- Re: The johnson graph
In article ,
Do you have access to Math Reviews online?
A search there for johnson graph turned up 72 results.
Here are the first 20.
MR2656274 Ning, Wantao; Li, Qiuli; Zhang, Heping Smallest generalized
cuts and diameter-increasing sets of Johnson graphs. Ars Combin. 95
- Re: Fourier series question
TCL schrieb:
NO. If \hat f(n)=0 for all integers n then f=0 Lebesgue almost
everywhere (Uniqueness Theorem)
Peter
p.s. didn't you post this on sci.math a few days ago????
- The johnson graph
Hi everyone...
Does anyone know of some good papers about the johnson graph ?? This
graph has as vertex set all m-subset of {1, ..., n } and two vertices
s1, s2 are adjacent if and only if |s1 \cap s2 | = m - 1. I have searhed
over the internet but i can only find litte information about this graph
- Z(t,t^-1) solutions to a(t)p(t)+b(t)q(t)=1
Greetings. Suppose that p(t) and q(t) are Laurent polynomials
with integer coefficients. I am looking for Laurent polynomials with
integer coefficients for which a(t)p(t)+b(t)q(t) = 1.
Over rationals, not integers, this could be unambiguously
determined by the GCD algorithm. However, in integers, the GCD
- Five papers published by Geometry & Topology Publications
Two papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 10 (2010) 1747-1780
On Davis-Januszkiewicz homotopy types II: Completion and globalisation
by Dietrich Notbohm and Nigel Ray
URL: [link]
DOI: 10.2140/agt.2010.10.1747
- Fourier series question
Does there exist a nonzero (i.e. not equal to 0 a.e.) Lebesgue
integrable function on [0, 2pi] whose Fourier series is 0, i.e. all
its Fourier coefficients are 0 ?
I don't think the famous Kolmogorov's example answers this question.
- E^(pi*sqrt(163)) and the solvable sextic 5x^6-640320x^5-10x^3+1 = 0
Hello all,
The sextics,
5x^6-15x^5-10x^3+1 = 0
5x^6-32x^5-10x^3+1 = 0
5x^6-96x^5-10x^3+1 = 0
5x^6-960x^5-10x^3+1 = 0
5x^6-5280x^5-10x^3+1 = 0
5x^6-640320x^5-10x^3+1 = 0
have some very interesting properties.
1. I'm sure some will also recognize the sequence {15, 32, 96, 960,
5280, 640320}. (Hint: Their cubes plus 744 are good approximations to
- Brouwer's choice sequences as a basis for measure theory and probability theory
In considering problems regarding the foundations of probability, I have
thought that Brouwer's choice sequences could be an interesting basis
for measure theory and probability theory. The class of choice sequences
can be regarded both as the codomain and (in essence) as the domain of
probability functions. A such approach could suggest possible solutions
- Question on the Polynomial Hierarchy
Is there any easily described parameterized problem sequence,
P1, P2, P3, ...., such that
the problem class Pk is exactly n^k poly-time?
- Diophantic approximations
I have a question about approximations of irrational numbers
by rationals. Roughly speaking, if x is an irrational, then there
exist an infinitely many distinct fractions p/q such that
of the continued fraction expansion of x. The converse is also true:
If p/q is a fraction such that |x - p/q| < 0.5*q^(-2) than p/q
- Re: Reference request: automorphisms of a product of two cyclic groups of prime power order
I guess this would be covered by the following references, which
handle split metacyclic p-groups. There is probably a better reference
for the abelian case!
MR2283679 (2007i:20055)
Bidwell, J. N. S.(NZ-OTG); Curran, M. J.(NZ-OTG)
The automorphism group of a split metacyclic $p$-group. (English
summary)
- Re: TQFT
You could try
Frobenius Algebras and Topological Quantum Field Theory, by Joachim
Kock
It's aimed at advanced undergrad level. The approach is via algebra
and category theory.
- Reference request: automorphisms of a product of two cyclic groups of prime power order
I'm looking for a reference to the following result (probably a
special case of a more general one):
Let p be a prime, and let a >= b > 0 be positive integers. let C_{p^a}
and and C_{p^b} be the cyclic groups of orders p^a and p^b,
respectively, and let A = C_{p^a} x C_{p^b} be their direct product,
- Exterior Jet Bundles
For field theory, when the field is based on natural objects such as
differential forms, a more suitable way to encapsulate its Lagrangian
appears to be a kind of bundle I've not seen discussed in the
literature anywhere -- the exterior jet bundle.
