HDTenEightyP/NetNews huggingface dataset:
From: ksanjay@cs.tamu.edu (Sanjay D Kamat)
Newsgroups: sci.math,sci.math.stat
Subject: Request for help - A Probability Problem
Date: 28 Jan 1993 18:09:09 GMT
Organization: Computer Science Department, Texas A&M University
NNTP-Posting-Host: sparc30.cs.tamu.edu
Keywords: Probability, random sums, beta distribution

Hi,
   I am a computer science student working towards my PhD degree. I 
   would very much appreciate your help/suggestions on the following 
   problem I recently encountered in my research.

   A random variable S is defined as the sum of n terms, each of the
   form u_i * w_i. 
   u_i and w_i are themselves random with the following properties.

   1) All u_i's are identically distributed -but not independent in the
      sense that their sum is fixed, say U. (All splittings of U
      considerted equi-probable).
   2) All w_i's are independent as well as identically distributed.
      They are also bounded between w_min and w_max.
   3) u_i's and w_i's are independent of each other.

   I can establish that 
      mean S = mean w * U
      variance S = (2/(n+1)) * U * U * variance w.

   Further, for the parameters of concern, "beta" distribution for S
   with above mean and variance seems to fit very well.

   My questions are:
   1) Is there a sound theoretical justification for "beta"
      distribution to be applicable?
      ( Also - is there some limit theorem which applies to S for large
	       n? )
   2) What is a good source for good approximations for the incomplete
      beta function?

Thanks  in advance,
Sanjay Kamat.
Dept of Computer Science 
Texas A&M University

ksanjay@cs.tamu.edu
From: ara@zurich.ai.mit.edu (Allan Adler)
Subject: Re: linear algebra problem
Organization: M.I.T. Artificial Intelligence Lab.
	<1993Jan24.175139.19561@sol.ctr.columbia.edu>
Date: Sun, 24 Jan 1993 20:03:26 GMT



If problems like this are equivalent to studying vector bundles on projective
spaces, what analogous problems are equivalent to studying vector
bundles on other varieties?

Also, what is the reference to Kronecker?

Allan Adler
ara@altdorf.ai.mit.edu
From: elkies@ramanujan.harvard.edu (Noam Elkies)
Newsgroups: sci.math
Subject: Re: Distribution of primes mod 4
Date: 24 Jan 93 17:36:37 GMT
Article-I.D.: husc3.1993Jan24.123639.19744
Organization: Harvard Math Department

In article <1993Jan21.212120.251@leland.Stanford.EDU>
ilan@leland.Stanford.EDU (ilan vardi) writes:
:In article <1993Jan21.141800.17997@linus.mitre.org>
:bs@gauss.mitre.org (Robert D. Silverman) writes:
:>
:>let u(x) = #{n <= x;  pi(n,1,4) < pi(n,3,4)}
:>
:>Then one would expect that u(x) = x/2 for almost all x. That is to say,
:>for large x, about 1/2 the integers less than x have pi(n,1,4) < pi(n,3,4)
:>and for about 1/2 the integers the inequality is reversed. This can be
:>made more precise;
:>
:>u(x) = x/2 + O(x^{1-epsilon})  for any fixed epsilon.
:
:
:Yo! This is clearly wrong, and you can't do better than epsilon = 1/2
:(which is the generalized Riemann Hypothesis). In other words 
:epsilon <= 1/2 in the above term. 

Careful here; this is different from the usual question of the number
of primes <x in a given congruence class.  In fact, even under the
optimal assumption that the extended Riemann Hypothesis holds for
the L-function  L(s) = 1 - 1/3^s + 1/5^s - 1/7^s - + ...  and that
the imaginary parts of the zeros in the upper half of the critical
strip 0<Re(s)<1 are linearly independent over Q, one does not expect
the set { n : pi(n;1,4) < pi(n;3,4) }  to have a natural density, only
a logarithmic one; and, more remarkably, that density is strictly
between 1/2 and 1!  (Thanks to Hugh Montgomery for clearing up
some of my confusion in this regard.)

