HDTenEightyP/NetNews huggingface dataset:
From: kdorma@ravana.eche.ualberta.ca (Kevin Dorma)
Subject: is there anybody out there, hmmm...
Organization: Dept. of Chemical Engineering, University of Alberta
X-Newsreader: Tin 1.1 PL3
Date: Fri, 28 Aug 1992 14:09:56 GMT

How's it goin', eh?
Say, we have a group for workstation related stuff but nobody has posted
anything yet.  What do we plan on discussing over this forum?  How many 
people have added this group to their .newsrc?  

just my $0.02
                                  | 
Kevin Dorma                       | Hi, my Lyapunov exponent is 2.31.
kdorma@ravana.eche.ualberta.ca    | What's yours?
Ph.D. type of student             | 
Dept. of Chemical Engineering     | Don't look at my disclaimer, your's
University of Alberta             | is much more interesting.
Edmonton, Alberta                 | 
                                  |

 




Newsgroups: sci.math.num-analysis
From: jonathan@chpc.utexas.edu (Jonathan Thornburg)
Subject: Re: 100 digit integer division?
Summary: use a symbolic algebra system
Keywords:  integer bignum divide arithmetic symbolic algebra Maple
Organization: U of Texas at Austin / Physics Dept / Center for Relativity
Date: Wed, 26 Aug 92 23:14:35 GMT

In article <1992Aug25.174608.1@camins.camosun.bc.ca>
comptec91065@camins.camosun.bc.ca writes:
>Can you help me find the easiest way to divide integers with a 
>minimum of 100 digits (possibly up to 4300 digits) ?

Any decent symbolic algebra system should be able to do this.
For example:

% maple
    |\^/|      MAPLE V
._|\|   |/|_.  Copyright (c) 1981-1990 by the University of Waterloo.
 \  MAPLE  /   All rights reserved.  MAPLE is a registered trademark of
 <____ ____>   Waterloo Maple Software.
      |        Type ? for help.
> Digits := 100;

                                 Digits := 100

> num := factorial(200);

num :=

788657867364790503552363213932185062295135977687173263294742533244359449963403\
342920304284011984623904177212138919638830257642790242637105061926624952829931\
113462857270763317237396988943922445621451664240254033291864131227428294853277\
524242407573903240321257405579568660226031904170324062351700858796178922222789\
623703897374720000000000000000000000000000000000000000000000000

> den := factorial(199);

den :=

394328933682395251776181606966092531147567988843586631647371266622179724981701\
671460152142005992311952088606069459819415128821395121318552530963312476414965\
556731428635381658618698494471961222810725832120127016645932065613714147426638\
762121203786951620160628702789784330113015952085162031175850429398089461111394\
8118519486873600000000000000000000000000000000000000000000000

> num / den;

                                      200

> quit();
bytes used=70232, alloc=65524, time=.150
%

- Jonathan Thornburg
  <jonathan@einstein.ph.utexas.edu> or <jonathan@hermes.chpc.utexas.edu>
  University of Texas at Austin / Physics Dept / Center for Relativity
  and (for a few more months) U of British Columbia / {Astronomy,Physics}
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: Abel's proof of the insolubility of the quint
Date: 3 Sep 92 18:01:28 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: elkies@ramanujan.harvard.edu (Noam Elkies)

In article <1992Sep3.122450.15337@husc3.harvard.edu>, elkies@ramanujan (Noam Elkies) writes:
>>I came across the proof in Rotman: identify the conjugacy classes of
>>A_5, and notice the impossibility of any of them forming a partition
>>for a size that non-trivially divides 60.

>This nice proof is reasonably well-known, but can one get a proof
>of the simplicity of all A_n (n>4) from such ideas?

I don't think so, although I don't know of a particular A_n where the
partition is possible, of course without forming a subgroup.  Rotman
redoes the partition proof for A_6, and then uses the result for A_6
to prove the result for A_n, n>6.

