HDTenEightyP/NetNews huggingface dataset:
From: gmmiller@mcs.drexel.edu (Michael R. Miller)
Newsgroups: sci.math
Subject: Applied Math - what do YOU do?
Summary: Survey of applied mathematicians
Keywords: visualization, applications, tools
Date: 5 Jan 93 05:21:18 GMT
Followup-To: gmmiller@mcs.drexel.edu
Distribution: sci.math, sci.math.symbolic, sci.math.num-analysis, sci.math.stat
Organization: Drexel University

(sorry about the repost; I think our news was unstable...)

I would like to gather information regarding some of the more 
interesting work done by applied mathematicians in industry and 
in academia.

I am especially interested in users of tools such as Mathematica, 
Maple, Matlab, et. al. in visualization, modeling, and data analysis work.

I welcome all responses, but am curious about the following areas:
     medical research
     image processing (esp. fractals)
     space, aeronautics
     weather forecasting
     physics (esp. lasers)
     signal processing
     information theory

Please e-mail your responses (short or long!) directly to me 
(gmmiller@mcs.drexel.edu).  The survey is for my own use (academic and 
career guidance).  If the responses warrant it, I will summarize and 
post the results.

If you love your job, here's a chance to brag about it!    :)

Thanks very much -- and happy 1993!

Mike Miller
(gmmiller@mcs.drexel.edu)
From: sundar+@cs.cmu.edu (Sundar Vallinayagam)
Newsgroups: sci.math
Subject: Re: What is the 'sinc' function?
Keywords: sinc
Date: 12 Jan 93 15:04:33 GMT
Article-I.D.: cs.C0qxw3.Ew.1
Organization: School of Computer Science, Carnegie Mellon


>I came accross it in a paper about the scattering of electromagnetic
>radiation. 
>
>Thanks.
>
>Darrell R. Hougen

Here is quote from Preface to the Second Edition of Ron Bracewell's book,
"The Fourier Transform and its Applications," (2nd edition, revised,
McGraw-Hill, 1986):

  Notation is a vital adjunct to thinking and I am happy to report that
  the _sinc function_, which we learned from P.M. Woodward's book, is alive
  and well and surviving erosion by occasional authors who do not know
  that "sine x over x" is not the sinc function.

Incidentally, the sinc function is sin pi x over pi x.  I have seen the
notation Sa(x) for sine x over x used in other books, but I do not know
if the latter is standard terminology.

BTW, Bracewell's book is one of the best books on Fourier Transforms, for
engineers, that is.  It has lots and lots of pictures and lends a lot of
physical insight into the topic.  The problems are quite challenging and
interesting.  Anybody else has used this book or taught out of it ?



ramli.



-- 
**************************************************
ramli@orca.ele.uri.edu
**************************************************
From: tadpole@ucrmath.ucr.edu (tad white)
Newsgroups: sci.math
Subject: Re: Closed forms for sums
Summary: Mathematica code
Date: 10 Jan 93 08:47:40 GMT
Organization: University of California, Riverside

In article <964.165.uupcb@hal9k.ann-arbor.mi.us> james.jones@hal9k.ann-arbor.mi.us (James Jones) writes:
* OB>Subject: sum(i=1 to n, i^3) = ??   URGENT !!
* 
* 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
* 
* where j went from 1 to about 12 or 13.  Can't remember exactly where I
* stopped at.
[ some formulas included...]

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.

-----
a[k_, n_] := (a[k,n] = Together [ 1/(k+1) ( (n+1)^(k+1) - 1 - 
   Sum[ Binomial[k+1,j] a[j,n], {j,0,k-1}])] ) /; k > 0;

a[0,n] := n;

a::usage = "a[k,n] returns a closed-form expression for 1^k+2^k+...+n^k,
when n >= 0 (possibly symbolic) and k is a fixed non-negative integer."
-----

In[2]:= a[3,n]

         2      3    4
        n  + 2 n  + n
Out[2]= --------------
              4
-----

[ Perhaps some motivation... Look at the integer points in
the (k+1)-dimensional cube of size n+1.  Assign to each point
the number of distinct values taken by its coordinates.  For
example, if k=1, we have something like this:

		2 2 2 1
		2 2 1 2
		2 1 2 2
		1 2 2 2

Then 1's occur along the (strong) diagonal; 2's occur in a union of
triangles (exercise: how many?); 3's in a union of tetrahedra, and so
forth.  In this way you write (n+1)^(k+1) as a union of the numbers in
question, and the recurrence relation falls out.]