To see how this happens, let \chi be the character mod 4 (i.e.
\chi(m)=0 if m even, +-1 if m=4k+-1), and let \Lambda be the
von Mangoldt function: \Lambda(p^k)=\log(p) for p prime and k>=1,
\Lambda(m)=0 if m is not a prime power.  Then one finds that
sum(\chi(m)\Lambda(m), m=1..x) is approximated by the sum of
x^rho/rho with rho running over the nontrivial zeros of L(s);
under our assumption on these rhos, this is sqrt(x) times an
almost periodic function of log(x) with zero mean, finite mean square
(this since the sum of 1/|rho|^2 converges) but attaining arbitrarily
large values (because sum(1/|rho|) diverges).  Now in the Prime
Number Theorem, when we pass from the sum of \Lambda(m) to the
count of primes <x the first thing we do is ignore the contribution
of all prime powers higher than the first, which contribute
"negligibly" to the sum.  However in our case this "negligible"
contribution is asymptotically sqrt(x) [note that chi(p^2) is
always 1 for p>2!].  Thus we find that pi(x;1,4)-pi(x;3,4)
is approximated by sqrt(x)/log(x) times an almost periodic
function of log(x) whose mean is -1!  Hence the estimate on
the set of x for which it is negative.

--Noam D. Elkies (elkies@zariski.harvard.edu)
  Dept. of Mathematics, Harvard University

P.S. Thanks to Paul C. Leyland for the references to Hans Riesel's
book and to Bays and Hudson's computational work.
Newsgroups: sci.math
From: victor@watson.ibm.com (Victor Miller)
Subject: Re: Frobenius Thm. on real dision algebras
Date: Wed, 27 Jan 1993 14:52:09 GMT
Reply-To: victor@watson.ibm.com
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
Organization: IBM, T.J. Watson Research Center

>>>>> On Monday, 25 Jan 1993 14:09:41 TUR, Melih Sener <E62802@TRMETU.BITNET> said:


Melih>   As far as I know there is a theorem due to Frobenius, which
Melih> states that the only associative divison algebras over real numbers
Melih> are complex numbers and quaternions (if you drop the requirement
Melih> of associativity octonions are also added to this list.)

Melih>  Here are my questions...
Melih> 1- Where can I find an explicit proof of this and related theorems?
Melih> (In Porteus' (Topological Geometry) , there is some info about the subject
Melih> but if there other sources, I'd like to know them.)

Melih> 2- Is this theorem valid only for finite dimensional case?
Melih> (i.e. Is there an infinite dimensional real divison algebra?)

Melih> Thanks for any information ....

Melih> Melih Sener<e62802 at trmetu.bitnet>

Melih, Look at "Studies in Modern Algebra" edited by A. A. Alber, MAA
Studies in Mathematics vol. 2, published by the Math. Assoc. of
America.  There is an article by Charles W. Curtis in there entitled
the "Four and Eight Square Problem and Division Algebras".
--
			Victor S. Miller
			Vnet and Bitnet:  VICTOR at WATSON
			Internet: victor@watson.ibm.com
			IBM, TJ Watson Research Center
From: victor@watson.ibm.com (Victor Miller)
Newsgroups: sci.math
Subject: Re: A strange recurrence and RESULT ABOUT PI
Date: 26 Jan 93 19:30:52 GMT
	<VICTOR.93Jan26142615@terse.watson.ibm.com>
Reply-To: victor@watson.ibm.com
Organization: IBM, T.J. Watson Research Center
Disclaimer: This posting represents the poster's views, not necessarily those of IBM

Scratch my remark about Weyl's criterion.  The problem with the binary
digits is covered under the name of "normal to base 2".  As far as I
know, no "naturally occuring" number has been proven normal (but I
might be wrong).
--
			Victor S. Miller
			Vnet and Bitnet:  VICTOR at WATSON
			Internet: victor@watson.ibm.com
			IBM, TJ Watson Research Center
From: neilfp@astro.ocis.temple.edu (Neil F. Palumbo)
Newsgroups: sci.math
Subject: HELP: Simul. Diag of matrices
Date: 23 Jan 93 02:28:59 GMT
Organization: Temple University
X-Newsreader: TIN [version 1.1 PL8]


Hi All,

Can anyone suggest a good reference on the simultaneous diagonalization of
several matrices? Thanks...