For beginners, the simple flat-out contradiction proof is probably ideal.
Later on the more commonly seen `complicated' proofs are better, since
structurally they resemble proofs for the classical groups.  And while
these later get superseded by the Lie theory proofs, these groups are
worth understanding on many levels.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: Groebner basis
Date: 29 Aug 92 15:00:16 GMT
Distribution: sci
Organization: M.I.T. Artificial Intelligence Lab.


Suppose I have a polynomial ring R in n variables over a field k and
a homogeneous ideal I in R generated by m elements f1,f2,...,fm of
degrees d1,d2,...,dm respectively. Let B be a Groebner basis for I
with respect to some ordering >.

Is there some useful bound for the cardinality of B and for the largest
degree of an element of B in terms of n,m,d1,...,dm and of some properties
of the ordering > ?

Allan Adler
ara@altdorf.ai.mit.edu
From: ap@levangerhs.no (Andrei Prasolov)
Subject: Re: Harmonic bi-sequences
Organization: Hogskolen i Levanger
Date: Thu, 27 Aug 92 17:16:33 GMT

I made a mistake in the previous article:

Newsgroups: sci.math
From: ap@levangerhs.no (Andrei Prasolov)
Subject: Elementary solution needed: harmonic bi-sequences
Date: Thu, 27 Aug 92 17:00:48 GMT

It was written:

"Let f(x,y) = Sum_i,j(delta(x-i,y-j))."

The correct version:

Let f(x,y) = Sum_i,j (a(i,j) delta(x-i,y-j).

              Andrei PRASOLOV
              Hoegskolen i Levanger
              Kirkegt 1, 7600 Levanger
              Norway

Tel. office 47-76-12650 (now), -12656 (later)
Telefax 47-76-12690
E-mail AP@LEVANGERHS.NO  
Newsgroups: sci.math
From: mccarthy@jezebel.wustl.edu (John McCarthy)
Subject: Re: Help - non-integral power of a matrix?
Organization: Washington University, St. Louis Mo.
Date: Sun, 23 Aug 1992 20:45:24 GMT

In article <KOSOWSKY.92Aug17163140@minerva.harvard.edu> kosowsky@minerva.harvard.edu (Jeffrey J. Kosowsky) writes:
>
>Just for clarification, the two mentions of finite-dimensionality above
>can be extended to compact operators on any Banach space. In the
>compact infinite dimensional case:
>	a] spectrum = closure of set of eigenvalues
>			  = {eigenvalues} U {0}
>	 so, it is still sufficient check the size of the eigenvalues
>	 plus the limit point 0. 
>	In the case of the logarithm, 0 does not lie in the radius of
>	convergence about 1. So, the Riesz functional calculus won't work
>	here. Actually, the Borel functional calculus won't work either
>	since the logarithm is not defined at 0.
>
>	So, is there any way to define the logarithm of a (compact)
>	operator on an infinite dimensional space that avoids this
>	problem of 0 being in the spectrum?
>
>	b]It is still true that normal iff diagonalizable
>	
>
>
>Jeff Kosowsky

No. If log(K) = A, where A is bounded, then 
spectrum(K) = spectrum(exp(A)) = exp(spectrum(A).
So if 0 is in the spectrum of K (always true if K is compact on
an infinite dimensional space), - infinity must be in the spectrum of A,
contradicting its boundedness.

John E. McCarthy
From: columbus@strident.think.com (Michael Weiss)
Newsgroups: sci.math
Subject: The thread that wouldn't die (was:You know, the integers)
Date: 27 Aug 92 11:49:30
Organization: Thinking Machines Corporation, Cambridge MA, USA
	<1992Aug11.190119.23518@ariel.ec.usf.edu>
	<1992Aug16.172642.13398@sics.se>
	<1992Aug24.153555.1298@ariel.ec.usf.edu>
	<1992Aug27.141149.14345@sics.se>
NNTP-Posting-Host: strident.think.com
In-reply-to: torkel@sics.se's message of Thu, 27 Aug 1992 14:11:49 GMT

As Torkel Franzen explains, if one is willing to use the phrase "the formal
system PA" without blushing, one shouldn't gag at "the integers".  (Note
that one might accept "the integers" without qualms and still feel nauseous
at "the universe of sets".)

