HDTenEightyP/NetNews huggingface dataset:
From: RSMA302@haifauvm.bitnet (Victor Harnik)
Subject: Opening at Haifa U.
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Haifa - Mt. Carmel Haifa, Israel.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Comments: Internet address: bimacs.cs.biu.ac.il. Bitnet address: bimacs.bitnet.
	 Old internet address (bimacs.biu.ac.il) is available only temporarily.
Date: Mon, 9 Nov 1992 12:02:11 GMT


The Dept. of Mathematics and Computer Science at the University of
Haifa, Israel anticipates an opening for a tenure track position
starting October 1993. Candidates holding a Ph.D. in mathematics
with a demonstrated strong research ability are invited to apply.
Both junior and senior level applicants will be considered.
Please send CV with list of publications and suggested names and
addresses of references to:
          Prof. Victor Harnik, Chairman
          Dept. of Math. and Computer Science
          University of Haifa
          Haifa 31905, Israel

          fax: 9724-246814

Our Department offers B.A. and M.A. degrees in pure mathematics and
in math with computer studies and Ph.D. degrees in all branches of
mathematics.

Newsgroups: sci.math.research
From: greg@math.uchicago.edu (Greg Kuperberg)
Subject: Re: A Conjecture About Packings of Balls
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Dept. of Mathematics, Univ. of Chicago
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Sun, 8 Nov 1992 23:52:32 GMT

In article <9211060833.AA05802@wisdom.weizmann.ac.il> you write:
>For a finite ball packing P in R^3 [with balls round but not
>necessarily congruent], let
>a(P)=2(number of tangencies)/(number of balls)
...
>Conjecture: A = sup a(P) = 12.
...
>I think I can improve the naive argument above to get something
>better than A<=24, but I don't expect to reach A=12.

Your expectation is true and your conjecture is false.  :-)

A regular dodecahedron in flat Euclidean space has angles slightly less
than 120 degrees.  On the surface of the 3-sphere, a very large
dodecahedron has angles close to 180 degrees, while a very small one is
close to flat.  Therefore there is one of intermediate size with angles
exactly 120 degrees and as it happens 120 of them tile the 3-sphere.
Inscribing a sphere in each one, we get a packing of the 3-sphere by
120 spherical caps of a certain size, each kissing twelve others.
I'll call this the hyperdodecahedral packing.

Stereographic projection preserves spheres, so we can project
this packing onto Euclidean space, sending some point not contained
in a sphere to the point at infinity.  Thus we get a finite cluster
D with a(D) = 12 exactly.  However, this is trouble, because the sup
of a(D) is not a maximum.  You can always take two clusters of the same
type and make them touch at a single point, increasing a(D) slightly.
In this case you get a(D+D) = 12+1/120.

If you are interested in the actual value of A, then here is my best
lower bound:   Take the above cluster D.  If you project it from a
point that lies symmetrically between four spheres, you get a regular
tetrahedron of four big spheres with 116 little spheres on the inside.
I'll call the interior arrangement "hyperdodecahedral grout".  You can
put hyperdodecahedral grout inside any other sphere packing with
tetrahedral crevices, including the dodecahedral arrangement itself,
which yields a better kind of grout.  If you do this once you get a
packing with average kissing number 7152/581 > 12.309, and if you
iterate, the supremum is (I think) 3486/283 > 12.318.

Interestingly, a lot of simpler constructions, like taking the
cannonball packing and placing a sphere in each octahedral crevice,
yield a(P) = 12 on the nose.  Perhaps there is one with a(P) = 13 or 12
1/2 or something like that.

This construction is vaguely similar to the example due to A. Bezdek
and W. Kuperberg of packings of long, flat ellipsoids whose density
exceeds the conjectured packing density of spheres in three
dimensions.  (I should finally mention that with a comment of J.  M.
Wills and another comment of mine, you get a sequence of ellipsoid
packings which, in the limit, have a density 2.4% greater than that of
the cannonball packing.)

Newsgroups: sci.math.research
From: kolount@leland.stanford.edu
Subject: Is the following problem in NP?
Followup-To: poster
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Illinois at Urbana
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Sat, 7 Nov 1992 08:15:04 GMT



INPUT: a polynomial F(x_1, ... , x_N) of bounded degree (say 10)
and integer coefficients (also bounded by say 100).

