HDTenEightyP/NetNews huggingface dataset:
From: sichase@csa2.lbl.gov (SCOTT I CHASE)
Newsgroups: sci.math
Subject: Mersenne again
Date: 14 Apr 92 20:53:55 GMT
Organization: Lawrence Berkeley Laboratory - Berkeley, CA, USA
Distribution: na
Reply-To: sichase@csa2.lbl.gov
NNTP-Posting-Host: 128.3.254.197
News-Software: VAX/VMS VNEWS 1.3-4   

This week's Science reported the new Mersenne prime and added that there 
is an expectation that at least one lower one has so far been missed.
Now I know from reading previous posts that certain intervals of primes
have not been thouroughly explored.  But what is the specific conjecture on 
the density of Mersenne primes that leads this Science article to claim 
that there is likely a missing one?

-Scott

--------------------
Scott I. Chase
SICHASE@CSA2.LBL.GOV
From: marc@vieta.math.uni-sb.de (Marc Conrad)
Newsgroups: sci.math
Subject: New SIMATH version on ftp !!
Summary: SIMATH version 3.5 on ftp
Keywords: computer algebra system, number theory
Date: 14 Apr 92 10:17:44 GMT


The new SIMATH-version 3.5 is now available via anonymous ftp 
from 
anonymous@ftp.math.uni-sb.de

For those, who don't know, what SIMATH is, here a short 
description
(the "official" README File, you will get, if you get SIMATH):

--- 
This file is part of the computer algebra system SIMATH. 
Copyright (C) 1992 by the SIMATH group in Saarbruecken.

The computer algebra system SIMATH is free software. This software is
distributed in the hope that it will be useful, but
		WITHOUT ANY WARRANTY.

Permission is hereby granted to copy the system for any non-commercial
purposes, provided the above notices are retained on all copies.

Upon reception of this software, please send an e-mail message to
		simath@math.uni-sb.de
to inform us that you got a copy of the system.

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

The computer algebra system SIMATH is written in C. It was developed
for research purposes by the SIMATH group of Prof. Dr. H.G. Zimmer at
the University of Saarland in Saarbruecken, Germany.

Up to now SIMATH is running on the following machines: 
	Sun 3/140 under SunOS 3.4,
	Sun 3/80 under SunOS 4.0.3,
	Sun SPARCstation under SunOS 4.1.1,
	Apollo DN 3000 under SR10.1,
	Apollo DN 4500 under SR10.1,
	Apollo DN 10000 under SR10.3,
	Siemens MX2 under SINIX V2.0, 
	Siemens MX2+ under SINIX V5.2 and
	Siemens MX300 under SINIX V5.2.

Even if you are using a different machine (and/or operating system),
you can (and you should) try to install SIMATH. If you are successful
please let us know. If you had to change some of the SIMATH source
files, please inform us of the changes to be made.

If you have any problems or suggestions, please contact us by mail:
	SIMATH-Gruppe
	Lehrstuhl Prof. Dr. H.G. Zimmer
	FB 9 Mathematik
	Universitaet des Saarlandes
	W-6600 Saarbrueken
or by e-mail:
	simath@math.uni-sb.de
or by phone:
	0681/302-2206.

The latest version of SIMATH may be obtained by anonymous ftp from
math.uni-sb.de (134.96.32.23).
--------

or send a respond to this article to me.

Marc.
 

--
     \   /                     | Marc Conrad 
      \ Luxemburg              | Universitaet des Saarlandes
France \|   Germany            | marc@math.uni-sb.de 
        \x <---- you are here! | phone: 0681 302-2297
From: rose@fsu1.cc.fsu.edu (Kermit Rose)
Newsgroups: sci.math
Subject: test of non-orientability of moibus strip.
Date: 3 Apr 92 18:32:46 GMT
Article-I.D.: mailer.1992Apr3.133246.28043
Reply-To: rose@fsu1.cc.fsu.edu
Organization: Florida State University
News-Software: VAX/VMS VNEWS 1.3-4

It was suggested that one test of the non-orientability of a moibus strip 
was that if you drew clockwise circle on the band, moving around the band, 
when you cam back to where you started, then you would be drawing the 
circles counterclockwise.   
I tried this.  I did not find it so.  Actually what I tried was drawing the 
circles counterclockwise.  When I came back to starting point, I was still 
drawing them counterclockwise.  
I assume that the non orientation comes from its having just one side. 
What is the real point behind the idea of drawing circles to test for 
orientation posibility?