			Neil
From: scavo@cie.uoregon.edu (Tom Scavo)
Newsgroups: sci.math
Subject: Re: NCTM math teaching standards
Date: 22 Jan 93 16:55:06 GMT
Article-I.D.: pith.1jp8taINN3os
Organization: University of Oregon Campus Information Exchange
NNTP-Posting-Host: cie.uoregon.edu

In article <1993Jan21.200907.12918@cs.rochester.edu> fulk@cs.rochester.edu writes:
>Does anyone know where I can pick up a copy of the NCTM(*) standards,
>and the related materials?  I understand that Houghton-Mifflin has
>published NCTM-based text books; if anyone knows the titles, etc,
>could they please post or email that also?
>
>(*) National Council of Teachers of Mathematics

_Curriculum and Evaluation Standards for School Mathematics_

Available for $25 from

	Dale Seymour Publications
	P.O. Box 10888
	Palo Alto, CA  94303
	(415) 324-2800

Their toll free order number is (800) 872-1100.

-- 
Tom Scavo
scavo@cie.uoregon.edu
Newsgroups: sci.math
From: jhusdhui@math.tau.ac.il (Gurel-gurevitch Ori)
Subject: Re: Integers
Organization: School of Math & CS - Tel Aviv University , Tel Aviv , ISRAEL.
X-Newsreader: Tin 1.1 PL5
Date: Fri, 22 Jan 1993 09:43:18 GMT



 Magnus Olsson wrote:
 >>One way of defining integers is the following:
 >>
 >>a) There exists an integer called 1.
 >>b) Every integer n has a successor n'.
 >>c) Every integer n except 1 has a predecessor m, i.e. there exists
 an
 >>   integer m such that m' = n.
 >>
 >>This defines the non-negative integers.
 ...What I wrote down above is a set of axioms for the integers (known

 as the Peano axioms)

 This is not true.
 the correct Peano's Postulate are:
 1)there exist an integer called 0(sometimes 1).
 2)every integer n has a successor S(n).
 3)for every intgers n and m S(n+m)=S(n)+m
 4)if A is a setof integers 0 belongs to A and for every n which
 belongs
   to A S(n) belongs to A too then A is N(the set of all integers).

   the axioms Magnus gives define a structure of the integers which
   can be
   very different from what we know, for example:R-(-N) (the set of
   all
   the real numbers except the non-positive integer).
   the third axiom is neaded to make use of + and the fourth one is
   known
   as the principle of induction (which make induction possible),
								   J.

--

Gurel-Gurevitch Ori			jhusdhui@libra.math.tau.ac.il

Newsgroups: sci.math
From: jhusdhui@math.tau.ac.il (Gurel-gurevitch Ori)
Subject: RE: call it FERMIN
Organization: School of Math & CS - Tel Aviv University , Tel Aviv , ISRAEL.
X-Newsreader: Tin 1.1 PL5
Date: Thu, 21 Jan 1993 12:31:28 GMT

I hope you do understand that proving FERMIN is ever increasing
automaticaly proves FLT,
			J.














Newsgroups: sci.math
From: norm@netcom.com (Norman Hardy)
Subject: Re: pyramid volume
Organization: Netcom Online Communications Services (408-241-9760 login: guest)
Date: Thu, 21 Jan 1993 23:29:01 GMT

In article <1993Jan21.140402.25519@mr.med.ge.com> carl@crazyman.med.ge.com (Carl Crawford) writes:
>
>how do show that the volume of a pyramid is 
>
>	1/3 * area of base * altitude 
>	
>without using calculus?

Papus' theorm (axiom?) says that two solids have the same volume
if horizontal cuts of the solids by a horizontal plane at the same
altitude always have the same area.
(Think of the two solids sitting on a table.)
Two pyramids of the same hight and whose bases have the same area
thus have the same volume.
It thus suffices to find one pyramid whose volume is 1/3 hight times base.

The unit cube can be divided into three congruent solids each of which
is such a pyramid. The points (0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0)
span such a body.

