HDTenEightyP/NetNews huggingface dataset:
From: steele@isis.cgd.ucar.edu (Alfred Steele)
Subject: Euclidean Domain
Organization: Climate and Global Dynamics Division/NCAR, Boulder, CO
Date: Fri, 8 Jan 1993 21:14:40 GMT


In article <HAMMOND.93Jan3134111@annemarie.albany.edu>, hammond@csc.albany.edu (
William F. Hammond) writes:
|> In article <Jan.3.02.05.44.1993.24643@spade.rutgers.edu>
|>    cadet@spade.rutgers.edu (Uniquely TiJean) writes:
[....]

|>If someone can answer the question:
|>Why there are not other candidates for the Euclidean function?

I have asked the very same question and do not know the answer.  The previous
posters have made reference to Hungerford's Algebra Text
Hungerford's definition does not use the norm - this is true of most
texts.  His problem #8 Chapter III section 3 (in my edition) asks to show
a + b(1 + sqrt(19)) a,b \in Q is a principal ideal domain but not a
Euclidean domain.  My guess is that any function that satisfies Hungerford's
definition of Euclidean domain:
f : R - {0} \arrow N
a) a,b \in R and ab \notequal 0 then f(a) \le f(ab)
b) usual definition with division and f(r) \lt f(b) or r = 0 in
   a = qb + r 
will be equivalent to a norm.  Something like this is Ostrowski's theorem
which states that non-trivial norms (or valuations) are either absolute
values or p-adic norms.

Any information netters know about this, I would be interested in hearing
about.  What is the "folklore" on the subject?
Alfred T. Steele
steele@isis.cgd.ucar.edu
Newsgroups: sci.math
From: kavuri@lips1.ecn.purdue.edu (Surya N Kavuri )
Subject: Re: sum of eigenvalues of a covariance matrix = trace ?
Organization: Purdue University Engineering Computer Network
Date: Mon, 11 Jan 1993 18:09:49 GMT

In article <1ipnacINNd5k@function.mps.ohio-state.edu>, edgar@math.ohio-state.edu (Gerald Edgar) writes:
> In article <1993Jan9.194845.8567@noose.ecn.purdue.edu> kavuri@lips1.ecn.purdue.edu (Surya N Kavuri ) writes:
> >
> >  Is the sum of the eigenvalues of a covariance matrix equal to 
> >   its trace ?
> 
> The sum of the eigenvalues of any square matrix is equal to its trace.
> You have to allow complex eignevalues, and you have to count multiplicity.
> This works even for matrices that are not diagonalizable.
                                      ^^^^^^^^^^^^^^^^^^^^

This is very interesting. Are there any restrictions on the 
type of the square matrix ?

> 
> 
> -- 
>   Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
>   Department of Mathematics      Bitnet:    EDGAR@OHSTPY
>   The Ohio State University      telephone: 614-292-0395 (Office)
>   Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: Fields Medal Winners
Date: 10 Jan 93 00:41:36 GMT
Organization: U of Cambridge, England

In article <1452@kepler1.rentec.com>, andrew@rentec.com (Andrew Mullhaupt) writes:

> I'm a bit surprised at the idea that the tripos still existed in 1950,
> since Hardy successfully abolished them but did not see 1950. Can
> anyone clear this up?

Er, what? I wonder what the exam I sat a year and a half ago was, then.
Hardy (and others) *reformed* the Tripos very greatly, but it's alive and
well, and Part III (what used to be Part II; now a post-graduate course)
is as crap as ever.

[Er, I need hardly add that the views expressed above do not represent etc.]

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
From: liuli@unixg.ubc.ca (Li Liu)
Newsgroups: sci.math
Subject: Re: proof wanted 2
Date: 10 Jan 1993 10:53:31 GMT
Organization: University of British Columbia, Vancouver, B.C., Canada
NNTP-Posting-Host: unixg.ubc.ca

>>Is it true that if  C  is a nonempty closed subset of R  and x is a point not
>>in  C  that there exists a point c in C that is closest in C to x.
>> 
>>i.e. such that:   |x-c'| >= |x-c| for all c' in C.

This is not true for general metric spaces. 

In a previous followup, I made
a stupid mistake. My example was 
{1/n | n=1,2,...} = "The metric space" = 
C. And x=0. Notice that x is not in the metric space!


