HDTenEightyP/NetNews huggingface dataset:
From: ara@zurich.ai.mit.edu (Allan Adler)
Subject: Re: Why are Some Journals so Expensive?
Organization: M.I.T. Artificial Intelligence Lab.
	<92221.182456U53644@uicvm.uic.edu>
	<1992Aug16.174406.8309@vax.oxford.ac.uk>
Date: Mon, 17 Aug 1992 04:19:11 GMT


Jocelyn Paine is under the impression that the number of mathematicians who
do not have access to email, LaTeX and other facilities that would make it
possible for them to receive math journals electronically is not significant.

Speaking as one mathematician who has from time to time taken his place
among this insignificant number, and who has no assurance of access for
the indefinite future, I caution against basing decisions of this nature
on the assumption of access.

Sci.math is hardly the place to collect data on the question of access.
Some who reads sci.math already has access and those without access are
not in a position to speak for themselves in this forum.

Universities are not in the business of providing logistical supports to
independent scholars. They are not necessarily even in the business of 
providing these supports to their own faculty. 

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math
From: heisen@convex.rz.uni-duesseldorf.de (Henner Eisen)
Subject: Re: Is Card(R)=Card(R^2)?
Organization: Heinrich-Heine-Universitaet Duesseldorf 
Date: Thu, 13 Aug 1992 00:09:28 GMT

In article <1992Aug12.102140.5231@nntp.hut.fi> samu@lammio.hut.fi writes:
>I have been wondering... It seems first that there are more pairs of
>real numbers than real numbers, but is it really so? And if not, I would
>like to see a bijective mapping f:R->R^2.     ...

Such mappings exist! To construct a mapping f(x,y) = z  choose a
unique decimal representation of x and y and then merge the digits.

i.E.:
x =  1 0 0 2. 7 1 8 2 8 2 . . . . . .
y =   3 0 3 .1 4 1 5 9 3 . . . . . . 
 
z =  1300032.174118529832............

This will be bijective for non-negative real numbers. In order to obtain a
bijective mapping R <-> R^2 this has to be combined with a bijection
which maps real numbers to non-negative real numbers (right now, I
don't remeber by heart how this is done, but it is possible).

------------------
Henner Eisen
 
  


Newsgroups: sci.math
From: roach@bikini.wri.com (Kelly Roach)
Subject: Re: Can you prove it?
Organization: Wolfram Research, Inc.
Date: Thu, 20 Aug 1992 21:04:00 GMT

In article <1992Aug20.055633.19046@nuscc.nus.sg>  
bhonsle@bhonsle.iss.nus.sg (Shailendra K Bhonsle) writes:
> Hi
> I have a simple problem, can you prove or disprove it? I will appreciate  
all replies:
> 
> Problem:
> 
> Prove that for primes p & q, q<p
> 
> if 2^(p-1) == 1 (mod q^2)
> 
> then either 2^(q-1) == 1 (mod q^2) or q | p-1  { q divides (p-1}


     The case q=2 is trivial, so suppose q is odd.  Let

     ord(2,q^2) == minimum x>0 such that 2^x==1 (mod q^2)

By elementary number theory,

(1)  ord(2,q^2) | phi(q^2) == q(q-1)

where phi() is the Euler phi function.  Now suppose

     2^(p-1) == 1 (mod q^2)
     2^(q-1) != 1 (mod q^2)

These equations give us

(2)  ord(2,q^2) | p-1
(3)  ord(2,q^2) does not divide (q-1)

Putting (1) and (3) together we get

(4)  q | ord(2,q^2)

Putting (2) and (4) together we get q | p-1.

				QED


      We need q prime to get (4).  We didn't really
need p to be prime nor q<p for the proof to work.  We
just need p to be odd (for the trivial case q=2).




Newsgroups: sci.math
From: dzk@cs.brown.edu (Danny Keren)
Subject: Re: Is Card(R)=Card(R^2)? (yes, and a question)
Organization: Brown University Department of Computer Science
Date: Thu, 13 Aug 1992 04:43:51 GMT

In article <1992Aug12.102140.5231@nntp.hut.fi> samu@lammio.hut.fi writes:

#I have been wondering... It seems first that there are more pairs of
#real numbers than real numbers, but is it really so? And if not, I would
#like to see a bijective mapping f:R->R^2. And furthermore, is there some  
#relation between Card(R) and Card(R^n)?