Hope this helps.  --tad

By the way, I'm not sure there's a standard terminology for these numbers
(triangular, tetrahedral, ...)?  Perhaps "simplicial numbers" is apt?
-- 
/********************************************************\
*  Tad White                  UCR Dept. of Mathematics  *      
*  tadpole@ucrmath.ucr.edu    Riverside, CA  92521      *
\********************************************************/
Newsgroups: sci.math
From: rivero@sol.cie.unizar.es (Alejandro Rivero)
Subject: Points, topos and geometry
Reply-To: rivero@sol.cie.unizar.es
Organization: Department of Theoretical Physics. University of Zaragoza
Date: Tue, 5 Jan 1993 18:54:51 GMT



I had one or two questions to add to Adler ones, perhaps
some naughty cathegorist there can answer easily.

First, is the category of conmutative C*-algebras a topos?
Being as it is the dual (or it was the antiequivalente?) of the
category of compact topological spaces, it would be a  topos or sort of, am I
correct?

Second, what about the category of all C* algebras, this is, including the no
conmmutative algebras? Following Connes, you can use ANY C* algebra to make
diferential geometry. And you have "points" and "arcs" (R-->M or dually
C(M)-->R). This would have a categorial counterpart.

Third, which is the difference  from the categorial point of view of the two
categories? This would be: Which is the correct categorial formulation of
conmuttativity? But I m not sure if there are more diffs.

I dont know if categorists are or not in the side of Connes but I think they
would have something to say about all this stuff of non conmutative geometry,
manifolds etc...

Alejandro Rivero
rivero@cc.unizar.es
From: edgar@math.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: transfinite real numbers? (...probably not. :( )
Date: 11 Jan 1993 15:03:37 -0500
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu
Keywords: well defined?


*  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.)

-- 
  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: mstemper@ems.cdc.com (Michael Stemper)
Newsgroups: sci.math
Subject: Re: Value of the US Dollar
Date: 12 Jan 93 18:33:36 GMT
Reply-To: mstemper@ems.cdc.com
Organization: Empros Systems International, a division of Ceridian

In article <1993Jan11.180318.6541@cs.unca.edu>, snodgras@cs.unca.edu (Ryan Snodgrass) writes:
>How do I compute the value of the US dollar?

I give up. How do YOU compute the value of the US dollar? :->

It really depends on what metric you use. The metric that I use is
actually a variable metric. It's the famous Beers function:
  "How many beers can I get for it?"

If I go to a trendy brew-pub and order a pint of Porter, the value of
the US dollar is about 0.25
If I go to the bar at the hotel next to work, the value is 0.50
If I stop at the bar near my house, the value has gone up to 1.2
And, after 01:00, the value drops to zero, because the bars are closed.

So, we have a metric that is non-linear in both space and time. It's
messy to work with, but really useful.

If you prefer a simpler metric, how about 100 US cents? This is a
constant metric in both space and time.

-- 
#include <Standard_Disclaimer.h>
Michael F. Stemper
Power Systems Consultant
mstemper@ems.cdc.com
Newsgroups: sci.math
Subject: Re: Combinatorial? problem
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 4 Jan 93 19:35:50 GMT
Organization: Beckman Instruments, Inc.
Keywords: binomial coefficients

In <1992Dec29.041921.29638@cbnewsm.cb.att.com> thf@cbnewsm.cb.att.com (thomas.h.foregger) writes:

>In article <Dec.23.18.15.49.1992.22657@pepper.rutgers.edu>, gore@pepper.rutgers.edu (Bittu) writes:
>> 
>> Someone please help me with the following problem. I have pretty much
>> given up on it after a lot of thinking. We want to show the following:
>> 
>> given m,n nonnegative integers, the quantity
>> 
>>      (2m)! (2n)!
>>     -------------      is an integer.
>>      m! n! (m+n)!
>> 
>> 
>> Note that this is very easy to show by the standard argument where for
>> every prime p, you find the highest power of p (say p^k) that divides
>> the denominator and then show that p^k divides the numerator as well.
>> 
>> I want a combinatorial proof of this. I have tried rewriting the above
>> as C(2m,m)*C(2n,n)/C(m+n,m) where C(a,b) is "a choose b" and also in
>> other ways, but I still haven't come up with a combinatorial proof.
>> 
>> --Bittu


>Without loss of generality assume m<=n so m+n <= 2m.
???                                            >=
>Write the ratio as

>(2m)! . n! . (2n)!
>----   ---   -----
>(m+n)!  m!   n! n!

