9N+yn1apNLv+ifBD9D1cQZVWobpczu0j8/+q5aPS8tmXQ7CyPc4NgT +c3/AMk1LbUfVYTbzxMKzQ1zoeNAo52K7EyXUu1A1afFp+iliOdqAJHdOoExJvfozctklHjgCPWP 0v6rJ5eH6nUcInrQ0EgyVA2y8EjQdkV5YWe46HhCH6ZjP/GbuQaYhPF/if8AR9LTybfZtgAuMkjw HZVSrOVWNjXgyJIKqkIxvgFhr8xwnOaJFVv/AOhLgJiEhKRJR0piHFxb2//Wv9IraWbRq4xA78rt el4xZWHObC866FmBlzDP+sLu8DqrNgEqPGRO5HT9F1+cwyhAY4Hi/SP8v8F2uVgdbynFrhMDyV67 rOOxp9wDvCdVyfVc5xDgSAfijkJqo6nwa/J4OGfHl9MR+88v1t8vdrKwnfRC1OouD3GXLEyLXMcW NOgTcfFj9U+ujazmGYcGIiweL90UuVXvBJEaqDnvPJKJRwU/3Bk9FVfXyYPZOD9YSJcP6P8Ae9KI VvP5pRGF1Rl+gOiKh3/QHxSOIQHECbigcxLJIYyAIy0NbqOQPApt/qnb9HvKCATwJRKwWulwIHjC ZHJORAPyndknhxwiSB6gNLN/81k+ox4juFSuxy0lzJLfDwWjvaoPIcNND4qWQA1B+jn6XuA5jXQd SiMdrA5PBVi6itwk6HxH8UL0XN+idw8kExkL1LJrnjR2gTOdrI1PgmJHLw6PA6JepWPomPFDr+3q ycYquIUf0do/98jtdrqIhC3E6DjyR7PTfESXd44SZQ8/yQiwylrQ2/BahhcfLv8ABaNTGObJGspq sYNbB08gnc41Ha3UHXVA6VKQBh9rZ5eBIPCSMp+X9Go/peprPHpmB4wfkgWau+OqsP8Ae8zoOdFC ysbZHPmhvqPkTONeiX873/8AQmvxqlylqdD2S4R/6LDt/fVMaFICDPZLnVIa+3udEv5BX5n5k9Ti AwtPxj4q+4CuHNHPKqUNDCA7TUQrbIBJeNDxKB3/AK0v/G//AEZt4gBHXWEOn+ev/vF4FbfEP/BD sYPT2GC/kQlMl3qH2t4UBa5zw48jhIdxoNh4fvqzZYx9M/UZeqVfp/5v/wBDQxrryEfHtDHbHase IKFa0zvHflQDuxR3DQNRlobHQt/YXMdQdXV+6s+LfBU9QfMKzVYbKg9v87T+LVHKY0EWM+g/UJoX SFjRGxwBg/RfofmtDptgdNT/AKTdIWYIIIPbsrGLY5tjHjk+0x4jhEoib0Pk7fpCddEvRb4n/X5K q+7Tc9+0HvMJ29VxaqnB7vUsb9ECTP8AaUeLN7k+HWO+svB0OZ+ESwYhlOXHMGtI71L9J1RTi4/S 35zX7r2GPTOpPu2+3/OVSu03sD+7vpfHwWI/rFr3bbj+iOuxvA/6rcr2J1HHYJ3j+6UMkpwJ/T8m pwCXCPkAFf3j+96nRYKq7qRkNDqnPaHg6+2fctlub0rF/omKxp8QAP8AqVx3UuseqdlOscuKz7ep 57jBuIb4CAhCEpDjyAi9ogs+OWOB4YSs/vcIl/i6vd5H1iva39GA0nhggE/BZHUuq5d1Dm5T21Vv 7PJcdPdo1v8A5FcocrIJn1HT5EhSfc+yHWvLj4uJJ/FSRxwJNjhroD/0jwr8ucRhwiJymVgyyWK/ uwxz4XXx+p0VmN0du8fe6FYvzLbiD9EDUeK50vb8VZx82ytrQ6HsHY6GPDcosnLAyvGdfFdyPMYc ZvmYyofJQuP+FB3cK4lzmOMk6gnlW3Oa3VxA+OiycfqnTyIfW6px/O+lHz+l/wBFR9Wt7jseH+YO qn93Jy+KIkBk39QO395sxx8vz2ecsczi0HoIHFL+76m3dW2+79C4Eke75KTcA/nv+QCr0+oHh1bS SD2V5+XUzR07u7Y1CjxDBk4smUcJvvww/wAFs8weaw+3h5eRmBGtozyx4f3v6v7qLIN1DWitx2RE mJVb1Xn6bi4HsSjXZgsaWbPae5OqPVjY+0OA3TqCUJ4/fmRiyXAAemRl6f7oTizfdMUZcxhrLIn1 QEDKf6XrkrGtDq4cdW9/EKTsmhvLwfhr+RO+ljqzWAGg8Rpqs0tcHFpHuGkKXLmy4IwjQnpXH/Y1 8HLctzeTLMGWIXxe0K2P6XEnZRXe9xrdtaDwRqjswqW8y4/GPyIGPVkMsDwwgcGdNPmjWZoY4tDC SNDOibh9kQ480OCV/pCXDL+7Fl5k81LJ7XLZfcgIj5JQ44fo/rJtfPNtRMuJY6IE6amIWQ7k+UrR zsp9lBDgANzeP6wWaTyEoGMjOUCTEn9JzPicckZYYZBGMo4/0evql6mDOVN3M/ioNUi4lPc9TQSQ O54TWndYQOBoJ8lJkbhPHP8AFDmTJ17lJb0YnlJJJJCXHE2cwQDEeKsXPc9on6Vz9x/1+aDS0hm6 OdJ/BWGjdktb2rb/ALf+/IHfyZyKhAdxf1kf+8iwzCNzKhw0SQllnZUyrvEn8pUR+mzD3Ex9yjlv 33GDIHCQ6LCfmPf0qrc9mO+Cdr9CP9f6qlTY+h1WQzsdPiPptP8AnJy6ttbWHXQn7/8AzlAD3NYW D6JcDHw/86RWO31qpmVhV5lWpYAT/Vd/5Fyx8R0OcD3H5Fcwct/ovxHHdW9pAafP6UKriEN3A6E/ wSjoautWTECZ3RlQJNfmzJrfYJ48VKyoFvt0IUCxjnw0wpWtcGiCSByE3XhmZREtd4uia48QhOUN PlnaM0OsYRwD4qg4Oa4tdoRoQtKl7uIJHiq+W1jzvaId+VKJiICiRfdZnx5JZJExB4RuP3en+E1Q UxhPCaE43XdqRriPR//Xw8e/0Bva47gtGnrNgEF5K543At2NILj2Umlw5dCgyYyTWMemum3E9Bg5 iMY8WY+u9OIerh/716KzrJjlVczqTrJ1WQXg8klUrMh7uXFGAOIeoXxfsWZskeZIEDQhvY/e/wDR W7kZAJMlZ9rXWPLm/RPBQ3OlGqP6MfP8qfGXunhIoD1NbJE4BxxPFI+nUafy9KL0D3KZ01aN1nmU coVrS8jbrHMJ0oCMSYD1dO7HjyyyTAyEcHW/lRm2w91Klxc/Uzp3TCh/kFLaahume0KOImCJSuhv bLM4jEwhw8UtI8PdI5waJPyCVNF+S6K27o5PACWJQ/NyA3ho1cfAK5k5QracbF/R01kNtsHMnwUk p3s5sibI7MTh4eP/AEm7c/uxikx3S3nazHteR4ST+D1Vsuppsrdigy2dz3gGSf5P0VGzLyHXC82H dESNICbS1tvq6XYfTcH4zv5c/wDft6y8ih+Pc6onjhw7g/RcrLMq6ux1k7i8bXb/AHA/GUO/a+rc TFjDo2NC066fu7Ugpr73eKfc88BM0AmCYRmsgwOEUgWxAJidPEKQGpEaogaOe6mATwJ+Cba8BZlk CHcgaeabb62v0Y0jlEFNhE7VEbq+QQCiKOh+XqGbFm4Lr5/0Zdu6KyvY2eT27IE79OFbcfV9o0I1 MoVlBr9418QlsfT/ADf8rbEgJAGX8/8Ay4P6jXfUAJ7oRree3Hhqjzv9vCiXtrPMnwS8vkYZR/e0 y9P5fKh2uGkH8iNXVt95OvKXqMfqTt7IjCXOFYEzpKPnt+iqMR+jrL9PySVM9U6aBnM+aK4+oNje W+PlonDfs7f3t3PbhNHp/pOd3b46pp63v/lPCP6LYgKA4dRvg/rT/TtHa6Q1n7vPxTUU2XWCusS4 /gol25xPiVqMLcDBa8D9Yv1BPYf+YtRJc3IbnI+JXd0Q7TFoJjgtj8Zcse6p9Nrq3iHNMFXa2ZD9 +Rv2urbvLnEgka/R/e+ii9VrN2MzKMG2uGWlvBBG6uxILXPotNVgd27jyVwtDmvo7fTrPx7LOVym wmoOGr6T97SlIdV8D0P8u6EaEz20hSq0sLSNHQR8eWqeS3a/c36LxIKFxtcOWlLcJ2JZ5DBuD+dw 7+SE5oLYR7DNJI1LYPyKqlzj3S4ogURq2ccZzqQOg7lE8GUmyNY07o8BzYQzpyjGAoG1mWZ4jHhY +p5Jp3ESm2knThOGeaXrKP1YGho19WQAHCZ4kT4JnOcCoyUZSGopEMcrErUGk9lMS0apwZEpEt7l IRA1tEpyJ4THrqGO8pNdJ157FMGT30UgwBAcZNrpHGAQNC3Kep5tMBthc0fmu9w/FFt6u6xzXPqG 7glp5/slZji6YJTJZJCUTCQsMnLzy4ZDJjnUv8Ya+bt030XD+cbX5PO1WGdQx6a9tdzXmeCCAJ+K wA4ESmLm/FNhihAExJEiNJW2MnxTmMpEckISgDcocOkq/rPQOy73/nQD+7ojYV5LjW8yTqCeVQ6L W3Ioc1zzNZ4jsfo6rVZiUtgwSRqCSf4IYsXM+4JmVgfvS+aP/ObuXmuRly5hGHDKQ2xw+Sf970cS YkDU6BU8pjLbG+k4F50IBQMhr2WFryXeBJnRDBIII0I4TOY5rjvHLHQB119WnZm5P4ecdZoZrJj6 aj6DxfvLdTxX1YFtjnD27dBr+c1ZxmTK1+q2ts6VaHHa8gHb8HNKx2u3M3eIBUwhjiB7ex1+1xef yZsma8w9QHCNKHDGUvlYzqnKY6FPB57BJpdFwSGuPaIPzQ+xRHAiuZ5MR8NUPskjsv2UUkhqY8Ul b6NvHboxuvMnw/11U6He267xkhMDAe8GdrNPiUz/ANHhAcbyms8/mPTh/wC59C2EI32HkAwfM8IA 99s8iZVmua8NzuC4xPwH/kkDG+mXfuifu938Ee5YjtEfVa8zYR4aaeWigewSMl3mUjyY47IrWVby 1wLTBGoKs07OCBuOv3qqxpc4ACe5+Ctt9Nx4g9kL9Udvq2uWhcMsyDoAAYsHVe+GEePPClY6xoHh 3Ki6tzX+zXuFKx7gIIGoQqhPeGvT5W4SZSxaxyiv0tJ+a9VgI2nQhAyQwvbtPPPgj1FhbAAB7oGR UQRt1HgieLgjtMd1npGTJXFjPY/K1bW7XR4hDR7WO2h3JHPwQJRNadGrrcjpLx7v/9DhqXfpB/r2 Vlz+yA5grYXCZHdVi5x5MqOMjiHCRZPqdfJEcxLjjKoj06jt6v8Aum4b2DlyD6LjyQEBXJTo1lJ4 h8u31Ysl8uBwH597/qoxQ3uSUKxzmuLWkho4COXtHJCE5hscXNOh7pZIgCofNfTekYckjIyyn01p xfLxIkXH/O+ScY47lRePSjYeefkmRhKB45DQMmTJDKPbgfVLb930+pOh3atgameEEvceSUwfDoHJ Cf7on6a+bS2P2DiHuGQPDrXd1Ok/oun5NwEPaXc8+xu5v/VKi6y4UnGcQNrtxAA1d4lyajqLqqr8 Y/RtB93mRtd/nITHQQfHQpVRLQluWY97Eh7m6/NIe15HY6hLh/kfypIXGog8hLkflSOjgex0KR0M +KSkDmlro+5HrdI15ChbAjxRKNtTDkP7aMHiUioGk8V1M33GPBvdJrsi0SB6NZ4HdDxqnWv+1Xe5 x+gOwHirJlBdq1n4eQ50tyXtB7an/v6rXnPxBuNnq1dyfd/nBy05Q8gt9JwImdIPmkCpz8fqFRf+ kbskRI1H4q057bWw3TvJ4gLNfUySCIjiEmufWwtBJYfvCPShsd2bFm4dZC5RHol2rbiZ22yfbxxP ih8pHXRLhIADQfKmU5TJlL+cKuNFYxLNj9eDx8VX51Um8x2Sr/0FUZGJsbj5/wCsOzqfzw92kcQo