HDTenEightyP/NetNews huggingface dataset:
From: ted@physics2 (Emory F. Bunn)
Newsgroups: sci.math
Subject: Fourier Analysis in Hyperbolic Space
Date: 13 Jan 93 00:42:32 GMT
Followup-To: sci.math
Organization: Physics Department, U.C. Berkeley
NNTP-Posting-Host: physics2.berkeley.edu

I want to do something like Fourier analysis on functions on three-dimensional
hyperbolic space.  That is, I want to find a complete set of eigenfunctions
of the Laplacian on this space so that I can write an arbitrary (sufficiently
nice) function as a linear combination of these functions.  I think I've
found all of the eigenfunctions of the Laplacian, but I'm having trouble
figuring out the orthogonality and completeness relations I need to
make use of them.  That is, if f_k(x) is an eigenfunction with eigenvalue
-k^2, I want to prove things like

\int f_k(x) f_{k'}(x) dV is proportional to \delta(k-k')
and
\int f_k(x) f_k(x') ...  is proportional to \delta(x-x')

(\delta is a Dirac delta distribution; dV is the volume element in hyperbolic
space, and the ... means that I'm not sure what to put there:  It's some
sort of volume element in k-space.)

(The eigenfunctions can be written in terms of associated Legendre functions
of complex order, in case you're interested.)

Can anybody point me towards a good source of information, either on this
specific problem, or on doing this kind of analysis on a general Riemannian
manifold?  I'm a physicist, not a mathematician, but I'm not quite as
ignorant of mathematics as mathematicians generally suppose physicists to
be.  I've looked around for such sources, but I don't even know what one
would call this particular branch of mathematics, so I haven't found anything
useful.

Replies by e-mail would be preferable, as I don't generally follow
this newsgroup.

Thanks.

-Ted
(ted@physics.berkeley.edu)
Newsgroups: sci.math
From: yeomans@austin.onu.edu (Charles Yeomans)
Subject: Re: High Prices of Math Books. I am pissed.
Date: Fri, 8 Jan 1993 16:33:24 GMT
Organization: Ohio Northern University

In article <1993Jan7.232629.25796@ryn.mro4.dec.com>, roth@3d.enet.dec.com (Jim Roth) writes:
> 
> 
> In article <1993Jan7.214312.5720@austin.onu.edu>, yeomans@austin.onu.edu (Charles Yeomans) writes...
> >In article <ARA.93Jan7012128@camelot.ai.mit.edu>, ara@zurich.ai.mit.edu (Allan Adler) writes:
> >> 
> >> In article <C0GEBz.98t@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
> 
> >>    The amount of effort required to produce a fairly good book when one
> >>    does not already exist for a one-semester to one-year course is two
> >>    or three person-years, and preferably involves more than one person
> >>    writing it.  An active faculty member does not have the time to do
> >>    very much writing.
> 
> >> Why is this so? I heard a rumor that Serge Lang can knock off a book in
> >> a weekend.
> 
> >I heard it was a month.
> 
> Wow.. it takes me longer to understand one of his books :-)
> 
> (I'm thinking of the ones I've studied closely like his _Elliptic Functions_)
> 
> >Lang's books tend to be of somewhat uneven quality; also, given his 
> >writing technique, the quality is actually quite high, I suppose.
> >And Lang's mathematical insight is an order of magnitude above that of 
> >most mathematicians.
> 
> Still, he's published a *lot* of what appear to me to be serious books.
> Not sure how he manages to do that.

When Lang was writing Number Theory III, he met Colliot-Thelene and 
decided he wanted to include a section on Brauer group, Hasse principle,
etc.  Apparently Lang quizzed Colliot-Thelene intensely, getting him
to explain the main ideas, then forced him to give Lang a list of
references.  Lang then showed up one day later with the section written.

Charles Yeomans

Newsgroups: sci.math
From: cs911301@ariel.yorku.ca (CHAK MAN TSUI)
Subject: Re: HELP: limit
Originator: cs911301@m09.ariel.yorku.ca
Keywords: limit, sum
Organization: York University, Toronto, Canada
Distribution: york
Date: Tue, 12 Jan 1993 20:06:03 GMT




This problem is probably related to the study of Gamma Function.
Euler's Def. for Gamma Fn:
                    infin
                   /       -t  z-1
      Gamma(z) =  |       e   t    dt   ;  Re(z)>0.
                 /
                   0

However, for the incomplete Gamma Function:
                       infin
                     /      -t  n-1
      GAMMA(n,x) =  |      e   t   dt        Re(n)>0
                   /
                     x

This can be shown to be: 
                                n-1
                                ---      i
                           -x   \       x
     GAMMA(n,x)  = (n-1)! e     /      ---
                                ---     i!
                                i=0


Then,

                            k+q
                            ---    i
     GAMMA(k+q+1,k)    -k   \     k
     -------------- = e     /    ---
        (k+q)!              ---   i!
                            i=0

and, what you want is...