I don't remember how Euclid proved this but these were all tools that
he had.
:
From: lordSnooty@cup.portal.com (Andrew - Palfreyman)
Newsgroups: sci.math
Subject: Help needed - Constraints Problem
Date: Thu, 21 Jan 93 19:20:59 PST
Organization: The Portal System (TM)
Distribution: world

I am interested in finding an efficient algorithm for solving
the following problem:

System
------
A bounded Euclidean 2-D surface with discrete coordinates (0<=x<=XMAX,
0<=y<=YMAX) is assigned numbers z(x,y) at each point. Nothing is known 
_a priori_ about this assignment. The range of z (0<=z<=ZMAX) is far
higher than the total number of points; 
	i.e. XMAX*YMAX / (dx*dy) << ZMAX/dz, where d(i) is the granularity.

Problem
-------
Given a fixed range of z-values RZ (RZ > dz), the problem is:
group contiguous points within the range such that, after covering
every point on the surface, the final grouping minimises the total 
number of groups.

Notes
-----
* "Contiguous" is taken to mean +/- dx or dy of the point under
  consideration, but not both (i.e. no diagonal connections).
* The minimum size of a group is one point.
* Note that RZ is a range = zmax-zmin, and we are free to choose the
  absolute value of one of {zmax, zmin} for any group.
---
Andrew Palfreyman
From: ferenbaugh-charles@math.yale.edu (Charles Ferenbaugh)
Newsgroups: sci.math
Subject: Re: THE DIVINE MASTERS OF THE UNIVERSE
Date: 26 Jan 93 14:51:23 GMT
Followup-To: alt.flame
Organization: Yale University Math Dept.
NNTP-Posting-Host: cauchy.math.yale.edu

In article <1993Jan25.194006.3333@cnsvax.uwec.edu> mcelwre@cnsvax.uwec.edu writes:
>
>                      THE DIVINE MASTERS OF THE UNIVERSE
>      
> [much deleted]
>
>                                           Robert E. McElwaine
>                                           2nd Initiate in Eckankar
>

A number of comments:

1.  This has nothing to do with math.  You should post it in one of
    the religion groups.

2.  Speaking as a Christian, I can tell you that you have grossly
    misrepresented Christianity in your posting.

3.  I would expand on #2 in more detail, but such would not be
    relevant to this newsgroup.

4.  This has _nothing_ to do with math.

5.  Your post consists entirely of unsubstantiated statements.
    You should make at least a token effort to justify them.

6.  This has NOTHING to do with math.

7.  You have accused Christianity, Islam, etc., of being
    perversions of the teachings of their founders.
    Can you back up this statement with evidence?

8.  THIS HAS NOTHING TO DO WITH MATH!


                                        Charles Ferenbaugh
                                        crf@math.yale.edu
Newsgroups: sci.math
From: pjp9q@honi2.acc.Virginia.EDU (Paul Joseph Perrone)
Subject: Number Theory
Organization: University of Virginia
Date: Tue, 26 Jan 1993 02:11:32 GMT


I am the non-mathematician who posted the question regarding prime
numbers a few messages ago, and I apologize for incorrectly phrasing
my question.

Here is my rephrased question:

What is the LARGEST set of prime numbers fulfilling the following
criterion,
        1) No prime number in this set can be greater than 1 million;
        2) No sum nor difference between any two of the primes in this
           set can be equal to the sum or difference between any other
           combinations of primes in this set.

I am looking for references or direction in how to compute such a
maximum set for the above problem, and for cases where I might
vary criterion one's bound.

Thanx again to those who pointed out my gross mistatement of the
problem, and to those who might help me out.

Sincerely,

Paul Perrone

pjp9q@virginia.edu
From: dubhashi@mpii01044.NoSubdomain.NoDomain (Devdatt Dubhashi)
Newsgroups: sci.math
Subject: Re: Frobenius Thm. on real dision algebras
Date: 27 Jan 93 14:48:32 GMT

See H-D. Ebbinghaus et al (eds): "Numbers", Springer-Verlag 1990.
From: nissim@mary.fordham.edu (Leonard J. Nissim)
Newsgroups: sci.math
Subject: Re: THE DIVINE MASTERS OF THE UNIVERSE
Date: 26 Jan 93 14:12:00 GMT
Distribution: usa
Organization: Fordham University
News-Software: VAX/VMS VNEWS 1.41
X-Posted-From: mary.fordham.edu
NNTP-Posting-Host: sol.ctr.columbia.edu

In article <1k3i81INNqor@CAUCHY.MATH.YALE.EDU>, 
ferenbaugh-charles@math.yale.edu (Charles Ferenbaugh) writes...