The cardinalities are the same, since Card(R)=2^aleph0 
(aleph0=Card(integers)). Hence:

Card(R^2)=Card(R) X Card(R) = 2^(aleph0+aleph0)=2^aleph0=Card(R).

(This extends immediately to show Card(R)=Card(R^n) for every integer n).

To build a bijection R-->R^2, take every real number, write it in its
decimal expression, and map it to the real pair of numbers consisting
of the odd and even digits in the expansion. Actually, there is even a
*continuous function* from the unit interval onto the unit square! Peano
gave the first such fuction, which stunned many mathematicians...

If I recall correctly, the fact that for *every* infinite cardinality
alpha it is true that alpha = alpha X alpha is equivalent to the
axiom of choice (help, anyone? I can prove that the axiom of choice
implies alpha = alpha X alpha, what about the other direction?).


-Danny Keren.
From: popx@vax.oxford.ac.uk
Newsgroups: sci.math
Subject: Re: Why are Some Journals so Expensive?
Date: 16 Aug 92 16:44:06 GMT
Organization: Oxford University VAX 6620

In article <92221.182456U53644@uicvm.uic.edu>, U53644@uicvm.uic.edu writes:
> You hit the nail on the head - the difference between profit and nonprofit
> publishing. The latter will obviously make for cheaper publications. The
> example given even is an example of someone doing what I recommended some of
> the previous posters should do : gather together some colleagues to form an
> editorial board, and put out your own journal at a lower price. 
> ...  
> Since the publishing houses are in this for the money (as is their right), if
> the Mathematics community wants to see cheaper publications, it should consider
> putting them out itself. It's already producing the contents - why not go the
> final step, and arrange production (desk-top publishing)...
> ... 
>                                               Joseph B. Dunphy
> 
How many mathematicians lack access to electronic mail, LaTeX, and
PostScript printers? Have all articles submitted (or re-cast) to
use LaTeX, with any diagrams that can't be handled by the picture
environment included as PostScript specials. Distribute the result to
subscribers by electronic mail, or from an FTP site. In the latter case,
you might want some method to prevent those who haven't paid from receiving
copies, but I should think that's feasible. It's the subscriber's
responsibility to print the articles: to help him/her decide which are
worh printing, include a table of contents and set of abstracts in 
plain ASCII text.

I am really surprised that no-one has considered this before (at least,
I have never seen it suggested).

Jocelyn Paine
Experimental Psychology
Oxford
From: schlegel@cwis.unomaha.edu (Mark Schlegel)
Subject: Re: tensors
Organization: University of Nebraska at Omaha
Date: Thu, 20 Aug 1992 20:41:58 GMT

frisinv@alleg.edu writes:

>  I was reading a book on general relativity and the author began talking  
>about tensor analysis, something I'd never heard of. I get the feeling  
>tensors are some sort of number, but I'm not sure. Could anyone enlighten  
>me as to what they are and how to use them?
>----
>Vince

Tensors are very useful in physics and are generally the next level of
complexity beyond vectors.  The simplest tensors are those of second rank
which contain nine terms (usually scalars and vectors are not called tensors
but they do belong to the tensor family) usually the name "tensor" refers
to those of rank 2 and above but tensors generally as a class also
contain scalars and vectors like this:

a tensor has 3^N terms where N is the rank number

tensors of zero order contain 3^rank terms --> or 3^0 = 1 term
which signifies only magnitude  this is a SCALAR

tensors of rank one contain 3^1 terms = 3 terms --> a VECTOR which symbolizes
a magnitude and direction

tensors of rank two, ---> 9 terms
           rank three --> 27     and so on
           

an interesting example of a second rank tensor occurs in solid state physics,
the tensor that describes the stresses in three dimensions including the
stress normal to and perpendicular to an area is the stress tensor

Pxx is the pressure in the x direction on a surface normal to the x direction 
term while Pxy is the shear in the y direction perpendicular to the x direction
so this tensor can be written

        Pxx  Pxy  Pxz           the P's are forces per unit area
        
        Pyx  Pyy  Pyz
        
        Pzx  Pzy  Pzz              this is written in the form of a matrix
                                        (3 by 3)
                                        
General Rel. uses even higher order tensors than the second order, however 
frequently many of the terms are zero.

Mark Schlegel
Newsgroups: sci.math
From: achim@unibi.uni-bielefeld.de (Achim Flammenkamp)
Subject: factorization algorithmn wanted
Date: Thu, 20 Aug 92 18:33:43 GMT
Organization: Universitaet Bielefeld

I am looking for an integer factorization algorithmn which is public availible.