tPqOLHfRbx8kxcYZs03AE/FTvrNcACHd45Te96mPz/1+zc0NV6Y5P5n/AFVfNJr49fq5DKv3nAH4 Sr3US6/NNVfFTY8tBvcgdKZPUKwfzdxPyBUbMh7cu8tMeoXsPwJR6uWdz5rZOS6+xthAa0NDNo4g KWPdtbbQ/wCha3afiNaz/wB9Vdves/JODoD3GhRQDRBRObtcW+CJj2bLBP0To74FPeJDX9+D8kJJ cRwysbbx8m8WbqnVn6VRlvwVUifnp81ZpsB2WHv7HoF7Nj3N8OE0Lzskph7C3xEE/wCvxVcMHco1 LgD4z+HdQscGvcPNGo36mTFKdcMPwYOEDTRBsbPu+9GL57Jw1scIECR9J2Z7MIfrAbJ0P8WuwwYK lub4qbq/DjwQCCDHdPJMQBu1xETkSbDIkOI7J9jVENd2CkXxpCAI3kFSB0ED9LWeNJCinLyVMRAI CVCR0SJGEfULYsMc8eKcvHxUkMtIMIm4gAarY8M5EnReQ466KW1vgoBjvgpF5GkapA9ZBMhZAgfp aniRPgoJy5xU2mQhQkdNE3LHHUW3ui5n2a51dgiu3v3Dh9FbLs9n5jSfjp/euZVynPboywGe7xr9 6GWWaEQMZ/C5fRu/D58rklKPM+n9w2Yw8puqL23Wt9Zo28aSIn5q62utn0WgfAKjXh2PAdLQ06gz OnyRrrbsdrWiHCI3ka6IYJzhGU80D3469bc5rHjyyx4uVyjrH2hKXt/vcQ/QYdYqFnT7ieWNLgfg ufpM1NPl+TRa2VddbRa0uPuY4QNOR5LGxjNceB/KiM0MpMogjvfVzuf5XJy5xxnISuJ4eHaOqQ+K lp4JjPBSGoRc8dl7BDW6yDJ/ghqdpMMB7A/lKgUlFZSq/nG+RlRKJjj3/L8qScYucfNO/Sl3bc4N j4f+cpZkBlVY+ad2raWnlxLj+Cjlndktb4ABNG66R0J71/3y+QduNW3x1+/X+CFX7aXu8dB8/wDz lEzzDms7ARH+vxQ3S3HaOzj+T/ztEbLZfN5CkTefhr9ydoLnBviYTDgqdABtE8aooiLkB3LYpYa9 0CR4p6yxzjIg9kqwQ47SC1MwtNh3iD/FNv5L/ePzaj/GdQRA9wRFDgH836Zf4WNZzHNfLdZ4UrHw 2HN1KZ7HNfLdSeE9jxtAe3UpbCY1j5+qKT6jhOmTxHoyKrbWWyOeD4ob63NMczwQiVNbEtJnuoOL 2PknVCQHBEkV/WinGScuQCXFp8mRE4loh414IVV7QHaCAeFo2bHsl2h7SqmwEkfgU+R1ABEvza3t jhkZAw1+YXwv/9HiLHNc0sBknhCFB7mEzPpD4o6bCstykNtHSzcWCoQPzDiJPdGKWDnVBc5xOpJV g2MHJCEKSTMiDwhkhdCAHjX7VYchFyyk/wBUy/HhRqxT/NhMKG9ySh2EtdtaSG+CEYnH6pDwXTnH P+rgf61nbROSByYQ7B6hAZrHKCi4/LvkiMnuHgIoFacPsxOQS4pR2009XpW9AgS4gAfNV3Db7p1V 1/0HfAqm/wBwgalPOOMRoNWE5pzIEj6evZpyUbHeSTWTz9H4hQfU5p407JhLDuB1HCFFglW2jeJ3 Vh3dqkfc2Rz2UKnCfJ2oUme0lvhwgxrj3N+Kcatg/NMNHEeOoT8O+KSkdswD4aFNlPBcKphlQDT8 fznKdhAaZ4j8ipgusgO/OJc75n/vySYizQdwAAADgDT4JFUqsl7WhoIIGglJ+S8yN0eQ/wBdyFLi K0bT7WVj3H5DlUcnKHJ5/NahWXiCW6n+KqfpHumC4nuiAgAjdKHl8mPiU4JBlNW0tku+CUxoimQO hWc3ZqODqAo7iUYN3sInj8iAfaSO6Xnsm9iN2W7sEQCBIQR4lGr1IHil4d9lwN6jp839Z0MV0VNc ee0/BSa+HF1mk8KBG5we0ewAa+QUnAW6gwG8pmvT5ofL/X/ek3gI1qfRkA46/wAnXyQS9MYWdSbP cOP4KlY8FpaPzXudPkY/8irNdjtwuHtLZHyIhUgddeDoU7TcbdHPzRMckgd7vTxZk8WD4FS0DvJ3 5VFmssKTZLI7t4SY0gG5jmH/AFIQEYO1Dh3/AIIdrdr9ODwkv3h4wP8AzZJMZ07qzw4afEI2QN1b LeCfa74hVGO2PDvAq6RLXsGsje3/AL8gd0w1FNWsx8ilkA+qT4gH+H8Em8/FSuIDmHxBH3R/5JKQ B3ZOXkRLREGOT6tHipqLiCIlHgEQSDqzDLKZAlG43sAxL3KJHJ+9TDCn2AfFCIndldkOExMRV+AR KDxJ058EnyDB4UQYMomYOlaMMcUom71HRcMPwUoLRpqpSIlRLm8J3DEdaWccpHUWO1MdzvFOwwY8 UgyRMqQYAmxjKwV0pQox/ILqLoPHKi6QYKZKU+lKhjqpWy2HxT7YGh1Th0iSmL2p1RAtaZZCaq66 UwknunaYcJ0HdOGhxP5FINaEwRkdbXynEAxI+j1lArrx62tdLGtAa49xHKhkW47qywuBPaNdViYN 5I9Fx+j9D4fuq4mZ+bkDLHwDatfVYdj4fyGLJDHnGWXeo+ngnH9H9Jsswd7QXPG1w7eC5vHDmWPr dy3Q/EGF02HdtaWv0aNQ7sFzmRtZ1K6NWmxxEeDjLf8Aqk7EMXtxMBRl8wvXRpfFffOWsp4owJEJ VUan6v8AGSOjsmbynKiNCnOZsWeRyz+qEM6It4kNPgAEI6klIKluVkXHn3EcgaflQkaiQ1x8YH3p FOP5r7CX/RbAH6xU3wb/AHoZ9+cfiB+RGZ/Sz/JaPyAoON7stx/lH+Kb/BJ6DvJhmmb3eWn4psjR tbfKfxUbdbz8QnyfpgeAH5Aj2WHcouyNjEh5IE9ig+CNQIEgw6dJ4RJrVl5aIllAPaX/AEU4DfV9 p2+SYuiz9IAQnsjeNwjzCT94cHfSb2TToD4S+n+FB0BqYk/pQoWfVp+5kitYyHBzDqeyd7oZD26l NcGEyDBPY6KTi5tfvG7xR2M6006eqH2I3GK/UQa19GT/AAZLVNbEtJnuoF1jHy4ypVBp1BIcouL2 Pk6+CadIRO2u8flXR1yzBqVj5Z+mX+DL91K51bme4wD96AKPUMtI0790Zxrc33GPCeUOtjp3MI0T p6zjoJf3fmW46GOYsw12n6sb/9LiDU1rSRyBIKrOLidTKtOsZBE6nRCOOeSY+CjyQsgYxp1p1cWS omWYkG/TxDp/VQK236I+CgKGDnVBeTuInQGAEo3i1Iu0TMeYIjEkcOtkNkvaOSEJzPUduadEJHo+ h80Yz9w8JGm62WL2I8cTctvDVYUDuU1g9MDZpPKKXNHJAQ3gWwGHjlOnCIiREDi6fvLMeScpAzJM P0tPQhJJ5MobW7X+SsjH8SmsrDGyOSY1UcYTj6pbDdlyZMeQe3E+o6R00REA6HUIT6mEQ3nwCm5k 9ynqpcX6EJ4yiRoDdglysoAyOvDqxraWNA/d1CM4/RePgU5ocGkkjTsoNMsLTyCjKNNSW91Vs3cB w5GqciWpqzLY7pM0lvh+RBDC8zQ8+SrUmGbu50+QVi8H0rAPCUJjSGARrCTJiqyT0ZAz8Qh2P2Dw PbyUxwB2j8qr2uJeSfmiyzNDT6MdxJ8yrGPc1tbmubq785VkasbRDhqeAkWPGTdhmeROjux8lFw1 mFIyPbzPJTO7EfR7JJmPSpsgGChvEvKKBoh3GHCO4SWx+ShvaOdY7I4+i2PJBIACJXEAHvCR7FdD ex06N+h0sNXdTEsd6QMgnU/FCqlhLxz/AHyjEbq5iXuTdf8ACj/6T/d/wm9CuEHeE9/9r+//AHYL OAa+OKxz4Ko9pa6O3IPkrbQHN9LiOSowLGEGC7hiQ/PUefWLHnxHJHf1Y9L/AHon5Z/4TXmCHfI/ JT+jZPZyGBy088/cpc1z3aUXPZARLfAyE9g3VyPzfyJTq13jofmpMEyzxBH9yS7HuR+8OH/vf+c1 1eofuZU7uJrPwKoqzima7GdwA4fEIS2TiNS/l0RuBbY4eBT26+nPiR+E/wAFLIg2B4GjwCoXuhjf J4/IUh0tdHSRA76MHTKipyHHVSDQOybwcRJB0bvuiAEZA8VLNcI1S3tSeNPghp0pyjp+K3HihkuW u/ysiwWT2KHtA7IjZBnso2EfSHzRgY1Z0LHmhMy9FkAdEbxBkKKkXzyNFIAdglwiRNFbxmEQJDVi w6GeE+9qkRIhCIgwiSYgBbERmSTp4MpDiJ0UtrfBQAd2CkXxyNUoncyH1VMHQQP+DanCR8FBSLz2 0TsgjzQNSOiYmUI6i2LZBmFIvAUlB4gz4okGI0WgxnLUUov8ls9DtNrn1WNDwG7mudqRrG1YgBPA Wr0bN+zF9TxIfq3xkJQIvimNBrZFs8BISjDFIxlI8PCJcPHbvloILSNDpC5TrNBx+oGeHgEHy+j/ AN9W8/OtP0QG/iVjdcL7BXa8yQS0n46hNnzGKc4iN8Wo4q0ptZ+Q5nHyuSU+HhBjMwvilxD08X7v 6aJrtzGuSIPyQ8Z0tg/ESiE/ii5J3SPAIaD3aNUFFd+aP5IQ3iHEJBUt7Yqxjj2HzI/KFXVjGOgH i6P9fuSOyce58i2KRORafDT8EHCPve4cgEhFqP6S8+BP4EoeCNLD/JKb3+iesfMoIm4/EpZAi5w8 DH3JMM3T2J4+Ka07rHHxJKcs/ixGhEqy0D0NBImT4hVjyrNI/RxxIncEj276M/KfOZfu6/8AOTV1 +oBBljeQeUQ01zMajzKngU23MdsbMaSIhTfTYww4QfAqMm/wZskzGRjxVVjT/wBBaeUANoA7Shtt 2sidfAo2W1weJBAgAFVy0J479SN2H3pj06SgDfCRp9qSosJ4h3ZM4WMeCCT4IbdzXaa/FSmXSzQ+ CBFRA6g7x0P2NnFzEJ5DZ4eKPy5PVD/Bn+ilc5jmjf7ZUK2umWEaKbnDZ+kbz4KFTZMtdEdkZazj 18vTNfj0xT14RfX9Zi/waf/T4Ecq2eNVBtLB2n4qu4knUyo43hGovi/Y68hHmSOEmPBvY34kxsYO Sh+lvJdMA6hCPKsVn9GEYy901IaDViyY/YFwJ4ieHVYUMHMlDu9pDW6COEU2MHf7lAtFp3AwBonT jGuGFcXhutxTnxcWW+D+t8toUajkqQoYOZKja0AAMEeKZHHKHrPToyTz48gOMGuL9I/KEpc0ckBD eRaNrTqNUP03KVY2Ok+EJ3uSloY1E7sP6nH6o5OKcfl7WuMcdz9yT2itss0J0lENjAJJUHEW+1p4 1lGUYAVGuLp+8mGTJIiUyTjHzaehCS48klQBhysihvckoWQxrSNohMjjlGzJHNTx5IgQBuOu2nD+ ks0w/wAink7gfHRQJ4PgnJBEpzSZW+5pb3hB1IEa6IpMgHiUOANByky4TqQtzz3VZ/ucT4lWj2/K qxEGPuRC7J0Rqy0Q0Nd9LhQawu18EdjQ4T+ekSrHHqf5eP8AcYGWiPHkpnfSAbx/FXcfJxq8PIot r33WQGP/AHVS2ntw3Upfy8vBWTY96+kv6y5MKFoA2+ICnDtu6OTAQrD747AQksjpD6sQUapu7Xs3 VBIJMBWqG+0VxqTqUj2K/GCTxDpqfANrGhzSXgR2Tgmtxc4c8BJ1e0gAe1o1KkYsaXxxMBN12/Tj