HDTenEightyP/NetNews huggingface dataset:
From: sibley@math.psu.edu (David Sibley)
Newsgroups: sci.math
Subject: Re: fun with primes
Date: 6 Apr 92 20:18:50 GMT
Reply-To: sibley@math.psu.edu
Organization: Dept. of Mathematics, Penn State University

In article 702587236@dn66, a_rubin@dsg4.dse.beckman.com (Arthur Rubin) writes:
>
>The best one I can remember is: in any Noetherian integral domain D which
>is not a field, there are infinitely many primes.
>
>Proof sketch:
>
> ... (omitted stuff)
>
>(3)  Suppose there are only finitely many primes; let x be the product of
>all of them plus 1.  If x is 0, then each p is a unit, a contradiction.  If
>p divides x, then p divides 1, and p is a unit, a contradiction.  Hence, in
>any factorization of x (guaranteed by (1)), no prime can occur, again, a
>contradiction.  Done.
>

Nope. x can be a unit and therefore have no prime factors.

David Sibley
sibley@math.psu.edu
From: fulk@cs.rochester.edu (Mark Fulk)
Newsgroups: sci.math
Subject: Re: Probability puzzle
Date: 10 Apr 92 17:41:57 GMT
Organization: Computer Science Department University of Rochester

In article <1992Apr10.171252.3102@leland.Stanford.EDU> algebra@leland.Stanford.EDU (Leong Weng Ng) writes:
>Puzzle:
>
>	Choose any straight line in a plane. The plane is then divided into two
>half-planes by the line. Select any two points on the plane not lying on the
>chosen line. What is the probability that both points lie on different half-
>planes? Is it 1/2 or something else?
>
>Cheers                                                                 Al
>

The answer depends on the distributions according to which the line and
points are chosen.  The following applies to one such answer:

Suppose we are given a probability distribution P on the plane.
Suppose that four points, p1 to p4, are chosen according to P.
What is the probability that p1 and p2 determine a line, and that
p3 and p4 lie on opposite sides of the line?

Answer: depends on P, but generally < 1/2.  Consider cases such that
p1-p4 form a quadrilateral, etc.  Note that every permutation of p1
to p4 is equally probable.  The proof is left to the reader.

Mark
-- 
Mark A. Fulk				Computer Science Department
fulk@cs.rochester.edu			University of Rochester
Omit needless words -- Strunk		Rochester, NY  14627
Newsgroups: sci.math
From: orourke@sophia.smith.edu (Joseph O'Rourke)
Subject: Re: Archimedes tomb (was: Did Archimedes prove radial-projection measure-preserving?)
Organization: Smith College, Northampton, MA, US
Date: Wed, 15 Apr 1992 10:51:16 GMT

In article <COLUMBUS.92Apr14133749@strident.think.com> 
	columbus@strident.think.com (Michael Weiss) writes:

>Has Archimedes' tomb been found?  I have a vague recollection of reading a
>review of a book by Howard Eves (ambiguity deliberate, I'm not sure which)
>where the reviewer said, approximately, "the book incorrectly refers
>to Archimedes' tomb as still missing".  Is my recollection even
>approximately correct?

William Dunham says [*] that Cicero stumbled upon Archimedes' tomb in
Syracuse, and implies (but does not say explicitly) that it hasn't
been reported as seen since.  So it was found, but a rather long
time ago (~50 B.C.).

[*] in "Journey Through Genius," p. 105.
Newsgroups: sci.math,sci.econ
From: kasdan@cunixa.cc.columbia.edu (John Kasdan)
Subject: Who is Bertrand?
Reply-To: kasdan@cunixa.cc.columbia.edu (John Kasdan)
Organization: Columbia University School of Law
Date: Mon, 13 Apr 1992 20:37:43 GMT

In article <1992Apr9.121105.22267@linus.mitre.org> bs@gauss.mitre.org (Robert D. Silverman) writes:
>In article <44268.979217512@crfm.gen.nz> karl@crfm.gen.nz (Karl Scherer) writes:
>:In 1845, Bertrand noted that consecutive primes were not
>:too far apart and conjectured q/p < 2 for consecutive primes.

