sci.math.research Google Group

Call for papers XA2010

afor...@gmail.com (afortis@gmail.com) — Mon, 15 mar 2010 13:40:50 UT

XA2010
"EUROPEAN CONFERENCE ON
COMPUTER SCIENCES & APPLICATIONS"
3rd Edition
Timi ?oara, Rom?nia, September 24-25, 2010
AIM
The 3rd European Conference on Computer Sciences and Applications
intends to stimulate the research activity and to establish
interactions between Romanian and foreign researchers, teachers, B.

Nine papers published by Geometry & Topology Publications

g...@msp.warwick.ac.uk (Geometry and Topology) — Sun, 14 mar 2010 02:24:30 UT

Seven papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 10 (2010) 525-530
Faithfulness of a functor of Quillen
by William G Dwyer, Andrei Radulescu-Banu and Sebastian Thomas
URL: [link]
DOI: 10.2140/agt.2010.10.525

Re: decomposing rationals

henne...@web.cs.ndsu.nodak.edu (Mike) — Fri, 12 mar 2010 22:06:54 UT

If a and b are rational,
this becomes an integer linear programming problem in two variables.
Such things are solvable in polynomial time.
I don't remember details.
I think that you can solve the linear relaxation
and plug away with Gomory fractional cuts.
Selecting the approximations could be tricky.

Re: minimum height of a 0-1 simplex

henne...@web.cs.ndsu.nodak.edu (Mike) — Fri, 12 mar 2010 19:13:15 UT

The above is roughly 1/n, but there are worse examples:
e_j for j in 1..k
k
SUM e_j + e_L for L in k+1..n
j=1
k n
The vertices satisfy SUM x_j + (1-k) SUM x_j = 1
j=1 j=k+1
For k=2n/3, the distance to zero is roughly sqrt(27/(4n**3)).

Call for Papers Reminder (extended): The World Congress on Engineering WCE 2010

imecs_2...@iaeng.org (IMECS 2008) — Fri, 12 mar 2010 10:42:22 UT

CFP: The World Congress on Engineering WCE 2010
WCE 2010: London, U.K., 30 June - 2 July, 2010
[link]
Draft Paper Submission Deadline (extended): 18 March, 2010
The WCE 2010 is organized by International Association of Engineers
(IAENG), a non-profit international association for the engineers and

Re: minimum height of a 0-1 simplex

henne...@web.cs.ndsu.nodak.edu (Mike) — Wed, 10 mar 2010 19:48:09 UT

That is what I get, also.
The base satisfies the linear equation
n-1
SUM x[j] + (2-n)*x[n] = 1
j=1
Lower bound, anyone?

Re: minimum height of a 0-1 simplex

henne...@web.cs.ndsu.nodak.edu (Mike) — Wed, 10 mar 2010 12:37:27 UT

I'm not sure what this means,
but I think that it is not true even in three dimension.
that a minimal-height-defining line segment of a
tetrahedron lies within the tetrahedron.
Consider a tetrahedron with the following vertices:
(0, 0, 0), (3, 2, 0), (3, -2, 0) and (4, 0, 1).
Its minimal-height-defining segment is (4, 0, 1)_(4, 0, 0).

Re: minimum height of a 0-1 simplex

corbenn...@googlemail.com (Corbennick) — Wed, 10 mar 2010 12:37:27 UT

Yes, but it seems I made a mistake there, as the height-defining
segment
does not always lie inside the simplex.
However, it does so, if the simplex has the property that all angles
between
edges are at most \pi/2.
Now for a simplex with vertices in {0,1}^n this condition is
satisfied!
By symmetry, it is enough to check this at the vertex zero.

Re: minimum height of a 0-1 simplex

anton.deit...@googlemail.com (Anton) — Wed, 10 mar 2010 12:37:29 UT

no, is not.
For example, consider the simplex spanned by zero, e=e_1+...+e_n, e_1,
e_2,...,e_{n-1},
where e_1,...,e_n is the standard basis.
A calculation shows that the vertex at zero has height equal to 1/
sqrt(n-1+(n-2)^2)
which for n>3 is less that 1/sqrt(n).

Whitehead Groups of Short Exact Sequence

wildstar...@hotmail.com (Jeffrey Rolland) — Wed, 10 mar 2010 12:37:28 UT

Hello, all!
The Whitehead group of a group G, Wh(G), is a functor from the category
of (finitely presented?) groups to the category of Abelian groups. A
reference is _A Course in Simple Homotopy Theory_ by Cohen.
If I have a short exact sequence of finitely presented groups 1 -> K -> G
-> Q -> 1, and I take the Whitehead torsion of the sequence, forming Wh

Re: minimum height of a 0-1 simplex

henne...@web.cs.ndsu.nodak.edu (Mike) — Tue, 09 mar 2010 18:12:37 UT

Excellent news. Thanks much.
I'm having trouble following the proof, though.
I'll get back to it when I'm not supposed to be working.
The crucial point that I didn't think of.
Once I can prove that both ends of the height-defining segment are in
n-cube,
the rest is easy.

Re: Do free abelian groups embed into connected semisimple complex lie groups?

corbenn...@googlemail.com (Corbennick) — Tue, 09 mar 2010 18:12:36 UT

Any such Lie group contains a complex torus isomorphic to C^*.
This group contains a subgroup isomorphic to the additive group R
of reals. Now let n be a natural number and choose v_1,...,v_n in R
which are linearly independent over Q.
Then the group Z v_1 + ... + Z v_n is free abelian of rank n and

Re: minimum height of a 0-1 simplex

corbenn...@googlemail.com (Corbennick) — Tue, 09 mar 2010 16:26:40 UT

The lower bound is 1/sqrt(n).
Proof as follows. Let e_1,...,e_n be the standard basis of R^n.
Let s be a simplex of dimension n in R^n.
The minimal height is taken at a vertex v_1 which lies opposite to a
face F of maximal area.
(This is so since the volume of the simplex is height times area(F)
times dimension factor.)

minimum height of a 0-1 simplex

henne...@web.cs.ndsu.nodak.edu (Mike) — Mon, 08 mar 2010 00:16:08 UT

What is the minimum height of a full dimensional n-simplex whose
vertices are members {0, 1}**n ?
Equivalently, what is the minimum non-zero distance to the origin from
a hyperplane defined by members of {0, 1}**n ?
The answer is at most 1/sqrt(n) .
The corner simplex provides an example.
A smaller answer might be possible if the simplex is oblique enough

Re: delta function as a continuous linear map?

mahdia...@yahoo.com (mahdiarnt) — Sat, 06 mar 2010 19:04:28 UT

Oh now I see. Thanks G.A and Dan for pointing out the caveat in my
argument.