qD+9/wCit2PCAOuOYAlH9z92P+Gs4FjhE66uKTjBFg76AJNkg1uncdSUm6yw99G/BLy0vb+rMJ23 1Mfm/r45fpfy/wAmgvAZbLeDqEzNHFvYqdwmvzYdPggzqCjd6udngYZJD6s2iWFvcKbXatd4/lCi IFnk4JDQEfumfkkxsbRFjo45CJhmLh4HQ/NRuGjT8vuTVOLXA9gQfuS6Mh0yWOpEv8b1Jrh7G/yS WoF5/Qg/yh+VWrBItETqHD56KlkfzI/rhAapOkv5fosgHTMKRePBSQ3jX4pEGEfSW1GUcs/WOmii 8lTbESFANd4J9WjxQgTdyuk5IxIEYEXewO7NCcIMJy9ydjtde6UpRnQ/FUITxgyNHT5UDq3A8aJ5 LQAdVYcJEIDxoR4J4jQNHVrynxSAI9NsN7lJhmZ5UdrvBOGEGZQjxWDqmfBwkCh5M1F4kT4KJe74 JpKMpgiqRDHIEGwvtd4J2tc3X8FIGRKdEQG9olkkbBARl5+CW4zKdzZOmqQYe6ZU76rwcYHQX9rN O1xaQ5pgjUFQMtGigSTyU8zrQhZHGTqDpeh6u7i78msPY0+B8J+KbqOBa7Btc6BsG+OTpz/0VV6H m+hkei4/o7tPg781dE6sWNNZEhwIPwKZh5XEfVZsHa9I9nUzfEc+TD7REanHglKvVL9GTxWO/aR9 x+atu/JoqllTsfIsof8ASrcW/cYVljtzB5aFOLjnbyXOm0/68p3+4bvA/gUzpGhTt00PB5QWlgj4 /wCb/X/gguG0wi4/5vk7+CR2TDr5NivnJ+LvylQxNKrCOYj7yp185Pxd+VybErf6TxEboifim9/o u6j/AAmrR/Ot+I/Kou1cSrtOCWOD3P1GsAfxRW4eO3XbuPmUbWdHMPJVytjvYQDEAEgSD8Vbaxjf otA+AhSSv+LJiyHHel8Q4Wz0y6rHxnts9ri8mNddAoWZNlujjp2EDRBTt5CbQVLIZSJoWWZ3Edig vxK3iY2O/k8I6RhLZJ1OzTGBGpf+CY4E/n/h/tV1JGytIDUbjOaNrnbh8P8AaojEAMhxHhCuEKJa kTdX02XRyZIAiMtDu//U4g3VjvPwURSHe4nQ6x8VWBhW63tFbZMaJkZDIfWBQ1DqzgcMR7RPFI0f 0leiwDifiq9ujyBx2CsG5g80PY2w7jI8kZiMhwwq76LYHJCRyZeLhqvV38kCNQQGmfFTFTB2+9Qc C+wMYJPAA8ShHGYHiJHksz81GUDEA+bJ1hOg48UejAybhu27Gc7n6BHbTRgNa64erku+jXyAh2W2 W2luc91YABFbR49v5P8AaSMiWgTe7L7LgVmLsncf5A/iN6f0ekf6d/3f+o1XbkU12uNdTXM0DRZ7 iPNNXlbbHuNVbt3DS0QP6rUqU2LOlMsrL8S0WAfmmP8AqgqNYNbnNf7SNCDorWJkV1P9TVtpfqG/ RLD9Jp/qqXXGNGQwjlzZP5ECeE8XZscqTInF+jk/Dh9TVNzB5qJaLml3EaAIQaTwJRWvFbdrufBG OQyPr0i2cmCMI1jszOnjwn5mt2hP+b8En6vJGk6pgUfJz5RMSYnQjRcfRI+ajJTgwUklQlwyBY2E 7T9yDvB5GvZGeJae3gq+qIZpnYjZKHxqNZ5RAS3VupPKrskIzdGy3XxlJMT/AC/7mS/M/vJ6n+mT pLYgjxTBs/R+ZUHvI9sapKlVa6jsdwkMTIiO45VYgk6CSUbZDAD35U2bWt+KWl1sjhlwgj5eg6sK mhnIl5/BWq6SGggGSdPghikx6h8dFbrdsbBnce3kmkj5Zadj2bGGBA9yHqreP70v+8iphDm+l4cl RnY+fzRoB5pnsI0ZPEuKUte2Y0bMfclR2Oko7fw/wWUyiPUNcc74vOX6X+Gye2PcJ11d8PBQda0k OEg9/gh7nEQT5qTK3vPtEpVv0vo1cnNSBAhR4bHF+8P+9SWDcN3Zw1H/AFKq9iFc9Kxn6K1u0kSJ /wCqVVwh5HCQ38/z6q5gCUIT7Cv8GXy/91Fcn2td4GFP87+sPyKDdWOHzUgfa0+cFFqqdrSfIg/w UGcH5IoEtc3xkD8qE36JPmkv6RP0+xtT7Zmd1f8A1KpZOlPwd/erG4eg2D7gS0jyOqq5moEeJ/KE AmR1BHZIXOSadfikGOKcM8SmgTJB1+rflLEImNgX+6zTOEhQc50xKZOlkGopjhgOkuIDqKXDXFOG eadhkfBSRjCNAoyZsgJjoOiMudMIdgJ933orhJ05S9PxTCJEmtWQHHwC6iSO2qJpkJ0z2bJ2ock8 qQy4QARq1Pb4iSDpbJwk6apbD3KiDBlFQiBKyUzMoAAHTuxILRooEk8ohIHKgGTwdEpDoPsTjloT L/GpTTBRFEVhO6t48giLiDaCBkkBHdRI7qAYT8FIV+JRKw1piE3jEiLZfYnCJILFlJkGY81v1ZRt qYQ/UiHNnWRysdRLwNQYI4IQzQEoEA8J82fkOZlgzCZh7sTpIEbf1o/uyY9Xq9PLFo4sE/Me1yFS 7UtPBWnmYrsno4yy4OspOoHhO13/AJNY7XHn8UscZRhETFED8OjD8QOKXNZJ4jcMlZB0qU/5wf47 d5b5jT71GISY8ODTGvf4p3Dv3TmlW65G5vmEbCqc8E9gQZKhjVG20NGg5cfJaora1vsEN8ECeiom tUTKmMLi3lxkqSc8pkEqSSSSUpJJO1rnGGgk+ASUspsHdTZh5T+K3fPT/qoVlnTMogTDfif/ACO5 C0xDVTq63pNv5z2j4Sf/ACKn+yP+F/6P/mSFhfTnJLTHSq41e4nygJx0qju934f3JcQVTlJ1q/sr H/ef94/8imPSqOz3/h/clxBRD//Z ------=_NextPart_000_029E_01C07B15.387204E0 Content-Type: image/gif; name="Hull17.gif" Content-Transfer-Encoding: base64 Content-Disposition: attachment; filename="Hull17.gif" R0lGODdhMAEwAfcAAP///+fn58bGxq2trXNzc5yUlGNaWpyMjHtSUpxjY5RaWoRKSmMYGHsAAGsA AFIAAFoIALWEe2sQAIxjWpRza6WEe+etnHMhCJR7c86cjK17a2MhCK2Ec3spCOfWzsa1rXtaSpRj SpRSMa1aMa1SIZSEe5xjQpRKIaVSIYxCGIQ5EK1KEJxzWsZaGN5jGJRCEKWMe5x7Y6WclJSMhHNr Y62lnJyEWq2ce4x7Uq2ljP/ee4x7QsatWqWUUt7Ga4yEY5yUa6Wca7WtWlJSQlpaQpSUUnN7Qlpj MYSUUnuUUoSMe4yce3OUUr3GtWN7UnutWoSta4zGa5SljFprUnuca3OUY2uUWlJjUmuUa3Oce2OE a3OchJS9rWOEe3uclKWtrZylpYyUlISMjM7e3oScnGuEhK3W1kJSUoSlpZS9vb3393ulpWucnBhS Y3uUnLXn95TG1lqMnBCUxghKY0qEnBil3mOtzjF7nClzlBBrlBB7rSFrlEJrhDFrlAg5WjlrlAg5 a0JSa8bO3muMzkJajHuc52N7tTlKc1JrrXuEnFJjlBgpWgghawAYWkpajFJjnFJrvTlKhGt7tRgp awghe2tzlFpjjEJSlCk5ezlSvTFKrRgxlK213oyUvWNrlFJahDlKnDFClBgpewAQY1pjlCkxYwAQ cykxe+fn962tvVJSWnt7jKWlvTk5QoyMpUpKY2trlEpKawgIIQAAGAAAEAAACDkxc3tznGNajL21 1mtjhJyMxiEYOZSMpXNrhHNjlFpKe1JCczkpWox7rUo5a1I5e3trlGtKnDEhSmNSe2NCjEoxa3tz hGtae1I5axAIGCEYKVpCa1pKY2tSc2NCa4yEjGtSayEYIRAAEJRrjIRae62MpXtac3NSa2tKY3Na a3tjc617nIRreyEIGMactYRac1pKUlJCSpx7jHNSY0opOWM5SmtCUpR7hHMpQkIQIXtKWnspQmsh OWMpOVohMYwxSjEQGFoQIXtSWoRSWnNCSnM5QsZ7hK1rc1IIEAAAACwAAAAAMAEwAQAI/wABCBxI sKDBgwgTKlzIsKHDhxAjSpxIsaLFixgzatzIsaPHjyBDihxJsqTJkyhTqlzJsqXLlzBjypxJs6bN mzhz6tzJs6fPn0CDCh1KtKjRo0iTKl3KtKnTpxwDDBgQJw6ePFizat3KtWueOW3ioPkCtaxZhwKm Vr2qp47bt3Djyp37Ng8dNmbU6FWDBkyAs4ChpgVTFascuogTz9WzJ86avZD3pkEzILDloVMJxzGs uLPnOnLsrskbuTTksX8vq6Y51U0cOlg/y/as506cNKZzm04DRsDq3yelUn0de7ZxxaHpjNbNPLeZ scCjaxS+Nk/b49gV177dvHvzNb2li/9nOLj69ezoESdf7r198+eVx4sf8wZOHDuc0+tPnOcOG9zu BdheX6nJd1kc+yXYmRx7KCfggwLy5puBZwXAh4L7bdXHhn388cgrbkAo4oPPfVEghUwF0AaG/GnF YYePxPhIITTWaKMkrOSyCoAj9uidhCgulYof+oWW1R4veiijjUw26WQhg7iSy5SsJEKaj1jqVmKQ R1UCSGJGYoUkhzI+YsiTaKaZJixTtplLLyFmKWdu4J3IZU8BfNIIVkmWeaaagAYaqCE5utnmjnMm Gtlk8d25UwCiUDKIoJRWaukqhhpa5ZWKKoqaozilIgomk1pq6qlOepLpqnB26qoaQIL/OlMYpkSC 6q24Errqroi+quiWsr70iSmI4GrsqZjuuuumvnYK3oTBohTAIZIeay2lqiqrbavN/kpZtCYJMGqp 15aLpq7apttrt4kSCG5IqZiCibn0oplsuukyy26ik0H7rkbDFlvvwDZmi+/B3O47pxlp+PsvRXlS 8ifBBA/Sy8EYT7muwlma4fDDEEE6CbkUD1xJxijryzGWaNgJckOpjDJvyRSTgvLNb8a5so9ivAxR JcTSTLHFOOO88c4k9uwzQ59ILDTFJxeNs8pIR9jo0gYFMMnITxNss9RSJ1x1gGW4jHUqk8zcdb1E gw320WN3dwbWBdEq8Nr1Ru022FTH/82cGQTQLVDTE+Nt7td77y2237pxUQ3W03JtOL1RJm65jjwy nlsXH4MrrtqTm8vm5Zb3rTlkV5gta7yEhF4vjqSTvvjpepkxxcOfMHK369dWHnvscJ/OhRLg5skI ybxbO/rvsZuuuRZNBAsp6MlbCzvzzM+ueeqgxtx69eX6jj32wcedhhOOdqI7+OYaPD72zo/txRJc KnI8++Wi+/772o8NPYWoGBX+zHWv/e2vfDszgxU6t5pUbOJ7A7SW+wy4v/itjAtVUJ1lOEGJ3UUw V4WioAj7t7It0C86kLjfB61VQBGKEIEKw4IUfhMAUFBvhbeaoAtFaEF2KTB6l9EaBP9xCMIdGrFN JGQXBjXYlAAswoNERFULj7hDGDYrC1UITABKgbwongpxVKRiD31lhROWJRWB6KIXLdW2MLoxia8y AxOA+JQBHGKNx9KbG/doxU554QlMLMoAZoRHXIFxj3sco6KyAIVACkUQaiwkpdqIyEr2QgxhWIMm u2UGKJgxKYkonCRNpcdKVrIaHkilB2bAyjC4kgya5FSP0hAFMCwlEpcYJaoOaUpEolKVwAxmDVh5 