To clarify this point, I offer the following variation on PA:

    1. There exists a first post in this thread.

    2. For any post in this thread, there is a reply to it.

I believe (2); I'm not so sure about (1).
From: ladd@oscar.cs.unc.edu (Brian Ladd)
Newsgroups: sci.math
Subject: Archives? Hexes?
Date: 31 Aug 92 17:12:20 GMT
Distribution: sci
Organization: UNC Department of Computer Science

I have been told, more or less reliably, that the shortest path on a
hexagonal grid has been discussed here. Since I am sure those who follow
this group regularly would rather not see such a disucssion again, could
someone point me to archives which would contain such an algorithm? E-mail
would be much appreciated, though I will follow this group for a while,
looking for responses. Thanks in advance -bcl

Brian C. Ladd
Graduate Student & *NIX Court Jester
Department of Computer Science
University of North Carolina - Chapel Hill
As usual, the University will disavow all knowledge of this posting and the
poster. This posting will self-destruct in 5 seconds. 5...4...3...2...<hiss>
From: srobbins@ringer.cs.utsa.edu (Steven Robbins)
Newsgroups: sci.math
Subject: M/D/1/B Queue reference requested.
Date: 1 Sep 92 13:56:18 GMT
Organization: University of Texas at San Antonio

I am looking for a reference on M/D/1/B queues.
These have exponential interarrival times, constant service time,
and one server with a finite number of buffers.

I do have a reference for M/M/1/B queues so please do not include this.
Please email and I will summarize if there is any response.
Newsgroups: sci.math
From: watson@maths.uwa.oz.au (David Watson)
Subject: Re: Question about polyhedra
Organization: University of Western Australia
Date: Wed, 2 Sep 1992 00:58:42 GMT

faustus@ygdrasil.CS.Berkeley.EDU (Wayne A. Christopher) writes:

>I need some information that must be in a book somewhere, but I can't
>seem to find it.  The question is this: for the various platonic
>solids, in particular the dodecahedron and the icosahedron, if the
>length of an edge is 1 and the polyhedron is centered about the origin,
>what are the coordinates of the vertices?  (For some convenient orientation.)
>Any references or numbers would be very much appreciated.  Thanks,

Each vertex of the icosahedron has coordinates which are signed 
permutations of (0, 0.5, (root(5)+1)/4)

The golden rectangle, with sides of 1 and (root(5)+1)/2, lies inside
this icosahedron on each pair of axes. 
--
Dave Watson                          Internet: watson@maths.uwa.edu.au
Department of Mathematics            
The University of Western Australia               Tel: (61 9) 380 3359
Nedlands, WA 6009  Australia.                     FAX: (61 9) 380 1028
From: watson@clark.edu (Dennis Watson)
Newsgroups: sci.math
Subject: Re: Proof of God's Existence
Date: 2 Sep 92 06:47:47 GMT
Article-I.D.: clark.1992Sep2.064747.26008
Organization: Clark College, Vancouver, Wa.  USA

In article <1992Sep1.090011.1@tnclus.tele.nokia.fi> hporopudas@tnclus.tele.nokia.fi writes:
>
>   If someone is arguing that "Existence Himself" does not exist, I think that
> at the same time he/she is arguing that he/she himself/herself does not exist.
>
>              Hannu.

 I/She/He/It thinks that this is TOO policticaly correct. I/She/He/It think that
we/wshe/whe/wit are not doing the English language any good by being TOO
policticaly correct!! Let's get a new word meaning "I am not a Man nor a Woman
but a Thing" and then we don't need these weird constructs anymore.  We
are lucky we don't have a language like German or Russian or French or...
where the words have gender!  We couldn't even write!!!