Kermit@FSU or rose@fsu1.cc.fsu.edu.bitnet
If you want to be sure I see your response, please e-mail me.
-----------------------------------------------------------------------
This is the signature file of Kermit Rose.

Believing in dichotomies leads to hardening of your logic.

What determines the existence of Free Will?
I strive to believe only what is true. I have faith that whatever is 
true will also be logically consistent and knowing truth will increase my 
capacity to be kind.
Peace is the way to peace.  Hostility is the way to hostility.
Newsgroups: sci.math
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Re: On consecutive primes: q<3p/2+1?
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Thu, 9 Apr 1992 12:11:05 GMT

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.
:Five years later this was proved by Chebychev.
:In this century Erdos improved on this, showing that, in fact
:q/p is not larger than 5/3.
:
:My question is how good the value 5/3 is compared to the
:actually calculated ratios q/p for known primes.
:Maybe 5/3 is a good approximation only for primes < 10,
:and 3/2 holds for all p >10, 6/5 for all p>100 and so on.
:To be precise:
 
stuff deleted.
 
You are essentially correct. The ratio does go to 1.


It can be shown on the PNT that q/p < 1 + o(1)   as q--> infty.

There is a paper in Math. Comp. by Rosser & Schoenfeld that gives
some explicit inequalities for primes and which tell you how big the
o(1) term is for various q's.
--
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: ky04@ns1.cc.lehigh.edu (KUN YU)
Newsgroups: sci.math
Subject: AX <= B  ---- HELP
Date: 10 Apr 92 00:53:12 GMT
Organization: Lehigh University


 AX=B, A=[a1 a2 a3 ... an], X=[x1 x2 x3 ...xn]' , a's and B are (mx1) vectors
                               x's are scalars.
 Known: only a1
 Sought: x1

 The problem seems ridiculous, but it does make sense and is important.
 If a1 is orthogonal to other a's,  the problem is perfectly soluble.
              x1=a1\B=a1^{+}B
 If a1 is linearly related to others, it's absolutely insoluble.

 There must be somthing between the extremes, especially if we add some
 constraints. The  physical meaning of my problem requires that nothing be
 negative, none of the elements of a's. x's and B. Thus, the problem becomes
      AX <= B,  A=[a1 a2 a3 ... an], X=[x1 x2 x3 ...xn]' ,
                     a's and B are (mx1) vectors
      rank(A)=n, A is well conditioned(not orthogonal, however).
                 All elements      of A and B are non-negative.
      Sought: X, which is all positive.

I don't know how to start the analysis.
Any advice/hints/help/references will be highly appreciated.
-- 
 
 
           /
         / _ \
       /  _I_  \
           I
         / I \
Newsgroups: sci.math,news.answers
From: ec120wee@sdcc4.ucsd.edu (Anthony Minkoff)
Newsgroups: sci.math
Subject: Test wanted for "groupness"
Date: 15 Apr 92 03:59:24 GMT
Organization: University of California, San Diego

More unenlightening babblings from the ignorant undergraduate who's
not even a math major:

I want a way to determine efficiently whether a given set and
operation constitute a group.  In particular:

Suppose I am given a set and an operation; the operation is
described by specifying a*b for all ordered pairs (a,b) in SxS.

I can write down the definition of the operation as a matrix.  The
element in the ith row and jth column is i*j.  Now I want to know,
is it a group?

For example,

     1 2 3 4 5
     2 1 5 3 4
     3 4 1 5 2
     4 5 2 1 3
     5 3 4 2 1

(This particular example, as you may have realized, is not a group.)

