HDTenEightyP/NetNews huggingface dataset:
From: ap@levangerhs.no (Andrei Prasolov)
Subject: Re: Is Card(R)=Card(RxR)?
Organization: Hogskolen i Levanger
Date: Thu, 13 Aug 92 16:12:32 GMT

Card(S)=Card(SxS) for any infinite set S,
if the Axiom of Choice is assumed.

              Andrei PRASOLOV
              Hoegskolen i Levanger
              Kirkegt 1, 7600 Levanger
              Norway

Tel. 47-76-89157 (office), Telefax 47-76-89155 
e-mail AP@LEVANGERHS.NO  
Newsgroups: sci.math
From: N020BA@tamvm1.tamu.edu
Subject: How do make custom wavelets given data?
Organization: Texas A&M University
Date: Fri, 14 Aug 1992 23:54:39 GMT

     Hello! I've got a wavelet problem. What I need to do is take a wave-
form and turn it into a basic wavelet. I know that basic wavelets can be
made from functions like splines.
     Why the custom wavelet? I'd like to take some EEG data, select a wave-
form from that data, and make the selected waveform into a wavelet.
     Thanks for your help. Please reply to N020BA@tamvm1.tamu.edu or post
your thoughts to this group.
From: wilson@web.ctron.com (David Wilson)
Newsgroups: sci.math
Subject: Length Scales in Physics
Date: 19 Aug 92 14:24:12 GMT
Reply-To: wilson@web.ctron.com (David Wilson)
Organization: Cabletron Systems INc.
Originator: wilson@web


In <1992Aug18.222608.501@galois.mit.edu> jbaez@riesz.mit.edu
(John C. Baez) writes:

> On the scale of the Planck length, it's possible that the structure of
> spacetime becomes quite different from the four-dimensional manifold we
> know and love. Spacetime itself becomes a foam (according to Wheeler)
> or a bucket of dust (according to Wheeler) or a bubbling sea of virtual
> black holes (according to Hawking) or a weave of knots or tangles
> (according to Ashtekar, Rovelli, and Smolin). In short, it's weird, but
> beyond that nobody really knows...

Others, such as myself, feel that spacetime at that scale is best
understood a hodgepodge of peanut butter, grass clippings, and
incessant reruns of "I Love Lucy."  Someday, we may be taken seriously.

-- 
David W. Wilson (wilson@ctron.com)

Disclaimer: "Truth is just truth...You can't have opinions about truth."
- Peter Schikele, introduction to P.D.Q. Bach's oratorio "The Seasonings."
From: uchpcjv@Msu.oscs.montana.edu
Newsgroups: sci.math
Subject: Re: eigen vectors
Date: 12 Aug 92 22:25:10 GMT
Reply-To: uchpcjv@Msu.oscs.montana.edu
Organization: Montana State University

In article <36562@sdcc12.ucsd.edu>, pak@cs.ucsd.edu (Suehee Pak) writes:
>Any information concerning to the following question 
>would be greatly appreciated.
>
>Suppose A1 and A2 are square matrices. Under what conditions, if any, are the
>eigen vectors of the two matrices same? 
>
>Strang gives one answer: IF the matrices are diagonalizable, they have the
>same eigenvectors if and only if A1*A2 = A2*A1. 
>
>What happens if they are not diagonalizable?
>                         ^^^
>
>
Isn't it true that for any matrices we'd be interested in (physcially) would
be "diagonalizable?"  Then not only would it be true for A1*A2 = A2*A1, but
for A1 = (constant)*A2 as well.  And to be religeous, wouldn't it REALLY be
A1(transpose)*A2 = A2(transpose)*A1?