Dennis
watson@clark.edu
From: toon@moene.indiv.nluug.nl (Toon Moene)
Newsgroups: sci.math
Subject: How to prove 1 = 0 with statistics, was: Re: mathematician's marrying ages.
Date: 30 Aug 92 19:41:12 GMT
Organization: Moene Computational Physics, Amsterdam, The Netherlands

In article <l9htbnINNr3@boogie.cs.utexas.edu> swisher@cs.utexas.edu (Janet  
M. Swisher) writes:
> In article <1992Aug24.134508.27438@cc.tut.fi> jk87377@cc.tut.fi
> (Juhana Kouhia) writes:
> >The problem in this kind of research is (I think) to examine:
> >-a person have problems ---> not married
> >-not married --> a person will get problems

> >The research which about I wrote did research the latter one, and I
> >recall it showed some relation.

> >Well, we don't have details so, it would be silly to argue on this
> >anymore. I think it is better to choose the one which causes
> >less harm:
> >-if you don't marry, then you don't have a wife and will have mental
> >problems
> >-if you marry, then you have wife and very fun  :-)

> Gee, I'm married and I don't have a wife.  What went wrong? :-) :-)

> But seriously, I have read (newspaper reports, unfortunately) about
> survey research which indicated that married men report being happier
> than unmarried men report being, while unmarried men report being
> happier than married women report being.  I think it also said that
> those who reported being happier tended to live longer, but I tend to
> be skeptical of such assertions.  Still, it gives us married women
> pause.

OK, I've long refrained from getting into this discussion - but as it gets  
sillier by the hour, here's my two cents:
Surveys showing married men being happier than unmarried man are wrong  
because they never interview me (at least the last part of the sentence is  
true). To put down the other half of the equation: I don't mind living  
half as long as the average married mathematician (I'm a physicist, BTW),  
as long as I don't have to marry!

And Janet, we seem to have read the same newspaper reports :-) The amazing  
thing about them is that they imply that people ARE getting happier as  
they marry - I've never understood why ...  Now if someone could dig up  
the real references, to enable us to shoot down this misuse of statistics
:-)
--
Toon Moene (toon@moene.indiv.nluug.nl)
Kantershof 269, 1104 GN  Amsterdam, The Netherlands
Tel.: + 31 20 6982029; Fax: + 31 20 6003411
No Disclaimers; a NeXT at home protects against this occupational hazard.
Newsgroups: sci.math
Subject: Godel and the US constitution
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 1 Sep 92 16:26:33 GMT

On the subject of a proof of God's existence,
In <1992Sep1.215331.89956@vaxc.cc.monash.edu.au> kevin@vaxc.cc.monash.edu.au writes:

>2. It will strike many as odd that even Godel believed he had a proof, using
>modal logic. If you can bother spending the time reading it (it is quite
>complex), I'm sure you'll spot the error. It's more sublte than most other
>ontological errors, but it's there, unavoidable, and unrectifiable. I suppose
>even great mathematicians can go loony every now and again.

This reminds me of a story I heard at a memorial seminar on Godel, on which
I would like confirmation.  When he was studying US Constitution for his
citizenship, it is reported that he found a way for the system to produce a
dictorship.  While talking with the judge, he commented that he left
Germany because it had become a dictorship.  The judge said something like,
"Thank God that can't happen here."  Godel was about to reply with his
observation, but his sponsor kicked him and got him to shut up.
--
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.
Newsgroups: sci.math
From: ara@zurich.ai.mit.edu (Allan Adler)
Subject: Re: Proof of God's Existence
Organization: M.I.T. Artificial Intelligence Lab.
Date: Fri, 4 Sep 1992 08:03:28 GMT

Matt Wiener has apparently missed my point. Without some agreement as
to what one is supposed to be proving, there is no possibility of
mathematical proof.