Here is a better example:

Let X be the set of all functions on [0,1]. For any two functions f and
g on [0,1], the distance d(f,g) is defined as

   d(f,g)= sup{ |f(r)-g(r)|, where r is in [0,1] }.

Then <X,d> is a metric space. 

Define:

f_n( 1/n) = 0.5 + 1/n
f_n( r ) = 0            for all other r in [0,1].

Then C={ f_n |n=1,2,3, ...} is a closed set. You can verify that there is no
converging sequence in this set because the distance between every pair
of functions is larger than 0.5  .

Take a point f_0 = 0. There is no closet point in C to f_0.
From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers)
Newsgroups: sci.math
Subject: Re: Fields Medal Winners
Date: 11 Jan 93 19:25:35 GMT
Organization: Computer Science Dept, QMW, University of London

In <1993Jan10.004136.11719@infodev.cam.ac.uk>
gjm11@cus.cam.ac.uk (G.J. McCaughan) writes:

>Part III (what used to be Part II; now a post-graduate course)
>is as crap as ever.

That must be why I got 0 marks in it. :-) :-)
--
Gus Rodgers,  Dept. of Computer Science, | Cinema's worst romantic dialogue? --
Queen Mary & Westfield College, Mile End | "Mechagodzilla's brain is  installed
Road, London, England.   +44 71 975 5241 | in my stomach!" "I don't care if you
E-mail (JANET):   arodgers@dcs.qmw.ac.uk | are a cyborg  --  I still love you!"
From: dboese@spartan.ac.BrockU.CA (Darcy Boese)
Newsgroups: sci.math
Subject: Re: bitonic sorting networks
Date: 10 Jan 93 19:22:58 GMT
Organization: Brock University, St. Catharines Ontario
X-Newsreader: Tin 1.1 PL4

> 
> Would someone define a bitonic sorting network and
> tell me where I might obtain some info? I believe
> they are used in signal processing. 
>

Try Knuth's _The Art of Computer Programming Volume 3_

I don't know about the signal-processing part, but the sorting network
is described in some detail... look for it under the headings bitonic
sorting network and Batcher's sorting network...
Newsgroups: sci.math
From: rsilver@world.std.com (Richard Silver)
Subject: bitonic sorting networks
Organization: The World Public Access UNIX, Brookline, MA
Date: Sun, 10 Jan 1993 10:47:19 GMT


Would someone define a bitonic sorting network and
tell me where I might obtain some info? I believe
they are used in signal processing. 

Thanks.
From: bevan@cs.man.ac.uk (Stephen J Bevan)
Newsgroups: sci.math
Subject: Re: High Prices of Math Books. I am pissed.
Date: 6 Jan 93 21:52:56 GMT
	<1idj1gINNhah@roundup.crhc.uiuc.edu>
	<1993Jan6.151149.7824@infodev.cam.ac.uk>
Organization: Department of Computer Science, University of Manchester
In-reply-to: gjm11@cus.cam.ac.uk's message of 6 Jan 93 15:11:49 GMT

In article <1993Jan6.151149.7824@infodev.cam.ac.uk> gjm11@cus.cam.ac.uk (G.J. McCaughan) writes:

   There is much to be said for providing education on equal terms for
   all, or at least for discriminating on the basis of ability rather
   than of wealth.  And it can be done without bankrupting the
   government; the UK has had such a system for ages, and it has
   worked all right.

I think the current government might disagree with your analysis, or
they wouldn't have introduced a partial loans scheme to save
themselves money.  As to the subject line: each new intake of students
complains about the price of books (I'm sure I did).  If you can't
afford a book, borrow it from a friend, club together with others and
buy one copy between you or make friends with a rich student and
borrow all their books :-)  Alternatly try asking a faculty member or a
graduate student if they are willing to lend out their books.
Personally I'm not so keen on this since the some of the books I
lent out came back looking rather worse for wear, but with enough
begging and promises to treat the book with reference, you might get
lucky.

bevan
From: menissie@ausone.inria.fr (Valerie Menissier-Morain)
Newsgroups: sci.math
Subject: Re: sum(i=1 to n, i^3) = ??   URGENT !!
Date: 8 Jan 93 10:37:40 GMT
Organization: INRIA * Rocquencourt BP 105 * F-78153 LE CHESNAY CEDEX* France