Thus, for a 1-form field the configuration variables would comprise a
- Re: This Week's Finds in Mathematical Physics (Week 300)
If this really is the last Baez Find I shall read in sci.math ,
may I thank you for an extraordinarily interesting and stimulating series
on an almost Eulerian scale over so many years.
You stand beside Martin Gardner in my mathematical pantheon.
- This Week's Finds in Mathematical Physics (Week 300)
Also available at [link]
August 11, 2010
This Week's Finds in Mathematical Physics (Week 300)
John Baez
This is the last of the old series of This Week's Finds - and the last
one that will appear on the newsgroups sci.physics.research,
sci.physics, sci.math.research and sci.math. Soon the new series will
- Arithmetic Coder Probability Model $100
[
Moderator's Note
If you want the job, contact them directly, not in the newsgroup.
We do post job listings, but this is a bit different: Is this sort
of thing appropreate for this newsgroup?
]
do you already knows Arithmetic Codings algorithm .... if so , has a
straight forward modification of Aritmetic coding job for you to
- Nine papers published by Geometry & Topology Publications
Six papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 10 (2010) 1609-1625
Continuous interval exchange actions
by Christopher F Novak
URL: [link]
DOI: 10.2140/agt.2010.10.1609
(2) Algebraic & Geometric Topology 10 (2010) 1627-1664
- Re: logarithm reciprocal limit
I settled now a proof for that, including lots more background:
[link]
- Re: Proof that there is a prime in ]m·n, (m+1)·n[
Hello,
This is well-known, when you look at it in the proper way :)
Set X = mn and eps = 1/m. You want a prime in the interval
[X, (1+eps) X].
A usual roundabout is to look at
\vartheta(y)=\sum_{p\le y} \Log p
If you find X0 such that
\vartheta(y) = y (1+O^*(epsprime)) (where z=O^*(u) means |z|\le u)
- Re: Logical problem: how is it possible for first-order logic to be at the same time complete and only semi-decidable?
Do not confuse his completeness theorem for restricted FOL
with his incompleteness theorem for full first-order functional
calculus with identity.
Up until Andrew Wiles' proof was tested and confirmed, FLT was very
often
cited as the very me of a theorem which was in principle undecidable
(in
Gödel's sense).
- functions from real to banach space
Hi all,
I am doing research in function spaces.
I have two questions_
1. i am stuck in the function of type----------
Let U be a domain in R^n and X be a Banach space then i want to study
about C^k(U,X) , k times continuous differentiable functions.
Can U suggest me some book for studing it?
2. if g is mollifier from U to R^n and f : U ---> X, X is a banach
- Re: Logical problem: how is it possible for first-order logic to be at the same time complete and only semi-decidable?
In article
,
This is not correct. For most A, neither A nor ~A is a theorem. For
example, suppose as our axioms we take the notion of group, and A the
commutative law. Then since some groups are commutative, ~A is not a
theorem, and since some groups are non-commutative, A is not a theorem.
- TQFT
Hello all,
This is my first post here and I hope this is appropriate to ask
here. I'm an undergraduate(senior) in math and I have a strong
interest in learning about TQFT. Most of what I've been able to find
is well above my current level. I'm hoping I might get some
suggestions on where I might start in my attack on this area.
- Proof that there is a prime in ]m·n, (m+1)·n[
Hi,
Someone could help me? Given m > 0. Using Prime Number Theorem, I want
to prove that there exists n_0 such that for all n > n_0 there is a
prime in the interval ]m·n, (m+1)·n[. Specifically I want to know a
upper bound of n_0.
All of my tries are in vanuous. Is there any know upper bound for n_0?
- retract
Hello,
I would like to check whether some set of probability distributions
form a retract. Would you kindly suggest how to proceed?
Best,
Skyline
- Re: About rigorous proof of chaos in dynamical system
In article ,
[cut]
Just a follow up on the letters and an article in American Mathematical
Society journal. The letters are interesting. They are stimulated by
an article by Freeman Dyson on types of mathematicians throughout
history, especially people he knew. He covers a lot including chaos,
- Unity Root Matrix Theory - arXiv endorser?
