sci.math.research Google Group

Re: minimum height of a 0-1 simplex

2010-03-09T18:12:37Z

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?

2010-03-09T18:12:36Z

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

2010-03-09T16:26:40Z

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

2010-03-08T00:16:08Z

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?

2010-03-06T19:04:28Z

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

Ten papers published by GT Publications

2010-03-04T12:35:16Z

Five papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 10 (2010) 315-342
An involution on the K-theory of bimonoidal categories with anti-involution
by Birgit Richter
URL: [link]
DOI: 10.2140/agt.2010.10.315

Call for Paper The International Journal of Computer Science (IJCS)

2010-03-04T17:28:40Z

Call for Paper
The International Journal of Computer Science (IJCS) publishes
original papers on all subjects relevant to computer science,
communication network, and information systems. The highest priority
will be given to those contributions concerned with a discussion of
the background of a practical problem, the establishment of an

Re: delta function as a continuous linear map?

2010-03-03T21:59:58Z

On Wed, 03 Mar 2010 13:40:02 -0600, Dan Luecking <LookIn...@uark.edu>
wrote:
I really meant n,m>0
and I meant \sum_{k <= n, j <= m}
And here || f ||_{n,m}
And here || f ||_{0,0}
Dan
To reply by email, change LookInSig to luecking

Re: delta function as a continuous linear map?

2010-03-03T19:40:02Z

On Tue, 2 Mar 2010 22:12:35 -0800 (PST), mahdiarnt
You have provided a proof that the delta function
is not continuous on L^2. To prove it _is_ continuous
on S, you have to use the topology on S, which is
provided by the fammily of seminorms || f ||_{n,m},
n >= 0, where || f ||_{n,m} is defined to be

Re: delta function as a continuous linear map?

2010-03-03T16:23:59Z

In article
<5b79b21d-efa8-4f42-979b-f3518 b89c...@g8g2000pri.googlegroup s.com>,
So, you refer to ||f||_S , but what is that? Of course, to determine
whether some function is continuous on S we need to know what is the
topology on S. In fact, this topology is not given by a norm.

Ten papers published by GT Publications

2010-03-03T12:52:23Z

delta function as a continuous linear map?

2010-03-03T06:12:35Z

Hi
I've come across a claim that has made me confused. In
[link] (which is for people like me)
it's claimed on page 17 that the delta function defined on functions
of Schwartz space S as
delta: S -> R, delta_{x_0} f = f(x_0)
is continuous. I think it's true, as implicitly mentioned there as

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

2010-03-03T11:19:01Z

Question:
Let A be a connected semisimiple complex lie group. Is it true that
any free abelian group G of finite rank can be embedded in A?
I know that it is the case that any free groups of finite rank can be
embedded into any connected complex semisimple lie group.
Do we have to make any assumptions about the dimension of A for the

Call For Manuscripts: International Journal of Signal Processing (IJSP)

2010-03-03T04:59:10Z

Call For Manuscripts
The International Journal of Signal Processing (IJSP) is currently
accepting original high-quality research manuscripts for publication.
The Journal welcomes the submission of manuscripts that meet the
scientific criteria of significance and academic excellence. All
research articles submitted for the journal will be peer-reviewed

Re: Three Elementary Planar Convexity Problems

2010-03-02T13:31:23Z

D'oh! and sincere regrets at errors due to haste in posting.
Long and thin rectangles show that both (i) and (ii) are incorrect.
Although it is possible to avoid that case by restricting the minimal
width of X it is probably best to consider case (iii) only.