In article <8979@lhdsy1.lahabra.chevron.com>, jgrij@lhdsy1.lahabra.chevron.com (Joey J. Griffin) writes:
|> 
[deleted]
|> 1^3 + 2^3 + 3^3 + ... + n^3 = (1 + 2 + 3 + ... n) ^ 2
|>        Proof by induction.
-- 

In fact there is a very beautiful geometrical proof of this assertion:

        If you consider two squares with each side of length
        (1+2...+(n-1)) and (1+2+...+n), the difference of the surfaces
        of these two squares is exactly n^3 as on the following
        figure:

              ------------------------
              |/ / / / / / / / / / / |
              |/ / / / / / / / / / / |
              |/ / / / / / / / / / / |
            n |/ / / / / / / / / / / |
              |/ / / / / / / / / / / |
              |/ / / / / / / / / / / |
              |/_/_/_/_/_/ / / / / / |
              |         |\ \ \ \ \ \ |
              |         |\ \ \ \ \ \ |
(1+2+...+n-1) |         |\ \ \ \ \ \ |
              |         |\ \ \ \ \ \ |
              |_________|\_\_\_\_\_\_|

             (1+2+...+n-1)    n

        The difference of the two surfaces is: 

                n*((1+...+n-1)+n) (the upper rectangle / / /)
        +       (1+...+n-1)*n     (the lower rectangle \ \ \)
        =       n*(2*(1+...+n-1)+n) = n^3

------------------- Vale'rie ME'NISSIER - MORAIN -----------------------------
INRIA Projet Formel			        Tel: (33 1) (16 1) 39 63 55 98
Domaine de Voluceau		                Fax: (33 1) (16 1) 39 63 53 30
78153 Rocquencourt			     e-mail: menissie@margaux.inria.fr
BP 105
------------------------------------------------------------------------------
Newsgroups: sci.math
Subject: Re: High Prices of Math Books. I am pissed.
From: pete@bignode.equinox.gen.nz (Pete Moore)
Date: 8 Jan 93 11:53:14 +1200
Reply-To: pete@bignode.equinox.gen.nz
Organization: Equinox Networks
X-Newsreader: TIN [version 1.1 PL8]

I've been following this thread with interest from the beginning (I still
get a smile from the subject line; we say `pissed off' in this part
of the world, and use `pissed' as a rude synonym for `intoxicated').

Allan Adler (ara@zurich.ai.mit.edu) wrote:

>I heard a rumor that Serge Lang can knock off a book in
>a weekend.

Ah! I guess that explains why

(1) there are so many books by Serge Lang
(2) `avoid Serge Lang' is a useful rule of thumb when looking for good
    textbooks.


On the subject of textbook prices, may I join the rest of the non-Americans
on the net in saying: I wish our paperbacks were as inexpensive as the
hardbacks you Americans are complaining about.
--
 +-------------------  pete@bignode.equinox.gen.nz  -------------------+
 | The effort to understand the universe is one of the very few things |
 | that lifts human life above the level of farce, and gives it some   |  
 | of the grace of tragedy   -  Steven Weinberg                        |
 +---------------------------------------------------------------------+
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: Finding best mate
Date: 5 Jan 93 04:41:01 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <your-email-addr-040193123900@microlab22.med.upenn.edu> your-email-addr@a1.mscf.upenn.edu (Jesse Goldman) writes:
>Dear Mathematicians;
>
>     This weekend I saw an interview on T.V. with a mathematician who
>stated that if a woman assumes she is to have 100 suitors in her life then
>her best
>chances of finding an ideal mate would be to reject the first 37 and then
>choose the next one better than the preceeding 37.
>     I am not a mathematician or physicist but I understand that this has
>something to do with e (root of natural log).  Could any of you math dudes
>or dudettes explain this to me?  Thanks in advance.

I've heard this called the 'princess problem' and it is completely worked
out in Sheldon Ross's _Introduction to Stochastic Dynamic Programming_
which is a smart little volume, BTW.

The general strategy to pick among n suitors is to pass on the first n/e
and then pick the first one you encounter which is better than what you've
seen so far. Your chances of getting the best one are about 1/e, which is
surprisingly large.

It might make more sense to minimize the down side on this one, however...