Thanks for listening.
Newsgroups: sci.math
Subject: Re: int(x*log(x)*((1-x)^n), x=0..1)
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 21 Aug 92 17:19:22 GMT

In <1992Aug21.100918.29780@ecrc.de> jeanmarc@ecrc.de (Jean-Marc Andreoli) writes:

>          1/2 + ..... + 1/(n+2)
>I(n) = - -----------------------
>              (n+1)(n+2)


Thanks, I should have seen that.
--
Arthur L. Rubin: a_rubin@dsg4.dse.beckman.com (work) Beckman Instruments/Brea
216-5888@mcimail.com 70707.453@compuserve.com arthur@pnet01.cts.com (personal)
My opinions are my own, and do not represent those of my employer.
My interaction with our news system is unstable; if you want to be sure I see a post, mail it.
From: jordan@euler.think.com (Jordan Ellenberg)
Newsgroups: sci.math
Subject: Tangles and Representations of Lie Groups
Date: 12 Aug 92 10:19:04
Organization: Thinking Machines Corporation, Cambridge MA, USA
NNTP-Posting-Host: euler.think.com




	A while back there was a thread going on this topic, of which I
unfortunately lost track;  could someone mail me pointers to relevant
books/papers?  Thanks.

Jordan Ellenberg
jordan@zariski.harvard.edu

Xref: sparky sci.math:10490 sci.physics:13255
From: benzvi@leibniz.geom.umn.edu (benzvi)
Newsgroups: sci.math,sci.physics
Subject: Re: tensors: How about 3rd, 4th rank?
Date: 21 Aug 92 19:15:59 GMT
Organization: Geometry Center, University of Minnesota

Just thought I'd liven up the discussion with the ""correct"" (  (:  :)  )
definition of a tensor- a (p,q) tensor on a manifold M (tangent
bundle TM, cotangent bundle TM*) is a section of the vector bundle
obtained by tensoring TM with itself p times and then tensoring with
TM* q times. Here the tensoring is the tensor product of 
vector spaces: given two vector spaces over a common scalar field,
V and W, V(tensor)W is defined as the set of elements
v(tensor)w (v in V, w in W). This tensoring is a formal operation
satisfying the relations (v1+v2)(tensor)w=v1(tens)w+v2(tens)w,
v(tens)(w1+w2)=v(tens)w1+v(tens)w2, and k (v(tens)w)=kv(tens)w=
v(tens)kw for k a scalar.
Of course there is arbitrary detail to be added to this explanation...
For a good treatment of tensors (the nice topological way instead of the
messy physics/diff geom way with local coordinates) see
Warner, Foundations of Differentiable Manifolds and Lie Groups.
 (Or see Lang's Algebra for tensor products, or Dubrovin-Fomenko-Novikov
and Gullot-Hulin-Lafontaine for the diff geom, or........)
David
From: sichase@csa2.lbl.gov (SCOTT I CHASE)
Newsgroups: sci.math
Subject: Re: Power series solution to ordinary differential equation
Date: 17 Aug 92 21:25:16 GMT
Reply-To: sichase@csa2.lbl.gov
Distribution: na
Organization: Lawrence Berkeley Laboratory - Berkeley, CA, USA
NNTP-Posting-Host: 128.3.254.197
News-Software: VAX/VMS VNEWS 1.3-4

In article <57030@mentor.cc.purdue.edu>, hrubin@pop.stat.purdue.edu (Herman Rubin) writes...
> 
>The method of power series is actually the oldest method of numerical
>solution of differential equations, but is now usually considered "not
>in style."  There ARE many cases in which it is far better than the
>usual ones, and of course many where it is not.  HOW is not much of
>a problem; as to WHEN, this is a matter of art, not science.

Interesting.  Why is is "not in style"?  As a physicist, I use only 
two methods of solving DE's.  I guess the solution that I already know or 
I use the Frobenius method.  With rare exception, I have not needed more.
(Once or twice I have had to solve a DE with a contour integral, but that's
unusual.)  In fact, the only time I have ever needed to know any of the 
host of standard techniques was when taking a Diff Eq. class as an 
undergrad.

