HDTenEightyP/NetNews huggingface dataset:
From: fc03@ns1.cc.lehigh.edu (Frederick W. Chapman)
Newsgroups: sci.math
Subject: Re: STRUCTURE OF TIME
Date: 8 Oct 92 01:14:37 GMT
Organization: Lehigh University

In article <1992Oct4.122333.1@tnclus.tele.nokia.fi>,
hporopudas@tnclus.tele.nokia.fi writes:

[...]

> You should say that you has nothing to say about morality.? Then why
> you then make these stupid comments. ?

For you to insult others who post to USENET news groups is senseless
and unbusinesslike.

Please refrain from making these personal attacks.  They contribute
nothing to the substance of the discussion.

-- 

o ------------------------------------------------------------------------- o
|  Frederick W. Chapman, User Services, Computing Center, Lehigh University |
|    Campus Phone:  8-3218     Preferred E-mail Address:  fc03@Lehigh.Edu   | 
|         "The day after yesterday is the second-to-last day before         |
|               the rest of your life the day after tomorrow."              |
o ------------------------------------------------------------------------- o
From: rodolfo@lo-yosemite.ucsb.edu (Resende)
Newsgroups: sci.math
Subject: isomorphic acyclic digraph problem
Keywords: graph isomorphic classes combinatorial algorithms
Date: 14 Oct 92 22:03:50 GMT
Organization: University of California, Santa Barbara

I would like to receive insights/references on the following problems
(unlabeled partial orders)

1)Is there a closed formula that gives the number of classes of
isomorphic acyclic digraphs with n verices?

2)How to generate a list of one diagram from each class of the question
above?

3)How to generate one diagram from a class such that each class has
uniform probability of being chosen?

Example:
n=3
1)I think there are 5 classes of isomorphic acyclic digraphs
2)the list

1. * * *   2. *->* *  3. *->*    4 *->*   5. *->*->*
                            ^      |
                            |      v 
                            *      *

Thanks in advance!

---Rodolfo      rodolfo@cs.ucsb.edu
Newsgroups: sci.math.research
From: greg@math.uchicago.edu (Greg Kuperberg)
Subject: Re: Permutation polytopes
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Organization: University of Illinois at Urbana
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Date: Thu, 8 Oct 1992 16:35:59 GMT

I have made a mistake.   I said that Mike's matrices have the property
that the k'th row has the same sum as the k'th column, and that
this was a linear constraint on the matrices in the space of all
anti-symmetric matrices.  Both halves are false in spirit.  The sum
of the k'th row is the negative of the sum of the k'th column, but
this is true for all matrices.  So there is no constraint at all.

Rather, Mike's matrices span the set of all anti-symmetric matrices.
If you take our original matrix A, which I would actually prefer 
to call a here, and let tau be the transposition of 1 and 2; tau's
effect on a is two switch the first two rows and columns.  Then
a-tau(a) = 2e_12 - 2e_21, where e_ij is an elementary matrix.
The orbit of e_12-e_21 under conjugation by permutation matrices
clearly spans all antisymmetric matrices.

The rest of what I said is still true I think, except that the polytope
U is even bigger than I said it was.

				Greg
From: alvisd@bronze.ucs.indiana.edu (dean alvis)
Newsgroups: sci.math.research
Subject: number theory question
Date: 14 Oct 92 19:12:01 GMT
Article-I.D.: usenet.Bw4LC2.Dnq
Organization: Indiana University
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Let $p$ be an odd prime, and assume $\beta$ is an algebraic
integer of the form $$\beta = \sum_\omega \mu_\omega (1-\omega),$$
where the coefficients $\mu_\omega$ are nonnegative rational
integers and $\omega$ ranges over the primitive complex $p$-th
roots of unity.  Assume further that $\beta$ is irrational,
so the coefficients don't assume a constant value, that the
coefficients of $\beta$ are relatively prime, and that
the product of the algebraic conjugates of $\beta$ is a power
of $p$ (so the norm of $\beta$, in the field-theoretic sense,
is a power of $p$).  Does it necessarily follow that $\beta$
has the form $1-\omega$ or $2 Re(1-\omega)$?

