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Robin Chapman
science forum Guru Wannabe

Joined: 25 Mar 2005
Posts: 254

Posted: Thu Mar 24, 2005 9:51 pm    Post subject: Re: Orthogonal latin squares of even side

Simone Severini wrote:

 Quote: Would you explain to me a more-or-less general (possibly simple!) method to construct orthogonal latin squares of even side?

At

http://www-math.cudenver.edu/~wcherowi/courses/m6406/cslne.html

there is a short account by Bill Cherowitzo of a construction by Zhu Lie.

--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
"Elegance is an algorithm"
Iain M. Banks, _The Algebraist_
Ruitao Zhang
science forum beginner

Joined: 24 Mar 2005
Posts: 1

 Posted: Thu Mar 24, 2005 9:51 pm    Post subject: Re: de Finetti's theorem de Finetti theorem said that if an infinite sequence is exchangeable then there exist a unique probability measure such that the de finetti hold. Is this probability measure the prior measure. In Bayesian we choose start from any prior measure. Here it seems that the prior is unique. I don't understand it. For infinite population with exchangeability, we can use relative frequency of an event to estimate the the probability of this event. But, For the finite population, why we need exchangeability? Thanks very much for your help Ruitao
John Baez
science forum Guru Wannabe

Joined: 01 May 2005
Posts: 220

G A Edgar
science forum beginner

Joined: 24 Mar 2005
Posts: 1

Posted: Thu Mar 24, 2005 9:51 pm    Post subject: Re: Brouwer's characterization of Cantor set

In article <cvkodf\$vq5\$1@news.ks.uiuc.edu>, John Ryskamp
<philneo2001@yahoo.com> wrote:

 Quote: The most important response of Brouwer to Cantor was Brouwer's formulation of an infinite ordinal number. He described this in his 1912 lecture. However, it is based on that idea that Cantor proved the well-ordering of the ordinal numbers. As Garciadiego has shown, not only did Cantor not do so, but also, he never claimed to have done so, and never used the term infinite ordinal number.

???
"Ueber unendliche, lineare Punktmannigfaltigkeiten, 5"
Math. Annalen 21 (1883) 545-586

available on-line:

http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN235181684_0021

I guess you could say Cantor did not use the term "infinite ordinal
number"
because, writing in German, he used "unendlichen Zahlen" (see page
547)...
But somehow I do not think that is what Garciadiego had in mind.
John Ryskamp
science forum beginner

Joined: 24 Mar 2005
Posts: 1

Posted: Thu Mar 24, 2005 9:51 pm    Post subject: Re: Brouwer's characterization of Cantor set

The most important response of Brouwer to Cantor was Brouwer's
formulation of an infinite ordinal number. He described this in his
1912 lecture. However, it is based on that idea that Cantor proved
the well-ordering of the ordinal numbers. As Garciadiego has shown,
not only did Cantor not do so, but also, he never claimed to have done
so, and never used the term infinite ordinal number. The term
infinite ordinal number has no meaning and you should examine your
interests in light of what Garciadiego has to say about the math
history of Brouwer's era.

On Thu, 09 Dec 2004 18:09:40 +0000,
=?ISO-8859-1?Q?Jos=E9_Carlos_Santos?= wrote:
 Quote: On 08-12-2004 12:46, Jorge Buescu wrote: Brouwer has given an equivalent characterization of the Cantor set as a perfect, totally disconnected, compact Hausdorff space with a countable base of clopen subsets. However, I can't seem to find a suitable reference for this fact (MathSciNet does not extend that far). But this is probably on some appropriate General Topology books. Can anyone point one out? There's a proof in Willi Rinow's Lehrbuch der Topologie. It's the last theorem of section 24. Best regards, Jose Carlos Santos
Axel Vogt

Joined: 03 May 2005
Posts: 93

Posted: Thu Mar 24, 2005 9:51 pm    Post subject: Re: The curse of dimensionality for integration

On Thu, 19 Feb 2004 06:38:52 +0000 (UTC), Greg Kuperberg wrote:
 Quote: In article <4033DA60.7060503@univie.ac.at>, Arnold Neumaier wrote: Numerically, integration is simpler than differentiation in one dimension, but in higher dimension, integration suffers from the curse of dimensionality while differntiation doesn't. In particular, it is very hard to get accurate integrals in dimensions >100, say. Readers may be interested in my new paper in which I fight the curse of dimensionality for numerical integration in high dimensions: a href="http://front.math.ucdavis.edu/math.NA/0402047">http://front.math.ucdavis.edu/math.NA/0402047

Is there an example available to look at for computing a cumulative
multivariate normal distribtuion?

--

use mail ät axelvogt dot de
Dave L. Renfro
science forum Guru

Joined: 29 Apr 2005
Posts: 570

Posted: Thu Mar 24, 2005 9:51 pm    Post subject: Re: fractional iteration of functions

qmagick@yahoo.com
[sci.math.research: January 28, 2005 14:00:05 +0000 (UTC)]
http://mathforum.org/epigone/sci.math.research/dralyoysli

wrote (in part):

 Quote: Wow, first, thanks for all the responses. I now have more then enough references to investigate. I have gotten a good response on this question. Second, I would like to respond to Mr. Geisler's last comment about axiomatic basis for function iteration. I think that will be the goal of the paper I write. Well, at least an axiomatic basis for well behaved functions over the complex plane.

Here's another reference that you might want to look at.
(I didn't see it among those suggested in this thread.)

Daniel S. Alexander, "A History of Complex Dynamics from
Schröder to Fatou and Julia", Aspects of Mathematics E 24,
Friedr. Vieweg & Sohn, Braunschweig, 1994.
[MR 95d:01014; Zbl 788.30001]
http://www.emis.de/cgi-bin/MATH-item?0788.30001

The Zbl review is especially long (the URL above takes you
to a publically available webpage). Two additional reviews
that I know of are:

Theodore W. Gamelin, Historia Mathematica 23 (1996), 74-84

Robert B. Burckel, SIAM Review 36(4) (Dec. 1994), 663-664.

Alexander's book is useful for its survey of early work
on what you're interested in. For example, Section 2.2
"Analytic Iteration", is preceded by this paragraph:

"Before reviewing the responses of Korkine and Farkas to
Schröder's study of functional equations it will be useful
to first say a few words about analytic iteration, and
then to briefly outline the respective approaches of
Schröder, Korkine and Farkas to this problem." (p. 24)

Dave L. Renfro
Annales de Toulouse
science forum beginner

Joined: 13 Jun 2005
Posts: 3

 Posted: Thu Mar 24, 2005 9:51 pm    Post subject: Annales de Toulouse, 1/2005 The issue 1/2005 of the Annales de la faculte des sciences de Toulouse has appeared. Contents: Michel Hickel Sur quelques aspects de la geometrie de l'espace des arcs traces sur un espace analytique Laurent Bernis Solutions stationnaires des equations de Vlasov-Poisson a symetries cylindriques Duc Tai Trinh Coefficients de Stokes du modele cubique : point de vue de la resurgence quantique Mohammad Daher Translations mesurables et ensembles de Rosenthal Andrzej J. Maciejewski, Maria Przybylska Differential Galois approach to the non-integrability of the heavy top problem The abstracts and some full texts can be downloaded at: http://picard.ups-tlse.fr/~annales (french version) http://picard.ups-tlse.fr/~annales/index_en.html (english version)
server
science forum beginner

Joined: 24 Mar 2005
Posts: 26

 Posted: Thu Mar 24, 2005 9:51 pm    Post subject: How real are the "Virtual" partticles? message unavailable

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