gFdq8jEC8kIU6GgUAWjiFLo0FSV76ctgWvOawWTlDFwZBliyxzRYaCRSKpGJTDgimpUqJTX3+Ets uvOdqhzmNo25hjR0kgpIOUU5bYX/zkBdb52nhKdABxrMJsyACFH4pFAGUM5MaEKU/WyS+ABaTYJa dKBAEMITmBkURzQ0E7mMKJqWR9GKXvSk2ASCDooAyKEEIBQfhaZInfTPkrITpTi1pkp1gARxBqUX Hy3nOWdqo4na1I3tzGlOd6qDJCi0J5EIaib4SVQakfSoSFWqVmGgg6764Am2/IkzpfrQqhaiplgN Y1K1etIZdNWrTGDgTRIh1XKGdKZGTSsV18pWi7r1rToQQgZ9EtW6ynSmOtTrEfna14H+FbBC0EJP GFpXoc5Uf4pVa2NR+ljAFmGGOyFnZac60ylm1oiM3ew7OwtYI3C0Ji8drUMhKsnE/552h6lVLTZZ C9gjOLIlQJUtSPuJ2dsuVrd+BaxyfUCEnHhUuIct5CAUgQtj+MK4WUWuY5W7XBrcZKzCNWchH2EJ Y+zivMO4GHaPq12B8la5QnhcTegaXtJG0RCk0MV593teXayXve1dLXe52wO5sqSw4S3rBwdBClwM g78Q3sV1/+vC3AZYlT0YsHJx8NtwaaK+dh3gdKsb4RIPQ0oUpqCFL+yBDGsYsD+YiWhBHF3ekde8 Jc7xLm4RwhSPb8UXdvGL35oDmegTxJZ1HX71q+MmS9jH+wNygIU8ZB0EISbBRbJ98cZgBzv5yyeG 8o9Z/E4qD7kHMXmulhUstBHj+P/LcOaxmJkn5faa+cU86HBIYqvlENPsxnAONH8nPGfS1Vm7d37x 1VaS5T7X2FxLFrSk9xvmQl9uFWR2Z6I1vGiVILjP4oV0gx886VLvwhg9tvTbMo3NTQ/4Bi4BL6i3 bKwRk9rUuPavqveGaVZb09XchXVL6Dvr2RrrESTGtbL3a9pdZ6zXvgYmsJWL5pYcudjDPZUhLMHk ZXv71Kl29rOjHUymVlkH1V4JZbGdiUerCb9e/ra8d6Frcd8M2uT2gLnP3WmTzJjdQ1WTredN8PM2 297Kwje5913lfpOEz+ymtZOQ/eaCExzVCB93vlPJ8CELOyWNZjebbbTtblv85PX/zri6Ns7xcwP2 4yhRc8SzTSN43/rkOH+yylfO8o6/+MopkfXMoTnwnBsdverdOa9Yrm+XvzXdJyH2zB0ai4of/egp V7qhFB5tn2vYBwb+yKcjHopiFOPmVz86obXuJq772uucRsm6Z24LZRzjGMFIu97Ty/atMx3uAy7y Sf6NbU0s4+53V8Yv9J72rLPd7awGfLBRcm1sn6IYiEc8MNDO+JOv/fFMf++QgV6SkINaE7bIvOqB 0fmjV7rvkM+06F8M9ZHIHNRlV73qFd96o8sZ9qF3+lvzXBKIg/oUdte96onRe6N/fuexJ/PsFV0S qa859cpXPuubf/LXKz36LJ6+/4ZrUJKxgzj32Ve+MqzOfXn//vvBF35XYQ4SoYO47ulPP/Pbb/Hn Ixz8FyZ+A0Z6IWF9CXZ4+Zd/28d/8+Z9GQeAASaABEYSlRdel5eACXh2DHhx4SZuENheEqhcxBcS cydcqIeBKJh3GzhvjueB8Sd/OuBwGnF7o4V+KIiBybCC83ZwlvaB2tUEPACDMbhnMGWByXeDGKiB OuhtGPeATNdiQkh/HGF6ZIV9SHiDKriEy9aCquaDiBaFIWF+QWWDV4iCvKeFy8aDPrYKq2AOJfCG 2qRNTUBm0zZgtbcR9hdU+FeGV7h5aKhsTQhlbMgMzCAO4kAO5EABFrCIjMiIEf9AAZAYiW84iSUQ h6xUAxdVhxP4EQbYUIbHh6C4gH9YalyoV72wCoRoiIi4ioi4DRHQiLAYi7IYixkQiZGIAZQIh6yk idwlgxYhhu2GeaDIh2c4iqXmfxR1iqkoDtvAis64iuIwi9I4jdQ4izYghEPYESVYTic4jMO4f8Y4 aXwHUMpYiMz4jOjojIpYjezYjrEYA9gohRhBeJlAht7Ih6IYjoFWii5UjobYjOkYkM7oiu5YkO5I AfHYEcbXbkd4j6C4fvo4acg4PqyAiuYIkAKZkc8YjQbZkdXIi4BFgBnRaN3okPcIjhEJZ+MIP4No iOigkTApkOvokTQpi9cIg3f/eBFqZo8mOYz5mJJNxo83U5Go6JIxeZQZiQ4ZUJNMCYvwCINgtxF8 toc96ZBKCJRfNpH50pLi8JJI+ZUayZFNOZYR4ANC6IsRQVefWJVVmYVY2WQOuCxc6ZVgWZcwOZNj 2ZQgSWQbEQkXyJZsmYNv6WTv13YW2ZV2mZhIKZZ52ZQ3KX/yOBECYIWAWZVXOZg5dl2DaI6K2Zlg yZiNWZNPKX8iWRED0JCV2ZNuiZn8NQzNMA3n4JmyaZd4GZo0mQFBKH85ORGqgICpWZXFyJquOQ3a EA7hkA10OZvKmZGgaZs0uZc6MIIXoQrC8JuA6YeYqQvEaZzcGQ7agJHLGZ4b/+mcY/mYwoeWDqEK vGCd1/mW2tkN3Rmf4fAN4lmfrEiQ5MmUCAmD5IcRtCAL7MmWwTmKxtAM8CmfCMoN9mmfzZmfBomb MBiZEUELtBCgbImSWlig1pANCNqhxgkOCyqetemgHQmdpTkRtDALwmihJvmT/OeaG+qhMnqc2RCi yomfJEqT5ulyuwkRAzALs+CbLHqPEMmAw1mcM5qk32mjstmgOXqQMCidFPGjs4AMQ9qTGNp6r4mk Sdql4dANTOqZI/qkBQmd6LkQVLqeV9qivfeeXvqm3KmgYWqXSkmmNbmj/DadQAqga2qVnIdzxjAN BwqnhBoOIDqnn2mnohmhev86CxXapw65mhanoRxaqJaaDTWKqEg5porKjvspfBKankCqopDqkIJZ cJRqqarKnUuqqTBZp53qkXvZow6RokAqpKXKh5e5bMNZqav6q94Jnq6ajk4aq9WIp2d2EbY6C2qa q8MoqeK4pcA6rXE6rBnJqcZKjaPpcicKEcvarM5KjItnatrJpdR6rodqreOZrR1ZlqBqEVQKpI8a rqH4pzrmpuear9yJqeq6ruxqkCAZqgwRr45Kr97oohFWoIOqrwwbrP3Kitj6r9KIrOMHr6N6qwb7 kONaYqnasB5rnK3ar8UqsdK4rQ1nEapwsUGasaCYpTDqqx8bs3LarxFLsrL/6K4ud6YJkbIXC64s i4Tbd6QxO7Txma7DiqM2246aKKUSEQYqCw0/S4zSsJ1EW7X7mqnDOrJJa5M8ehEEW7BRW4YLa7VW i5zWWrNbC4ufmqwWEQDL6qioGbb5twxkW7esKqxMirRpS40QWmXd6q0qi6tym350a7d2S5+aqrV7 C4t1KLAN0QoqW52Di4HOYLiGO7NhiraLy4gU+3IYwbOj6rOTq3zRYLl2y69hCqubW41rG3de+7Sj m4DUYLqnm5wLqriru4h9S32ve7HzGrvKN7a0S7Qhu6Cam7sW0LldpbML8ba0ELfAe3fCO7xDi7gL qrrIO40mS20a8bYrG72q/1e41Fu3mCueuJu9rcu9GQG6QGql4Jt54ju+ZGu04Xm82etqtAoR7Mus 75t5lSu/dYu64Xm+2Zu8L+a4DvG1fNq/x1C6AFy3xTubBJy92/tWCNwQX/u77zu7D1y3YLqcelvA 0pi+FrwR3rui7zu9HSyzyznBBbxpzMsQ3iu4wKvCK/yx9KuY9ivCFBvDC7G/7vu+8XvDVSvAihnC IlyyAxaVGkEAKiu6sTvEREy8eJuoSdyOOAtY+RsRCszAxDDFdhvBYLnDSXxnWwwRAqCyGgy8DgzG ZFu+X4m9V0yNePq3FDHD/dvGbmy1OXyULpzE23vBDwENgdu/NrzHDWvEm/86x+64u/PXEfsLxZN7 yIjMsGKskXLMyNNoZoK3EU7cs+9bDDBbyVT8lX98xTvqwwOrxkJMynYLx9eqyVAKWKq8EGnsu+/7 xa5ct31MrLLcyLmpA0zMEXgcvXq8y0SryAF5ynMsZGcsEYR8sZLLxsgcwLabjmSsyY/5zBERyeBL ydWsr5fMisw8x59qxxXhtBcLtdELzuGcr9aLzb8MsI/sERkcvaL8zuQbkEg8zxNbzwrpvNAbtVKs zzGrzIhYzoz8lP3pEcU8ugVt0B9rts+Yzb+8n7X8uJFLzRJNthHcz/4sjRmW0QzhzbF7zB1dvc6o 0NrMtBuhzqPKzqNrDSn/vc+raNHzHAPcLBH3HLvuXNPoioiZHNLUGAE7sGcnPLrKYK5APbT8ytKy PAQi8dByG9FN7bHfidP+fAAiAbkXG8RVfdUevJREXZAgEHaNGtOji9Ji7bHZoAATUNZYfAIwMBJf WwvQMND0ytZtzbD4wA/8ENdyLY0ZIAItsAJ6NqUqWwu08Aw0TK803dcxmw6ADdiCPdiwqAEk4AIu UNcksay0wNihDdYZ+9OSXajl0A+VbdmYzYiF3QKcLQImAdoUWtt5zbJLfdqJrACrXdmXLdeazdmc LQMmAbqiXduN/dh9atW6vap/3du+LdevLdwuYAInYdzIXdu1QNqlytzN/12ozw3d0R3SCrAC1O0C LYDWGxGvx53dtMALes2ifP3dqK3a4r3av83IhX3enM0Ccjeq7e3ez4DCfTrf9P2m2ZAA9w3d+Z3E 5c3fLoDYKZGi7l3htTDNfcrBB76q+bDg4t3gyLvfEN7ZKkHhFV7h8A2ppr3h8hneHt7bIL65IWDe Iz4Cia0RKRvgJ06hA96nK87i3EnZL37fMb61EXACIy7cxK0STqzjOx7aGB6g3g3kCKoN9j3kH567 IQDbSe4Csq1us+DkT/7e8V2VU07l3fnWWO7hRc6uR97lnJ3eLCEAoT3mJ97jAfq/aN6lLr7mWZ60 GbDlcM7Z1t0SYm7nUP8eoAa+50Hu50Pe5nYa3IOO3uodEteA6E+e4r+p4Yzeoant6I/+r9M96STu EqqA6U+O55X54weu5qD+4v3AAdkq6aQu4S4RANCA6jt+4anJ6vTd4a8+5LHeqaNO6i6w5C8RAIeu 65I8jGdO5X0e7As+7GT64MYe2zMxAMuO6s9Q5kj47Cz+6dKO5dTuoCJ+7cPNGtuO6bWg3Feo552e 5go+7mte7s5p7ehe3TZx6rq+682OhIsO5K5O7/Uu67Z57vku5/ve76nu7fkX8Cwe7QQP6waflzOe 79Tt3zeB6wy/6+6egL4u2UI+8Y5u7zT55hgv3La+8bne8Rb+7/kX8m3/beUk/+omb5CCnvLC7dk5 IQDrruvdXob5HO/Hyds1b/MVX5Aor/PYzhPa7vIn3u5XCO7NLfFHT+5Jz445z/Tp3hMEAPVRD/OZ p8vxPvJXj/TtqAFIzvXC/eU+we9gL+AOD/HNLe5nH+w3D4vFzvYK/xOtEPcW/vENHO8Df/d4n/WN SOtsT+hCwfGAn921APMyD9TAbvjjfvN7v/grDxTK/vhyn36Tn9JWb/kln/QKsNmLf948v1A/z/CO rXxDj+Z2T/qXL+sIn/qcvfms7/mQz91UL9YJTvsk3w8gQOO4T93IXhRwz/u23ZBkL/BGL/wELwLH z99ufxTLz/zJjXh0/9/Woy/9fr4A1X/eLfABSuH42k+h23133X/VZg/+wa4AXD7+jL8U6J/+tJDX of/Osw8Q/AQOJFjQ4EGECRX2Q+HC4UOIESVOlNhCAACMGTVu5NjR40eQIUMKqEXL5EmUKVWuVPlM