    

       lim      Gamma(k+q+1,k)
               ----------------  = Ans.
     k->infin       (k+q)!


---------------------------------
  From then on, I don't know how to proceed anymore...
  You may pick up any book on special functions, it usually contains
details about Gamma function...
  I hope this will help...
  
---------------------------------
  Will you post solutions to the newsgroup, if you solves it, or
you got someone's solution about it... thanks.

                 Jacques.
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Subject: Re: Frankly,my dear......was: Fermat's Last Theorem
Organization: U of Cambridge, England
Distribution: usa
Date: Sat, 9 Jan 1993 14:49:16 GMT

In article <1993Jan9.031339.6646@nuscc.nus.sg> matmcinn@nuscc.nus.sg (brett mcinnes) writes:

>Astrology and alchemy also gave rise to important things. Actually, you
>almost seem to be agreeing with me: FLT is of historical interest only.

No; I'm just not sure what you regard as making a problem interesting,
and I thought perhaps you were concerned with its relations to other
areas of mathematics.

>: Perhaps I'll understand better if you tell me what you think of some other
>: famous conjectures. What do you think of:
>:  * the twin prime conjecture?
>:  * the Goldbach conjecture?
>I try to think of them as little as possible.                            
> :  * the four-colour problem?                                           
> Amusing and entertaining, but not the stuff of Fields Medals.          
>  :  * the Poincare conjecture?                                          
> Now you're talking. This is really significant, and would be so even if
>it had no applications.                                                  
>:  * the Riemann hypothesis? :  : -- 
>Utterly boring in itself, like FLT; but unlike FLT, it is important
>because you need it to prove things that are interesting. Just imagine the
>sensation if it turns out to be wrong.                                    

You think the four-colour conjecture is more "amusing and entertaining"
than FLT? I'm astonished. Basically, it sounds to me like you're just
prejudiced against number theory (not, despite your comments, just the
recreational sort); very well, you don't find number-theoretical results
interesting, but plenty of mathematicians do, and it doesn't seem very
reasonable of you to try to decree that they're all wrong. Just different
tastes to yours.

But perhaps I'm wrong about you being prejudiced. What *do* you think
makes a mathematical problem worth considering?

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
From: cazelaig@ERE.UMontreal.CA (Cazelais Gilles)
Newsgroups: sci.math
Subject: proof wanted 2
Date: 8 Jan 93 19:56:46 GMT
Organization: Universite de Montreal


                                                       n
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.
 
If it is true I would appreciate if someone could give me a proof
of the result.
 
                Thanks in advance.
Newsgroups: sci.math
From: rgep@emu.pmms.cam.ac.uk (Richard Pinch)
Subject: Re: HELP: INTEGRAL
Summary: Do it by partial fractions
Organization: Department of Pure Mathematics, University of Cambridge
Date: Mon, 4 Jan 1993 11:37:15 GMT

In article <4540017@hpcc01.corp.hp.com> selee@hpcc01.corp.hp.com (Lee Say Eng) writes:
>
>
>I am running an experiment to find a constant n and the situation
>is such that I need to find an expression for the following integral
>(in which n appears) first. 
>
>
>	   /
>	   |       p
>	   |   __________  dp       where k1, k2 and n are constants
>	   |            n  
>	   |   k1 - k2*p 
>	   /
>
>
Express 1 - a p^n (where a = k2/k1) as \prod_j=1^n 1 - \zeta^j p
where \zeta = exp(2\pi i/n).  Then split up the product by partial
fractions into \sum b_j/(1 - \zeta^j p) where the b_j are suitable
constants.  Now you have to integrate a sum of terms each of the
general form p / (1-cp) for c a (complex) constant.  You get a lot
of logarithms.

Richard Pinch
From: tim@maths.tcd.ie (Timothy Murphy)
Newsgroups: sci.math
Subject: Re: transfinite real numbers? (...probably not. :( )
Keywords: well defined?
Date: 12 Jan 93 16:20:12 GMT
Organization: Dept. of Maths, Trinity College, Dublin, Ireland.

edgar@math.ohio-state.edu (Gerald Edgar) writes:

>*  As Cantor claimed, his transfinite numbers exist concretely. I wonder if
>* a process similar to the construction of real number (e.g.Dedekind cut)
>* can be extended.