Of course, it is simple to determine, at a glance, whether an
identity exists, and whether each element has an inverse.  But
associativity?  How am I to test associativity, without testing all
ordered triples?  For a reasonably large group, there are
approximately n^3 triples that need to be tested.

I have figured out some things to look for.  E.g., if any element is
duplicated in any row or column, then it's not a group.  If the
positions of the identities are not symmetric about the diagonal,
then it's not a group.

I have also determined that certain triples certainly do not need to
be tested, once the above conditions are satisfied.  For example, if
e is the identity, then certainly (ae)b = a(eb), and there is no need
to test such triples.  Furthermore, if a is the inverse of b, then
there is no need to test aba.

Is there a way, short of testing all the triples, to determine
whether it's a group?  A couple of professors I asked here at UCSD
were unable to answer this question, and a couple of textbooks I
consulted did not even address this issue.

I'm mostly looking for something I can use myself, to determine
withing a reasonable amount of time whether a given operation,
specified as above, is a group on a given set.  But, more
rigorously,

Given an operation over the integers 1..n, specified as above (i.e.,
a*b is given, for all a, b in 1..n), what is the most efficient
algorithm for determining whether the operation and the integers
1..n constitute a group?  Is it possible to do better than o(n^3)?

My gut tells me that it must be possible to do better than o(n^3),
but I don't know how.

Tony
-- 
Tony Minkoff
aminkoff@sdcc13.ucsd.edu
ec120wee@sdcc4.ucsd.edu
From: sichase@csa1.lbl.gov (SCOTT I CHASE)
Newsgroups: sci.math
Subject: Re: A simple question about R2 - Q2 (irrational points of the plane)
Date: 13 Apr 92 19:44:31 GMT
Reply-To: sichase@csa1.lbl.gov
Distribution: na
Organization: Lawrence Berkeley Laboratory - Berkeley, CA, USA
NNTP-Posting-Host: 128.3.254.196
News-Software: VAX/VMS VNEWS 1.3-4

In article <1992Apr11.175123.360@math.okstate.edu>, gindrup@math.okstate.edu (Eric `'d'kidd' G..) writes...
> 
>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...
> 

sqrt(2) + -sqrt(2) = 0 is not irrational.

(1+sqrt(5))/2 + (1-sqrt(5))/2 = 1, and so forth.

-Scott
From: moews@math.berkeley.edu (David Moews)
Newsgroups: sci.math
Subject: Re: polyomino classification
Date: 15 Apr 1992 06:53:14 GMT
Organization: UC Berkeley Math Department
Distribution: world
NNTP-Posting-Host: sizzlean.berkeley.edu
Keywords: polyomino
Originator: moews@sizzlean.berkeley.edu

In article <seghkINNd3c@agate.berkeley.edu>,
   reid@durban.berkeley.edu (michael reid) writes:
|...i don't know if the implication 
|
|              three-quarter plane  ==??==>  half plane 
|
|is valid...

If a polyomino tiles the three-quarters plane, copies of it can be used to
cover arbitrarily large squares in such a way that one edge of the square is
`smooth', that is, it has nothing hanging out over it.  Then we can use
Koenig's lemma (which Mike Reid hints at in his post.)  Koenig's lemma
says that if a rooted tree has infinitely many vertices and finite degrees 
everywhere, it has an infinite path from the root.  In this case the vertices
are coverings of squares with one edge smooth and there are edges leading from
a covering to its immediate enlargements.  An infinite path from the root
then gives a tiling of the half-plane.