nbdu3bKFo1nT5k2cOXXu5NnTZ85sChQOJVrU6AmKSZVSZCHS6VOoUT8OKMnS6lWV4+ptlUeP3rx1 62J2+1nW7Fm0NPEZZduWrYilceOuCCDV7l28HAlg5Yu1lrytgQVv9UovLLuY2tIuZswznVvIkQ0q aCHXMkUYeTVvjqqq7+eV7waPJl0vnlew62DKbNy6bLl+kmVDTlD58v/thyI47+b98Rpo4CaxlSZe vF7Xr2HHumYeLluC2dGNMsRd3YWM3tm1B4AWHDg94+HFoz6cuHnZfNLVD0Vq/bYJ7fF7B6jqna9W 8fn1myavOubM89Rab8CD4HLvMovkU5Azquzjq5Z49pNwwuO8CkusmBiDjUAOBaLswMvgW3DEvMJw kC/RKFRxxf4Q60axnbSJrUMCawPRMrpI1PEuz060argVgxRyq9OS80+moGgkkLob5cpsRyg789Eq 8Ia08soKhVJyPQObXKqpKMN0irspV7IHSzSHjEfLLWdbwMu4wBRzTpDILBMlCNPUU8U125TtQzgp aqECOgsFqcE7T7r/Z09GJYxnAT8h62eFQAX9wFBMPUI0USAb9VS8fSJli8lKI2rh0kxT3WivRGn5 61NYjQtVVKK6LPWhEVBVdVeMekz0zFiDJW1WWhF681aIRqiLV2YB+C3RPIWVNjB5ZiyWIECRdUHZ Zpu1885FpxXXHWuvnVRbh0xYtltm6UsUP3GnJfdagVJA1wU52W12Ux9fjVde6Iq19dZ89W3WxDtT /FfaPkU9FtlBDZbY134XFrfhNrMt9VSJO6b4xHAtFhZjGkndWNeO9f32RHhFDjYefba0F9lcU055 ZfuidVlYYgkcOFBubU6ZX/sU3jnYntV7uNSghR66Pvs6PRrpATUO/1Rdp51m9cQqpw52nnIlMznQ grNO+ePgWvYa1nlna6/Uss1O+dmcI1w72LYj+7nJFuKWO+UwWoEaNKPv/tSdgN2ymm+U/zZbAMGD k9rwT0kuysZKOXZ8cwAEIGDwq/ylHFbLF2qo0hUa5/zvAD7/DNjRSWeTPabXXX31AMKg2yqdY/c0 nqQLrP124jXSHXSUQvb90+CxtQ1OEWwvvnjIkadl8uUbbZ4fzOH0e3riBVAFdNGz93SfsMe+8Xvw i299cNjN9zRvfvZ2r+/28++odbprkT/Wti3tRprTXwE3ojuTKO9/jCLX4u6nOgNGcACtUNsC90SP DVCqSamLYAc7Iv+AcnTNgmi6xwMc0AAHQKADLzhQ0zz4Qo0MIIQjVFMJG3BDHN7wARdg4W1cCEMg ZmQA8AAMDSUkj3ucMIdLxOEDJKCC5yUlekGkIkcCUAAiGjE89PCHEpn4RRymsAMalAj7qhjEK2ZR i4OxIRjdyMQU8hAiZjxjFQPQDnfYjYbxaOMb/fjFHb6AjnWsowDwqEfzIdGLf2QkCh+AAAwMQHqE pKRHDCnC0XFxkY0EowMesA8ESLKSo5SKDDE5tT5yEpAMCOVFSPlKvMiwiC7j4wNUycQHsPIAA4Bl LzmTxlmKSx5dvOUNPQlJXvpSmfPBYjBhdQ9ictKT+4jkJJd5zd2JXDGPv0ulHz/ZSmyGk0SG3Caa +LjJVSJgl+JkZ5TIaaVhojOMj4xkO+1JJ1OqCJronGY17/lPTOVTPLXM4TTBCVCEqmqIzhSMInWo S1cmVKK8AmZD/fGAR65zohtVGRbfYQACiJKjIyVpSU16UpSmVKUrZWlLXfpSmMZUpjOlaU1telOc 5rRjAQEAOw== ------=_NextPart_000_029E_01C07B15.387204E0-- ========================================================================= Date: Wed, 10 Jan 2001 11:50:14 PST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: 'Bill' 'Eagleton' Subject: Re: [Re: [Re: waterman poly 25]] Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: quoted-printable A second post was lost, I retell it here... Kirby Urner wrote: >>I will try IE also tho just to watch it slower... >>Nope. Ran them side by side and they kept pace exactly! >Must be something with my version/platform. _All_ my anim GIFs seem sluggish in IE. *I asked a gal w 28.8 who is in the sticks. Hers in ie dnld'd slowly, bu= t ran better after dnld, and equally, BUT only if nothing else was tasked, even= the keyboard. MS IE wants full control, so this makes sense. It is all TOO t= ied into the OS. >>If you meant download, I cannot say, as I have a fast download ability.= >Me too, DSL. *Our dsl slowed to minimum after a while so we dumped it at our yr point = and got cable. We also started getting poor uptime too. Cable is usually do= wn for only a minute, not hrs here. Also $10 a month cheaper. Cable TV, we don't have. 1 other on the block who does not... LOL. >Hmmmmm, that's what I use, plus IE 5.5 *5.5 also here, not sure what ie she uses, she does not like ie, but I th= ink I recall she has 5.0 which is par enough with 5.5 speedwise. *I do use a 700MHz duron w 128M and fast ram, where as she is a 266 penti= um w 64M. BillSF9c Name, area, very own usda zone, and IM name. ____________________________________________________________________ Get your own FREE, personal Netscape WebMail account today at http://home= =2Enetscape.com/webmail ========================================================================= Date: Wed, 10 Jan 2001 15:19:49 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: scaling MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_02BF_01C07B18.C6896AE0" This is a multi-part message in MIME format. ------=_NextPart_000_02BF_01C07B18.C6896AE0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable >I know W1 - W15 were all drawn after scaling to be the same size >diagram, so the whites in W6 are (on screen) slightly closer together >than the oranges in W5, right? I can't tell with W24to25, is it getting >bigger on screen? This is a good point. Yes, the final data is always divided through by 1/root, clever approach BASE to make all the polys approximately the same size for rendering. This means they are not really "to scale" i.e. not all to the same scale. It's as if the movie camera were backing away from an expanding balloon, keeping it always about the same size on screen. my personal viewing choice here. >If M is the next generation with only 6 new spheres, then I bet M+1 = will >surround those 6 like 25 surrounds 24. So M+1 will draw in orange and >green, like W25. But I don't bet a billion dollars. > Lots of fun investigations suggest themselves.=20 you bet....go for it BASE. I'm hoping that at least one or two folks will go to the trouble to download Python + Povray (since this is the combo I'm pushing throughout my Oregon Curriculum Network website). If you go that far, then it's just a little hop to grabbing Qhull as well, and then you're in a position to generate Watermans all the live long day. DO DAH DO DAH Steve, are you listening? A P133 should be sufficient. i fear getting all screwed up. i have done some bases myself. i would love to stay at 2d island and have the ccp teach me more stuff, now that it is nearing complete computerization.=20 it did teach me stuff, and i can no longer stay at 2d island.=20 i am absolutely delighted to be able to link to all the graphics. it is in capable hands, matie. i must be ready for the long voyage ahead.=20 i need YOU at BASE, whether or not you=20 come for the Trip. steve ------=_NextPart_000_02BF_01C07B18.C6896AE0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