I have typed in one, Shanks algorithmn, which can handle up about 40 digit
numbers in a reasonable amount of time.
I know today there is no problem to factorize arbitrary numbers of 80 decimal
digits and even longer! But I don't want to spend time to implement, test and
refine one of the well known sophisticated factorization methods if other
people have done this already. :-)

achim
From: kriman@acsu.buffalo.edu (Alfred M. Kriman)
Newsgroups: sci.math
Subject: Indices (was Re: Littlewood's Three Principles)
Date: 22 Aug 92 08:16:47 GMT
Organization: "UB" = State University of New York at Buffalo

In <16di3cINNpd2@function.mps.ohio-state.edu> (an article acknowledging net
assistance finding a Littlewood quote), Gerald Edgar
(edgar@function.mps.ohio-state.edu) complains:
>One of my most frequent complaints about technical books is inadequate
>(or even nonexistent) index!

My two cents:  I believe that Kurt Vonnegut has one of his characters
complain that authors should not write the indices of their own work,
because the writing of a good index is a specialized professional task
they rarely are suited for.  I think this appears in
_God bless you, Mr. Rosewater_ (which I don't have near to hand),
and I also think that book has no index.
-------
"Reading is sometimes an ingenious device for avoiding thought."
  [_Friends in Council_, Sir Arthur Helps]
(Or work.)
Newsgroups: sci.math
Subject: Re: Can you prove it?
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 20 Aug 92 15:47:05 GMT
Keywords: Number theory

In <1992Aug20.055633.19046@nuscc.nus.sg> bhonsle@bhonsle.iss.nus.sg (Shailendra K Bhonsle) writes:

>Hi
>I have a simple problem, can you prove or disprove it? I will appreciate all replies:

>Problem:

>Prove that for primes p & q, q<p

>if 2^(p-1) == 1 (mod q^2)

>then either 2^(q-1) == 1 (mod q^2) or q | p-1  { q divides (p-1}


Actually, Bob's "proof" is wrong.  However, ....

2^phi(q^2) == 1 (mod q^2), so (as phi(q^2) = q(q-1)), 
2^GCD(p-1,q(q-1)) == 1 (mod q^2).

If q does not divide p-1, then GCD(p-1,q(q-1)) = GCD(p-1,q-1) | q-1, so
2^(q-1) = 1 (mod q^2).
--
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: rickert@NeXTwork.Rose-Hulman.Edu (John H. Rickert)
Newsgroups: sci.math
Subject: history of radians
Date: 13 Aug 92 21:45:10 GMT
Organization: Rose-Hulman Institute of Technology


Today a student asked me when radians were 
first used as measures of angles.
I know that degrees came from the Babylonians, 
but who came up with radians?

john rickert
rickert@nextwork.rose-hulman.edu
Newsgroups: sci.math.research
From: Allan Adler <ara@zurich.ai.mit.edu>
Subject: Bott-Tate formula
X-Submissions-To: sci-math-research@uiuc.edu
Organization: M.I.T. Artificial Intelligence Lab.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Sat, 22 Aug 1992 02:18:04 GMT


Does anyone know of a paper in which the formula of Bott and Tate is stated
and proved? The formula gives a number f(n,r) such that every nonsingular 
hypersurface of degree d in projective n space has an automorphism group
of exponent f(n,r).

Allan Adler
ara@altdorf.ai.mit.edu

Newsgroups: sci.math.research
From: victor@watson.ibm.com (Victor Miller)
Subject: Re: The character group of k((x))
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
Reply-To: victor@watson.ibm.com
X-Submissions-To: sci-math-research@uiuc.edu
Organization: IBM, T.J. Watson Research Center
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Mon, 17 Aug 1992 20:07:36 GMT

I received the following answer, which is just what I'm looking for:



Date: Mon, 17 Aug 92 21:08:24 +0200
From: Torsten Ekedahl  <teke@matematik.su.se>
Message-Id: <9208171908.AA11751@candida.matematik.su.se>
To: victor@watson.ibm.com
Subject: The character group of k((x))

Andre Weils Basic Number Theory (Springer Grundl d. math. Wiss. 144),
particularly II:5, discusses this. Indeed, k((x)) is self dual as
topological dual, k[[x]] is a compact subgroup with discrete quotient
and is its own annihilator for a suitable normalisation of the self
duality.

