HDTenEightyP/NetNews huggingface dataset:
From: lee@dutiag.tudelft.nl (Marcel van der Lee)
Newsgroups: sci.math
Subject: Contents of n-dimensional sphere.
Keywords: n-dimensional sphere.
Date: 31 Aug 92 12:35:02 GMT


 Hello,

There exists a formula to compute the contents of an n-dimensional sphere.

        pi^(n/2)
C(n) = ------------- r^n
        gamma(n/2+1)

Where C denotes the contents, n denotes the dimension and r the radius of 
the sphere. I am wondering why the gamma function occurs in this formula.
If you have a proof or a good reference, please post it on Newsnet or send
it by e-mail to me.
Thanks.


-- 
   Marcel van der Lee -- lee@dutiaa.tudelft.nl

       /
      /        ___/    ___/
     /        _/      _/
    _____/   ____/   ____/

Newsgroups: sci.math
From: cyeomans@ms.uky.edu (Charles Yeomans)
Subject: Re: Godel and the US constitution
    <1992Sep02.134107.33391@watson.ibm.com>
Date: Wed, 2 Sep 1992 21:17:29 GMT
Organization: University Of Kentucky, Dept. of Math Sciences

In article <1992Sep02.134107.33391@watson.ibm.com> platt@watson.ibm.com (Daniel E. Platt) writes:
>In article <1992Sep1.203402.4257@magnus.acs.ohio-state.edu>, regeorge@magnus.acs.ohio-state.edu (Robert E George) writes:
>
>Taft was wrong.  Abraham Lincoln, under the state of emergency, revoked the
>writ of habeas corpus, effectively making it possible to imprison people
>indefinitely only upon an accusation.  The powers associated with a state of
>emergency might be adequate to keep a sufficiently popular president in
>office effectively as a dictator.  It was through the state-of-emergency 
>mechanisms in the German government that Hitler obtained his power.
>
>
>Dan

Fortunately there is the second amendment of the Bill of Rights.

Charles Yeomans
yeomans@austin.onu.edu
cyeomans@ms.uky.edu

Newsgroups: sci.math
From: shallit@graceland.uwaterloo.ca (Jeffrey Shallit)
Subject: "amslookup" shell script to search AMS database
Organization: University of Waterloo
Date: Wed, 2 Sep 1992 19:02:37 GMT

I got a copy of Ken Ribet's shell script below, which he calls
"amslookup", from Jerry Tunnell.  Ken told me he's posted this 
to the net before, but I never saw it, so he agreed I could post
it again.

Here it is:

---------------------------------cut here-------------------------
#
#From ribet@math.berkeley.edu Tue Sep  1 14:31:59 1992
#
#I did indeed write it, and I think that I posted it to sci.math
#at one point.  You're 100% welcome to spread it around.  The
#"sed" part of the pipe is to get rid of control-M's that are
#visible if you use "less" instead of "more".  If you really use
#"more", there's no need to strip out the control-M's.
#
(echo ${1} | /usr/etc/mconnect -p 2050 e-math.ams.com) | sed  's/^M//' | /usr/ucb/more

--------------------cut here-------------------------------------------

This script takes as an argument a mathematician's name (such as "ribet")
and returns the record stored in the AMS/CML database (with address,
phone, e-mail address, etc.)  Pretty useful!  No guarantee it works
everywhere, but it works on my Sun.