>I know W1 - W15 were all drawn = after scaling to=20 be the same size
>diagram, so the whites in W6 are (on screen) = slightly=20 closer together
>than the oranges in W5, right? I can't tell with = W24to25,=20 is it getting
>bigger on screen?

This is a good = point. Yes,=20 the final data is always divided through
by 1/root,

clever approach BASE

to make all the polys = approximately the same=20 size for
rendering. This means they are not really "to scale" = i.e. not=20 all
to the same scale. It's as if the movie camera were backing = away
from an expanding balloon, keeping it always about the same = size
on=20 screen.

my personal viewing choice = here.

>If M is=20 the next generation with only 6 new spheres, then I bet M+1 = will
>surround=20 those 6 like 25 surrounds 24. So M+1 will draw in orange = and
>green, like=20 W25. But I don't bet a billion dollars.
>

Lots of fun=20 investigations suggest themselves.

you bet....go for it BASE.

I'm hoping that
at least one = or two folks=20 will go to the trouble to download
Python + Povray (since this is the = combo=20 I'm pushing throughout
my Oregon Curriculum Network website). = If you go=20 that far, then
it's just a little hop to grabbing Qhull as well, and = then=20 you're
in a position to generate Watermans all the live long=20 day.

DO DAH DO DAH

Steve, are you=20 listening? A P133 should be sufficient.

i fear getting all screwed up. i = have done=20 some bases

myself. i would love to stay at 2d = island and have=20 the

ccp teach me more stuff, now that it is = nearing=20 complete

computerization.

it did teach me stuff, and i can no = longer=20 stay at 2d island.

i am absolutely delighted to be able=20 to

link to all the graphics. it is in = capable hands,=20 matie.

i must be ready for the long = voyage ahead.=20

i need YOU at BASE, whether or not you=20

come for the=20 Trip.