Later,
Andrew Mullhaupt

Newsgroups: sci.math
From: clin@eng.umd.edu (Charles Lin)
Subject: Re: High Prices of Math Books. I am pissed.
Date: Sat, 09 Jan 93 20:20:15 GMT
Organization: College of Engineering, Maryversity von Uniland, College Park
Originator: clin@modulation.eng.umd.edu


In article <pete.03o4@bignode.equinox.gen.nz>, pete@bignode.equinox.gen.nz (Pete Moore) writes:
>
>On the subject of textbook prices, may I join the rest of the non-Americans
>on the net in saying: I wish our paperbacks were as inexpensive as the
>hardbacks you Americans are complaining about.

    I have heard (and seen) paperbacks sold in India (and possibly Taiwan)
which are sold for a fraction of the cost in the US.   I suspect these
countries have pretty lax copyright laws, and no one could really afford
the equivalent of a thirty dollar American book in rupees, anyway.  The
two combined means that companies that want to make any money on the book,
have to sell it dirt cheap.   The paper quality is usually not quite as
good though.

    I suppose it might be possible to have professional societies attempt
to sell books.   Assuming the mathematicians are the ones in control
of their own professional societies, they could probably find ways of
keeping the prices reasonable, and still get a decent royalty.

--
Charles Lin
clin@eng.umd.edu

Newsgroups: sci.math.research
From: "John C. Baez" <jbaez@BOURBAKI.MIT.EDU>
Subject: surfaces in R^4
Originator: dan@symcom.math.uiuc.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: MIT Department of Mathematics, Cambridge, MA
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Sat, 9 Jan 1993 00:38:26 GMT

I am getting interested in compact 2-manifolds embedded in R^4.
Consider such a thing and call it S.  Let S_t be the intersection of S
with the surface {(x,y,z,t): (x,y,z) in R^3}.  If S is generic it seems to
me that for all but finitely many values of t, S_t will be a link in
R^3, and at the finitely many "bad" values of t S_t will be a link
with a single transverse selfintersection OR a link union a single
isolated point.  I guess we can use Morse theory to show this, taking t
as a Morse function and noting that there are 2 kinds of critical
points, saddle points and extrema, which give the 2 cases above.

There is a little about this in the section Knotted 2-spheres in an
article by Fox in Topology of 3-manifolds and Related Topics, ed. Fort.
The references there all antedate 1962; can anyone direct me to more
recent stuff, especially surveys?  Can anyone tell me what, if anything,
this has to do with Donaldson theory and link invariants?  

Can anyone direct me to similar stuff that treats the case of generic
immersed rather than embedded surfaces?  Generically an immersed surface
in R^4 should have some transverse double points and these should spice
things up a bit.  I would like to know how the picture I paint in the
first paragraph generalizes to this case; I *think* I know but haven't
gone through it carefully.

Of course, not only references but also general wisdom about this kind
of thing would be greatly appreciated.  

Newsgroups: sci.math.research
From: milanfar@athena.mit.edu (Peyman Milanfar)
Subject: Standard Beta Function
Originator: dan@symcom.math.uiuc.edu
Followup-To: milanfar@athena.mit.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Massachusetts Institute of Technology
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Mon, 11 Jan 1993 20:03:00 GMT

I have a sort of mundane question.
Let the standard Beta function be defined by

B(\frac{a+1}{2},\frac{b+1}{2})=
 2 \int_{0}^{\pi/2}\sin^a(\theta)\cos^b(\theta)d\theta.

I need a tight upper and lower bounds on $B$ when $a$ and $b$ are even positive
integers. A very simple upper bound in this case is B((a+1)/2,(b+1)/2) < \pi .
I need something stronger.
Any references to the literature, etc. is appreciated.

Thanks
Peyman Milanfar

Newsgroups: sci.math.research
From: aap@cs.brown.edu (Andrea A. Pietracaprina)
Subject: Question regarding PGL groups
Originator: dan@symcom.math.uiuc.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Brown Computer Science Dept.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Mon, 11 Jan 1993 15:05:35 GMT

Hello,
does anyone know a solution to the following problem?

Let PGL(2,k) be the Projective General Linear group of 2 X 2 matrices
with entries from the finite field with k elements, where k is a
prime power. Let q be an even prime power and n and integer > 2. Consider
the quotient

                  PGL(2,q^n) / PGL(2,q)

As known, it consists of [(q^n+1) q^n (q^n-1)] / [(q+1) q (q-1)] elements,
i.e., cosets of PGL(2,q). Is there an ordering of these cosets such that
given an index i it is easy to determine the i-th coset? By easy I mean
requiring *a few* operations in the field.