-Scott 

--------------------
Scott I. Chase			"The question seems to be of such a character
SICHASE@CSA2.LBL.GOV		that if I should come to life after my death
				and some mathematician were to tell me that it
				had been definitely settled, I think I would
				immediately drop dead again."      - Vandiver
From: oliveira@durban.berkeley.edu (Jorge-Nuno Oliveira Silva)
Newsgroups: sci.math
Subject: >>math books for sale<<
Date: 22 Aug 1992 22:19:43 GMT
Organization: U.C. Berkeley Math. Department.
Distribution: ba
NNTP-Posting-Host: durban.berkeley.edu



			Math books 4 sale

		(see them at 1058 Evans Hall)
			




	R. P. Boas, "A primer of Real Functions"
		Third edition
		MAA 1981.........................................$10.00


	P. R. Halmos, "Problems for Mathematicians Young
		and Old"
		MAA 1991.........................................$10.00


	C. L. Liu, "Elements of Discrete Mathematics"
		3rd printing, softcover
		McGraw-Hill 1987 ................................$25.00


	W. M. Boothby, "An Introduction to Differentiable Manifolds
		and Riemannian Geometry"
		softcover
		Academic Press 1986..............................$25.00


	J. Guckeneimer & P. Holmes, "Nonlinear Oscilations,
		Dynamical Systems and Bifurcation of
		Vector Fields" 3rd printing
		Springer 1990....................................$25.00


	S. Wiggins, "Introduction to applied nonlinear
		Dynamical Systems and Chaos"
		Springer 1990....................................$25.00


	Hartshorne, "Algebraic Geometry"
		4th printing 
		Springer 1987 (used).............................$25.00


	Hartshorne - same as above but New.......................$42.00


	Wiener, "The Fourier Integral and Certain of its 
		Applications"
		Dover............................................$8.00


	Birkhoff & MacLane, "A Survey of Modern Algebra"
		6th printing
		Macmillan 1967...................................$10.00




-- 
Jorge-Nuno Oliveira Silva		home:		
Department of Mathematics		328 Wilson St.	      
University of California		Albany, CA 94710   USA
Berkeley CA 94720 USA  e-mail: oliveira@math.berkeley.edu
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: Bott-Tate Formula
Date: 19 Aug 92 18:20:37 GMT
Article-I.D.: camelot.ARA.92Aug19132037
Distribution: sci
Organization: M.I.T. Artificial Intelligence Lab.



Can someone tell of of a paper where the formula of Bott and Tate is stated
and proved? It is a formula for an upper bound, in the sense of least common
multiple, of the orders of the elements of the collineation group of a
nonsingular hypersurface of degree d in projective n-space. It is not in
general equal to the least common multiple.


Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math
From: shillsp@leonardo.cs.curtin.edu.au (Stephen Hill)
Subject: linear programming HELP REQUIRED!
Keywords: linear programming
Organization: Curtin University of Technology
Date: Tue, 18 Aug 1992 07:44:14 GMT



Currently I am working on the Vehicle Routing Problem under
Capacity constraints. I am using a cutting planes technique
to get lower bounds which are then incorporated
in a branch and bound technique. I have programmed
the dual and revised simplex with upper bounds, using an LU
decomposition to solve equations involving the basis, and these both
work for problems with around 450 variables and 50 constraints.

With larger problems I encounter numerical instability and cannot
get a solution.

I am looking for ways to get rid of this problem. Alternatively I am
willing to purchase a linear programming package, either commercial
or otherwise (to run on a Sun SPARC station 2) or working source code
which I can incorporate into my own code. 

I hope that someone out there can provide me with references, advice or
code. Thanks in advance. 