steve

------=_NextPart_000_02BF_01C07B18.C6896AE0-- ========================================================================= Date: Wed, 10 Jan 2001 09:48:21 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: [Q-P] Reaction to the plague <> Brian �Quincy! Hutchings 10-JAN-2001 9:48 r001806@pen2.ci.santa-monica.ca.us thank you, KS, for the dyscussion of U in coal!... I had always wonered, how it was removed from the smoke; is it not?... how does the release from nuke plants compare to that of coal ones, again? "The 'scientific understanding' in our case is virtually a concensus." "virtually," I think, should be quoted, or just italicized, when "climate change" is covertly morphed into "overall warming," as is typical with the UNIPCC and the scince press -- mostly by the use of computerized simulacra, appropos! for example, look at the USDA's hardiness-zone maps, as a series, and check against these models (note that the connection between GCMs and weather forecasting is interesting, but hardly a proof-of-principle; I've spoken with Stephen Schneider from NCAR, which was illuminating --for me-- and he's a big promoter of the "overall" warming model (circa 1896)). the thing to note is that these simulacra have no particular *conceptual* model, other than "overall" warming, to which the tools of weather forecasting may be applied, in an ad hoc fashion. unfortuntaly, the overly-well-known concept of "sensitive dependence upon initial conditions" militates against taking the "future" of these models with any seriousness (the floating-point arithemtic of the hardware is "inherently chaotic" for these obvious reasons, and one can show this graphically on any workstation) -- any more than you'd think that the #2 glasshouse gas, CO2, could "double" without some sort of feedback -- "it's the water vapor, Silly!" then we have the serious modelling of a glass house, or a greenhouse as we Americans say it, which, as well, has massive "anomalies" with evaporation and condensation: it does not warm "globally" in the sense of "global warming;" dig it?... in such a model, as might be made by a manufacturer or farmer, one can prefer the phrase, proximal dependence upon intermediate cognition, or some thing (taking what is obvious, that one does not begin with "initial conditions," but simply an approximation of some intermediary state, whose initial condition is somewhat unknowable. --beyond petroleum (tm) !! http://www.tarpley.net/bush8.htm ========================================================================= Date: Wed, 10 Jan 2001 10:03:08 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: distance calc for frequencies <> Brian �Quincy! Hutchings 10-JAN-2001 10:03 r001806@pen2.ci.santa-monica.ca.us well, I wasn't giving any attention to the watermans that happenned to be roots of "squares," although I vaguely recall some that were cuboctahedral -- if not one with unit edges (proportionally). once you mentioned it, it's easy to see that there'd be a lot of spheres, say in the root(10000) waterman, outside of the cuboctahedral hull, noting that the ratio of the vertex-to-vertex diameter of the latter to the tetragonal and trigonal face-to-face diameter, is root(2):rott(4/3):root(1) (or, to "integerize the radicals," root(6):root(4):root(3). (one has to "scale-up" to the big shape .-) --beyond petroleum (tm) ??... It Came from Rocks; It Must Be Fossilised! http://www.tarpley.net/bush8.htm ========================================================================= Date: Wed, 10 Jan 2001 10:21:10 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: distance calc for frequencies <> Brian �Quincy! Hutchings 10-JAN-2001 10:21 r001806@pen2.ci.santa-monica.ca.us or, to put it another way, if you want to "normalize" the center-to-vertex dystance as 1 (root(1)), then the center-vertex:center-trigface:cnter-tetragface is, root(1):root(2/3):root(1/2), for any "frequency" of cuboctaheron (or "vector equilibrium" .-) so, what is the *raison d'etre* for using other than unit-diameter spheres? --beyond petroleum (tm) !! http://www.tarpley.net/bush8.htm ========================================================================= Date: Wed, 10 Jan 2001 12:03:13 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: [Q-P] Reaction to the plague <> Brian �Quincy! Hutchings 10-JAN-2001 12:03 r001806@pen2.ci.santa-monica.ca.us opinions have appeared in the press, along the lines of "George is to Climate as Richard was to China," as our CEO, which certainly belabors the obvious inclinations of the tripartite 'WAND' Corp. presence in the incoming Cabinet (since Rice is grabbing for economic warfare, as well, she's *in*, whether you like it or what ever, as head of NSZ; yahoo .-) it'd be even more obvious to you, if you lived in Santa Monica, "the home of Harry Shearer" and Warren Olney: every thing they do that is "green" in LA, they prototype here, firstly, like DWP head Dave Freeman and his "green-e," which he developed at the Grobachov Foundation (I spoke against the adoption of that programme 4 times, including when it was brought to LA Council, because it was intimately linked to deregulation, as recently told by Freeman in the Times; he apologized !-) I'm not against all things "small-g green," but I do have a problem with the Mayor, at the moment, a big, Green thing. last night, for instance, at the last oppotunity for them to do some thing, or say some thing about the nearly third of the WAND board that was on the G2Kcmte., they said nothing, and I was cut-off, twice, for supposedly being off-topic (even after the radio shuts down, after midnight), trying to speak to energy (as their own presenter did, extensively, for the Budget Item), and to my own case against the City in Public Comment (for their violation of the State Elections Code, in keeping me off of the ballot, and from even being a qualified write-in). in both cases, I was encompassing WAND's probable or possible influence, as abundantly portrayed in the Fall issue of WAND Weview, which I got from their lobby (it's across from City Hall), which is incredibly over-the-top, with its positioning (and misattribution to Chardin) of "noopolitik" in the noosphere. (weirdest quote: truth-seeking teams of "special media forces" with the tools of the media; why didn't they just title it, Big Mother Is Telling You ?-) the most truthful, if not the only truthful thing in it, was the statement about how NGOs are totally unaccountable, and not really able to promote the general welfare (my term). then, they go on to rpomote the Hell out of NGOs, including the Neighborhood Councils that they'd just instituted in LA (without mentioning these ones or their role in their creation) -- and avoid the obvious, that they are one of the oldest NGOs, or "quango" in their case! this was spelt-out in the cover article, "Transcendental Destination," but the other articles were not too bad (except that they didn't mention that the Littleton kids were *on* the "Doses" of the title, but not so metaphorically). if you want proof that WAND is so dang green, the whole article on the electricity dereg crisis in California, mentioned nuclear power only once, in passing. oh, yess; the new CM (former ACM) is married to the Lead Author of the Charter Reform Study that was made after Milken and Riordan's "LABA" ponied-up $98K; they segued into being the Primary Consultant for both of the Commissions that created it -- without too dang much pulbicity, I might add (only one person knew, at one of the Councils a-starting, last week). --The Duke of Oil! http://www.tarpley.net/bush8.htm ========================================================================= Date: Wed, 10 Jan 2001 12:54:57 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: distance calc for frequencies <> Brian �Quincy! Hutchings 10-JAN-2001 12:54 r001806@pen2.ci.santa-monica.ca.us I'm not at a graphical terminal, so taht I don't grok how you can maintain congruence with the grid (either cubical or IVM) by rotating 45 degrees and making the spheres root(2) larger (relative to the grid); assuming that your roatation's on the Z axis? ========================================================================= Date: Wed, 10 Jan 2001 14:01:11 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: [Q-P] Reacting to the plague <> Brian �Quincy! Hutchings 10-JAN-2001 14:01 r001806@pen2.ci.santa-monica.ca.us I'm not saying that I don't have *other* problems; oy! the City fooled me into copping a plea, the other day, for their silly trespassing case, with the faint hope that I might take the original plea, back (that's not quite correct, but I'll have to speak to my counsel, Bri .-)... if that's the case, that was *defintely* the *very* last time that I'll cop a plea on that particular charge (although their's no "strikes" law on it, at least). the moral of the story is --and I can certainly, partially grok their side of "limiting the field," as we just saw, big time, with two of the worst candidates ever to appear in a National Democlition Derby-- you cannot fight City Hall on its terms; not that I *really* expected to win, in spite of many false hopes. I think, the proper gambit to apply to one is, after all on his third run in 2 years (we had a Special Election), Crush'im like a bug (or make sure that know one *knows* that he's running, again !-) trying to see from their vantage: people who are really into the base of ten, as an icon unto itself a la some clown like Nostradamus (as opposed to some sort of regular purge, like a Jubillee Year of 2000), may have been dysappointed that hte Age of Aquarius, presumably a very Green thing, or at least, Teal --whether of not the precession of the equinoxes really corresponds, very well, to our odometer roll-over-- has all-of-a-sudden been beset with a collapsing economy -- other than the fact that such an age might correspond to the reintroduction of feudalism, "across the board," as it were. --The duke of Oil! http://www.tarpley.net/bush8.htm ========================================================================= Date: Thu, 11 Jan 2001 01:32:12 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Steve Waterman Subject: abc of ccp MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_002E_01C07B6E.52C90A60" This is a multi-part message in MIME format. ------=_NextPart_000_002E_01C07B6E.52C90A60 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable kirby,=20 Mission accomplished. Unless someone can show me a flaw in the algorithm (or prove that Qhull is unreliable). =20 a job well done indeed, kirby thanks for the mountain of work you have put in. .........................................................................= ..... I suppose I should do a "stress test" and really try to compute Waterman 10000 again. If there's a "hole" in my algorithm, it'll probably relate to the fact that I don't go "deep enough" to pick up all the relevant spheres. So far I'm only going down to N-4, which has been sufficient for all Watermans so far computed (at least I think so). =20 i think so too, because the urner generator seems=20 to handle ALL the 1-15, and looks right ( to me ) for those higher values you show.=20 .........................................................................= . I think the manual/tabulation methods have this same "hole".=20 =20 yes, the same "hole".... (which additional lower n's to use?) = .........................................................................= .... We don't have a proof that X-layers will always be sufficient, =20 not yet .........................................................................= ..... nor do we have a way to mathematically prove a sphere is part=20 of the hull _except_ through methods like those used in Qhull, can the planes in question be quantified by equation ? .........................................................................= ..... which neither Steve nor I go into at our respective websites. =20 nothing there for sure. i do not know. .........................................................................= ......... ccp =3D ccp no matter what procedure you have mathematically devised to decode its structure. That's true, but how does that help you? all the answers lie within all the various different bases. .........................................................................= ................ Short of building a physical model=20 and what would be the harm in doing some of that ? build the first few....and you will see. .........................................................................= ................ and trying to wrap it with cellophane, the information is already there, ask the right question and the ccp MUST reveal that answer. if you only have the aba of ccp ...you only get to ask about 75 percent of the questions. .........................................................................= .............. how can you tell whether a certain N-3 sphere is or is not a part of the convex hull? You need to do some math. i agree. some math needs to be done. series of series.... ....................................................................... CCP is the PATTERN of spheres. yes. The diameter you assign the spheres depends on the measuring stick. BASE, as i see it, can only have unit spheres by MATHEMATICAL definition. ..................................................................... As you define it, yes.=20 not my arbitrary choice. it MUST be....make it so number one. .................................................................... You're free to define anything you like. as are we all. however, to define/think of/visualize BASE as not unitary,=20 is counter-productive in my opinion=20 .........................................................................= .................. you needed to learn my jargon to design the urner generator. The "urner generator" is finished, except with regard to this matter of how many layers deep is relevant -- and so far I'm not getting any answers to that from your website. it is not there. i do not know. .........................................................................= .................. i do not need to know how you do it, and fear i will just get lost in stuff i already do not comprehend. I think that'd be a good experience,=20 me too, however it appears that your documentation on this has been well done. i hope to understand how you did it in due time. i think the information is there. you have=20 offered to get me set up on my P133, and perhaps very soon i will try that too....i am still concerned about my lack of computer skills here.. .........................................................................= ....... as you've pretty much eaten everything on your plate.=20 much on the related ccp stuff, yes. you too kirby, you did the urner generator in about=20 a week or was it a day, it was hard to believe, but=20 since you were getting all the lower polyhedra perfectly,=20 there is not a chance in hell that it is wrong... just my opinion. .........................................................................= ............ i can see now, that the whole mass/physical thing is where this journey stops for you. i realize that=20 this list is a GEODESIC list, and that i respect.=20 you have adequately expressed that you have no=20 personal desire for Physics as well, and that i can respect=20 as well. you came all this way....i did not think we would ever get this far....let alone in maybe just a dozen days ? .........................................................................= ............. What do you plan to do next I wonder?=20 i am planning to take that Trip... it is=20 now in dry-dock, though with this all this recent help it now has a fresh new coat of paint. .........................................................................= ................... More with the empirical constants of nature I guess.=20 this is the path that ccp has led.=20 i am simply following its path. ................................................................... That doesn't seem a productive tack to me,=20 mathematics is your passion,=20 you are most productive here. ................................................................. but if it turns you on... that is not at all why i am doing it. .............................................................. But only Steve speaks Steve. thanks. i appreciate the compliment. i really do. .....................................................................=20 I'm not really motivated to learn it you already have... related to aba. .................................................................... i trust that the urner generator will work perfectly over time, even if it does not now. eventually it can be cross checked with the abc method to also replicate the ccp. It needs to be audited now, and I think we can do this without the benefit of an abc cross-check. either you want to understand ccp=20 in which case you must learn abc or you can be complacent with now knowing aba and hence still have ALL the ccp coding. but you are missing 1/2, and until that is done, you will NEVER otherwise verify the aba... and hence NEVER verify the ccp. i would bet a billion dollars on that. .........................................................................= . Just getting the same results by exhaustive tabulation would not constitute a "proof of concept". you have the method...learn abc distances. .........................................................................= .......... more importantly, than even having it work, is your faith that it can eventually be accomplished, by you and/or others Mostly what I wanted was the very pretty pictures. I don't want the BASE tables. .........................................................................= ........ i suspect we have the pattern both mathematically=20 definable and physical definable in doing visual=20 comparative analysis by as little as root 100. "Visual comparative analysis" sounds very imprecise. I wouldn't trust it. Too stone age. by that, i meant ...build each model=20 physically/visibly and steal its information. =20 make a chart, and record the n-1, n-2 ... condition of each. i suggest that with the power you now have with the 100 percent working urner generator for the ccp in aba, that a least one series will be mathematically definable by stealing this data from this incremental analysis. in ccp, once you know ( n-1, n-2, n-3....you have it all....and can mathematically know all n- whatevers) try it ...you will like it. build them and see what happens. .........................................................................= ... yes, i think so too, give me the raw data 1-100 i would like a crack at it. I think my "raw data days" are probably over. But the software tools are all freely downloadable. by raw data i mean the mathematical results from the "visual comparative analysis" .........................................................................= ..... I so far trust Qhull to get the right answers, in large part because I'm feeding it a diet of 100% integers. sounds like a good strategy. .................................................................... But I certainly wouldn't have the same faith in you or I, left alone with the BASE,=20 but without Qhull. the convex hulls you have made are another leap forward. a very huge giant leap....the rest should be fun. you are BASE. ...................................................................... I wouldn't -- not out to the higher numbers, like 117. I don't think there's a visually precise way to solve these things.=20 i suspect you might change your mind one day. .........................................................................= I'd always be going back to the computer for the "right answer" -- so why kill yourself doing it manually in the first place? perhaps you did not understand how i was using my term ....manually... ( but i do not really know the context here ) i mean mathematically. with 4 masters.... sphere centered aba......evens void centered aba.....odds and as i had written you in 93 with abc charts i sent you then with the distances and=20 distance formulas... sphere centered abc.....0,3,6,9.... void centered abc......1,2,4,5,7,8... the mathematical guts.=20 no stone age no mysticism no hocus pocus this is math dude i have faith in you Kirby. we have years to get the BASE right if we need to. .........................................................................= ................... I'm not going to be generating BASE numbers. Unless someone shows where my algorithm is wrong, or that Qhull is somehow unreliable,=20 until you cross check it...how reliable is it ? I'm going to trust that those very pretty pictures are also mathematically accurate and complete. they are. .........................................................................= A huge BASE wouldn't give me any more than I have already. true, but abc analysis will. .........................................................................= ............ you guys have done more work, got more results, understanding, muses, feedback, depictions, ideas, scrunched into 2 weeks, than i did in over 10 years on my own. .........................................................................= ..................... steve =20 ------=_NextPart_000_002E_01C07B6E.52C90A60 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