>Each of the 3 factors is clearly an integer, so the ratio is an integer.

--
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; please mail anything important.
From: edgar@math.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: sum of eigenvalues of a covariance matrix = trace ?
Date: 10 Jan 1993 12:44:44 -0500
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu

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.

Similarly, the product of the eigenvalues of a square matrix is equal
to its determinant.



-- 
  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: henebry@matt.ksu.ksu.edu (Geoffrey M Henebry)
Newsgroups: sci.math
Subject: Re: Looking for random permutation generation algorithms
Date: 8 Jan 1993 12:26:30 -0600
Organization: Kansas State University
NNTP-Posting-Host: matt.ksu.ksu.edu

rayw@ee.ubc.ca (raymond w m woo) writes:

>Hi, does anyone know, or can provide any pointer in the literature to, any 
>random permutation generation algorithm that can be easily implemented as a 
>function in a computer program?  

>But of course, I am interested in knowing *all* kinds of permutation generation 
>algorithms. 

try: 1) Combinatorial Algorithms, A. Nijenhuis & H.S. Wilf, Academic: New York,
        1975, ISBN: 0-12-519250-9, 253 pp.
     2) Elements of Combinatorial Computing, M.B. Wells, Pergamon: New York,
        1971, ISBN:none evident, Lib. of Congress: 77-129633, 258 pp.

good luck!
From: berling@informatik.uni-koblenz.de (Roland Berling)
Newsgroups: sci.math
Subject: analytic geometry
Date: 23 Dec 1992 13:27:38 GMT
Organization: Universitaet Koblenz
Distribution: world
Reply-To: berling@infko.uni-koblenz.de
NNTP-Posting-Host: klee.uni-koblenz.de
Keywords: polynomial curve, locus of mobile point


Hi,

I would like to know the equation(s) which describe the locus of a 
mobile point which is in the same distance from two given 
polynomial curves and/or straight lines. 
For example, given a circle and a straight line,
the locus of the point is a kind of parabola settled between 
circle and line. I am especially interested in the equations 
describing the locus-curves between conic sections and/or
straight lines. 

In order to compute a set of solution points, I am looking
for an algorithm which is able to compute all intersection points
between conic sections in the plane. Does an algorithm exists for
computing intersections of general polynomial curves?

I will thank you for any hints on textbooks etc.

Best regards,
		Roland


-- 
+----------------------------+-----------------------------------------+
|                            |                                         |
|  Roland Berling            |  Tel.:   +49 261 9119 436               |
|  Universit"at Koblenz      |  Fax.:   +49 261 9119 499               |
|  Institut f"ur Informatik  |  e-mail: berling@infko.uni-koblenz.de   |
|  Rheinau 3-4               |                                         |
|  D-5400 Koblenz            |                                         |
|  Germany                   |                                         |
|                            |                                         |
+----------------------------+-----------------------------------------+

Newsgroups: sci.math,alt.books.technical
From: steve@monu6.cc.monash.edu.au (Steve Balogh)
Subject: Re: High Prices of Math Books. I am pissed.
Organization: Monash University, Melbourne, AUSTRALIA
Date: Tue, 5 Jan 1993 18:39:53 GMT

In article <1993Jan5.173010.19718@Princeton.EDU> bathurst@phoenix.Princeton.EDU (Bruce Bathurst) writes:
>Generations of Americans educated their children for a better life.
>The fact that the educated go without luxuries, or sometimes food, is
>not a fact that Americans will soon believe.
>
>Glad you're pissed.  Wish everyone were.
>

You think you have it bad. Have a look at the cover price for any text book
and then DOUBLE it. That is about what we have to pay in Australia; and we
don't get paid any more than you guys do.

I am also pissed off at the prices charged, and often wish we had the
"cheap" prices that you have in the states.