OUTPUT: YES iff there are _real_ numbers x_1, ... , x_N that satisfy F=0.

Please reply to "kolount@cauchy.stanford.edu".

Mike Kolountzakis





Newsgroups: sci.math.research
From: schramm@wisdom.weizmann.ac.il (Schramm Oded)
Subject: Re: A Conjecture About Packings of Balls
Originator: dan@symcom.math.uiuc.edu
Summary: The average number of contacts is <= 8 + 4*3^(1/2)
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Weizmann Institute of Science
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 13 Nov 1992 09:59:41 GMT

In article <9211082352.AA24164@zaphod.uchicago.edu> greg@math.uchicago.edu (Greg Kuperberg) writes:
>In article <9211060833.AA05802@wisdom.weizmann.ac.il> you write:
>>For a finite ball packing P in R^3 [with balls round but not
>>necessarily congruent], let
>>a(P)=2(number of tangencies)/(number of balls)
>...
>>Conjecture: A = sup a(P) = 12.
>...
>>I think I can improve the naive argument above to get something
>>better than A<=24, but I don't expect to reach A=12.
>
>Your expectation is true and your conjecture is false.  :-)
...
>which yields a better kind of grout.  If you do this once you get a
>packing with average kissing number 7152/581 > 12.309, and if you
>iterate, the supremum is (I think) 3486/283 > 12.318.
...

Thanks G. Kuperberg.  Without much sweat I can show that
A <= 8 + 4 Sqrt[3] = 14.9282...  Unless there is some miraculously
ingenious idea, I expect that better and better estimates will
become very difficult.  Anyway, the actual value of A is not as
interesting as the near-optimal packings.  Do you think, G. K., that
your construction gives the true A?

Oded Schramm                schramm@wisdom.weizmann.ac.il
From: sutin@helios.ucsc.edu (Brian Sutin)
Newsgroups: sci.math.research
Subject: Geometry Conjecture
Date: 5 Nov 92 00:31:56 GMT
Article-I.D.: darkstar.1d9q1sINN9ms
Organization: Lick Observatory UCSC
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu

I need the following result (which may be common knowledge):

Let D be a region of R^3 with a reasonable boundary S and let dS be any
measure on the surface of D.  If

    INT(S){ 1/|x - y| dS(y) } = 1	for all x in D,

then D must be an R^3 ball.

Brian Sutin				sutin@lick.ucsc.edu
Lick Observatory, UCSC			Santa Cruz, CA 95064
    Fred:   "May I rescue you?"
    Ginger: "No, thank you.  I prefer being in distress."
Newsgroups: sci.math.research
From: dan (Daniel R. Grayson)
Subject: Weight filtrations in algebraic K-theory
Reply-To: dan@math.uiuc.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Illinois at Urbana
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Sun, 8 Nov 1992 19:46:19 GMT


I've made my preprint entitled "Weight filtrations in algebraic K-theory"
available for anonymous ftp in 
	math.uiuc.edu:~ftp/pub/papers/grayson/seattle.{tex,dvi}
This is an expository paper which was delivered at the Motives conference at
University of Washington in 1991, and is now in final form.  Here is the
first paragraph of the introduction.

    The recent search for a motivic cohomology theory for varieties,
    described elsewhere in this volume, has been largely guided by certain
    aspects of the higher algebraic K-theory developed by Quillen in 1972.
    It is the purpose of this article to explain the sense in which the
    previous statement is true, and to explain how it is thought that the
    motivic cohomology groups with rational coefficients arise from
    K-theory through the intervention of the Adams operations.  We give a
    basic description of algebraic K-theory and explain how Quillen's idea
    that the Atiyah-Hirzebruch spectral sequence of topology may have an
    algebraic analogue guides the search for motivic cohomology.


Newsgroups: sci.math.research
From: Allan Adler <ara@zurich.ai.mit.edu>
Subject: deriving the octahedral axiom
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: Sun, 8 Nov 1992 07:04:12 GMT


I'm looking at the definition of a triangulated category and I find
the octahedral axiom rather puzzling.