I would greately appreciate suggestions and/or pointers to the literature.
Thanks in advance.

andrea pietracaprina


Newsgroups: sci.math.research
From: squash@math.ufl.edu (Jonathan King)
Subject: Rectangular tiling conditions
Originator: dan@symcom.math.uiuc.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Florida Department of Mathematics
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Mon, 11 Jan 1993 16:14:37 GMT

Given a finite set T of rectangular tiles, with integer sidelengths, I'm
interested in characterizing those rectangles NxK which can be tiled by copies
of the tiles in T.  Here, copies are all parallel to the axes.  (Actually, for
my purpose it is permissible to allow negative copies; to allow part of one
copy to cancel-out part of another copy.)

Can someone provide a pointer to an "iff condition" for when NxK can be tiled
by T?  [I know a necessary condition, and a sufficient condition, and wish to
decide if it is worthwhile determining if they are equivalent.]

		Jonathan,		squash@math.ufl.edu 

Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: spell this?
Organization: Computer Science Department,  Stanford University.
Date: Tue, 12 Jan 1993 07:00:26 GMT

In article <1isvrsINNe11@master.cs.rose-hulman.edu> goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard) writes:
>
>The raging debate here is the correct spelling of (choose one and 
>supply a reference):
>
>a) nilpotentcy
>b) nilpotency
>c) other

"Nilpotentcy" describes Dan Quayle's chances for the 1996 presidential
elections.

To decide between nilpotency and nilpotence I grepped for "potenc" in
some 300 technical papers I had online and found 37 occurrences of
"idempotenc..".  Generally "idempotency" was preferred, only a couple
of authors used "idempotence."  (I confess to being one of them.)

I then browsed around in Webster's New World Dictionary, Funk and
Wagnall's Standard College Dictionary, and the Oxford English
Dictionary (unabridged, 16,464 pages).  None had either "idempotent" or
"nilpotent".  However all three explained "-ence" vs. "-ency".  F&W
(US) and OED (UK) agreed that "-ency" was used for static qualities and
"-ence" for dynamic (cf. state of emergency vs. act of emergence---if
you disagree write to the dictionaries, not me), whereas Webster did
not draw this distinction and gave the same meaning for both endings.
On the other hand both F&W and Webster gave "impotence" as the primary
usage and "impotency" as a secondary equivalent.  But so as to be truly
democratic in such matters they both reversed this for "potence" vs.
"potency", preferring the latter.

This is enough ammunition for any mercenary willing to argue either
side, almost guaranteeing a win against a more lightly armed opponent.
And you should have no difficulty arguing either side of whether
nilpotence is a static or dynamic quality.

As for me I'm going to stick to "idempotence" and "nilpotence," which
somehow sound nicer to my ear.
-- 
Vaughan Pratt			There's safety in large condition numbers.
From: isaacs@hpcc01.corp.hp.com (Stan Isaacs)
Date: Mon, 4 Jan 1993 06:51:43 GMT
Subject: Re: Banach-Tarski (_NOT_ Re: Bayes' theorem and QM)
Organization: the HP Corporate notes server
Newsgroups: sci.math

> 
> What would really help me at this point is if someone
> could email me a decent explanation of this (or at least
> a direct pointer to a sufficient reference):

The clearest discussion I know is the article "The Banach-Tarski
Theorem", by Robert M. French, in the Fall, 1988 issue of The
Mathematical INtelligencer, Vol 10, No. 4, pp. 21-28.  It was the
first article that made clear to me (as a non-mathematician) just what
was involved in the proof, how it worked, what it meant, etc.

I would expect the book "The Banach-Tarski Paradox", by Stan Wagon, to
be even better for a mathematician.  I understand that the first few
chapters are "...an entertaining and lucid introduction to the "paradox"
which is perfectly accessible to any graduate student.  Furthermore,
the book as a whole is an in-depth guide to the subject and will
probably be the standard text for many years." (quoted from
R.J.Gardner in a letter to MI in Spring, 89.)

  -- Stan Isaacs
  -- isaacs@corp.hp.com
Newsgroups: sci.math