Jeff Shallit
Newsgroups: sci.math
From: mab@wdl39.wdl.loral.com (Mark A Biggar)
Subject: Re: Solitaire games
Organization: Loral Western Development Labs
Date: Wed, 2 Sep 1992 20:49:31 GMT

In article <Btyo5z.D8q@cs.psu.edu> morgan@math.psu.edu (Ilene Morgan) writes:
>My game with license plates is to try to find a word that contains the
>letters of the license plate in order, not necessarily consecutively.
>For example, XPV -> expressive.  My license plate used to have XPF; I never
>did think of one for that.

expeditefull
excerptfull
exemplify
exemplification

--
Mark Biggar
mab@wdl1.wdl.loral.com
From: drc@gauss.math.usf.edu. (David Cabana)
Newsgroups: sci.math
Subject: topological question
Date: 25 Aug 92 18:55:19 GMT
Distribution: usa
Organization: Univ. of South Florida, Math Department

Problem 3, chapter 5-3 of Munkres' Topology asks: under what
conditions does a metrizable space have a metrizable compactification?
I have torn a few hairs out trying to answer this, and have come to
believe that I am overlooking something.  I would appreciate whatever
light you might shed on this question.
		David Cabana
From: maspr@levels.unisa.edu.au
Newsgroups: sci.math
Subject: Directed Graph Display Software - LOOKING?
Date: 26 Aug 92 01:33:37 GMT
Organization: University of South Australia


I want the nodes and directed links of a given directed
graph to be displayed in a pleasing way - where clusters
of tightly connected nodes are automatically arranged on
the diagram in a local region.

I am sure there are programs out there which display 
directed graphs nicely, but where?

I need to get out a paper on the evolution of random
directed graphs, my graphs are evolving, but currently
I transcribe the directed matrix to xfig and muck around
with it four a couple of hours.  I could write a program
- but I want to shake the bushes first.

Kind suggestions anyone?


******************************************************************
***   Simon Ronald                                             ***
***   "There's a fly in my soup"                               ***
***   Email: maspr@lux.unisa.edu.au                            ***
******************************************************************
Newsgroups: sci.math
From: bns@cse.iitb.ernet.in (B Nagendra Srinivas)
Subject: Ph D in Maths and Computer Science
Organization: Department of Computer Science,IIT, Bombay
Date: Mon, 31 Aug 1992 09:02:46 GMT


   I'm an undergraduate in computer science . But I am a lot interested in
Mathematics too.I attend some courses in math on and off.  
Since my intrest shifts from one to the other periodically, I wonder if I  
can get Ph.Ds in both simultaneously without skimping on either. If this is  
possible, which grad schools are best for it and how long will it take? If  
not, what's the closest I can get?


-- 
BNSrinivas
Newsgroups: sci.math
From: takriti@engin.umich.edu (samer Takriti)
Subject: Re: Triangular systems of equations.
Date: Fri, 28 Aug 92 12:03:08 EDT
Organization: University of Michigan Engineering, Ann Arbor

In article <1992Aug28.002556.7374@amc.com> kenb@amc.com (Ken Birdwell) writes:
>I'm looking for a method to help me solve large systems of 
>simultanious equations (10,000+) that are related to one another in 
>the form of an irregular triangular mesh.  My problem seems to be in 
>not being able to order the points into a tight enough diagonal 
>sparse matrix.  If you know of any references on solving systems 
>like this, please forward them.
>
>
>The problem:
>    Given an irregular non-overlapping 2D open triangular mesh of a N 
>    points, with known coordinates for all edge points,  calculate "good" 
>    coordinates for all the interior points while maintaining the feature of 
>    non-overlapping triangles.  
>
>    The problem, I think, is that I don't have a good way to order the 
>    points in the matrix so that connected points keep a tight enough 
>    diagonal.  What I do now is to pick a single starting point, and 
>    interate outward from that point, numbering each point as they get 
>    farther and farther away from the starting point.  This creates (in the 
>    matrix) what look like a central band with two other parallel bands, one 
>    on each side of the central band, that bow out in the middle. This 
>    bowing in the middle ends up causing the matrix to fill up with non-zero 
>    values, and also killing performance.
>
Are you doing "Surveying" ? If this is the case there is a least
square method that will give you the "best" coordinates by solving
a system of equations. (There is no need for iterations). I worked
on this more than ten years ago and cannot find the name of the 
reference. You should check with civil engineers. The method is
well known. (There are two: direct and indirect but both of them
use least squares).
If you want to "exploit" the structure of your matrix in a better 
way, there is a computer package called sparcepack. It uses graph
theory to minimize the fill-in of the matrices. There is a book 
written by J. K. Reid, E. M. L. Beale and a third Professor about
sparse matrices. You could chec in the Mathematical Programming
journal. For example, there is an article in Math. Programming 24
(1982), pp. 55-69 by Reid: A sparsity-exploiting variant of the
Bartels-Golub Decomposition for Linear Programming. You can start
there.
-Samer
From: 8321207d@levels.unisa.edu.au
Newsgroups: sci.math
Subject: Help with Calculus
Date: 1 Sep 92 06:34:09 GMT
Organization: University of South Australia