Is this the same Bertrand who is known in economics for introducing
the "Bertrand equilibrium" in duopoly?  The story is that he reviewed
a book by Cornot in which what was essentially the Nash equilibrium
was introduced. In the review, he criticized the choice of quantity as
a control variable and noted that in the model Cornot proposed, the
choice of price as the control variable leads to a unique 
price = marginal cost equilibrium.

If this is the same person (and even if it isn't) I would appreciate
any reference for this story.  (I could use it for a footnote in a law
article I am writing.)

By the way, despite its sound, duopoly is NOT the excercise of market
power in the market for 1950s music.

/JK (.sig closed for repairs)
Newsgroups: sci.math
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Re: Mersenne Composites
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Thu, 2 Apr 1992 17:03:19 GMT

In article <1992Apr2.161916.3027@venice.sedd.trw.com> gay@venice.sedd.trw.com (Lance Gay) writes:
:If we restrict the definition of Mersenne numbers to those integers of the
:form (2^p)-1 where p is prime, I believe it is still unproved that there
 
If we restrict??  If??   That IS the definition.

:are an infinite number of composite Mersenne numbers.  Thus, it is possible
:that we might reach a point where all the Mersenne numbers are prime.  
	^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

I can prove this is impossible.

:That there are an infinite number of Mersenne composites must be among one of
:the most obvious, yet unproved, conjectures.  Does anyone know if any work 
:has been done on this problem?

Yes, there is someone who knows.  :-)
--
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: fry@zariski.harvard.edu (David Fry)
Newsgroups: sci.math
Subject: Erdos problems
Date: 10 Apr 92 18:40:19 GMT
Article-I.D.: husc3.1992Apr10.144022.10926
Distribution: world
Organization: Harvard Math Department


There's a famous Erdos problem involving a combinatoric
problem P for a given integer n.  Unfortunately I can't
remember what the problem P was, other than it was deceptively
simple. I think P(1) and P(2) is pretty easy and P(3) has been
solved, although with effort.

The story is that aliens from another planet come to Earth and
say they will destroy it in one year unless we can prove our
worth by solving P(n).  Erdos says that if the aliens set n=4,
we should stop all computers on the planet from their normal
work, and set them to solving P(4), and possibly we'll get it
done in one year.  But if the aliens set n >= 5, we should
spend the time figuring out how to destroy the aliens.

So does anyone know what P(n) is?

David Fry                               fry@math.harvard.EDU
Department of Mathematics               fry@huma1.bitnet
Harvard University                      ...!harvard!huma1!fry
Cambridge, MA  02138            
Newsgroups: sci.math
From: gerry@macadam.mpce.mq.edu.au (Gerry Myerson)
Subject: Re: A simple question about R2 - Q2 (irrational points of the plane)
Organization: ceNTRe for Number Theory Research
Date: Sun, 12 Apr 92 23:50:37 GMT

In article <1992Apr11.180450.559@math.okstate.edu>, gindrup@math.okstate.edu (Eric `'d'kidd' G..) writes:
> 
> In article <1992Apr11.175123.360@math.okstate.edu> gindrup@math.okstate.edu (Eric `'d'kidd' G..) writes:
> >In article <1992Apr7.233720.12411@newshost.anu.edu.au> gerry@macadam.mpce.mq.edu.au (Gerry Myerson) writes:
> >>In article <1992Apr7.174510@masg1.epfl.ch>, baumgart@masg1.epfl.ch (Marcel Baumgartner) writes:
> >>> 
> >>> Keywords: In R2 - Q2, does there exist an oblique straight line ?
> >>
> >>Sure; x+y=pi. 
> >
> >Can you PROVE that the sum of any two irrational numbers is irrational?
> >From my humble memories comes a rumbling that that is still an open idea...
> >
> >-- Eric Gindrup ! gindrup@hardy.math.okstate.edu
> 
> Mayhaps I mean "... that the sum of any two transcendental numbers is 
> transcendental..."
> 
> --Eric Gindrup

I don't have to prove that the sum of two transcendentals is transcendental 
(good thing, too, since there are trivial counterexamples), just that if two 
numbers add up to pi, they can't both be rational---but that follows instantly 
from the irrationality of pi. 