------------------------------------------------------------------------------
                 Stephen Hill- shillsp@euler.cs.curtin.edu.au                  

                 Curtin University, Perth, Western Australia                  
------------------------------------------------------------------------------
--
------------------------------------------------------------------------------
                 Stephen Hill- shillsp@euler.cs.curtin.edu.au                  
                                                                                
                 Elvis: Too young to die, too fat to live!                     
------------------------------------------------------------------------------
Newsgroups: sci.math
From: jbaez@zermelo.mit.edu (John C. Baez)
Subject: Re: Puzzles
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Fri, 14 Aug 92 19:27:10 GMT

In article <israel.713746423@unixg.ubc.ca> israel@unixg.ubc.ca (Robert B. Israel) writes:
>In <1992Aug13.172531.10744@galois.mit.edu> jbaez@nevanlinna.mit.edu 
>(John C. Baez)writes:
>
>>Some kind soul pointed out that one needn't write a program in C that
>>can accept and run C programs to get the job done. Let me give away the
>>answer to the problem (how to prove the "almost-paradox" A-P above).
>  
>>One need only write
>>a program that looks through statements in ZFC to find those of the form
>>"N cannot be printed by a program in C of length < E", and check
>>which are provable in ZFC.  If it finds one, the program should print
>>out the number N.
>
>Well, if you can write a program that checks whether a statement is
>_provable_ (and terminates in finite time if it isn't), then by Godel's
>Theorem ZFC is inconsistent!  What you want your program to do is look
>through all strings until it finds a _proof_ in ZFC that ends with
>a statement of the form "N cannot be printed by a program in C of length < E",
>and then print N.  If this program prints out N, then it is a counterexample
>to the proof.  I might point out that, in concluding that no such proof
>exists, we are using the consistency of ZFC, which is not part of ZFC itself.
>If ZFC were inconsistent, every statement would be provable in it.

Thanks for correcting my sloppy wording.

>Your _program_ needn't be able to run C programs, but your statement
>"N cannot be printed by a program in C of length < E" is really an abbreviation
>for a very long formal statement in ZFC, which must contain a description of
>the C language and how programs will be run.

That's true.  

What I'd really like (as I keep hinting) are some good estimates for the
magic constant E!
Newsgroups: sci.math
From: israel@unixg.ubc.ca (Robert B. Israel)
Subject: Re: algo. determining closed form integral from c.f. function
Organization: University of British Columbia, Vancouver, B.C., Canada
Date: Thu, 13 Aug 1992 23:13:12 GMT

In <5115QKM@minnie.zdv.uni-mainz.de> polani@Informatik.Mathematik.Uni-Mainz.DE (Daniel Polani) writes:

>In article <4699@balrog.ctron.com>, wilson@ctron.com (David Wilson) writes:

>   It occurs to me that there is an algorithm for determining if a closed-form
>   function has a closed-form integral.  Would a varition of this algorithm
>   apply to the grazing goat equation?

>An algorithm which was said to do this, I have been told, has been devised by
>Risch (sorry, I cannot be more precise) based on an idea of Liouville from the 
>last century. That's all I know. 

>Does anybody know the general idea used by this (or a similar) algorithm ?

>-- 
>Daniel Polani - polani@informatik.mathematik.uni-mainz.de

See the following book for part of the algorithm:

AUTHOR:     Davenport, James Harold, 1953-
TITLE:      On the integration of algebraic functions / James Harold 
             Davenport. --
CALL NO:    QA 341 D33 1981
PUBLISHED:  Berlin ; New York : Springer-Verlag, 1981.
DESCRIPTION: 197 p. ; 25 cm. -- Bibliography: p. [186]-197.
SERIES:     Lecture notes in computer science ; 102

As of 1981, there were cases (mixed algebraic and transcendental functions)
which did not have a complete algorithm.

The basic idea is, in a way, a development of the "method of undetermined
coefficients".  You prove that if a closed-form integral exists, it has
a certain basic form, then examine functions of that form to see if any
can have the given function as derivative.  For example, as a consequence
of one of Liouville's results, if f(x) exp(g(x)) has a closed-form 
integral, where f(x) and g(x) are rational functions and g(x) is not 
constant, then that integral must be of the form p(x) exp(g(x)) + C,
where p(x) is a rational function.
-- 
Robert Israel                            israel@math.ubc.ca
Department of Mathematics             or israel@unixg.ubc.ca
University of British Columbia
Vancouver, BC, Canada V6T 1Y4
Newsgroups: sci.math
From: bs@faron.mitre.org (Robert D. Silverman)
Subject: Re: Prime conjecture
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Wed, 12 Aug 1992 22:58:20 GMT