I am trying to find an arXiv endorser for a paper I have written
entitled "Unity Root Matrix Theory". The usual method is to search on
arXiv and I have done so. My problem is that the paper is a complete
mishmash of mathematical physics, number theory and linear algebra. It
could be all of them and none of them. The title is a bit too specific
- Re: About rigorous proof of chaos in dynamical system
In article ,
Thanks. I'll check those out. I know Jim Yorke and he gave me the
impression that this is a closed book. But maybe that's because he has
his own approach that he likes. Not a criticism there. I certainly am
partial to my own views. I could also have missed some subtly that he
- A proof of the Riemann hypothesis ?
Dear Professors of analytic number theory,
I would like to receive your attention for the proofreading
and dissemination of the following paper, which is
available as the version 14th of the preprint
titled
"An integral formula for 1/|zeta(s)| and a proof of the
Riemann hypothesis"
- Re: Order of arithmetic and geometric means
The proofs above show AG(A) <= GA(A). It seems interesting to test out
if AG(A) <= GA(A*), where A* is the transpose of the matrix A, is also
true, ie take the geometric and arithmetic means of the COLUMNS
first.
Of course this cannot be true for general matrices (take a 1xn
matrix), and it is also false for square matrices, but just barely. A
- Re: About rigorous proof of chaos in dynamical system
I refer you to Letters to the Editor in the November 2009 issue
of the Notices of the American Mathematical Society, where James
Yorke and David Ruelle appear to have different definitions of
chaos. Not a "nasty spat"; on the contrary, very, very polite.
Lee Rudolph
- Re: About rigorous proof of chaos in dynamical system
In article ,
Really? That's news to me. I thought most people were settled on the
definitions of attractor and chaos (ignoring Hamiltonian systems for
now). Can you give me an example of definitions of chaos that differ
and which people are debating?
Thanks.
- Re: About rigorous proof of chaos in dynamical system
A couple of leads, perhaps.
Dynamical Systems, Stability, Symbolic Dynamics and Chaos
Robinson C. (Clark), ISBN 0-8493-8493-1
Chaos and Integrability in Nonlinear Dynamics
An Introduction, Michael Tabor, ISB 0-471-82728-2
If nothing else, the list of references at the back should be of use.
Richard M.
- Re: About rigorous proof of chaos in dynamical system
In article
<0d68e51a-a81f-4205-83ff-71e93 e9d7...@t2g2000yqe.googlegroup s.com>,
Try Google Scholar. I came up with this:
Rigorous verification of chaos in a molecular model, Thomas Rage, Arnold
Neumaier, Christoph Schlier, Phys. Rev. E 50, 26822688 (1994)
I think for certain parameters Sparrow may have proven the Lorenz system
- Re: About rigorous proof of chaos in dynamical system
You must first decide on rigorous definitions of "chaos" and
"dynamical system" (though the latter isn't in much dispute
now, the former still is, and there continue to be occasional
nasty spats about whether one person's "chaotic dynamical
system" is another person's "chaotic dynamical system").
Lee Rudolph
- About rigorous proof of chaos in dynamical system
Hi,
I search for a good referene about rigorous proof of chaos in
dynamical system.
thanks to all.
John Claud, U of Michigan
- Re: Order of arithmetic and geometric means
On Mon, 2 Aug 2010 07:13:30 -0700 (PDT), Heine Rasmussen
It can also be seen as Holder's inequality (extended
by induction to n factors):
If 1/p_1 + 1/p_2 + ... 1/p_n = 1 then
\int f_1 f_2 ... f_n d\mu \le
(\int f_1^{p_1} d\mu)^{1/p_1}...(\int f_n^{p_n} d\mu)^{1/p_n},
Apply this with all p_j equal n, f_k(j) = x_{kj}^{1/n} and
- Re: Order of arithmetic and geometric means
It seems you have a corollary of Mahler’s inequality.
Assume your matrix has m rows and n columns. First, note that by
dividing each element in the matrix by n, you can replace all the
arithmetic means with ordinary sums and still get the same values for
AG and GA.
You then have Mahler’s inequality:
- Order of arithmetic and geometric means
Consider a matrix of positive real numbers. Take the geometric means
of each of the columns, and then the arithmetic mean of the result,
and call this AG. Also take the arithmetic means of the rows of the
matrix, the geometric mean of these, and call it GA. I think I have a
proof that AG is always less than or equal to GA.
- Continuous-time Markov chains
Often, continuous-time Markov chains with n_S states are defined by the
differential equation
d P(t) / d t = P(t) Q, P(0)=I_{n}, Q \in R^{n x n}
where
q_{ij} >= 0 for i != j and q_{ii} = \sum_{i != j} (- q_{ij}).
The solution of this differential equation is the transition matrix
P(t) = exp( Q t )
- True or False Logarithm
Let |b|<1 and consider the following polynomial sequence f_n(x):
f_n(x) = -sum from k=1 to n: binomial(n over k)*(-1)^k * (1-x^k)/(1-b^k)
I can show by elementary transformations that
lim_{n -> oo} f_n(b^m) = m for every integer m>=0 and
lim_{n -> oo} f_n(0) = -oo
Does this function sequence converge also for other points |x|<1 than
- Re: Linked or not
It is a nice book (reachable e.g. via Google books). An example on the
unsplittable links is at page 94, 2-sphere and spun trefoil (something
knotted by itself before its n-sphere embedding yielding rotation).
See e.g.
[link]
[link]
- Re: logarithm reciprocal limit
No, in my formula above there is a fraction \frac{k (-1)^k}{1-b^k}
without LaTeX: k * (-1)^k / ( 1 - b^k)
while in your formula it is a product (!) even omitting k,
thats something completely different.
For clarity the whole formula in ASCII:
b_n=sum(from k=1 to n) binomial(n over k) * k * (-1)^k/(1-b^k)
- Re: logarithm reciprocal limit
Henryk Trappmann schrieb:
a_n =sum_{k=1}^n k binomial{n}{k} (-1)^k(1-b^k)
=sum_{k=1}^n k binomial{n}{k} (-x)^k |_x->1
-sum_{k=1}^n k binomial{n}{k} (-x)^k |_x->b
=(x d/dx sum_{k=0}^n binomial{n}{k} (-x)^k) |_x->1
-(x d/dx sum_{k=0}^n binomial{n}{k} (-x)^k) |_x->b
= (x d/dx (1-x)^n) |_b ^1
= n b (1-b)^n
- Re: logarithm reciprocal limit
Your formula $\frac{1-(1-b)^n - nb(1-b)^{n-1}}{1-b^n}$ can not be true,
it does not give the correct values;
The values of a_n with b=2 are for n=1,2,...
1, 4/3, 10/7, 152/105, 314/217, 940/651, 5678/3937, 1447504/1003935,...
yours:
0, -4/3, 4/7, -8/15, 8/31, -4/21, 12/127, -16/255, 16/511
I think you can not apply summation by parts if the v depends on two
- Re: logarithm reciprocal limit
I found some mistakes in my proof above, because i was a bit careless
with boundary terms. The corrected derivation in LaTex can be viewed
here:
[link]
- Re: logarithm reciprocal limit
The sum can be calculated in closed form.
Using the formula for summing by parts: \sum_{m=1}^{n-1}u \Delta v =
uv|_{m=1}^n -\sum_{m=1}^{n-1}E[v] \Delta u, where E[f(x)]=f(x+1).
In this case u=a_m; \Delta v = \left(n\\m\right) (1-b)^{n-m} b^m.
Therefore, \Delta u = a_{m+1}-a_m, v=(1+1-b)^n=1 (binomial formula),
- Re: logarithm reciprocal limit
Ok, here the latex set formula:
a_n = \frac{1}{1-b^n}\sum_{m=1}^{n-1 } a_m \left(n\\m\right) (1-b)^{n-
m} b^m
Yes, (n over m) means the binomial coefficient. "over a_m ..." was
meant to take the sum "over" the rest of the line.
That's true this case has to be excluded. However if the conjecture is
true we can continue the function (in variable b) to b=1.
- Re: logarithm reciprocal limit
What's (n over m)? Is it n/m, the Jacobi symbol or something else?
Is the sum from 1 to n-1 or from 1 to (n-1) over a_m?
No, that's confusion of variables. What does over a_m mean? 1/a_m?
What's a_n if b = 1?
Factoring b^n from the sum, let's look at
lim(n->oo) b^n / (1 - b^n) = lim(n->oo) 1/(b^-n - 1)
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