Hi There!

I am in the midst of reviewing some calculus material from days gone by.
This is for the purpose of getting myself up to speed for some extra
study that I intend to undertake. I am experiencing some difficulty
with the following problems (mainly due to foggy memories). Any hints
are gratefully accepted.

1)  Let Phi(a)=Int from 0 to Inf of [exp(-ax)*Sinx/x]dx. Explain briefly
    why it is plausible to write Phi(a)=Pi/2 - ArcTan a. Could this 
    result be used to evaluate Int from 0 to Inf of [Sinx/x]dx ?

The second part of this I can establish quite easily using limits.
My attempts at the first part have led to dead ends.

2)  Let Psi(r)=Int from 0 to Inf of [Sin rx/x(1+x^2)]dx for r >= 0.
    Explain briefly why it is plausible to suggest that
    Psi''(r) - Psi(r) = Pi/2 with Psi(0)=0 and Psi'(0)=Pi/2. Hence
    deduce that Psi(r) = Pi/2*(exp(r) - 1).

The solution Psi(r) can be easily established by solving the DE with
the initial conditions. The first part, however, has flumoxed me!!

I will persist with these and try other avenues of solution but any
useful help will save lots of frustration.

E-mail to 8321207d@lv.levels.unisa.edu.au or post.

Thanks in advance
Paul.
From: jtien@venice.eng.uci.edu (Joe Tien)
Newsgroups: sci.math
Subject: need math functions
Date: 3 Sep 92 20:00:41 GMT
Reply-To: jtien@venice.eng.uci.edu (Joe Tien)
Organization: University of California, Irvine


Hello everyone,

Does anybody know where I can get the software for computing math functions
such as bessel, erf, and matrix inversions. FTP sites would be okay too. 

Please send email to jtien@balboa.eng.uci.edu.

Thanks much,

Joe Tien
From: rogers@epx.cis.umn.edu
Newsgroups: sci.math
Subject: Psuedo Random sequences   Help needed
Summary: Binary psuedo random sequence,  which bits or XORed in?
Date: 29 Aug 92 23:00:20 GMT
Organization: University of Minnesota


   I am need a random sequence for a graphics effect, and I can't
remember which bits to exclusive or together.  About ten years ago
I used data in a book to generate 24 bit sequences, but right now I need
a 12 bit sequence.   This is how it works:

      xxxxxxxxxxxx
   -->010101011001   <- a 12 bit binary number that will be shifted right
   |          |  | 
   |          |  |  <- two bits to be excluse ored together (and the result 
   | <-bit    \  /         inverted and shifted back in)
   |  shifted  []  
   | back in    |
   \            /
    ------------

The sequence will lock up if all ones are in the register, but otherwise
should give every number between zero and 4095 (inclusive) in an apparently
random order.  This is just what I need for what I am doing because I
need every number once to clear every location on the screen in a random
order.  
  
   The problem is I cannot remember which bits to XOR (or XNOR) together
and I think I have tried every combination. (of two bits)  I know that
some of the larger (bit length) sequences needed four bits to XNOR together.

  Does this sound familer to anyone?  Does anyone know what book I could 
find it in?