Gerry Myerson
From: ecarsten@next1.cs.umr.edu (Edward Carstens)
Newsgroups: sci.math
Subject: factorial puzzle
Date: 7 Apr 92 20:04:19 GMT


How many zeros are at the end of 1000! ?

No, the answer isn't 3.  The exclamation represents factorial of course. :-)

-Ed Carstens
Creator of JugglePro
Newsgroups: sci.math
From: gindrup@math.okstate.edu (Eric `'d'kidd' G..)
Subject: Re: A simple question about R2 - Q2 (irrational points of the plane)
Organization: Oklahoma State University, Math Department
Date: Sat, 11 Apr 1992 17:51:23 GMT

In article <1992Apr7.233720.12411@newshost.anu.edu.au> gerry@macadam.mpce.mq.edu.au (Gerry Myerson) writes:
>In article <1992Apr7.174510@masg1.epfl.ch>, baumgart@masg1.epfl.ch (Marcel Baumgartner) writes:
>> 
>> Keywords: In R2 - Q2, does there exist an oblique straight line ?
>
>Sure; x+y=pi. 

Can you PROVE that the sum of any two irrational numbers is irrational?
From my humble memories comes a rumbling that that is still an open idea...

-- Eric Gindrup ! gindrup@hardy.math.okstate.edu
Newsgroups: sci.math
Subject: Re: Erdos (was Re: Fermat's Last Theorem)
From: maschler@vms.huji.ac.il (MICHAEL MASCHLER)
Date: 11 Apr 1992 19:22 IDT
Distribution: world
Organization: The Hebrew University of Jerusalem
News-Software: VAX/VMS VNEWS 1.41    Lines: 21

In article <1992Apr7.235418.12640@newshost.anu.edu.au>, gerry@macadam.mpce.mq.edu.au (Gerry Myerson) writes...
>In article <1992Apr7.051902.4889@rata.vuw.ac.nz>, harper@kauri.vuw.ac.nz (John Harper) writes:
>>
>>
>>  >Pardon my ignorance. Who is this Erdos dude?
>> Several people have been abusing one another instead of answering the
>> question. Paul Erdos is a very famous Hungarian mathematician (aged around
>> 80 I'd guess)
>
>79; he'll be 80 next March. Does everyone know his story about being three
>billion years old? It seems that when he was a young man, the geologists
>said the world was a billion years old; now, they say it's four billion years
>old; ergo....
>
For people who do not know who Erdos is, they certainly do not know who
Erdos3 is.

Well (if I count correctly), Erdos1 is any person who wrote a paper with
Erdos. Erdos2 is any person who wrote a paper with an Erdos1 person, etc.


Newsgroups: sci.math
From: orourke@sophia.smith.edu (Joseph O'Rourke)
Subject: Re: Art Gallery Problem
Organization: Smith College, Northampton, MA, US
Date: Wed, 15 Apr 1992 23:53:44 GMT

In article <1363@hydra.bucknell.edu> 
	cwalker@client10.bucknell.edu (carleton walker `93) writes:

>	I'm looking for information on the art gallery problem. I'm more
>interested in books than papers on the subject, but any help is
>appreciated.

	I wrote a book on the topic: Art Gallery Theorems and Algorithms,
Oxford University Press, 1987.
Newsgroups: sci.math,rec.music.dementia
From: stephen@mont.cs.missouri.edu (Stephen Montgomery-Smith)
Subject: Re: Math songs?
Organization: University of Missouri
Date: 17 Apr 92 20:28:04 GMT

In <1992Apr17.200026.11761@midway.uchicago.edu> duve@ellis.uchicago.edu (michael andrew duvernois) writes:

>In article <22787@dog.ee.lbl.gov> sichase@csa1.lbl.gov writes:
>>In article <1992Apr17.142606.920@drycas.club.cc.cmu.edu>, fenthe@drycas.club.cc.cmu.edu writes...
>>>Does anyone have any mathematical songs (mnemonic ideally, but
>>
>I seem to recall a novelty song on the radio about Nicholai Alexander
>Lobachevski.  (Spelled incorrectly no doubt.)  It was about the whole
>publish or perish situation in math and science.  It stuck with me
>for a while and the words "Nicholai Alexander Lobachevski was his name"
>occasionally come into my head for no good reason.