In article <9204101706.AA21144@sun1.aic.nrl.navy.mil>, Dan Hoey mentions 
diagonal quadrants, half-planes and three-quarters planes.  If a diagonal
                                     #
                                    ##
quadrant has a corner looking like ### we cannot abut a quadrant and a rotated 
                                    ##
                                     #
quadrant to form a diagonal half-plane, since there will be a defect where
the two corners come together.  However the infinity lemma can be used as 
above to show (diagonal three-quarters plane ==> diagonal half-plane).  For
(diagonal quadrant ==> diagonal three-quarters plane) and, of course,
(diagonal half-plane ==> diagonal plane), abutment does work.  Thus
we have the same implications as proved in the orthogonal case.
-- 
David Moews                             moews@math.berkeley.edu
From: George.Harris@bbs.oit.unc.edu (George Harris)
Newsgroups: sci.math
Subject: Re: On knowing who's who (was: Fermat's Last Theorem)
Date: 14 Apr 92 16:20:05 GMT
Organization: Extended Bulletin Board Service

In article <COLUMBUS.92Apr9091341@strident.think.com> columbus@strident.think.com (Michael Weiss) writes:
>Our story so far:
>
>   Derek Abbott: "Who is this Erdos dude?"
>   Robert D. Silverman: "You're kidding, right? How could you not know one
>    	of the foremost mathematicians of this century?"  (approximate
>    	quotation)
>   Various posters: give the guy a break.
>   Other posters: give *us* a break.
>
>In an interview in Scientific American a few months back, then Chief of
>Staff John Sununu did not know (or professed not to know) who Leon Lederman
>is.  I leave it for the reader to decide which side of the debate (if
>either) this factlet supports.

	Gee, I don't know.  Who is this Lederman dude?

--
"If you take cranberries and stew them like applesauce, they taste more like
prunes than rhubarb does."		-Groucho Marx

George.Harris@bbs.oit.unc.edu	or, preferably	gharris@jade.tufts.edu
--
   The opinions expressed are not necessarily those of the University of
     North Carolina at Chapel Hill, the Campus Office for Information
        Technology, or the Experimental Bulletin Board Service.
           internet:  bbs.oit.unc.edu or 152.2.22.80
From: trivedi@curie.uchicago.edu (Anil Trivedi)
Newsgroups: sci.math
Subject: Re: Zero, "Arabic" numerals, etc.
Date: 9 Apr 92 00:37:28 GMT
Organization: Enrico Fermi Institute, University of Chicago.


In article <1992Apr8.221529.29450@usenet.ins.cwru.edu> somos@ces.cwru.edu (Michael Somos) writes:
>Does anyone know of a really good source for the study of zero?  I know
>that Martin Gardner wrote about "Nothing", but this didn't cover the
>topic very well.  The concept of the number zero, the digit zero, and
>nothing, are closely related and very subtle.  A glance at history will
>demonstrate this.  Even today, I don't think we really understand all
>the nuances.  This study would cover the history, the philosophy, and
>the mathematics and science of zero.  A highly non-trivial undertaking.

I am not sure what kind of source you are looking for: the number zero,
its use and representation through history are well documented.
The PHILOSOPHICAL mystery that seems to intrigue you has shifted, as far
as mathematics is concerned, to the concept of "null set". 
In physics, the concept of "vacuum" has turned out to be extremely dynamic
and nontrivial, and is still being sorted out.
From: teacher@netlink.cts.com (Daniel Pick)
Newsgroups: sci.math
Subject: A Proof about Groups
Date: 13 Apr 92 03:12:08 GMT
Article-I.D.: netlink.X3F6iB1w164w
Organization: NetLink Online Communications, San Diego CA

In Joseph Landin's book, 'An Introduction to Algebraic Structures,'
the author makes the following definitions:
A group G which contains only a finite number of elements is a 
finite group.
An element x of a group G has finite order if and only if
there is a positive integer n such that x^n = e, where e
is the neutral element.
Then he asks the reader to prove that if G is a finite group,
then every element in G has finite order.
This proof stumps me.  If you induct on the number of elements in
the group, how do you show that each successive element has finite
order?