>This sounds like J. H. Conway's "surreal numbers".  His text on it is
>called _On Numbers and Games_.  (Part Zero is on numbers.)

I've never understood why Conway's definition of number has not caught on.
Why isn't it taught in universities everywhere,
instead of Dedekind sections or Cauchy sequences?
Is it just that mathematicians are conservative?

With Conway's definition of number,
infinitesimals are real quantities, not limits.
Surely this would make the teaching of calculus much easier?


-- 
Timothy Murphy  
e-mail: tim@maths.tcd.ie
tel: +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland
Newsgroups: sci.math
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Subject: Re: High Prices of Math Books. I am pissed.
Organization: U of Cambridge, England
Date: Fri, 8 Jan 1993 01:20:16 GMT

In article <thompson.726445179@daphne.socsci.umn.edu> thompson@atlas.socsci.umn.edu writes:
>In all of this discussion I have not seen any reference to the
>following argument that helps explain why textbook prices are high:
>
>Those who buy textbooks (students) do not get to choose.
>Those who sell textbooks (publishers) like high prices.
>Those who choose textbooks (instructors) get them for free.
>
>So none of the parties involved in determining prices have any
>personal incentives to keep prices low.  To the extent that there is
>any price competition at all, it comes only through the altruistic
>concerns that instructors might have about their students' budgets.

That may have something to do with it, but I'm not sure how much. 
Perhaps things are different in the USA? In my four years taking
taught/examined courses, I don't think I've ever bought a textbook
to match a course; I've bought books that have interested me, and
done the course from lectures, using libraries for the occasions
when I've needed to look up something course-related in a book I
don't have. -- Books aren't needed so much for courses which are
lectured, as for independent reading, surely?

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
From: selee@hpcc01.corp.hp.com (Lee Say Eng)
Date: Mon, 4 Jan 1993 05:41:00 GMT
Subject: HELP: INTEGRAL
Organization: the HP Corporate notes server
Newsgroups: sci.math



I am running an experiment to find a constant n and the situation
is such that I need to find an expression for the following integral
(in which n appears) first. 


	   /
	   |       p
	   |   __________  dp       where k1, k2 and n are constants
	   |            n  
	   |   k1 - k2*p 
	   /


I've tried a few ways of doing it but haven't had any success. 
Any help will be greatly appreciated.

Thanks.

ALAN PHANG

alan@hpmalr50.mal.hp.com

---
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: Re: probability = 0
Date: 5 Jan 1993 18:08:34 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu

In article <9301051655.AA22441@aplpy.jhuapl.edu> louis@aplpy.jhuapl.edu (Louis  
Vasquez) writes:
> Hello,
[...]
> 	Anyone care to comment?
> 	Lou,
> 	louis@aplpy.jhuapl.edu

Even though the probability of an event is zero, it can happen.
(The probability that I would attain this exact physical stature was zero,
and yet, here I am, living proof...)  You're both right.

bart
Newsgroups: sci.math
From: UNM40F@rhrz.uni-bonn.de
Subject: article titles: any file?
Organization: RHRZ Uni-Bonn
Date: Sat, 09 Jan 93 19:10:54 MEZ

Hi,
is anything existing like "titles of articles published in journal xxx,
vols nn - NN" in machine readable form or even any kind of (I don't dare
to say) database with additional keywords?
Something similar for book titles?
 
Answers please via e-mail (for collection etc.).
Thanks a lot.
  Ralf Valerien
Newsgroups: sci.math
From: roth@3d.enet.dec.com (Jim Roth)
Subject: Re: High Prices of Math Books. I am pissed.
Organization: Digital Equipment Corporation
Date:  7 JAN 93 18:18:05    


In article <1993Jan7.214312.5720@austin.onu.edu>, yeomans@austin.onu.edu (Charles Yeomans) writes...
>In article <ARA.93Jan7012128@camelot.ai.mit.edu>, ara@zurich.ai.mit.edu (Allan Adler) writes:
>> 
>> In article <C0GEBz.98t@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:

>>    The amount of effort required to produce a fairly good book when one
>>    does not already exist for a one-semester to one-year course is two
>>    or three person-years, and preferably involves more than one person
>>    writing it.  An active faculty member does not have the time to do
>>    very much writing.

>> Why is this so? I heard a rumor that Serge Lang can knock off a book in
>> a weekend.

>I heard it was a month.

Wow.. it takes me longer to understand one of his books :-)

(I'm thinking of the ones I've studied closely like his _Elliptic Functions_)

>Lang's books tend to be of somewhat uneven quality; also, given his 
>writing technique, the quality is actually quite high, I suppose.
>And Lang's mathematical insight is an order of magnitude above that of 
>most mathematicians.