Let's say one is just sitting down to invent triangulated categories.
How does one discover that one wants to write down the octahedral axiom?

Allan Adler
ara@altdorf.ai.mit.edu


Newsgroups: sci.math
From: kgrant@alfred.carleton.ca (Ken Grant)
Subject: Topology Problem
Organization: Carleton University
Date: Wed, 11 Nov 1992 21:04:10 GMT

Topology problem:
If X is the continuous image of a countable successor ordinal with the
order topology by a map with all fibers finite, then is there a
compact Hausdorff topology finer than the topology of X ?

(If so then X countable T1, X the cts image of a compact Hausdorff
space ==> X is the cts image of a compact Hausdorff space under a
bijective map.
Is there a counterexample for X uncountable?)

Ken Grant.
From: dreier@durban.berkeley.edu (Roland Dreier)
Newsgroups: sci.math
Subject: Re: a first year grad student freaks out.
Date: 10 Nov 92 23:52:43
Organization: U.C. Berkeley Math. Department.
NNTP-Posting-Host: durban.berkeley.edu
In-reply-to: 's message of Monday, 9 Nov 1992 17:02:55 EST

In article <92314.170255RVESTERM@vma.cc.nd.edu> <RVESTERM@vma.cc.nd.edu> writes:
   i'm a first year grad student.  i can do most of the homework assigned
   to me.  i can pass tests i have to take.  i can usually understand
   proofs of theorems that we're studying, given some thought.  i think
   that with a lot of work, i can pass my orals.

   however, what's the deal with this thesis thing? what happens if you
   simply cannot prove whatever your advisor assigned?

   bob vesterman.

Guess what, kid.  It's even harder than that.  Consider yourself
extremely lucky if your advisor even gives you a question.  More
likely, not only are you gonna have to solve a problem, you're gonna
have to find the problem yourself.  But the advantage of this is that
you can usually find a problem you can solve if you look hard enough.
It's still not easy to come up with a problem you can do and also that
interests other people enough so that they're willing to give you a
degree.

--
Roland Dreier                                        dreier@math.berkeley.edu
From: ross@ecr.mu.oz.au (Ross McAree)
Newsgroups: sci.math
Subject: geometry question
Date: 12 Nov 92 23:14:10 GMT
Organization: Computer Science, University of Melbourne, Australia


What follows is a question that I've been pondering over for some time, but
I haven't so far found an answer. It concerns the number of different 
configurations of three identical annuli (i.e. having the same inner and 
outer radii) so that they have some form common intersection. 

If this sounds confusing, the following background material might help. 
Consider two circle of the same radius. By Bezout's theorem there
are (2 * 2 =) four intersections. These can be (i) all complex conjugate;
(ii) 1 repeated real and two complex conjugate (i.e. circles are tangent);
(iii) 2 distinct real and 2 complex conjugate (i.e. circles intersect);
(iv)  complete intersection, i.e. the circles coincide. Accordingly 
there are four different ways in which the two identical circles intersect.

For three circles the same logic can be used to arrive at ten different
configurations where the circles have some type of common intersection 
(for nine of these variations three circles have some common point or 
they overlap in some way. The tenth type is generic in that it 
corresponds to there being no common intersection amongst the 
three circle, although here two of them might have some common intersection). 
How about two identical annuli. By similar arguments there are ten different 
types of intersections.

So far so good. But when I come to finding the number of different
configurations for the common intersection of three identical annuli
I get all messed up. surely this is not a difficult problem! If 
anyone can see a simple answer or direct me to an appropriate 
reference I'd be most appreciative. 