--                    
INTERNET:  teacher@netlink.cts.com (Daniel Pick)
UUCP:   ...!nosc!ryptyde!netlink!teacher
NetLink Online Communications * Public Access in San Diego, CA (619) 435-6181
Newsgroups: sci.math
From: cyeomans@ms.uky.edu (Charles Yeomans)
Subject: Re: Question on Connectedness
Keywords: Topology
Organization: University Of Kentucky, Dept. of Math Sciences
Date: Wed, 15 Apr 1992 13:44:11 GMT
X-Bytes: 

In article <36937@gremlin.nrtc.northrop.com> jbarnett@nrtc.northrop.com (Jeff Barnett) writes:
>Is the following true in the topology of Euclidean n space:
>
>P is a collection of non-empty (pairwise) disjoint closed sets.  P is
>a partition of S.  Claim -- if S is connected, then the cardinality
>of P is either 1 or uncountable.
>
>Jeff
>
I'm not sure what the collection P has to do with the question.  It
is easy to show that a countable set in R^n is not connected. Let
p_i be the Ith projection map.  For some i, p_i(S) is countable.
Now, p_i(S) is a subset of R^1.  Since the continuous image 
of a connnected set is also connected, it will suffice to show w
that a countable subset of R^1 cannot be connected.

Let T be a countable subset of R^1.  Since R^1 is uncountable, there
is a point p in R^1 - T.  Then (-oo, p) intersect T, (p, oo) intersect
T is a separation of T by disjoint open sets.  Thus T is not 
connected.  We conclude that S is not connected, either.

I should say that the point p chosen above should lie between 
two points of T for this argument to be correct.

The case S = finite set is trivial.

Charles Yeomans
cyeomans@ms.uky.edu
yeomans@austin.onu.edu
From: tobias@maths.lth.se (Tobias Ryden)
Newsgroups: sci.math
Subject: Ergodic theory for general Markov chains
Date: 9 Apr 92 14:11:31 GMT
Distribution: sci.math,sci.math.stat
Organization: Dept. Statistics & Math, Lund Institute of Technology, Sweden

For a stationary ergodic process X_n it is well known that

       N
  1   ---
  -   \
  N   /    f(X_n) -> E(f(X_1))
      ---
      n=1

with probability 1 and in L_1 provided E|f(X_1)| is finite. Now, let
Y_n be a Markov chain on a general state space E for which there
exists a stationary distribution v, but the initial distribution of
Y, i.e. the distribution of Y_1, need not necessarily equal v.
Under which conditions does

       N
  1   ---
  -   \
  N   /    f(Y_n) -> v(f)
      ---
      n=1

hold, where f is in L_1(v) and the convergence is w.p.1, in L_1 or in
probability?

All references are appreciated!

+- Tobias Ryden                          Internet: tobias@maths.lth.se
   Dept. of Mathematical Statistics      Tel:   int+46 -(0)46 104276  
   Lund Institute of Technology          Fax:   int+46 -(0)46 104623   
-- P.O. Box 118, S-221 00 Lund, Sweden   
-- 
+- Tobias Ryden                          Internet: tobias@maths.lth.se
   Dept. of Mathematical Statistics      Tel:   int+46 -(0)46 104276  
   Lund Institute of Technology          Fax:   int+46 -(0)46 104623   
-- P.O. Box 118, S-221 00 Lund, Sweden
From: shepard@athena.cs.uga.edu (William Erik Shepard)
Newsgroups: sci.math
Subject: Re: Fermat's Last Theorum
Date: 11 Apr 92 04:27:13 GMT
Organization: University of Georgia, Athens

In article <1992Apr8.081134.19685@augean.eleceng.adelaide.edu.AU> dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott) writes:
>One of the tantalizing things about FLT is the fabled note that Fermat
>left before he died saying that he found an elegant proof.
>
>There are two main possibilities:
>
>(a) He really found the proof, and the historical record is lost
>
>(b) He had a mental abberation, and this mistaken proof is lost too

Actually, from what I understand, Fermat stated that he had discovered the
elegant proof but as he was making notes in the margin of a book, he did
not have enough room to write out the entire proof.  In either words, he
either discovered the proof but ran out of room or THOUGHT that he discovered
the proof but ran out of room.