--
			Victor S. Miller
			Vnet and Bitnet:  VICTOR at WATSON
			Internet: victor@watson.ibm.com
			IBM, TJ Watson Research Center
From: albers@fields.UWaterloo.ca (Sheri L. Albers)
Newsgroups: sci.math.research
Subject: Conference on Conservative Systems and Quantum Chaos
Date: 12 Aug 92 17:28:08 GMT
Organization: University of Waterloo
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu


THE FIELDS INSITITUTE FOR RESEARCH IN
MATHEMATICAL SCIENCES

presents
a five day workshop on

"Conservative Systems and Quantum 
Chaos"

Wednesday October 21 to Sunday October 25, 1992

Workshop Coordinators:

Larry Bates,University of Calgary
David Goodings, McMaster University
David Rod, University of Calgary

The workshop will focus on bifurcation and integrability 
problems in Hamiltonian systems.  Nonlinear normal 
modes and normal form theory in classical and quantum 
contexts will be considered.  Furthermore, the classical-
quantum correspondence in nonintegrable Hamiltonian 
systems will be explored by means of the Gutzwiller trace 
formula and its extensions, including dynamical zeta 
functions.  The list of confirmed speakers to date includes:  
M. Berry, T. Bridges, P. Brumer, P. Cvitanovic, M. 
Gutzwiller, M. Kummer, E. Lacomba, E. Lerman, D. 
Lewis, J. Marsden, K. Meyer, J. Montaldi, D. Offin, G. 
Patrick, J. Robbins, R. Sjamaar, B. Sleeman, F. Steiner, I. 
Stewart, J-C. Van der Meer, S. Wiggins.

Please register for the above no later than October 16, 1992. 
Return the registration form by fax at (519)725-0704 or 
e-mail: chaos@fields.waterloo.edu and include name, 
mailing address, 
e-mail address and fax number.

During the workshop (October 22, 23 and 24, at 9:00 
am each day) Professor Michael Berry will present 
three lectures as part of the Fields Institute 
Distinguished Lecture Series.
Newsgroups: sci.math.research
From: victor@watson.ibm.com (Victor Miller)
Subject: The character group of k((x))
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
Reply-To: victor@watson.ibm.com
X-Submissions-To: sci-math-research@uiuc.edu
Organization: IBM, T.J. Watson Research Center
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Mon, 17 Aug 1992 15:47:12 GMT

Can anyone point me to an article which discusses the group of
continuous characters of k((x)) (Laurent series in x) where k is a
finite field?  I vaguely seem to remember that using this groups
should give some sort of duality between k((x))/k[x] and k[x].
--
		Victor S. Miller
		Bitnet: VICTOR at WATSON
		Internet: victor@watson.ibm.com
		IBM, TJ Watson Research Center
		"Great artists steal; lesser artists borrow" Igor Stravinsky

Newsgroups: sci.math.research
From: rfedkiw@math.ucla.edu (Ronald Fedkiw)
Subject: Axisymmetric Navier Stokes Equations
X-Submissions-To: sci-math-research@uiuc.edu
Organization: UCLA Mathematics Department
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Sun, 16 Aug 1992 21:31:11 GMT

I'm trying to do a calculation of the full compressible Navier Stokes
equations for flow past an axisymmetric blunt body.
So, I put the equations into axisymmetric form and multiply
through by 1/Jacobian = r = distance from centerline (of axisymmetry).
I need to do this to put the equations back into conservative form for 
my method.
The obvious problem is that the equations are no longer valid along
the axis of symmetry (where r = 0). The Jacobian here is infinite.
I'm not quite sure what the implications of an infinite Jacobian are,
but from looking at my equations it becomes obvious that they cannot 
be used to solve the flowfield at r=0.

I was wondering what sorts of methods ae in common practice to solve
for the flowfield near r=0.
The solution is important here since this is where the flow passes
through the strongest portion of the shockwave. (It's a normal shock
at r=0 and the heating is high, also this is the where the stagnation
streamline lies.)
So, I need a good method, this might be the most important part of the flow!

Any help is greatly appreciated.

(I've thought about bounding the domain of the grid away from r=0,
 by 1/2 of a grid cell, but what boundry condition would I use?)