In C, the algorithm looks like this: (R=num, P= 2^p, Q= 2^q , p and q are bits)
(bits 0 and 3 were used in the example above,
  which would give P=2^0=1 and Q=2^3=8 )

if (((R&P)&!(R&Q))||(!(R&P)&(R&Q)))   /* R bit p XORed with R bit q */
   R = R >>1;                         /* R = R/2 */
else
   R = (R+4096)>>1;                   /* R gets a one shifted in */


Thanks in advance,
Brynn

rogers@epx.cis.umn.edu         (612) 536-6444
Newsgroups: sci.math
Subject: Re: polynomial roots and zero divisors
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 27 Aug 92 22:39:47 GMT

In <27AUG199211450866@cs.umass.edu> rcollins@cs.umass.edu (Bob Collins) writes:


>  I would like to find the eigenvalues/vectors of a square 
>matrix.  Unfortunately, the elements of the matrix are not 
>members of a field.  In particular, they are "dual numbers",
>defined in Yaglom's "Complex Numbers in Geometry" as a type of
>complex number (a + b E), a and b being reals, and E being a
>nilpotent imaginary unit; so E^2 = 0.  Dual numbers form a
>commutative ring, but they are not a field since any number 
>of the form (0 + a E) is a zero divisor.

>Question: Can I find the eigenvalues of a matrix (roots of a
>characteristic polynomial) whose elements (coefficients) are 
>from a commutative ring, but not a field?

In the general case, perhaps not; but in this case, we have:

M = A + B E; l (lambda) = a + b E; (A, B real matrices; a, b real numbers)

Det[M - l I] = Det[A -a I + E (B - b I)]
             = Det[A -a I] + E (Sum(i) Det[A-a I with row i replaced by B - b I]) + E^2 ...
             = Det[A -a I] + E (Sum(i) Det[A-a I with row i replaced by B])
                           - b E (Sum(i) Det[A - a I with row and column i removed]);

which can be solved if the characteristic polynomial of A has distinct roots.

If the characteristic polynomial of A does not have distinct roots, either
here are fewer than n eigenvalues, or (a + x E) are eigenvalues for all x
(for some a).

Alternatively, a + b E is an eigenvalue of A + B E if

(1) a is an eigenvalue of A of multiplicity 1 and the corresponding
eigenvalue of A + B eps is a + b eps + o(eps) (for eps small), or

(2) a is an eigenvalue of A of multiplicity > 1 and the corresponding
eigenvalue(s) of A + B eps are a + O(eps).

(This may not be obvious, but I believe it to be true.)


--
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; if you want to be sure I see a post, mail it.
Newsgroups: sci.math,sci.philosophy.tech
From: jackson@soldev.tti.com (Dick Jackson)
Subject: Re: Proof of God's Existence
Organization: Transaction Technology Inc.
Date: Thu, 3 Sep 1992 21:52:53 GMT

In article <Btx5E0.2Kw@usenet.ucs.indiana.edu> chalmers@bronze.ucs.indiana.edu (David Chalmers) writes:
>
> Building on a suggestion communicated in conversation by Hilary Putnam, this
> article provides a definite answer to a previously disputed question of
> philosophy by establishing the existence of God. In outline the argument
> (which the reader may find somewhat familiar) goes as follows: Everything has
> a cause; therefore there is a First Cause, namely God.

I know that you prefaced this quote by saying it was not entirely serious,
and that the main point of your article lies elsewhere. But if I (as a
very amateur voyeur of philosophy) make a corresponding argument but
substitute the string FCA (which might stand for first cause agent) for
the string God, how would a defender of this argument rebut my claim that
I have proved the existence of FCA but that FCA has no other properties of
the entity commonly called by many, but not a majority of people, God.

Dick Jackson
From: wilson@web.ctron.com (Dave Wilson)
Newsgroups: sci.math
Subject: Folding numbers
Date: 4 Sep 92 17:44:52 GMT
Reply-To: wilson@web.ctron.com (Dave Wilson)
Organization: Cabletron Systems INc.