Any information on this problem would be helpful. 
Please respond via e-mail to alvisd@natasha.iusb.indiana.edu
From: greg@math.uchicago.edu (Greg Kuperberg)
Newsgroups: sci.math.research
Subject: A 14th class of pentagons that tile?
Date: 13 Oct 92 17:51:27 GMT
Article-I.D.: zaphod.9210131751.AA17215
Organization: University of Illinois at Urbana
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I hear persistent rumors that they have found a 14th class of pentagons
that tile.  Does anyone here know the tiling or know a reference?
If so, please send a copy of your reply by mail.  Thanks.
Newsgroups: sci.math.research
From: "John C. Baez" <jbaez@bourbaki.mit.edu>
Subject: Re: Variational method for PDE with first derivatives
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Organization: MIT Department of Mathematics, Cambridge, MA
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Date: Wed, 14 Oct 1992 16:54:45 GMT

In article <1992Oct14.085015.150@news2.cis.umn.edu> burchard@horizon.math.utah.edu (Paul Burchard) writes:
>In article <1992Oct13.202915.29039@galois.mit.edu> "John C. Baez"  
><jbaez@bourbaki.mit.edu> writes:
>>
>> Laplacian u = f(u,Du)
>> 
>> where Du is the gradient.  (Actually she is doing much fancier stuff,
>> but I'll keep it simple here.)  She was trying to find a variational
>> principle good for the latter kind.  Is there any functional of u and
>> Du that when extremized gives you the latter PDE?
>
>Although there are certain obvious costs to this, you can always use |P(u)|^2
>as an energy, when solving P(u)=0, and look for absolute minima.

This is getting close but is still not quite what
I was looking for, since it requires finding the absolute minimum.  I
think my question may not have been loudly stated enough the first time,
so here it is again: for which if any equations of the above form is
there a functional of u and Du that when extremized gives you the
equation??  It's easy when there is no Du, of course.  

I am not looking for other methods of solving such PDE, general results
about such PDE, and so on - Mary knows lots of these and is in fact
trying prove existence in an extremely delicate case, which she has
managed to do using variational techniques in the case when there is no
Du.




Newsgroups: sci.math.research
From: loader@vax.oxford.ac.uk
Subject: Kreisel Lacombe Shoenfield and HEO
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Oxford University VAX 6620
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Date: Thu, 8 Oct 1992 14:12:57 GMT

The Kreisel-Lacombe-Shoenfield theorem states that any partial recursive
function f that gives a well defined functional on recursive functions ( ie
if {a} and {b} are total and equal then f(a)=f(b) ) is recursively continuous
( i.e. If {a} is total then there is recursive n(a) such that f(a)=f(b)
whenever {b} is total with {a}(x)={b}(x), x=0 ... n(a) )

(For a proof see eg 'Foundations of Constructive Math.', M Beeson, 1985)

It is not hard to see that the conclusion is equivalent to saying that there
is a recursive functional F with F({a})=f(a) whenever {a} is total.

Thus in terms of the model HEO, the KLS theorem states that:

   Any equivalence class of (N -> N) -> N is                         (*)
   given by a recusive functional of this type.

Question: What happens to (*) at other finite types?

For types of rank 1, this is the trivial statement that a recursive functional
with no function parameters is a recursive function.

For types of rank 2, the question can be reduced to (*).

What happens at higher types???

R Loader, Oxford
From: greg@math.uchicago.edu (Greg Kuperberg)
Subject: Re:  Permutation polytopes
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Illinois at Urbana
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Date: Wed, 7 Oct 1992 23:39:36 GMT

As I understand it Michael Cohen's question is this:  Let A be
the anti-symmetric n x n matrix with all 1's above the diagonal
and all -1's below.  Let U be the convex hull of the orbit of
A under the action of conjugation by permutation matrices.
What are the codimension one faces of U?