Regards,
         Steve

----_--_-_-_--_-__-_------_-__---_-___-_----_-____-_-_--__-_--_--___-_-_-_--__-_
Steve Balogh  VK3YMY   (Maths G.14)   | steve@monu6.cc.monash.edu.au
Monash University, Clayton Campus     |      37 54'38.8"S  145 07'47.1"E ...ICBM
Wellington Road, Clayton.  	      |      +61 3 565 4747 Voice (Office)
Melbourne, AUSTRALIA. 3168	      |      +61 3 565 4746 Fax
Newsgroups: sci.math
From: ilan@leland.Stanford.EDU (ilan vardi)
Subject: Re: condoms
Organization: DSG, Stanford University, CA 94305, USA
Date: Wed, 6 Jan 93 12:25:24 GMT

I have solved the general problem of the least number of condoms it
takes for m men and n women to have all mxn heterosexual encounters.
The answer is

   m = n = 2 => 2 condoms

   m = 2k+1, n = 1 => k+1 condoms

otherwise, it's the smallest integer greater or equal to m/2 + 2n/3.
I assume that m >= n, otherwise interchange m and n. 

The same method solves the problem for m homosexual men all having
sex, and m bisexual men and n heterosexual women (posed by A. Orlitzky
and L. Shepp).

The problem was almost solved by Hajnal and Lovasz [``An algorithm to
prevent the propagation of certain diseases at minimum cost,'' in
``Interfaces between computer science and operations research,''
edited by J.K. Lenstra, A.H.G. Rinnoy Kan, and P. van Emde Boas,
Matematisch Centrum, Amsterdam 1978] who showed that the number was
within 2 of m/2 + 2n/3. In any case, showing that 6 men and 6 women
require only 7 condoms pretty characterizes the algorithm (Hajnal and
Lovasz required 8 condoms).

My solution appeard in my book ``Computational Recreations in
Mathematica'', Addison--Wesley, 1991. The reason it appeared there is
that I suspected that interest in this problem might last longer than
interest Mathematica.

-ilan 
Newsgroups: sci.math
From: NAHAJ@CC.UTAH.EDU (John B 'Nahaj' Halleck, UUCC)
Subject: SUMMARY of answers:  What is this factoring algorithm called?
Organization: UNIVERSITY OF UTAH COMPUTER CENTER
Date: Wed, 6 Jan 93 18:50:27 GMT
X-News-Reader: VMS NEWS 1.24

[I posted a factoring algorithm, and asked what it was called, and where
 I could read up on it.]

Algorithm in question:   (C version)

           q=p=(long) sqrt(n); guess = p*q;
 
           while (guess != n) {
                 if (guess>n) { guess -= p; q--; }
                 else         { guess += q; p++; }
           }
           printf ("two possibly non-prime factors are %ld, %ld.\n",q,p);

Summary:

  Every single reply, without exception, received to date has pointed out
  that it can't be used to factor large numbers.    I thought this was
  self evident, but since everyone that answered pointed this out, I'm
  putting it in the summary.

  Nobody had a specific name or literature references for the algorithm
  itself.   Although several people miss-identified it as Fermat's method.
  Since it factor's by addition and subtraction, and there is a square
  root in the setup, and it adjusts two parameters, it does have superficial
  resemblance to Fermat's method.   But a closer look will show that it is
  not.

  The most generally usefull answer was that this is one of the infinite
  class of "potential function" factoring algorithms.   These are in form
  identical to certain potential function curve drawing algorithms.  The
  graphics routines draw curves by trying to stay as close to the zero 
  curve of the function as they can, while staying on the latitice.  The
  factoring algorithms do the same (for a curve known to go through the
  factors) but also check to see if we are on a lattice point.
  This point is somewhat obscured in the form given by the test
     guess == n
  if one rewrites the test as   guess - n  =  0   then the potential function
  character of the algorithm becomes more clear.
  [Answer provided by LeRoy Eide <lneide@cc.utah.edu> in a phone call]
From: hougen@focus.csl.uiuc.edu (Darrell Roy Hougen)
Newsgroups: sci.math
Subject: Re: High Prices of Math Books. I am pissed.
Date: 6 Jan 1993 03:18:08 GMT
Organization: Center for Reliable and High-Performance Computing, University of Illinois at Urbana-Champaign
NNTP-Posting-Host: focus.csl.uiuc.edu

goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard) writes:

% In articles <> several well-meaning but misguided souls write:
%% Have they suddenly lost the ability to use the libraries?
% Just how many copies of a text book do you suppose a library carries?

You said that college students didn't have the opportunity to read,
*not* just that text books were expensive.  But if you want to devise
a solution, why not ask professors to require less expensive books in
their courses?  There are many very high quality books that appear as
paper backs.

%%  The idea that some are going without food is ridiculous.