[He re-posts an entire *long* article in what I would describe as theology
which is totally inappropriate for this newsgroup.]

>In article <1993Jan25.194006.3333@cnsvax.uwec.edu> 
mcelwre@cnsvax.uwec.edu writes:

[He posted the original article, which does not belong here.]

Go find the appropriate newsgroup, and cease cluttering sci.math with this
stuff. 
-------------------------------------------------------------------------------
Leonard J. Nissim  (nissim@mary.fordham.edu)   
Disclaimer:  "I speak only for myself."
-------------------------------------------------------------------------------
Newsgroups: sci.math
From: amlogan@phoenix.Princeton.EDU (Adam Meredith Logan)
Subject: Re: Irrational stamp problem
Originator: news@nimaster
Organization: Princeton University
Date: Wed, 20 Jan 1993 23:44:27 GMT

In article <C16DI1.MD@cantua.canterbury.ac.nz> wft@math.canterbury.ac.nz (Bill Taylor) writes:
>In article <2338@sjfc.UUCP>, dmc@sjfc.UUCP (Cass Dan) writes:
>|> 
>|> You have an ink stamp which is so amazingly precise that, when inked
>|> and pressed down on the plane, it makes every circle of irrational
>|> radius (centered at the center of the stamp) black.
>|> 
>|> Question:  Can one use the stamp three times and make every point
>|> in the plane black?  [assume plane was white to begin with, and
>|> ignore the fact that no such stamp is physically possible]
>
>A very nice problem !
>
>Why not do it with only two stampings, where the second one is moved an
>infinitesimal distance from the first one, thus covering all the points
>left out by the first ?          JUST KIDDING !!
>
>Here's the real answer, that it can be done with three stampings.
>
>It is a constructive proof, but the details are *very* messy, and probably
>incomplete. I hope the idea is clear.
>
(proof deleted)
>Well, I warned you it was messy.  I feel sure that some more elegant
>construction/proof must exist.
>
>Can anyone find one ?
>
>------------------------------------------------------------------------------
>              Bill Taylor              wft@math.canterbury.ac.nz
>------------------------------------------------------------------------------
>                          You are what you remember.
>------------------------------------------------------------------------------

Here, how's this?

Punch first at (0,0), then at (1,0).  If (x,y) is still unstamped,
then x^2 + y^2 and (x-1)^2 + y^2 are both rational numbers, whence by
subtraction x is too, and so y is the square root of a rational number.
Therefore, punching a third time at, say, (0, pi) will work.

Adam

(This was on the 1990 Putnam, right?)



Newsgroups: sci.math
From: mfreiman@magnus.acs.ohio-state.edu (Mark R Freiman)
Subject: Can Anyone Solve this?????
Summary: Linear Algebra Problem
Organization: The Ohio State University
Date: Sat, 23 Jan 1993 21:07:32 GMT


             If W={f such that f"-2f'+f=0}
               What is the dimension? and what is a Basis?

I know the answer for the dimension is 2, and a basis is
               x          x
              e  and    xe

             but how would one go about obtaining these answers?
From: dufresne@act.ulaval.ca (Francois Dufresne)
Newsgroups: sci.math
Subject: Hardy-Littlewood maximal function
Date: 27 Jan 93 20:46:20 GMT
Organization: Universite Laval

Hi!

Could someone give me a precise definition of the Hardy-Littlewood
maximal function  HY(.)?   A recent reference to this topic would
                   ^+--subscript
be greatly appreciated.

