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Quantum Gravity 316.2: V - S (volume - surface area) Obeys the x^n
Solution Type Riccati Differential Equation
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On Mon, 23 Mar 2009 14:37:54 -0700 (PDT), OsherD <...@ca.rr.com
From Osher Doctorow
Having shown in a recent subsection here that V/S for V = volume, S =
surface area, under quite general conditions, when changed to V - S,
relates closely to the Total Gaussian Curvature and the Euler
Characteristic and Betti Numbers, let's see what type of Riccati
Differential Equation V-S satisfies under quite general conditions.
Since V/S under general conditions is bounded by the same for the
sphere, let's look at V - S for the sphere:
1) V - S = (4/3)pi r^3 - 4pi r^2 = 4pi r^2 ((1/3)r - 1)
But S is the derivative of V with respect to r:
2) S = d(V)/dr = d[(4/3)pi r^3]/dr = 4pi r^2
Hence we have, rewriting (1):
3) V - dV/dr = 4pi r^2((1/3)r - 1)
But (4pi r^2 = 4pi(r^3)/r = 3(4/3)pi r^3/r = 3V/r, so substituting
this into (3) yields:
4) V - dV/dr = [3V/r)][(1/3r - 1]
and therefore:
5) dV/dr = V - [3V/r][(1/3)r - 1] = V - V + 3V/r = 3V/r
This has the form, with t = r:
6) dV/dt = 3V/t = (1/t)3V
which is the same form as the Riccati Differential Equation for x^n
discussed earlier in breaking up the Gamma distribution function
(which is Maximum Probable Causation/Influence (PI) Entropy and
Maximum PI Expectation) into factors of form x^n and factors of form
exp(-x). The latter equation is:
7) d(x^n)/dx = nx^(n-1) = nx^n/x
so that with y = x^n, x = t, (7) says:
8) dy/dt = (1/t)y
Osher Doctorow
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On Mon, 23 Mar 2009 18:31:15 -0500, "frogma" <...@invalid.com
"OsherD" <...@c18g2000prh.googlegroups.com...
Duck/Quack ratio, or squeeze the Duck =
Quark/Quack = kOsher/Jewish + Riccati Cheese function
............ and UNITS man UNITS !
This is PHYSICS !!
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On Mon, 23 Mar 2009 21:08:37 -0700 (PDT), OsherD <...@ca.rr.com
From Osher Doctorow
The Gauss-Bonnet Theorem is to geometry and topology in mathematics as
Quantum Theory or GR is supposed to be to physics. If you had read
carefully, you would notice my applications to Gauss-Bonnet Gravity.
Look back a few posts in this thread. Not that I expect you to look
back, but heck, Miracles might happen. You might even learn to
appreciate physics history, mathematics history, not to mention human
history including old people's histories in a time of young spoonfed
spoiled brats.
Osher Doctorow
On Mar 23, 4:31 pm, "frogma" <...@invalid.com
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On Tue, 24 Mar 2009 10:47:10 -0500, "frogma" <...@invalid.com
**topposting smuckster, "If the units do not match, it is garbage", the
first rule of physics
And you always ignore that fact, therefore you post garbage most of the
time.
This is transparent, You don't know it, but everyone else does.
put that spoon back in you mouth! ***
"OsherD" <...@d38g2000prn.googlegroups.com...
From Osher Doctorow
The Gauss-Bonnet Theorem is to geometry and topology in mathematics as
Quantum Theory or GR is supposed to be to physics. If you had read
carefully, you would notice my applications to Gauss-Bonnet Gravity.
Look back a few posts in this thread. Not that I expect you to look
back, but heck, Miracles might happen. You might even learn to
appreciate physics history, mathematics history, not to mention human
history including old people's histories in a time of young spoonfed
spoiled brats.
Osher Doctorow
On Mar 23, 4:31 pm, "frogma" <...@invalid.com
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