In article <18990@nntp_server.ems.cdc.com> mstemper@ems.cdc.com writes:
:In article <1992Aug11.162953.13961@uwm.edu>, radcliff@csd4.csd.uwm.edu (David G Radcliffe) writes:
:|> 
:|>    Conjecture:  There exists a k > 0 so that p + k is prime 
:|>                 for infinitely many primes p.
:|> 
:|> Does anybody know the status of the this conjecture?
:
:I believe that
:  There exist infinitely many primes p
:  Such that p+2 is prime
:has been proven, which would prove this conjecture by showing k=2.
 
No. The twin prime conjecture is still open. The closest anyone has come
is Chen's result on Goldbach's conjecture which says that all even
integers are the sum of a prime and a number which is the product of at
most two primes. This result can be extended to show that there exists
an infinite number of primes p such that p+2 has a bounded number of
prime factors. 

This conjecture is a special case of Schinzel's conjecture, which in
turn is a special case of the Bateman-Horn conjecture. I discussed these
conjectures just a couple of months ago. I am not going to repeat that stuff
here.
 
If you would like to see where the difficulty lies in obtaining proofs
of these conjectures I would suggest you start with Halberstam & Richert's
"Sieve Methods". A superb book IMO [but very difficult and somewhat terse].

--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: Continued Fractions
Date: 20 Aug 1992 13:59:44 -0400
Organization: The Ohio State University, Dept. of Math.
Distribution: na
NNTP-Posting-Host: function.mps.ohio-state.edu
Keywords: Help, Continued Fractions


The classical reference on continued fractions is the book by O. Perron,
_Kettenbr\"uche_.  It may still be the best reference, if you are interested in
the non-number-theoretic part of the subject.
-- 
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
From: bhonsle@bhonsle.iss.nus.sg (Shailendra K Bhonsle)
Newsgroups: sci.math
Subject: Re: u(v^n)w prime puzzle
Date: 20 Aug 92 03:54:06 GMT
Organization: Institute of Systems Science, NUS, Singapore


   1751	Info on GRE testing guides                     [9] eppler@frith.msu.eduIn article <1992Aug19.173515.19841@wri.com>, roach@bikini.wri.com (Kelly Roach) writes:
|> In article <1992Aug19.024106.25588@nuscc.nus.sg>  
|> bhonsle@bhonsle.iss.nus.sg (Shailendra K Bhonsle) writes:
|> > The approach is to take a integer x (let's say prime integer) and prove  
|> that by repeating 
|> > v one gets a string u(v^m)w (for positive integer m) which is divisible  
|> by x.
|> > 
|> > Let's take x=9 (because it has nice properties for base 10 numbers).
|> 
|> 
|>      OK, but x=9 is not prime.
|> 
|>  
|> > then for a number "uv"(ie. 10u+v) 
|> >      uv=u+v (mod 9)
|> > 
|> > 
|> > In our problem definition:
|> > 
|> > let u+w=m(mod 9)
|> > 
|> > Now it is possible to find a n for given v such that
|> > 
|> >                      v^n==n.v== 9-m (mod 9) ==> simple number theory 
|> 
|> 
|> 
|>      I see some of the techniques I'm expecting to see in a
|> correct proof.  But my puzzle is not solved so easily.  What
|> would happen to your proof if v is divisible by 3 and m is not
|> divisible by 3?  Solving n.v== 9-m (mod 9) for n will be
|> impossible.  As a particular case, consider
|> 
|>      u="56",v="0",w="39"
|>      5639, 56039, 560039, 5600039, 56000039, 560000039
|> 
|> Any example with v="0" cannot be handled by your proof.
|> 
|> 				Kelly
|> 
|> 
|> 

-- 
I concur. The proof is incomplete because any instance with v=3.x {x=0,1,2...}
 will not work. In all cases it will work.