>Michael DuVernois                              m-duvernois@uchicago.edu
>Disclaimer: They really don't care what I say.

Yes, this song was by Tom Learer (well, I have no idea how to spell
his name).  He also had a song called ``New Math.''

Stephen Montgomery-Smith

Newsgroups: sci.math
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Subject: Re: "Half or plus".
Organization: The Ohio State University, Dept. of Math.
Date: Mon, 13 Apr 1992 16:57:33 GMT

>In article <1992Apr10.180746.4628@csc.canterbury.ac.nz> wft@math.canterbury.ac.nz (Bill Taylor) writes:
>>This one has bothered me for a long time.
>
>
>>"HALF-OR-PLUS" is a simple discrete-time stochastic process. 
>> ~~~~~~~~~~~~
>>Start with value 1; and at each time step, either halve or add one to the current
>>value, with probability 1/2 each, independently of what's happened before.
>
>
>>Formally....    Y   = 1
>>                 0
>
>>                        /   Y  + 1  .....   if  X = 0
>>                       /     n                   n
>>              Y     = <
>>               (n+1)   \    Y  / 2  .....   if  X = 1
>>                        \    n                   n
>
>>where { X  } is a Bernoulli sequence with parameter 1/2 .
>>         n
>
>			.......................
>
>>It seems reasonably easy to calculate (numerically), coarse approximations to 
>>the limiting distribution; i.e. the limiting discrete distribution on the set 
>>of disjoint intervals of unit width; or of half-unit width; and so on. 
>>But it's frustrating trying to extend the results to a continuous distribution.
>

In article <44968@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) replies:
>The limiting distribution is continuous, as is the case for just about any
>situation of this kind.  It clearly does not depend on the initial value.
>
>One way to get at it is to use the moment generating function.  If we call
>this function m, we get
>
>	m(t) = .5*m(t)*e^t + .5*m(t/2),
>
>from which m(t) is the infinite product of the reciprocals of the
>quantities 2 - exp(t/2^j), j = 0, 1, ... .  The characteristic function
>computed for u = 2^j * pi is a non-zero constant, so there cannot be a
>density.
>

An interesting variant replaces the constant 1/2.  Let 0 < c < 1 be given.
Then define:
Y_{n+1} as either Y_n + 1  or  c*Y_n (each with probability 1/2).
The existence of the limiting (continuous) distribution is as
before.  BUT is the limiting distribution absolutely continuous?
Herman Rubin's proof that it is not works only when c = 1/k (k an integer),
but not for other values of c .  What happens for these values of c ?

--
  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)
Xref: sparky sci.math:5750 sci.math.num-analysis:1410
From: jess@gn.ecn.purdue.edu (Jess M Holle)
Newsgroups: sci.math,sci.math.num-analysis
Subject: Need help with complex functions in C
Date: 8 Apr 92 05:39:10 GMT
Organization: Purdue University Engineering Computer Network

I have need of a set of complex number routines in C.  I can figure out
the basics (addition, subtraction, multiplication, division, and 
exponentials) and have seen formulas for sines, cosines, and logarithms,
but nothing else.

  1)  Can anyone provide portable (ANSI preferred) C code for complex
      number functions?  Hopefully this would include powers, trig,
      inverse trig, hyperbolic, inverse hyperbolic, etc.  An ftp site
      containing such a source would also be quite appreciated.

  2)  Can anyone recommend good texts that would provide definitions of
      these functions in terms of real functions where possible and good
      algorithms where it is not?  I would prefer something along the
      lines of a handbook, i.e. lists of what I need rather than endless
      derivations that I don't need.

Thanks to all who replay in advance.  PLEASE reply via e-mail, I do not
read this group (my apologies to those who do not appreciate this type
of request; those wanting a summary can send me e-mail).

