/sci/ - Science & Math

I guess you guess right, mhm..
http://en.wikipedia.org/wiki/Rate_law#Equilibrium_reactions_or_opposed_reactions
For elementary reactions, I would say that the rate law can be motivated by looking at cross sections, as in the statistical theory of reactions.
There the m,n,x,y are the stoichiometric coefficients.
I, too, would guess that if you've got different exponents, it should be because the reaction is not elementary.

>>5383545
..true

Well depending on what it's for, I'd just compute all the values...

Table[a^2 + b^2, {a, 1, Sqrt[50]}, {b, 1, Sqrt[50]}]
Select[Union[Flatten[%]], # < 50 &]

>>5073542
I though that too at first, but by the "=1 condition", d and n (or k and n) are not independend. I think.

Here are some ideas for a pedestrian version, I didn't get far thoug:

We investigate
(n choose k)*p^(k choose 2)
and for fixed k, this would of course blow up.
Now appearently this seems not to happen, and that means that the only real difficult part seems to be the "=1" condition, i.e. the dependence of n on k (or resp. d).

For starters, let's set

k=d+x
with
x=1+y,
with
y>=0
as the problem says.
(For y=0 you have the k=d+1, for y>0 you have k>d+1)

z choose 2 = -z/2 + z^2/2

so

(d+x) choose 2
= -d/2 + d^2/2 + x*(x-1+2d)/2
= (d choose 2) + c

with
c := x*(x-1+2d)/2 >0
which is > 0, because x>1 (assuming d>0)

p^(k choose 2)
=p^((d+x) choose 2)
=p^(d choose 2) * p^c (now using condition "=1")
=(n choose d)^-1 * p^c
=(n choose d)^-1 * C

with some number 0<C<1

so

(n choose k) * p^(k choose 2)
=(n choose (d+x)) * p^(k choose 2)
=(n choose (d+x))/(n choose d) * C

...?

>>4599827
>You're a smart ass retard that like talking out of your ass
Why do you insult me?
>Question of semantics and syntax are the same with Gödel's completeness theorem and soundness so fuck off with the formality when they don't matter.
OP was asking a question withing Predicate Logic and was using specific set. I pointing out to the second poster that 'true' or 'false' are relevant in semantics, not in pure logic. The purpose was to find out why he seems to associate the notion of an empty set with truth or falsehood. I don't see how you've cleared that up. Truth or false are relevant concepts when it comes to Gödels theorems, as you rightly say. "empty set", "no set", that has a priori not to do with falseness.

>The null set always exist. It's in the axiom of set theory and exist everywhere you go in math.
It exists in set theory true. In Zermelo–Fraenkel set theory it comes from the axiom of infinity
http://en.wikipedia.org/wiki/Axiom_of_infinity
The empty set is not a priori to be found in predicate logic.

>The null set always exist. It's in the axiom of set theory and exist everywhere you go in math.
Also we practically never EVER care about how the underlining ordered pair structure is made in proofs, (a,b) could just as easily be {{a},{a,{b}}}. >And we never care about the set theoretic construction of the natural numbers unless you want to write {0,1} lazy as 2.
I was just constructing models to show the use of the constructions in OPs post. This was the answer of the question. The answer is "yes, in a set theory context, these constructions are valid."

>>4496935
as n -> infinity, z -> infinity.

There is a formula for n up to 4. you will have a very hard time finding an analytic formula for n>4, if it exists, which I doubt.
In any case, if <span class="math">y \in [0,1][/spoiler], then there is a numerical solution iff <span class="math">z \in [n,2^(n+1)-2][/spoiler].

Related:
I saw this TEDx video a few days ago

http://www.youtube.com/watch?v=BoT7qH_uVNo

The talk is quite interesting and on 11:30 they show mice experiments, which suggests that it's unhealthy (to watch too much TV, at least as a child)

Oh and you can only just smash random numbers into that machine:

http://www.wolframalpha.com/input/?i=1-%3E2%2C+2-%3E3%2C+3-%3E1%2C+3-%3E4%2C+4-%3E1

http://www.wolframalpha.com/input/?i=Petersen+graph%2C+icosahedral+graph

>>4257982
Is she a better target than any other woman on the street? how do you choose your victims?

>>4142037
open sets.

>>4142031
what is the connection between symplectic topology and propability theory???

>>4097643
The information theoretic is the more fundamental one.
The fundamental postulate of statistical mechanics says that all microscopic states are equally probably, i.e. p_i=const for all i. If there are Omega possible states, then all p_i are 1/Omega

S=-sum_i p_i log(p_i)

is then


S=-sum_i p_i log(p_i)
=-(log(p_i))*sum_i p_i
=log(1/p_i)*sum_i p_i
=log(Omega)*(sum_i 1)/Omega
=log(Omega)

>>4082869
>>4082879
one of my favorite physics paper names is
http://en.wikipedia.org/wiki/An_exceptionally_simple_theory_of_everything

But seriously, the short technical argument would be power counting.
related:
Josef, are you somehow familiar with the whole gauge-gravity-duality thing which is getting more and more popular?