% No it isn't.  I can't imagine a time in my future when I will cease to be 
% bitter about the ignorant comments made by middle-class frat boys who've
% had everything handed to them on a silver-plated platter.

I resent that.  I have never belonged to a fraternity, I attended an
inexpensive undergraduate institution for lack of much choice and I
have worked hard for every penny in grad school.  But I cannot see
sticking it to others to make my life easier.  Enough of special
interest politics.  

Darrell R. Hougen
Newsgroups: sci.math
From: clarke@acme.ucf.edu (Thomas Clarke)
Subject: Re: How to Add White Gaussian Noise to Variables?
Organization: University of Central Florida
Date: Tue, 5 Jan 1993 22:07:53 GMT

In sci.math article <1993Jan5.195505.22186@wuecl.wustl.edu> you wrote:
> Hi fellows!
> Could anybody tell me how to add white gaussian noises to the process
> measurements?
> Any response is greatly appreciated!
> Lots of thanks in advance!
> 
> My address: ma@wuche2.wustl.edu
Don't have references at fingertips but if you mean to generate
samples of Gaussian noise in software to add to your data there are
standard methods to generate Gaussian or normally distributed random
variables from the uniformly distributed random variables that
computers usually supply. [try Abramowitz and Stegun, Special
Functions for a possible reference source]

The generatl idea is to take two uniformly distributed random 
samples, say A and B on [0,1] for definiteness.  Then turn one into
an exponentially distributed variable, R=exp(-S/A), where S is
standard deviation (my memory is rusty here, be sure to check 
other sources), and another into a uniform [0,2pi]=2pi*B.  
Then two Gaussian RVs are given by X=Rcos(B) and Y=Rsin(B).
I don't recall the constant relating S and the standard deviation 
of X and Y, but the constant is of order unity.

The trick is that the comples Gaussian RV (X+iY) goes into
exponential and uniform [0,2pi] in polar notation.
--
Thomas Clarke
Institute for Simulation and Training, University of Central FL
12424 Research Parkway, Suite 300, Orlando, FL 32826
(407)658-5030, FAX: (407)658-5059, clarke@acme.ucf.edu
Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Bayes' theorem and QM
Keywords: infinite
Organization: Computer Science Department,  Stanford University.
Date: Wed, 6 Jan 1993 06:41:40 GMT

In article <5915@osc.COM> jgk@osc.COM (Joe Keane) writes:
>A mostly unrelated observation is that if you mix 1 liter of water and 1 liter
>of alcohol, you get about 1.8 liters of something like vodka.

...and if you mix 1 liter of marbles and 1 liter of sand, you get about
1.52 liters of stuff.
-- 
Vaughan Pratt				There's safety in certain numbers.
Newsgroups: sci.math
From: brumleve@clio (Danny Brumleve)
Subject: Re: probability = 0
Organization: University of Illinois at Urbana
Date: Fri, 8 Jan 1993 22:20:13 GMT

louis@aplpy.jhuapl.edu (Louis Vasquez) writes:

>Hello,
>	My friend and I got in a debate about the probability of 
>something happening.  The event was that another friend of ours
>could win the superbowl.  Not that he would play on a winning team
>in the superbowl but that he would win it.
>	My thinking is that anything at all is possible and there are
>ways that this could happen however unlikely they are.  For example
>the rules of the superbowl could change to allow a single person to 
>be a team and this friend of ours would by some incredible luck, win it.
>I also say that there are many many other ways that it is possible.  
>Therefore I say there is a probability of greater than zero of this
>happening.
>	His arguments (although I must admit I probably don't fully 
>understand them) are that by definition a single person cannot win
>the superbowl.  And the case that I gave is a finite case in an 
>infinite number of possible cases and therefore the probability is
>n devided by infinity, a limit which approaches zero.  Therefore he
>says there is a probability of exactly zero that this will happen.
>	Anyone care to comment?
>	Lou,
>	louis@aplpy.jhuapl.edu

Your friend is mistaken when he says there is only 1 possible case for
a single person winning the superbowl, unless the exact state of the
universe (i.e., an infinite set) can be described at the time your
friend wins the superbowl.  There are an infinite number of possible
ways that your friend could win the superbowl, taking into account
where he is, what color clothes he's wearing, what the angle between
the planet Zog and Earth is, etc.  Therefore it's possible that your
friend could win the superbowl because "winning the superbowl" and
"the universe" are both infinite sets.

-Dan
Newsgroups: sci.math