Still, he's published a *lot* of what appear to me to be serious books.
Not sure how he manages to do that.

As for the base note - I'm actually a bit more annoyed at the fact that
some really neat books have gone out of print.  I've resorted to getting
a copy via interlibrary loan in some cases and copying it, but it sucks.
I'd rather buy a copy. (In fact, I did this with Lang's Elliptic Fns when
it was finally reissued by Springer, years after I first read it.)

I've tried book searching, but without too much success.

By the way, have you seen the reviews of books in the Monthly - I have to
chuckle when they say "note the price!" - usually for a slim book on some
esoteric subject from someone like Kluwer or Gordon & Breech for $199.00.

- Jim
From: simpson@matt.ksu.ksu.edu (Phillip C Simpson)
Newsgroups: sci.math
Subject: Re: Points on Sphere
Date: 11 Jan 1993 16:53:24 -0600
Organization: Kansas State University
NNTP-Posting-Host: matt.ksu.ksu.edu

scotj@pinet.aip.org (scot_shinderman) writes:


>  Given n points that exist on the unit sphere in 3-space (s2), what is
>their distribution such that the sum of distances from each other is
>maximized.
>   | Pn | = 1.0;
>   maximize   sum(j = 1,n)  sum(i = 1,n)  | Pi - Pj |

>  any ideas?  If the points are considered charges, does the answer
>correspond to a point of equilibrium?
>- thanks!
>- scot shinderman (scotj@aip.org)

I would also be interested in any solutions or references to this question. 
This is problem I have been looking at over the past few weeks, in one or 
more different flavours. There are many similar and related n-points on 
a sphere problems:

1) Maximize the minimum distance between any two points.

2) Minimize the sum of the reciprocals of the distances.

3) Minimize the energy of repelling points.  

The problem I have been fooling around with is this: Given n point charges 
on the unit sphere how many local energy minima exist in the space of all 
possible configurations. This the same as asking how many unique zeros of 
the gradient of the potential function are there.

The best materials I have found on the problems are 'Regular Figures' by 
Fejes Toth ( mostly addressing 3) and a column Martin Gardner in Scientific 
American (circa 1959) which deals with 1. Of particular interest to me is 
which of these problems are 'equivalent' (ie their solutions look the same),
and which (if any) of these problems give rise to degenerate solutions. 

I would appreciate any help/references and am willing to post a summary if 
interest merits,

David Skinner
skinner@next1.cs.ukans.edu
Xref: sparky sci.math:17954 alt.books.technical:436
From: mccolm@darwin.math.usf.edu. (Gregory McColm)
Newsgroups: sci.math,alt.books.technical
Subject: Re: High Prices of Math Books. I am pissed.
Date: 6 Jan 93 21:21:11 GMT
Organization: Univ. of South Florida, Math Department

In article <1993Jan5.203717.11913@Princeton.EDU> bathurst@phoenix.Princeton.EDU (Bruce Bathurst) writes:
>I graduated from Princeton years ago, Gentlemen.  My observations on
>how the trebling of technical book prices has affected education are
>not complaints.  The poverty of the scholar is historical.  (It
>pre-dates modern political hate-labels.)
>
>The defending of American book prices as reasonable because they are
>expensive to produce misses the point that students can't buy them.

Huh?????  When Paul Cohen's book---camera-copy of 150 typewritten pages---
went out of print two decades after publication, it was $ 40.  It couldn't 
have been more than a few bucks to produce.  A more recent example is 
Fraisse's Relations, also camera-copy of 400 pages.  It is $ 90.  How 
could it cost anywhere near that for Elsevier to make a copy?  Modern 
publishers (at least in mathematics) often have no typesetting costs 
(it is camera-copied or already written in TeX), so most of the margin 
is profit.  If you don't believe that, look at how much MAA books cost.

-----Greg McColm
--
SHAMELESS AD:  Math PhDs in Analysis, Discrete Math./Th. of Comp., Num. Anal., 
Prob., are invited to apply to the Math. Dept. of Univ. of S. Florida for 
research/teaching positions that may be available: contact K. L. Pothoven at 
mathdept@math.usf.edu. Deadline 2/1/93. USF is a politically correct employer.
From: markc@smsc.sony.com (Mark Corscadden)
Subject: term for the "angle" of a complex number
Organization: Sony Microsystems Corp, San Jose, CA
Date: Tue, 12 Jan 1993 21:21:36 GMT

A complex number Z can be expressed in these ways:

rectangular -   X + Yi         where X and Y are real
polar -         R  exp(Ai)    where R>=0 and A are real (A is not unique)

Terminology for these quantities:

X - the real part of Z
Y - the imaginary part of Z
R - the magnitude of Z or the absolute value of Z
A - ???  I have no idea ???