Ron Fedkiw

--
Ron Fedkiw (rfedkiw@redwood.math.ucla.edu)

A plan is made by someone who is sitting and thinking ...
while others are doing.
From: ara@martigny.ai.mit.edu (Allan Adler)
Newsgroups: sci.math.research
Subject: Re: Bott-Tate formula
Date: 23 Aug 92 14:40:02 GMT
Article-I.D.: life.9208231435.AA06548
Organization: University of Illinois at Urbana
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu

I have found the answer to my question about the Bott-Tate formula. There is
a paper by J.E.Schneider in J.Alg.27 (1973) 112-116 which contains this.
Newsgroups: sci.math.research
From: Allan Adler <ara@zurich.ai.mit.edu>
Subject: Re: The character group of k((x))
X-Submissions-To: sci-math-research@uiuc.edu
Organization: M.I.T. Artificial Intelligence Lab.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Mon, 17 Aug 1992 19:44:51 GMT

In article <VICTOR.92Aug17114712@terse4.watson.ibm.com> victor@watson.ibm.com (Victor Miller) writes:

   Can anyone point me to an article which discusses the group of
   continuous characters of k((x)) (Laurent series in x) where k is a
   finite field?  I vaguely seem to remember that using this groups
   should give some sort of duality between k((x))/k[x] and k[x].




See Andre Weil's book Basic Number Theory.

Allan Adler
ara@altdorf.ai.mit.edu


Newsgroups: sci.math.research
From: shillsp@leonardo.cs.curtin.edu.au (Stephen Hill)
Subject: linear programming HELP REQUIRED
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Curtin University of Technology
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Tue, 18 Aug 1992 07:45:27 GMT
Keywords: linear programming



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!                     
------------------------------------------------------------------------------
From: agw@ibc.cs.columbia.edu (Art Werschulz)
Newsgroups: sci.math.research
Subject: Analyticity of solutions of elliptic PDEs
Date: 12 Aug 92 16:51:16 GMT
Reply-To: agw@cs.columbia.edu
Organization: UTexas Mail-to-News Gateway
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu

Hi.

% If you want to TeX this, uncomment the next line
%  \input amssym.def  \input amssym

Let $\Omega\in{\Bbb R}^d$ and $\Omega_1\in{\Bbb C}^d$ be simply
connected regions having analytic boundaries, with the closure
of~$\Omega$ contained in the interior of~$\Omega_1$.  Let $L$ be a
strongly elliptic operator of order $2m$, whose coefficients are
analytic in~$\Omega_1$.  Let $B_0,\ldots,B_{m-1}$ be boundary
operators on~$\partial\Omega$, whose coefficients are analytic functions.
Let $(L,B_0,\ldots,B_{m-1})$ be a strongly elliptic boundary value
problem over~$\Omega$.  Let $u$ be the solution of the problem
$$\displaylines{
Lu=f \qquad\hbox{\rm in }\Omega,\cr
B_0 u=\ldots=B_{m-1}u = 0 \qquad\hbox{\rm on }\partial\Omega.
}$$

If $f$ is analytic on~$\Omega_1$, is it true that $u$ is also analytic
on~$\Omega_1$, and that
$$\|u\|_{\sup,\Omega_1} \le C \|f\|_{\sup,\Omega_1}$$
for some constant~$C$, independent of~$f$ and~$u$?

Thanks.

%      Art Werschulz
%      InterNet:  agw@cs.columbia.edu
%      ATTnet:    Columbia University (212) 854-8348 854-2736
%                 Fordham University  (212) 636-6325
From: MTURELLA@cmsa.gmr.com
Newsgroups: sci.math
Subject: Re: mathematician's marrying ages.
Date: 13 Aug 92 15:25:27 GMT
Organization: GM Research Labs

In article <hubert.713379330@spica>
hubert@spica.ucsb.edu (Chang;Hung-Hsien;H.;;;COMS;Graduate;930630;;;8-402525-199

>
>My friend (yu@math.harvard.edu) keep advocating that marrying
>early is good for mathematician.  He gave several examples
>( most of them are number theorist, according to his statemnet)
>Examples he gave are Delinge, Gauss, Milnor, Serre, Zariski.
>He told me that he got these information from bibliography
>(maybe from introduction to authors...etc)
>
>Any counterexample? ( Marry late and have quite an achievement )
>
>
>

Not much info is given above to have any statistical basis.

I will although make an assumption ...  I assume your friend is
married.

You know that misery loves company ...

Mark

P.S.
  I'm 34 and will be getting married in October ... but I don't
  consider that early in life.