Jess Holle
Newsgroups: sci.math
From: gindrup@math.okstate.edu (Eric `'d'kidd' G..)
Subject: Re: Calculating the # of primes < n
Organization: Oklahoma State University, Math Department
Date: Fri, 10 Apr 1992 20:59:21 GMT

In article <1992Apr7.154940.2753@ifi.uio.no> einarr@ifi.uio.no (Einar Andreas R|dland) writes:
>
>In article <1992Apr2.014052.1514@cunixf.cc.columbia.edu>, pvl2@cunixb.cc.columbia.edu (Priscilla V Loanzon) writes:
>> I was trying to compute what fractions of the positive integers are
>> prime. I was doing this by getting the fraction left if from the
>> positive integers we remove everything divisible by the primes
>> p_1,p_2,p_3,...  
>> 
>> I get the following infinite series that gives the fraction of integers
>> left: 
>> 1 - (1/p_1) - (1/p_2)(1-1/p_1) - (1/p_3)(1-1/p_1)(1-1/p_2) -
>> (1/p_4)(1-1/p_1)(1-1/p_2)(1-1/p_3) - ...
>> 
>      oo
>    -----
>     | |  ( 1 - 1/p_i ).
>     i=1
>
>Taking the logarithm, we get a sum
>
>      oo                   oo
>     ---                  ---
>     >    ln (1-1/p_i) <  >    - 1/p_i  =  -oo.
>     ---                  ---
>     i=1                  i=1
>
>Hence, the product converges to 0. This would apply to any sequence p_i
>such that p_i=\=1, p_i -> oo.
>

I may be very confused, but I remember that zeta(1) diverged...

-Eric Gindrup ! gindrup@hardy.math.okstate.edu
Newsgroups: sci.math
From: moore@aiag.enet.dec.com ()
Subject: Knotty Views - references please
Keywords: Knot Theory
Reply-To: moore@aiag.enet.dec.com ()
Organization: Digital Equipment Corporation, Marlboro, MA
Date: Fri, 10 Apr 1992 02:52:35 GMT



In the March 21, 1992 issue of Science News (Vol. 141,No.12) on page 186 there
was an article - "Knotty Views, Tying together different ways of looking at
knots." The article was very interesting but short on references.

The article mentions work done by Victor A. Vassiliev of the Russian Academy of Sciences in Moscow about a radically different way of looking at knots. Apparently based from Vassiliev's approach Joan S. Birman of Columbia
University, New York City described recent developments at a joint meeting
of the American Mathematical Society and the Mathematical Association of
America in January.

Ties between  Vassiliev's original equations and Feynmann diagrams, used to
provide an intuitive interpretation of interactions between subatomic
particles were discovered by Dror BarNatan of Harvard University. 

Louis H. Kauffman of the University of Illinois is quoted "Vassiliev's work
provides a very good insight into the nature of knot invariants generally.
It's entirely possible that all of the invariants we know arte built of the
building blocks coming out of Vassiliev's picture."

I would be greatly appreciate references or any additional insights anyone
out there can provide.

	Jim Moore
	moore@aiag.enet.dec.com
From: bs@faron.mitre.org (Robert D. Silverman)
Newsgroups: sci.math
Subject: Re: factoid about new prime
Date: 9 Apr 92 11:18:09 GMT
Article-I.D.: linus.1992Apr9.111809.19221
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA

In article <1992Apr7.150455.22306@news.eng.convex.com> dodson@convex.COM (Dave Dodson) writes:
:In article <1992Apr1.201324.25572@linus.mitre.org> bs@gauss.mitre.org (Robert D. Silverman) writes:
:>In article <3987@crl.LABS.TEK.COM> scott@ferrari.LABS.TEK.COM (Scott Huddleston) writes:
:>:It was mentioned on CNN that the new prime number discovered
:>:recently is four times bigger then the previous record.
:> 
:>This is a (slight) exaggeration. 756839/216091 = 3.5024 times as big.
:
:I thought the original posting was supposed to be humor:  If the previous
:largest known Mersenne prime was P, CNN was saying that the new one is 4P,
:which obviously has 4 as a factor, and therefore is not prime.
 
No, No, No!!!