Erik Shepard
shepard@athena.cs.uga.edu
From: msp@dcs.warwick.ac.uk (Mike Paterson)
Newsgroups: sci.math
Subject: Anyone seen one of these before?
Keywords: PDE
Date: 7 Apr 92 10:01:59 GMT
Organization: Department of Computer Science, Warwick University, England

I have the following partial differential equation which is unlike 
any I know about. It arises from the analysis of a flow in a 
network. (All the d's should be curly for partial derivatives.)

	exp(dV/dx).(d^2 V/dx^2) + exp(dV/dy).(d^2 V/dy^2)

I have just one particular solution, which is 

	V = x ln x + y ln y - 2(x+y) ln (x+y)

but would like others, preferably with a free parameter, 
or the general solution. Any ideas, please?

Mike Paterson

-- 
 Internet,EARN/BITNET,UUCP: msp@dcs.warwick.ac.uk | Mike Paterson 
 JANET: msp@uk.ac.warwick.dcs                     | Dept. of Computer Science
 PHONE: +44 203 523194                            | University of Warwick     
 FAX:   +44 203 525714                            | Coventry, CV4 7AL, ENGLAND
From: vcr+@EDRC.CMU.EDU (V C Ramesh)
Newsgroups: sci.math.symbolic,cmu.sci.math.symbolic
Subject: Mathematica-2.0 question
Keywords: mathematica, listdensityplot, densitygraphics
Date: 13 Apr 92 18:30:28 GMT
Article-I.D.: cs.1992Apr13.183028.288211
Reply-To: vcr@cs.cmu.edu
Organization: Carnegie Mellon University

I am trying to get ListDensityPlot/DensityGraphics to display a 2-D array of
pixel values *in color*.  First, I tried:

% ListDensityPlot[{{0.3, 0.5}, {0.7, 0.1}}]
	      and
% Show[DensityGraphics[{{0.3, 0.5}, {0.7, 0.1}}]]

Both of the above default to grey-level.

I then tried:

% Show[DensityGraphics[{{0.3, 0.5}, {0.7, 0.1}}],
	ColorOutput -> RGBColor[0., 0.5, 1.]]

% Show[DensityGraphics[{{0.3, 0.5}, {0.7, 0.1}}],
	ColorFunction -> RGBColor[0., 0.5, 1.]]

Neither of these worked either; apparently, wrong usage for the options.

The Mathematica book I have is old, and does not document these options
well (dunno if the latest edition does).  The on-line requests:

% ??ColorOutput
% ??ColorFunction

didn't help much.

I am running version 2.0 on a Dec5000 (running CMU's mach operating system
- Unix 4.3BSD server -, if that is relevant).

Thanks for any help.

Ramesh

ps: I would also like a legend of z-values & colors, if one is available.
From: gaylord@UX1.CSO.UIUC.EDU
Newsgroups: sci.math.symbolic
Subject: beauty contest. the winner is...
Date: 10 Apr 92 14:46:52 GMT

well,  quite a few people entered the pageant and there was alot to learn
from all of the entries

the rules of the contest were changed a bit to allow for a more general
startlist (deeper nesting) 

startlist = {{a, a, a}, {{{b, b}, {b, b, b}}}, {a}} ;

the consensus was that pattern matching was the best 'flattening' tool. 

in no particular order:  

startlist //. {a___,{b__List},c___} :> {a,b,c}
{{a, a, a}, {b, b}, {b, b, b}, {a}}

Cases[ startlist, {_Symbol..}, -1]
{{a, a, a}, {b, b}, {b, b, b}, {a}}


(#//.{b__List} :> b)&/@startlist
{{a, a, a}, {b, b}, {b, b, b}, {a}}


not alot to say here except that the last program is interesting from the
viewpoint of a functional programming style because it applies Map to a
list and produces a longer list. This is very 'unfunctional' and it arises
because M allows you to change datatypes in the list (a list is changed
into a sequence - as we know, Sequence is an odd duck of an M definition
which is quite useful). 'real' functional programmers, ML, Miranda, Haskell
types (this is a pun), hate this sort of thing since they are into B&D
programming (of course, they also hate side effects so there's no
accounting for taste).

thanks to everyone who participated. it was very educational and of course,
preferable to actually working.
Newsgroups: sci.math.symbolic