Ross McAree,
Dept. of Mechanical Engineering,
The University of Melbourne,
Parkville, Melbourne Australia.
Xref: sparky sci.math:14773 sci.physics:18699
From: chrisman@sizzlean.berkeley.edu (chrisman)
Newsgroups: sci.math,sci.physics
Subject: Re: Three-sided coin
Date: 11 Nov 1992 19:40:18 GMT
Organization: University of California, Berkeley
Distribution: usa
NNTP-Posting-Host: sizzlean.berkeley.edu

In article <1992Nov11.045329.21895@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
.In article <1992Nov10.051702.24907@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
.>In article <1992Nov10.032643.10467@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
.>>My best shot at answer invoked an idea from stat mech, namely,
.>>equipartition.  This says that the solution occurs when the *energy* of
.>>standing upright equals the energy of lying on edge.  Guess this means
.>>the radius should equal half the thickness of the coin, or if you
.>>prefer, the diameter should equal the thickness.
.>
.>Wouldn't that give the coin a 1/2 chance of landing on its edge rather
.>than 1/3?
.
.Well, not according the stat mech principle that equal-energy states
.have an equal chance of being occupied.  Since there are 3 states of
.equal energy (heads, tails, edge), each should have a 1/3 chance of
.being occupied.  That is, if the reasoning was right here.  However, I
.no longer think it is.

Yes, the reasoning is incorrect.  Let me "prove" using this reasoning
that the probability of a (flat) coin landing heads is twice that of
its landing tails.  Assuming the coin is flat and will not stand
on its edge, there are three possibilities:

	1. the coin lands tails;
	2. the coin lands heads, with angle of head between 0 and pi;
	3. the coin lands heads, with angle of head between pi and 2pi.

All three outcomes have equal energy states, so... the probability
of outcome 1 (i.e. tails) is 1/3.

I HOPE there is something wrong with this reasoning!  ;-)
From: mckay@alcor.concordia.ca (John McKay)
Newsgroups: sci.math
Subject: Re: Three-sided coin
Date: 9 Nov 92 12:20:27 GMT
Organization: Concordia University, Montreal, Quebec
Originator: mckay@alcor.concordia.ca


 von Neumann was asked, when about to enter a taxi,

"How thick should a coin be to have equal (=1/3) probability
 of landing on its head,tail,or edge?"

He turned, told the taxi where to go, then answered and was 
away.

Surprisingly, making "reasonable" assumptions, this can be
done in your head.

The only person from whom I have had an immediate correct
answer was the late John Leech.

To standardize on answers, let us assume the answer to be
Thickness/Diameter.




Newsgroups: sci.math
From: tim@gold.iss.nus.sg (Tim Poston)
Subject: Re: What is catastrophe theory?
Reply-To: tim@iss.nus.sg (Tim Poston)
Organization: Institute of Systems Science, NUS, Singapore
Date: Thu, 12 Nov 1992 04:15:17 GMT

In article <1992Nov11.180552.14797@progress.com> neil@progress.COM (Neil Galarneau) writes:
>I have heard of something called catastrophe theory.
>
>I am looking for recommendations on articles/books (in English!) readable by a
>non-math major.

If you are a sociology major, don't.
The only readable accounts are full of stuff that
(looked at closely by an expert)
may or may not be technically incorrect,
but induce weird misconceptions in those who read them.
Published examples in the social science journals
are too numerous to mention.

If you have some physics/engineering background,
Bob Gilmore's "Catastrophe Theory for Scientists and Engineers"
is full of good stuff on using it properly.
You could also look at the book I wrote in 1977 with
Ian Stewart, "Catastrophe Theory and its Applications"
which begins with the bare minimum
of calculus in several variables needed to make
sense of what Thom's theorem (really a cluster of results)
actually says.
Without calculus, expressed in words only,
catastrophe theory produces gibberish in the same way
Special Relativity does.

On the other hand,
if you're looking for the real mathematical power and glory of it all,
look at "Catastrophe Theory" by V.I.Arnold.
Elegant, but succinct.

Tim Poston.