What do you call "A"?  Ideally this would be a term that you could expect
to be recognized in a discussion about quantum field theory, for example.

Mark Corscadden
markc@smsc.sony.com
work: (408)944-4086
From: neilfp@astro.ocis.temple.edu (Neil F. Palumbo)
Newsgroups: sci.math
Subject: OOPS on HELP Quadratic Eqns
Date: 10 Jan 93 20:05:36 GMT
Organization: Temple University
X-Newsreader: TIN [version 1.1 PL8]

[ Article crossposted from sci.engr.control ]
[ Author was Neil F. Palumbo (neilfp@astro.ocis.temple.edu) ]
[ Posted on Sun, 10 Jan 1993 20:05:01 GMT ]

Oops, the Bi matrix is (1x100) NOT (100x1) as I posted. Thanks again in
advance...

				Neil
Newsgroups: sci.math
From: thompson@atlas.socsci.umn.edu (T. Scott Thompson)
Subject: Re: High Prices of Math Books. I am pissed.
Reply-To: thompson@atlas.socsci.umn.edu
Organization: Economics Department, University of Minnesota
Date: Thu, 7 Jan 1993 22:19:39 GMT

In all of this discussion I have not seen any reference to the
following argument that helps explain why textbook prices are high:

Those who buy textbooks (students) do not get to choose.
Those who sell textbooks (publishers) like high prices.
Those who choose textbooks (instructors) get them for free.

So none of the parties involved in determining prices have any
personal incentives to keep prices low.  To the extent that there is
any price competition at all, it comes only through the altruistic
concerns that instructors might have about their students' budgets.

Perhaps some reorganization of the textbook market is called for in
order to get the incentive structures right.  One step in the right
direction would be to eliminate the current system of providing free
desk copies of books to instructors.
--
T. Scott Thompson              email:  thompson@atlas.socsci.umn.edu
Department of Economics        phone:  (612) 625-0119
University of Minnesota        fax:    (612) 624-0209
Newsgroups: sci.math
From: ilan@leland.Stanford.EDU (ilan vardi)
Subject: Re: Closed forms for sums
Organization: DSG, Stanford University, CA 94305, USA
Date: Mon, 11 Jan 93 20:59:37 GMT

In article <24833@galaxy.ucr.edu> tadpole@ucrmath.ucr.edu (tad white) writes:
>* While we're on the subject, I was killing some time with Derive, a
>* Mathematical Assistant one day waiting form my Finite class to begin
>* and found the closed form for
>* 
>*         ---
>*         \     j
>*          >   i
>*         /
>*         ---
>*         i=1
>
>Mathematica doesn't seem to have them built-in either, and I needed
>them for my calculus course last quarter.  So here's Mathematica code
>for them, with a sample.
>

How about 

   s[m_, n_]:= (BernoulliB[m, n+1] - BernoulliB[m, 0])/m

-ilan
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: Fermat's Last Theorem
Date: 6 Jan 1993 20:01:07 GMT
Organization: The Ohio State University, Dept. of Math.
Distribution: usa
NNTP-Posting-Host: function.mps.ohio-state.edu


* I thank those who were polite about it.

Mathematicians receive so many of these amateur attempts (with elementary
mistakes in them) that they tend to get impatient with them...

An interesting book on the topic of this phenomenon is:

MATHEMATICAL CRANKS, by Underwood Dudley, published by the MAA.
--
  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: columbus@strident.think.com (Michael Weiss)
Newsgroups: sci.math
Subject: Re: Frankly,my dear......was: Fermat's Last Theorem
Date: 7 Jan 93 00:00:55
Organization: Thinking Machines Corporation, Cambridge MA, USA
Distribution: usa
	<1993Jan7.021308.10566@nuscc.nus.sg>
NNTP-Posting-Host: strident.think.com
In-reply-to: matmcinn@nuscc.nus.sg's message of Thu, 7 Jan 1993 02:13:08 GMT

[I omit McInness's OpEd (or diatribe, as he calls it) on why mathematicians
should not care about Fermat's last theorem]

    It is true that M. Fourier had the opinion that the principal
    aim of mathematics was public utility and the explanation
    of natural phenomena; but a philosopher like him should have
    known that the sole end of science is the honor of the human
    mind, and that under this title a question about numbers is worth
    as much as a question about the system of the world.

                                   --Jacobi, quoted in Bell's
                                       Men of Mathematics

Plus ca change...