4 times as big as P does NOT equal 4P. Size is measured by number of
bits. 4 times as big means 4 times as many bits. CNN got it RIGHT.
Most people here are getting it wrong.
--
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"
Newsgroups: sci.math
Subject: Re: SYMMETRIC MATRICES
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 6 Apr 92 18:59:49 GMT
 <1992Apr3.184134.26546@zaphod.mps.ohio-state.edu> <1992Apr4.015751.15194@math.okstate.edu>
Distribution: na
Organization: Beckman Instruments, Inc.
Keywords: symmetric matrix sleepless zombie proof

In <1992Apr4.015751.15194@math.okstate.edu> gindrup@math.okstate.edu (Eric `'d'kidd' G..) writes:

>In article <1992Apr3.184134.26546@zaphod.mps.ohio-state.edu> edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:
>>>In article <1992Apr2.173036.5644@cs.mcgill.ca> pone@cs.mcgill.ca (Daniel (...) Shields) writes:
>>>>
>>>>Given nxn matrix A, A and transpose(A) are similar to each other.
>>>>By Similar I mean that there exists a matrix P, such that 
>>>>transpose(A) = P A P^(-1)
>>
>>In article <1992Apr3.171308.28982@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>>> it's an easy consequence of the Jordan canonical form
>>
>>What if you are using a field other than the complex numbers?  (Say, the
>>rational numbers, the real numbers, or a finite field.)
>>
>>--
>>  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)

>It doesn't matter.  All you want to show is that A and transpose(A) are 
>diagonalisable to the same thing.  (Proof of equivalence of statement left
>to the reader.  And I've yet to meet a newsreader(program) that can prove a
>thing worth reading...)

WRONG.  We don't know that A is diagonalizable.
--
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.
Ich bin ein Virus.  Mach' mit und kopiere mich in Deine .signature.
From: arocho@acsu.buffalo.edu (Vance A. Arocho)
Newsgroups: sci.math,sci.math.num-analysis
Subject: Request for Info
Date: 8 Apr 92 04:07:49 GMT
Distribution: na
Organization: UB

I'm taking my 2nd course in numerical analysis and I'm looking for articles
and texts for information that would help me model the solar system. Please 
send email if you know of any.

Thanks in advance. 



-- 
"A young man who is a conservative has no heart; an old man who is a liberal 
has no brain." (Winston Churchill)
"Sin trabajo, no hay nada." ("Without work, there is nothing.")
Vance Arocho: arocho@acsu.edu (SUN)/V068PZYD@ubvms  (VAX)
From: jlam@ariel.ucs.unimelb.edu.au (James Lam)
Newsgroups: sci.math
Subject: Re: factorial puzzle
Date: 10 Apr 92 07:24:17 GMT
Reply-To: jlam@ariel.ucs.unimelb.edu.au (James Lam)
Organization: University of Melbourne

In article <4782@umriscc.isc.umr.edu>, ecarsten@next1.cs.umr.edu (Edward Carstens) writes:
|> 
|> How many zeros are at the end of 1000! ?
|> 
|> No, the answer isn't 3.  The exclamation represents factorial of course. :-)
|> 
|> -Ed Carstens
|> Creator of JugglePro

What is the point? There are 249 zeros at the end ....

Lin Can
=========================================================================
.-- .... --- . ...- . .-. -.. . -.-. --- -.. . -.. - .... .. ...
--. . - ... -. --- - .... .. -. --.   .-.. .. -. -.-. .... .- -.
=========================================================================
From: rcronh@wsres1.info.win.tue.nl (Ron Helwig)
Newsgroups: sci.math
Subject: Info needed about OR related PC-programs
Keywords: Operations Research, PC
Date: 14 Apr 92 10:08:57 GMT
Reply-To: rcronh@info.win.tue.nl


I want to find out, what kind of MS-DOS programs are available nowadays 
for Operations Research in general and topics like linear programming,
non-linear programming, simulation (discrete and continuous),
Markov-process analysis etc.

Any hints, including information about the vendor and a description of the
programs will be appreciated.

Thanks in advance,

	Ron Helwig
-- 
e-mail: rcronh@win.tue.nl               | Ron Helwig
phone:  +31 (0)40 472724                | Eindhoven University  of Technology
fax:    +31 (0)40 436685                | P.O. Box 513, 5600 MB Eindhoven, NL
Newsgroups: sci.math