____________________________________________________________
 "Division is esteemed one of the busiest operations of
  Arithmetic, and such as requireth a mynde not wandering,
  or setled uppon other matters."
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Newsgroups: sci.math
From: fburton@nyx.cs.du.edu (Francis Burton)
Subject: Surface area of ellipsoid
Organization: Nyx, Public Access Unix @ U. of Denver Math/CS dept.
Date: Thu, 5 Nov 92 14:26:35 GMT

For an ellipsoid with three axis radii a, b and c, two of them equal
e.g. a=b, the surface A area can be obtained by integrating the swept-
round perimeter (surface area of solid of rotation) thus:

               /x=c   ___________________
            2 |      /  4     2    2   2
A = 2 pi a/c  |     /  c  + (a  - c ) x    dx
              |   \/ 
              /x=-c
              

For c > a, this turns out to be

                 -1                        ___________ 
             (sin  (z) + a.z/c)           /     2  2   
A = 2 pi a c ------------------,   z =   / 1 - a /c    
                     z                 \/              
                                
                                
and for c < a

                  -1                        ___________ 
             (sinh  (z) + a.z/c)           /  2  2   
A = 2 pi a c -------------------,   z =   /  a /c  - 1
                      z                 \/              
                                
(note sinh vs sin).


That's about as far as my math goes, and I am having trouble finding
an expression for the surface area of an ellipsoid where a, b and c
are ALL UNEQUAL. Why is it that the expression for surface area
becomes so complicated when a sphere is squashed, in marked contrast
to the equivalent volume formulae?

Can any of you REAL mathematicians supply a useable formula?

I should mention that this is not homework: I'm a physiologist with
an interest in the mechanical properties of sarcolemmal vesicles (tiny
deformable spheres of muscle membrane).

Thanks in advance for your help.

--
Francis Burton      Physiology, Glasgow University, Glasgow G12 8QQ, Scotland.
041 339 8855 x8085  | JANET: F.L.Burton@glasgow.ac.uk  !net: via mcsun & uknet
"A horse! A horse!" | INTERNET: via nsfnet-relay.ac.uk BITNET: via UKACRL
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: definition of topological space
Date: 5 Nov 1992 12:36:14 -0500
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu

In article <1992Nov5.033835.5180@leland.Stanford.EDU> ledwards@leland.Stanford.EDU (Laurence James Edwards) writes:
>The definition of a topological space is:
>
>    :a set with a collection of subsets satisfying the conditions that 
>    both the empty set and the set itself belong to the collection, the 
>    union of any number of the subsets is also an element of the collection, 
>    and the intersection of a finite number of the subsets is an element 
>    of the collection
>
>What is the purpose of this definition?

Some math educators say that we should begin with the abstract (like the
above) and later specialize to the concrete.  Obviously, that approach is
not good for Mr. Edwards.

The definition above should come only after many, many examples have been
studied.  At that point, the purpose of the definition may be more
apparent.
-- 
  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)
Newsgroups: sci.math
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: What can we have for an educational system?
Organization: Department of Chemistry, University of Toronto
Distribution: usa
Date: Tue, 10 Nov 1992 17:52:02 GMT

In article <1dmhluINN1um@agate.berkeley.edu> chrisman@purina.berkeley.edu
(chrisman) writes:
>>baldwin@csservera.scs.usna.navy.mil (J.D. Baldwin) writes:
>>some work, perhaps even some training is required for most of us to become
>>good teachers.  Personally, I wouldn't mind knowing a little more
>>developmental and cognitive psychology; I especially would like to learn
>>something about these subjects if I were to teach younger children.  I
>>have developed a set of rules of thumb which seem to get me through
>>undergraduate teaching assignments, but there is no science to my
>>approach.  While I reserve the right to disagree with someone else's
>>theories, I would at least like to know what the evidence is and what
>>other people's thinking has produced before I claim that I know anything
>>about how children and adults learn anything.
>
>I also would like some "training".  As with most skills, one can improve
>one's skill at teaching by making use of other people's experience.
>If I had my choice, this "training" would consist of hearing about
>other teachers' rules of thumb and hearing about how they handled 
>particular students under particular situations - in short, gaining
>their personal experience.
>
>Why aren't education courses like that?  In my experience, teachers of
>education courses try to make teaching into a _science_ (as baldwin 
>would have it), putting out lots of unsubstantiated generalizations as 
>"theorems" of developmental and cognitive psychology.  I can learn
>more about teaching from a one-hour conversation with a good teacher
>than I can learn in a ten-hour education course or seminar.

     J.D. Baldwin is being unjustly blamed for my opinions.  The quoted
excerpt attributed to him was in fact written by me, Marc R. Roussel.

                                Sincerely,

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
Newsgroups: sci.math