I think the complete solution can be given by considering divisibility by prime 

p="uv" {ie. p=u*10^|w| + w } where |w|=number of digits in w.


Shailendra.
From: elkies@ramanujan.harvard.edu (Noam Elkies)
Newsgroups: sci.math
Subject: Erthstns' Sv
Date: 13 Aug 92 02:41:59 GMT
Article-I.D.: husc3.1992Aug12.224159.14681
Distribution: world
Organization: Harvard Math Department

Some years ago I read of a variation of Erathostenes' Sieve that
manages to compute the primes up to N in time o(N) [perhaps order
N/log(log(N))?] by compressing the sieve using the first few
primes (e.g. pre-sifting the multiples of 2,3,5,7 so one is
dealing with only 1*2*4*6=48 potential primes out of every
2*3*5*7=210 integers).  Unfortunately I have lost the reference.
Can any member of the computational number theory contingent on
sci.math provide a pointer to this paper?

Thanks,
--Noam D. Elkies (elkies@zariski.harvard.edu)
  Dept. of Mathematics, Harvard University
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.math
Subject: Re: Power series solution to ordinary differential equation
Date: 18 Aug 92 13:34:03 GMT
Distribution: na
Organization: Purdue University Statistics Department

In article <25544@dog.ee.lbl.gov> sichase@csa2.lbl.gov writes:
>In article <57030@mentor.cc.purdue.edu>, hrubin@pop.stat.purdue.edu (Herman Rubin) writes...

>>The method of power series is actually the oldest method of numerical
>>solution of differential equations, but is now usually considered "not
>>in style."  There ARE many cases in which it is far better than the
>>usual ones, and of course many where it is not.  HOW is not much of
>>a problem; as to WHEN, this is a matter of art, not science.

>Interesting.  Why is is "not in style"?  As a physicist, I use only 
>two methods of solving DE's.  I guess the solution that I already know or 
>I use the Frobenius method.  With rare exception, I have not needed more.
>(Once or twice I have had to solve a DE with a contour integral, but that's
>unusual.)  In fact, the only time I have ever needed to know any of the 
>host of standard techniques was when taking a Diff Eq. class as an 
>undergrad.

What do you mean by "solve"?  Numerical methods of solving a differential
equation can be quite a problem.  But if one looks at the current numerical
analysis books, the emphasis is almost entirely on methods which do not
involve computing derivatives anywhere.  These methods propagate rounding
errors, etc., and getting lots of accuracy is VERY difficult.

On the other hand, power series methods run into problems with radius of
convergence.  But a good nasty example is the Thomas-Fermi equation, where
the boundary conditions make real problems.  Now one can carry out numerical
approximations, and eventually get something reasonable, but a method, for
which I believe there is a paper by Hille, points out that by using two
power series, one in x^.5 about 0, and one which, apart from a simple factor,
is in x^a, where a is a quadratic irrational, about infinity, and matching
them, these major problems can be avoided.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)
Newsgroups: sci.math
From: dak@messua.informatik.rwth-aachen.de (David Kastrup)
Subject: Re: Primes
Organization: Rechnerbetrieb Informatik  /  RWTH Aachen
Date: 17 Aug 92 12:18:48 GMT

bill@waikato.ac.nz writes:

>How many primes are there less than 2 to the power of p?

>Is there a way of calculating this, or does anyone know of where I can get my
>hands on a list of primes so I can find out how many primes there are
>less than 2^16 or 2^32 for example?

>Is there some way of determining (or estimating) the expected magnitude of the
>nth prime? Or of the growth of the difference between the nth and (n+1)th
>prime?

The number of primes up to~$n$ is called $\pi(n)$. There are approximations
in the mathematic world to this function. See number theoretic treatises
(the function~$\phi$ has similar flavour). If I remember right, one
approximation was~$n\ln n$, but there might have been a constant factor.

Don't flame this inaccuracy, see Concrete Methematics by Graham, Knuth,
Patashnik for sensibly understandable treatise of this matters and others.
Newsgroups: sci.math,sci.physics