F. Dufresne
----------------------------------------------------------------------------
Francois Dufresne      | dufresne@act.ulaval.ca
Ecole d'actuariat      | 
Laval University       | 
Quebec (Qc) Canada     |
----------------------------------------------------------------------------
Newsgroups: sci.math
From: solan@smaug.uio.no (Svein Olav G. Nyberg)
Subject: Re: Non-Standard Analysis and philosophy
Reply-To: solan@smaug.uio.no (Svein Olav G. Nyberg)
Organization: University of Oslo, Norway
Date: Fri, 22 Jan 1993 09:41:20 GMT

In article <TORKEL.93Jan21223508@bast.sics.se>, torkel@sics.se (Torkel
Franzen) writes:
|> In article <1993Jan21.203027.27202@ulrik.uio.no> solan@smaug.uio.no 
|> (Svein Olav G. Nyberg) writes:
|> 
|>    >Surely finitist mathematicians will not
|>    >allow for infinitely large integers.
|> 
|>   Your question then was not about the possibility of the existing
|> field of non-standard analysis, but whether a version of non-standard
|> analysis has been developed within constructive mathematics.

Obviously. I am doing some non-standard analysis myself, so I
am not trying to ask a philosophically sceptical question along
the lines of Descartes whether there really exists something
called "non-standard analysis" or whether there's just an evil
demon seducing me to believe so.

What I wanted to know is under which philosophies NSA is a valid
type of mathematics. Finitists, as mentioned above, surely will
find it to be non-valid mathematics, and perhaps just nonsense.
I don't care too much about them, but since I wonder a little
about the philosophical justifications and validations for what
I am actually doing myself, I wanted to know what was (philosophically)
needed to say NSA is valid. It will affect both my choice of philosophy
and my approach to NSA. [NSA  Non Standard Analysis.]


Solan
Newsgroups: sci.math
From: gaur@cs.sfu.ca (Daya Gaur)
Subject: Totally unimodular matrices
Keywords: Unimodular,Matrices
Organization: CSS, Simon Fraser University, Burnaby, B.C., Canada
Distribution: na
Date: Fri, 22 Jan 1993 02:07:40 GMT

Q.  What is the fastest algorithm for determining
	 whether a matrix is unimodular.

It is polynomially solvable.

Any pointers will be appreciated. You can repsond
by e-mail (preferred). If there is enough interest
i will post a summary.

Thanks in advance.
-daya
From: des@thrain.anu.edu.au (David Stewart 249-4502 room 134)
Newsgroups: sci.math
Subject: Re: Non-Standard Analysis and philosophy
Date: 27 Jan 1993 22:17:45 GMT
Organization: School of Mathematical Sciences, Australian National University
Distribution: world
NNTP-Posting-Host: 150.203.15.22


In article <1993Jan21.203027.27202@ulrik.uio.no>, solan@smaug.uio.no (Svein Olav G. Nyberg) writes:
|> In article <TORKEL.93Jan21204806@bast.sics.se>, torkel@sics.se (Torkel
|> Franzen) writes:
|> |> In article <1993Jan21.180359.21766@ulrik.uio.no> solan@smaug.uio.no 
|> |> (Svein Olav G. Nyberg) writes:
|> |> 
|> |>    >Under which philosophies of mathematics is non-standard
|> |>    >analysis possible, and to what extent?
|> |> 
|> |>   Your question makes no apparent sense. Non-standard analysis is simply a
|> |> field of mathematics that exists, hence is possible.
|> 
|> I am serious, Torkel. 
[stuff deleted]

Just to throw my 2c worth in...

In 1988 I heard Peter Loeb give a series talk on non-standard analysis at
Gothenburg, explaining how to get non-standard constructions using ultrafilters
(so that the full theory of types can be used, and you can use n'th order
predicate calculus etc and do, e.g., non-standard topology).

Being a computational type I did a bit of thinking and came to the conclusion
that it is impossible under any reasonable model of computation to do anything
with ultrafilters.

First order theories may be different.  Add a symbol w satisfying

w > 1,  w > 2,  w > 3, ....

I think you can get away with any other consistent assumptions about w.
Is it prime?  Is it even?  Is it a perfect square?  Making consistent assumptions
about w might become a bit of a head-ache, but working in the world of
expressions with w does not seem outside constructive mathematics.

Ultrafilters on the other hand....


------------------------------------------------------------------------
David Stewart			Program in Advanced Computation
des@thrain.anu.edu.au		School of Mathematical Sciences
				Australian National University
------------------------------------------------------------------------
David Stewart			Program in Advanced Computation
des@thrain.anu.edu.au		School of Mathematical Sciences
				Australian National University
Xref: sparky sci.math:18758 sci.physics:23467