I can't answer this question, but I have evidence that the answer
could be very complicated.  First, here are some properties of U:

U actually lives in a vector subspace of A because the k'th row of a
matrix in U must have the same sum as the k'th column.  However, since
the whole matrix adds to zero this is really only n-1 constraints, so
we've identified a subspace V of dimension (n-1)(n-2)/2 that contains
U.  But in this subspace U has content, because the linear span of U
must be a representation of the symmetric group, and V is an
irreducible respresentation.  Note also that U is a centrally symmetric
polytope, because conjugation by the antidiagonal negates the
matrix A.

There is a theorem due to Milman (and perhaps Bourgain?) that the
number of faces times the number of edges of a centrally symmetric
polytope in k dimensions is bounded below by some C^k.  Perhaps C=2 is
a viable value, but the proof only derives that C is 1 plus a small
number not worth worrying about.  For us, however, k=n^2, and C^n^2
grows much faster than n!.  There will asymptotically be a huge number
of orbits of faces under the action of the permutation group.
Therefore there is no a priori symmetry reason that the faces are
nice.

However, I do know of one example of a polytope with many more faces
than symmetries which is nevertheless nice.  It's the convex hull of
permutation matrices which are symmetric and have zeroes on the
diagonal.  Do you want to do linear programming?  For the polytope I
have just mentioned, there is a way to do linear programming in
guaranteed polynomial time where you never consider all faces at once,
only those you encounter.  It's possible that there is also such an
algorithm for your polytope.

				Greg
From: jbaez@bourbaki.mit.edu (John C. Baez)
Newsgroups: sci.math.research
Subject: Variational method for PDE with first derivatives
Date: 13 Oct 92 20:29:15 GMT
Article-I.D.: galois.1992Oct13.202915.29039
Organization: Department of Mathematics, UCR
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A student here at UCR, Mary Legner, was trying to extend some theorems
about elliptic PDE of the form

Laplacian u = f(u)

to those of the form

Laplacian u = f(u,Du)

where Du is the gradient.  (Actually she is doing much fancier stuff,
but I'll keep it simple here.)  She was trying to find a variational
principle good for the latter kind.  Is there any functional of u and
Du that when extremized gives you the latter PDE?

I told her I was dubious becuase 1) if there was, some of the papers
she'd read would have mentioned it, and 2) in mechanics, there doesn't
seem to be any Lagrangian that gives the equations of motion

x'' = -x'

(which describes a particle with friction).  

What a drag that'd be if variational methods weren't applicable to 2nd
order elliptic ODE with first-derivative terms!
From: velo@sicsun.epfl.ch ((Martin Ouwehand EPFL-SIC/SE))
Newsgroups: sci.math.research
Subject: Re: Variational method for PDE with first derivatives
Date: 14 Oct 92 16:55:26 GMT
Article-I.D.: sicsun.1992Oct14.175526
Organization: Ecole Polytechnique Federale de Lausanne
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In article <1992Oct13.202915.29039@galois.mit.edu>, jbaez@bourbaki.mit.edu (John C. Baez) writes:
|>                                                 there doesn't
|> seem to be any Lagrangian that gives the equations of motion
|> 
|> x'' = -x'
|> 
|> (which describes a particle with friction).  
|> 

There is : L = exp(t) * ( x')^2 
where t is the "time" or independant variable. The corresponding
Hamiltonian is H = (1/4) exp(-t) * p^2, which describes the decaying
of the kinetic energy due to the friction.

--
Martin Ouwehand, Swiss Institute of Technology in Lausanne
Newsgroups: sci.math.research
From: conrad@boucher.harvard.edu (Keith Conrad)
Subject: Mahler expansion of p-adic gamma function
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Dept. of Math, Harvard Univ.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Thu, 15 Oct 1992 19:58:04 GMT


I have some questions about the growth of the Mahler coefficients of the
p-adic gamma function, which I'll denote by Gamma_p.  Let a_p(n) denote the
nth coefficient of the Mahler expansion (NOT the Taylor expansion) of
Gamma_p, and A_p(n) = ord_p( a_p(n)).  With some assistance I have produced
the following data:

For p = 2, 0 <= n <= 509, write n = 4k + r with 0 <= r <= 3.  Then
A_2(4k) = k
A_2(4k + 1) = k + 1
A_2(4k + 2) = k + 2
A_2(4k + 3) = k + 3 + ord_2(k + 1) = k + 3 + ord_2(k - 1/(1 - 2))