    Suppose we have a leaflet of N connected pages, e.g:

        +-------+-------+-------+-     -+-------+-------+
        |       |       |       |       |       |       |
        | TITLE |   2   |   3   |  ...  |  N-1  |   N   |
        |       |       |       |       |       |       |
        +-------+-------+-------+-     -+-------+-------+

    Let f(N) be the number of ways to fold the leaflet along its
    perforations to the size of a single page so that the title page
    appears on top of the folded leaflet.  I have computed the
    following values for f(N):

            N       f(N)

            0        1
            1        1
            2        1
            3        2
            4        4
            5       10
            6       24
            7       66
            8      174
            9      504
           10     1406
           11     4210
           12    12198

    I have verified these values by hand up to N = 5.

    1.  Is there a closed form or generating function for f(N)?

    2.  If we do not restrict the title page to be on top of the
    folded leaflet, the number of foldings appears to be N*f(N),
    in all cases I have computed (N <= 10).  Is there a
    straightforward argument as to why this should be so?


-- 
David W. Wilson (wilson@web.ctron.com)

Disclaimer: "Truth is just truth...You can't have opinions about truth."
- Peter Schikele, introduction to P.D.Q. Bach's oratorio "The Seasonings."
From: ahaley@eoe.co.uk (Andrew Haley)
Newsgroups: sci.math
Subject: Re: dividing 100 digit nos.?
Date: 27 Aug 92 09:45:42 GMT
Organization: EO Europe Limited, Cambridge, UK
X-Newsreader: Tin 1.1 PL3

comptec91065@camins.camosun.bc.ca writes:
: Hello,
: 
: 	Can you help me locate the easiest method of dividing
: 	integers of at least 100 digits (possibly up to 4300 digits) ?
: 
: 	I have a 386-DX at home linked to a VAX at school 
: 	(in case that matters).
: 
: 	Thank you ...
: 
: Sincerely,
: 
: 	Allan Curry (in beautiful B.C. / CANADA)

FTP gmp 1.2 from prep.ai.mit.edu.  This is a full multiprecision
arithmetic package in C from those wonderful people at GNU.

Andrew.
Newsgroups: sci.math
From: breuker@cs.rulimburg.nl (Dennis Breuker)
Subject: Re: Solitaire games
Organization: University of Limburg
Date: Thu, 3 Sep 92 12:53:17 GMT

morgan@math.psu.edu (Ilene Morgan) writes:

>In article <4906@balrog.ctron.com> wilson@web.ctron.com (David Wilson) writes:
>>
>>
>>    I used to put three hours a day on the road to and from work.  My
>>    game was to factor license plate numbers in my head (preferably
>>    before I lost sight of the car).  A simpler game was to try to
>>    break the numbers on the license plate into two groups whose sum is
>>    the same. 
>>
>>
>>
>>-- 
>>David W. Wilson (wilson@ctron.com)
>>
>>Disclaimer: "Truth is just truth...You can't have opinions about truth."
>>- Peter Schikele, introduction to P.D.Q. Bach's oratorio "The Seasonings."

>My game with license plates is to try to find a word that contains the
>letters of the license plate in order, not necessarily consecutively.
>For example, XPV -> expressive.  My license plate used to have XPF; I never
>did think of one for that.

>Ilene

How about exemplify? (grep 'x[a-z]*p[a-z]*v' /usr/dict/words)

Dennis Breuker
(breuker@cs.rulimburg.nl)
Newsgroups: sci.math
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart Goddard)
Subject: n doesnt divide 2^n-1
Organization: Rose-Hulman Institute of Technology
Date: Fri, 28 Aug 1992 19:43:50 GMT



If someone could prove the following for me, I would be forever in 
his debt.

If n > 1, then n doesnt divide 2^n-1.

This _is_ a problem in a book, but I don't _DO_ homework anymore, I'm  
just curious.