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math
From: radford@cs.toronto.edu (Radford Neal)
Subject: Re: Godel and the US constitution
Organization: Department of Computer Science, University of Toronto
Date: 2 Sep 92 22:30:52 GMT

In article <1992Sep2.170531.11675@ms.uky.edu> cyeomans@ms.uky.edu (Charles Yeomans) writes:
>In article <92Sep1.205802edt.637@neuron.ai.toronto.edu> radford@cs.toronto.edu (Radford Neal) writes:
>>In article <1992Sep1.175844.16825@nas.nasa.gov> asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:
>>
>>>Out of curiosity, does anyone know how Godel envisioned a
>>>consitutional dictatorship possibly arising in the U.S. ???
>>
>>
>>Well... My recollection is fuzzy, but can't the US congress create new
>>states just by passing a bill? It should be no problem for them to
>>create several hundred of them, each containing only a single
>>resident, namely, one of themselves. They can then run in these new
>>states come next election, elect themselves, and out-vote any
>>uncooperative representatives from the old states...
>>   
>>    Radford Neal
>
>Not quite.  To form a new state out of pieces of one or more old states
>requires both the consent of congress and the consent of the legislatures
>of the states involved - this is explicitly stated in the Constitution.


Ahhh! But in Godel's time, there were also _territories_. Surely Alaska
was plenty big enough for hundreds of states?

For that matter, do states have to occupy any land? 

    Radford
Newsgroups: sci.math
From: bwallet@apssgi.nswc.navy.mil (Brad Wallet)
Subject: Re: Proof of God's Existence
Organization: Naval Surface Warfare Center
Date: Tue, 1 Sep 1992 12:35:33 GMT

In article <1992Sep1.090011.1@tnclus.tele.nokia.fi>, hporopudas@tnclus.tele.nokia.fi writes:
|> 
|> In article <17ui6kINNsft@matt.ksu.ksu.edu>, bubai@matt.ksu.ksu.edu
|> (P.Chatterjee) writes:
|> > I was told by somebody that there is a mathematical proof of God's existence;
|> > was wondering if somebody could shed some light on the same.
|> >
|> > Thanks. Looking forward to the response.
|> 
|>    I think that God's existence is an axiom. He says in the Holy Bible (Second
|>  book of Moses 3:14-15 in Old Testament and also in Johannes 8:28-29 in New
|>  Testament) that He is "Existence Himself".
|>    If someone is arguing that "Existence Himself" does not exist, I think that
|>  at the same time he/she is arguing that he/she himself/herself does not exist.
|> 
|>               Hannu.

Mr. Space Potato has left/was run off sci.physics and has found a new home.
Please, before this gets started, take it to alt.talk.does.not.belong.here.
Newsgroups: sci.math
From: nickh@CS.CMU.EDU (Nick Haines)
Subject: Re: Solitaire games
Originator: nickh@VOILA.VENARI.CS.CMU.EDU
Organization: School of Computer Science, Carnegie Mellon University
	<NICKH.92Sep3143716@VOILA.VENARI.CS.CMU.EDU> <7230@charon.cwi.nl>
Date: Fri, 4 Sep 1992 15:58:37 GMT

In article <7230@charon.cwi.nl> dik@cwi.nl (Dik T. Winter) writes:

   In article <NICKH.92Sep3143716@VOILA.VENARI.CS.CMU.EDU> nickh@CS.CMU.EDU (Nick Haines) writes:
    > I play a game with triplets of digits (such as one finds on 99% of
    > British numberplates),
   Sorry.  900 out of 999 is not 99%.

Indeed not, but not all the 1- and 2-digit plates get issued.

Nick
Newsgroups: sci.math
From: Dave Dodson <dodson@convex.COM>
Subject: Re: Polygon point enclosure
Originator: dodson@bach.convex.com
Date: Thu, 27 Aug 1992 19:37:51 GMT
Reply-To: dodson@convex.COM (Dave Dodson)
Organization: Engineering, CONVEX Computer Corp., Richardson, Tx., USA
X-Disclaimer: This message was written by a user at CONVEX Computer
              Corp. The opinions expressed are those of the user and
              not necessarily those of CONVEX.