For p = 3, 0 <= n <= 1082, write n = 9k + r with 0 <= r <= 8.  Then 
A_3(9k) = 2k
A_3(9k + 1) = 2k
A_3(9k + 2) = 2k
A_3(9k + 3) = 2k + 2
A_3(9k + 4) = 2k + 1
A_3(9k + 5) = 2k + 3 + ord_3(2k + 1) = 2k + 3 + ord_3(k - 1/(1 - 3))
A_3(9k + 6) = 2k + 2
A_3(9k + 7) = 2k + 2
A_3(9k + 8) = 2k + 3

I have looked at A_p(n) as well for p = 5, 7, 11, 13, and 17 for n running
up to at least 400 (in the case of 5 and 7 for n up to 1400), and what
seems to be happening is 
      A_p(n) = (p - 1)[n/p^2] + r_n,   ( [ ] = greatest integer)
where r_n >= 0 and for "most" residue classes n(mod p^2) it turns out that
if m = n (mod p^2) then r_m = r_n.  For example, when p = 2 this "mod p^2"
periodicity of r_n" occurs for all classes mod 4 except for the class 3(mod
4).  When p = 3 there is one exception, namely the class of 5 mod 9.  When
p = 5 there seem to be (at least) four exceptions: the classes of 4, 7, 16,
and 22 mod 25.  When p = 7 I have so far found only one class mod 49 for
which  the n in that class don't have the same r_n value - it's 19 mod 49.
Due to the slower growth of A_p(n) as p increases, there are probably some
more exceptions to this when p = 7 which I have not located. Even in the
(seemingly) few exceptional classes mod p^2 not admitting a constant r_n
value, it seems that r_n = const. + s_n where the const. only  depends on
the residue class and s_n increases very slowly with n (see the data above
for p = 2 or 3 and the classes of 3 mod 4 or 5 mod 9).  

I'd like to hear from anyone who can explain this behavior of A_p(n),
ESPECIALLY the periodicity of the r_n's mod p^2.  The fact that A_p(n)
grows like (p - 1)n/p^2 seems to be due to Gamma_p(n) being analytic on
cosets of pZ_p but not on Z_p (well, for p > 2), although I haven't worked out
the details on this.

Responses can be given on this newsgroup, although I'd also appreciate it 
if they could be sent to me as well.  Thanks.

Keith Conrad
conrad@zariski.harvard.edu
From: albers@fields.UWaterloo.ca (Sheri L. Albers)
Newsgroups: sci.math.research
Subject: News of the Fields Institute
Keywords: Newsletter, Fields Institute, Mathematical Research Institute
Date: 8 Oct 92 16:04:54 GMT
Organization: University of Waterloo
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To: Any Interested Parties
From: Sheri Albers
Re: Electronic Newsletter for The Fields Institute

In order to provide timely information about programs and 
activities at the Fields Institute, we will be sending out an 
electronic newsletter every two weeks.  If you are interested 
in receiving this newsletter via e-mail, please fill in the 
following form.  Completed forms should be returned to 
news@fields.uwaterloo.ca or faxed to (519) 725-0704.

**************************** Cut here ******************
Professor ()  Dr.()  Mr.()  Mrs.()  Ms.()  Miss ()
Name:
Department:
University or Institution:
Address:
Phone:
Fax:
e-mail Address (Important):
******************************************************
Newsgroups: sci.math.research
From: Jonathan Borwein <jmborwei@orion.uwaterloo.ca>
Subject: Simon Fraser Centre for Experimental and Constructive Mathematics
Fax:   (519) 746-6530
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Illinois at Urbana
Phone: (519) 888-4829    Dept: (519) 885-1211 x2696
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Date: Thu, 15 Oct 1992 19:23:03 GMT

\documentstyle[12pt]{article}
\parskip=0.5ex

\begin{document}
\begin{center}{\Large \bf 
   Simon Fraser Centre for Experimental and Constructive Mathematics
} \end{center}

This Centre located in Burnaby, British Columbia (Greater Vancouver)
is intended to further research and graduate education in Computation in
the Mathematical Sciences. The Centre aims to provide a sophisticated
environment for Mathematical research on topics that require a substantial
mix of computation, experimentation and mathematics. Of interest are questions
on how one uses the computer: To build intuition?  To generate hypotheses?
To validate conjectures or prove theorems? To discover nontrivial examples
and counter-examples?

The centre will commence full operation July 1, 1993. Activities will
include the following.

(i)  Provision for and sponsorship of Post-Doctoral Fellowships in areas
related to Experimental and Constructive Mathematics.

(ii)  Sponsorship of regular short-term and longer-term research visitors
to the Centre.

(iii) Organization of regular Colloquia and occasional Conferences on
advances in Experimental and Constructive  Mathematics.

(iv) Participation in the training of graduate students in Experimental and
Constructive  Mathematics.

(v) Establishment, development and maintenance of accessible software
archives.

(vi) Collaboration with similar centres and appropriate individuals at
other Canadian and foreign Universities and Institutes.

The initial steering committee consists of J. Borwein (Director), P. Borwein
and R. Russell. Enquiries can be directed to jborwein@math.sfu.ca .

The Centre  is soliciting applications for {\bf two Post-Doctoral Fellows}
commencing after July 1, 1993, in any areas compatible with the interests
of the centre.  The stipend will be set on the NSERC PDF scale.  These are
primarily research positions though some teaching may be involved.
Potential Post-Doctoral Fellows should send a curriculum vitae and arrange
for three letters of reference to be sent to Dr. J.M. Borwein,
Department of Combinatorics and Optimization,University of Waterloo, N2L
3G1, Ontario preferably by December 15, 1992.


The Centre will be soon be soliciting applications for the position of {\bf
Computer System Administrator} commencing April 1, 1993.  Salary range is
\$42,846-\$54,955. This person will be responsible for the installation and
operation of the CECM computing facility and will be expected to provide
technical leadership for this and related projects.  A post graduate degree
in Computing Science or Electrical/Electronic Engineering and five years'
experience (or an equivalent combination of experience and training) are
required.


\end{document}

Newsgroups: sci.math.research
From: rajiv@cs.uwa.edu.au (Rajiv Ellepola)
Subject: Toroidal ( r,theta,z) coordinates
Summary: Is there anyone who has discretized the toroidal coordinates in 3-D
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Dept. Computer Science, University of Western Australia.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Thu, 8 Oct 1992 12:26:08 GMT
Keywords: Toroidal

Is there anyone who has discretized the toroidal coordinates in 3-D
for the problem of diffusion and convection?  ( i.e Conservation equation )

Numerical Heat transfer and Fluid flow, by Patankar has it in the
cartesian coordinate system.

Thankyou for your cooperation.

Jerome ( ENGP2176@NUSVM.NUS.SG )
-- 
Email	-  rajiv@cs.uwa.edu.au
phone	-  389 1610 (home)      
           380 3458 (lab)
address -  1/114 Broadway, Nedlands, WA 6009.

Newsgroups: sci.math.research
From: "John C. Baez" <jbaez@bourbaki.mit.edu>
Subject: Symmetric algebra over a Banach space
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: Tue, 13 Oct 1992 05:24:31 GMT

Say I have a Banach space V.  Now I form the symmetric algebra SV, that
is, all formal (commuting) polynomials in elements of V.  I'd like to
form a Banach algebra completion of SV in some especially nice way.  In
particular, I want the norm on V to coincide with that on S^1V, the 
homogenous polynomials of degree one (a subspace of SV which may be
canonically identified with V).  

This must have been studied, no?  It seems there must be a good way to
do it.  I suppose one could do something like the "universal enveloping
C*-algebra construction," where you start with a *-algebra and give it
a C*-norm which is essentially the sup over all norms of Hilbert space
representations.  This norm has a universal property and in my case too
one could try to define a norm on SV by a universal property -- though
I'd be happier if one could *also* describe the norm a bit more
explicitly.

In any event, what I'd really like is references.

Thanks,
John Baez