kirby,

Mission accomplished.

Unless someone can show me a flaw
in = the=20 algorithm (or prove that Qhull is unreliable).

a job well done indeed, kirby thanks = for the=20 mountain

of work you have put=20 in.
..................................................................= ............
I=20 suppose I should do a "stress test" and really
try to compute = Waterman 10000=20 again. If there's a
"hole" in my algorithm, it'll probably relate = to
the=20 fact that I don't go "deep enough" to pick up
all the relevant = spheres. So=20 far I'm only going
down to N-4, which has been sufficient for=20 all
Watermans so far computed (at least I think so).

i think so too, because the urner = generator seems=20

to handle ALL the 1-15, and looks right = ( to me=20 )

for those higher values you show.=20
.....................................................................= .....
I=20 think the manual/tabulation methods have this
same "hole". =

yes, the same "hole".... (which = additional lower=20 n's to use?)

................................................................= .............

We don't have a proof that X-layers = will always be=20 sufficient,

not yet

................................................................= ..............

nor do we have a way
to = mathematically prove a=20 sphere is part

of the hull _except_ through methods = like those=20 used in
Qhull,

can the planes in question be = quantified by=20 equation ?

................................................................= ..............

which neither Steve nor I go into at=20 our
respective websites.

nothing there for sure. i do not=20 know.
................................................................= ..................
ccp=20 =3D ccp no matter what procedure you have mathematically
devised to = decode its=20 structure.

That's true, but how does that help = you?

all the answers lie within all the various different bases.

....................................................................= .....................

Short of building a physical model

and what would be the harm in doing some of that ?

build the first few....and you will see.

....................................................................= .....................

and trying to wrap it with cellophane,

the information is already there, ask the right question

and the ccp MUST reveal that answer. if you only have

the aba of ccp ...you only get to ask about 75 percent = of

the questions.

....................................................................= ...................

how can you tell whether a
certain N-3 sphere is or is not a = part of=20 the
convex hull? You need to do some math.

i agree. some math needs to be done.

series of=20 series....
...........................................................= ............
CCP=20 is the PATTERN of spheres.
yes.

The diameter you assign
the = spheres=20 depends on the measuring stick.

BASE, as i see it, can only have = unit=20 spheres

by MATHEMATICAL definition.

....................................................................= .

As you define it, yes.

not my arbitrary choice. it MUST be....make it so number one.

....................................................................=

You're free to define anything
you like.

as are we all.

however, to define/think of/visualize BASE as not unitary,

is counter-productive

in my=20 opinion
........................................................= ...................................

you needed to learn my jargon = to=20 design the urner generator.

The "urner generator" is finished, except with regard
to this = matter of=20 how many layers deep is relevant --
and so far I'm not getting any = answers to=20 that from your
website.

it is not there. i do not=20 know.
................................................................= ...........................

i do not need to know how you do it, and fear i will just
get = lost in=20 stuff i already do not comprehend.

I think that'd be a good = experience,

me too, however it appears that your documentation

on this has been well done. i hope to understand how you

did it in due time. i think the information is there. = you have=20

offered to get me set up on my P133, and perhaps very soon i

will try that too....i am still concerned about my lack of

computer skills here..

....................................................................= ............

as you've pretty much eaten everything on your plate.

much on the related ccp stuff, yes.

you too kirby, you did the urner generator in about

a week or was it a day, it was hard to believe, but

since you were getting all the lower polyhedra perfectly, =

there is not a chance in hell that it is wrong...

just my opinion.

....................................................................= .................

i can see now, that the whole mass/physical

thing is where this journey stops for you. i realize that

this list is a GEODESIC list, and that i respect.

you have adequately expressed that you have no

personal desire for Physics as well, and that i can respect

as well.

you came all this way....i did not think we would ever

get this far....let alone in maybe just a dozen days ?

....................................................................= ..................

What do you plan to do next I wonder?

i am planning to take that Trip... it is

now in dry-dock, though with this all this recent

help it now has a fresh new coat of paint.

....................................................................= ........................

More with the empirical constants of nature I guess.

this is the path that ccp has led.

i am simply following its path.

...................................................................<= /DIV>

That doesn't seem a productive tack to me,

mathematics is your passion,

you are most productive here.

.................................................................

but if it turns you on...

that is not at all why i am doing it.

..............................................................

But only Steve speaks Steve.

thanks. i appreciate the compliment. i really do.

....................................................................= .

I'm not really motivated to learn it

you already have... related to aba.

....................................................................=

i trust that the urner generator will work perfectly over = time,
even if=20 it does not now. eventually it can be cross checked
with the abc = method to=20 also replicate the ccp.

= It=20 needs to be audited now, and I think we can = do
=20 this without the benefit of an abc cross-check.

either you want to understand ccp

in which case you must learn abc

or you can be complacent with now knowing aba

and hence still have ALL the ccp coding.

but you are missing 1/2, and until that is done,

you will NEVER otherwise verify the aba...

and hence NEVER verify the ccp.

i would bet a billion dollars on that.

....................................................................= ......
Just=20 getting the same results by exhaustive
tabulation would not = constitute a=20 "proof of concept".

you have the method...learn abc=20 distances.
...........................................................= ........................
more=20 importantly, than even having it work, is your faith
that it can = eventually=20 be accomplished, by you = and/or
others

Mostly=20 what I wanted was the very pretty pictures.
I don't want the BASE=20 tables.
..............................................................= ...................

i suspect we have the pattern both mathematically

definable and physical definable in doing visual

comparative analysis by as little as root 100.

"Visual = comparative=20 analysis" sounds very=20 imprecise.
I = wouldn't trust=20 it. Too stone age.

by that, i meant ...build each model

physically/visibly and steal its information.

make a chart, and record the n-1, n-2 ...

condition of each. i suggest that with the power you = now=20 have

with the 100 percent working urner generator for the ccp

in aba, that a least one series will be mathematically=20 definable

by stealing this data from this incremental analysis.

in ccp, once you know ( n-1, n-2, n-3....you have it all....and = can

mathematically know all n- whatevers)

try it ...you will like it. build them and = see what=20 happens.

....................................................................= ........
yes,=20 i think so too, give me the raw data 1-100

i would like a crack at = it.

I think my "raw data days" are probably over.=20 But
the software tools are all freely=20 downloadable.

by raw data i mean the mathematical results from the

"visual comparative=20 analysis"
............................................................= ..................

I so far trust Qhull to get the right
answers, in large part = because I'm=20 feeding it a
diet of 100% integers.

sounds like a good = strategy.

....................................................................=
But=20 I certainly wouldn't
have the same faith in you or I,

left alone with the BASE,

but without Qhull.

the convex hulls you have made are another leap forward.

a very huge giant leap....the rest should be fun.

you are BASE.

....................................................................= ..
I=20 wouldn't -- not out to the higher numbers,
like 117. I don't think = there's a=20 visually
precise way to solve these things.

i suspect you might change your mind one day.

....................................................................= .....

I'd always
be going back to the computer for the = "right
answer" -- so=20 why kill yourself doing it manually
in the first place?

perhaps you did not understand how i was

using my term ....manually...

( but i do not really know the context here )

i mean mathematically.

with 4 masters....

sphere centered aba......evens

void centered aba.....odds

and as i had written you in 93

with abc charts i sent you then

with the distances and

distance formulas...

sphere centered abc.....0,3,6,9....

void centered abc......1,2,4,5,7,8...

the mathematical guts.

no stone age

no mysticism

no hocus pocus

this is math dude

i have faith in you Kirby. we have years to get the
BASE right = if we=20 need=20 to.
..................................................................= ..........................

I'm not going to be generating BASE numbers.
Unless someone = shows where=20 my algorithm is wrong,
or that Qhull is somehow unreliable,

until you cross check it...how reliable is it ?

I'm going to
trust that those very pretty pictures are=20 also
mathematically accurate and complete.

they are.

....................................................................= .....

A huge BASE wouldn't give me any more than I have already.

true, but abc analysis =20 will.
................................................................= .....................
you=20 guys have done more work, got more results, understanding,
muses, = feedback,=20 depictions, ideas, scrunched into 2 weeks,
than i did in over 10 = years on my=20 own.
.................................................................= .............................

steve

------=_NextPart_000_002E_01C07B6E.52C90A60-- ========================================================================= Date: Thu, 11 Jan 2001 01:08:33 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: distance calc for frequencies In-Reply-To: <200101102054.f0AKsvH14329@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Probably too hard to explain and I expect lurkers are burned out on all this math stuff. When you get to a graphics terminal someday, check http://www.inetarena.com/~pdx4d/ocn/wmalgorithm.html Steve and I do our Z-plane spheres is a different orientation. I do a square grid with spheres running "diagonally". Kirby > I'm not at a graphical terminal, so taht > I don't grok how you can maintain congruence > with the grid (either cubical or IVM) by rotating 45 degrees and > making the spheres root(2) larger (relative to the grid); > assuming that your roatation's on the Z axis? > > ========================================================================= Date: Thu, 11 Jan 2001 04:32:39 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings