sci.math.research Google Group

Order of arithmetic and geometric means

hob...@newpaltz.edu (David Hobby) — Sat, 31 Jul 2010 18:00:05 UT

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

johnsinete...@yahoo.de (Ivo Siekmann) — Thu, 29 Jul 2010 16:00:09 UT

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

bo198214'remove-quo...@googlemail.com (Henryk Trappmann) — Tue, 27 Jul 2010 15:30:06 UT

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

logarithm reciprocal limit

bo198...@googlemail.com (Henryk Trappmann) — Tue, 20 Jul 2010 07:00:01 UT

In my current research I encountered the following intriguing
sequence:
Define a_n recursively in the following way (for any b>0):
a_1 = 1 and for n>1:
a_n = 1/(1-b^n) * sum from m=1 to n-1 over a_m * (n over m) * (1-b)^(n-
m) * b^n
For ASCII handicapped people here the typeset formula:
[link]frac{1}{1-b^n}\sum_{m=1}^{n-1} %20a_m%20\left(n\\m\right)%20( 1-b)^{n-m}%20b^m

Six papers published by Geometry & Topology Publications

g...@msp.warwick.ac.uk (Geometry and Topology) — Wed, 14 Jul 2010 17:04:39 UT

Four papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 10 (2010) 1437-1454
Multiplicative properties of Morin maps
by Gabor Lippner and Andras Szucs
URL: [link]
DOI: 10.2140/agt.2010.10.1437

How to combine linear constraints on a matrix and its inverse?

frederick.tra...@gmail.com (Frederick Eberhardt) — Wed, 14 Jul 2010 11:05:16 UT

Suppose there exists a (n x n) matrix A that is real and invertible
(nothing unusual or special about A). We do not know the entries of A.
However, we do have linear constraints, some of which are on the
entries of A and some of which are on the entries of its inverse
A^{-1}. All constraints are assumed to be consistent with the true

System Identification methods

christopher.mad...@wiremetrics.com (Christopher) — Wed, 14 Jul 2010 00:08:43 UT

I am looking for any papers that address the problem of solving y=Ax
for A where y and x are vectors. I assume many techniques have been
developed and would be really interested if a compilation of methods
has been published.
For any single y and x, there may be multiple solutions for A, but I
believe given a sufficient number of different y and x vectors, A can

Linked or not

stev...@roadrunner.com (S. B. Gray) — Tue, 13 Jul 2010 21:03:57 UT

Circles in 3D can be either linked (topologically inseparable) or
separate. In 4D, what if anything defines whether two spheres are
similarly linked? Is this situation even defined? I know that in 4D
there are no knots, so maybe there are no links either.
Steve Gray

GCD reduced lattices

genewardsm...@gmail.com (Gene Ward Smith) — Sun, 11 Jul 2010 10:39:44 UT

Suppose we have an integer lattice. If there is a basis given by a
kxn integral matrix M with linearly independent rows, such that one of
the rows has a GCD greater than one, we may divide this out and and
obtain a sublattice. If this cannot be done, call the lattice GCD
reduced. Another way of defining GCD reduced would be that the

Curvature via Koszul's formula?

florifulgura...@googlemail.com (Martin Gisser) — Tue, 06 Jul 2010 15:30:51 UT

I need a coordinate-free expression of Riemannian curvature involving
only vector fields and metric. I guess such a thing can be derived by
iterating Koszul's formula for the Levi-Civita connection - with quite
excruciating computations involving many dozens of terms. Has anybody
done (and published) this?

Fractional operator

ilario.maz...@gmail.com (ilario980) — Fri, 02 Jul 2010 23:42:27 UT

Fractional integral and fractional derivative can be evaluated using a
unique operator. In my site [link] can
be downloaded a pdf document that presents such operator; document
contains also a sketch of proof about the equality of this operator
respect traditional fractional operators.

Call for papers: WSOM 2011, 8th Workshop on Self-Organizing Maps

jaakko.pelto...@tkk.fi — Fri, 02 Jul 2010 18:18:11 UT

============================== ============================== =======
First Call for Papers
for
WSOM 2011, 8th WORKSHOP ON SELF-ORGANIZING MAPS
13 - 15 June 2011, Espoo, Finland
Aalto University School of Science and Technology and

MetaOptimize Q+A site

tur...@gmail.com (Joseph Turian) — Sat, 03 Jul 2010 00:57:35 UT

Question: What is an accurate technique for computing the moving
variance?
Answer: [link]
I have just launched a machine learning + statistics Q&A site:
[link]
I announced it initially to ML people, and am now announcing it more

New website devoted to Differential Equations

Wed, 30 Jun 2010 21:30:01 UT

A Website Devoted to Differential Equations
A couple of months ago we posted a message here to announce
the availability of a new website, devoted to the subject of
Differential Equations, and whose goal will be to present
that subject in an as an intuitive and conceptual a way as
possible. The URL is:

Degree sequences of triangle-free graphs

fred.gal...@gmail.com (Fred Galvin) — Wed, 30 Jun 2010 13:30:05 UT

What sequences can be realized as the degree sequence of a triangle-
free graph? Is there a characterization or a good algorithm?