In article <1992Aug27.180024.2843@linus.mitre.org> bs@gauss.mitre.org (Robert D. Silverman) writes:
>I have a question.
>
>I will assume that the polygon is given by a set of points.
>
>Counting how many sides it intersects seems to require computing the
>equation for the line containing each side and determining whether
>the ray intersects the line between the two points. This requires
>computing O(N) equations and intersections.
>
>Why is this any faster than simply representing the interior of
>the polygon as a set of linear inequalities and simply checking
>whether the desired point satisfies each inequality?? This is also O(N).
>This is essentially equivalent to whether a solution is feasible
>in linear programming.

Yes, but only a convex polygon can be represented by a set of linear
inequalities, whereas counting the edge crossings of a ray from the
point in question to infinity can be made to work whether the polygon
is convex or not.

----------------------------------------------------------------------

Dave Dodson		                             dodson@convex.COM
Convex Computer Corporation      Richardson, Texas      (214) 497-4234
Newsgroups: sci.math
Subject: Re: Summer Problems
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 3 Sep 92 20:36:06 GMT

In <1992Sep2.104741.12452@greco-prog.fr> loeb@greco-prog.fr (Daniel LOEB) writes:

>(DMITRI) - A door has a very strange lock. It contains n holes
>arranged in a regular polygon. There are buttons at the bottom of the
>holes. When all buttons are up or all down, the door opens. Buttons
>can only be examined or changed by sticking your arms in the holes.
>When your arms are removed from the holes, the lock spins very quickly
>and then stops at an unknown point. How many hands h(n) must you have
>in order to be SURE to open the doors after a finite number of
>manipulations. 
>Partial results: if p is prime, then h(p)=p-1. Otherwise, h(4)=2 and
>h(1)=0.
>Is there a general rule? Generalizations?

h(n) = n(1-1/p), where p is the largest "prime" divisor of n (prime including
1, to handle h(1)=0).  I think I've seen this problem before; probably in
the American Mathematical Monthly or Mathematics Magazine, both published
by the Mathematical Association of America.  I think I see a fairly
straightforward proof that that number is sufficient; I don't see how to
proof necessity at the moment.

Standard disclaimers apply.
--
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; please mail anything important.
Newsgroups: sci.math
From: ceblair@ux1.cso.uiuc.edu (Charles Blair)
Subject: p prime, p divides ab => pdivides a or b
Organization: University of Illinois at Urbana
Date: Wed, 2 Sep 1992 17:21:47 GMT

   My recollection is that a number theory course I took presented
this as a difficult result, only proved after doing some stuff
with the Euclidean algorithm.  Is there a proof which avoids that?
Newsgroups: sci.math
From: ppc1@cec2.wustl.edu (Peter Pui Tak Chiu)
Subject: Probability
Organization: Washington University, St. Louis Mo.
Date: Sat, 29 Aug 1992 13:52:11 GMT



Hi everyone!


Some of my friends and I have been discussing a question and
we came up w/ an answer and would like to verify if its correctness.

Please give any comments freely!!!

Thanks...

Question:

Assume there are m kinds of balls in an infinitely large pool
(i.e. there are infinitely many balls)
and the distributions of different kinds of balls are equal.
Find the probability of getting all kinds of balls if n balls
are picked.

Solution:

First group the n balls you picked into m groups according to
their kinds using m-1 sticks.  So the number of possible
arrangements for the sticks and balls is (n+m-1)C(m-1).

Then we are to find the number of possible arrangements of:
(m balls of different kinds) + (n-m balls of whatever kinds) + (m-1 sticks)
since the m balls are fixed (to satisfy the constraint that there
exists at least one ball of each kind) and what we are trying to
find is the number of arrangements of n-m balls and m-1 sticks.
So, the possible arrangements is:    ((n-m)+(m-1))C(m-1) = (n-1)C(m-1)

Therefore, the probability is:    (n-1)C(m-1)
				---------------
                                 (n+m-1)C(m-1)