Bart
goddard@nextwork.rose-hulman.edu
From: pwk@wsinfo01.win.tue.nl (Pieter Kuppens)
Newsgroups: sci.math
Subject: Why don't we split the group?
Date: 4 Sep 92 09:46:30 GMT
Reply-To: pwk@win.tue.nl

For those who don't read this group about twice a day,
there are too much articles, of which some aren't interesting
enough.
My suggestion whould be to split the group even more
Currently we have:
sci.math
sci.math.num-analysis
sci.math.stat
sci.math.symbolic
sci.math.research
I would like to see:
sci.math.coding        (with error correcting/cryptology/information theory)
sci.math.group         (group theory)
sci.math.misc          (whatever...)
sci.math.puzzles       (well, puzzles appear sometimes)
and many more.

Pieter Kuppens     (pwk@win.tue.nl)
-----
Pi is about 3.2 if you want to calculate the earth's surface.
From: laydin@solar.usc.edu (Levent Aydin)
Newsgroups: sci.math
Subject: Integral Eqn --> Diff. Eqn.
Date: 26 Aug 1992 16:04:05 -0700
Organization: University of Southern California, Los Angeles, CA
Distribution: world
NNTP-Posting-Host: solar.usc.edu



	Hello;
	
	I am a PhD student at the Communication Sciences Institute of the
University of Southern California.In my research I had to solve an integral
equation and learned that a usual approach is to convert that eqn. to an
"equivalent" differential eqn. and then try to solve that.
	I have sources which does this conversion without giving the details.
I understand that the procedure is to differentiate on both sides of the
int. eqn. first, simplify it, then differentiate a second time and substitute
for the terms recognized from the previous step and so forth..
	The integral equation in question is as follows:

				       1
				     /    sin[c*(t-s)]
       lambda_n * psi_n(t) = P*T/2 * |    ------------  * phi_n(s) ds
				     /        c*(t-s)
				      -1
	                                                          for |t| <=1

	and the related differential equation is given to be:

                ..       .     
	(1-t^2)*f(t)-2*t*f(t)+[mu(c)-c^2*t^2]*f(t)=0              for |t| <=1


         I tried several times to apply the procedure to end up with the
diff. eqn. but could not do it.Any help will be greatly appreciated.Please
respond me at laydin@solar.usc.edu.Thank you...


							L  E  V  E  N  T	
Xref: sparky sci.math:11012 sci.philosophy.tech:3115
From: holmes@opal.idbsu.edu (Randall Holmes)
Newsgroups: sci.math,sci.philosophy.tech
Subject: Re: Proof of God's Existence
Date: 4 Sep 92 19:34:45 GMT
Organization: Boise State University Math Dept.

In article <1992Sep3.215253.23999@ttinews.tti.com> jackson@soldev.tti.com (Dick Jackson) writes:
>In article <Btx5E0.2Kw@usenet.ucs.indiana.edu> chalmers@bronze.ucs.indiana.edu (David Chalmers) writes:
>>
>> Building on a suggestion communicated in conversation by Hilary Putnam, this
>> article provides a definite answer to a previously disputed question of
>> philosophy by establishing the existence of God. In outline the argument
>> (which the reader may find somewhat familiar) goes as follows: Everything has
>> a cause; therefore there is a First Cause, namely God.
>
>I know that you prefaced this quote by saying it was not entirely serious,
>and that the main point of your article lies elsewhere. But if I (as a
>very amateur voyeur of philosophy) make a corresponding argument but
>substitute the string FCA (which might stand for first cause agent) for
>the string God, how would a defender of this argument rebut my claim that
>I have proved the existence of FCA but that FCA has no other properties of
>the entity commonly called by many, but not a majority of people, God.
>
>Dick Jackson

Some of the premisses of the argument are very dubious; as someone
pointed out, every backward sequence of causal antecedents must itself
have a common causal antecdent.
-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu