HDTenEightyP/NetNews huggingface dataset:
From: jjpan@unixg.ubc.ca (James Jun Pan)
Subject: Help! Numerical Analysis?  ???
Summary: Looking for a solution to a numerical analysis probelm. Find
Keywords: Numerical analysis, approximation, fit, software, routine
Organization: University of British Columbia, Vancouver, B.C., Canada
Date: Tue, 15 Sep 1992 22:28:23 GMT

Hi, there.  I have come across the following problem in my work. I am
a chemist so please be patient if it is too simple for you guys. 

In general, for an equation , 

	y + a/y + b*LN(y)   ==  u + w*LN(x)	(1)

where a,b,,u, and w are constants,  we want to find a approximate solution    
of y in the form

	y = A + B*LN(x)				(2)

for a given range of x, where x > c, u+w*LN(c)=0.

This is mentioned in a paper and it is assumed to be trival so no explanation
is given.  I could only figure out one way to do this. The above problem is  
the same as to find the parameters A'and B' for

       A'*y + B'* = y + a/y +b*LN(y)   		(3)

i.e. use a straight line to approximate the curve.  And I had to do it 
by first plotting out the curve, fit the points to a straight line and
find out the slope and intercept. The reults are not satisfactory and
it heavily depends on how big the range of the ploted curve is.

Is there a general way to solve the probelm? Is there a way to get a pair
of A and B for a very large interval where the curve is "good" enough?

In particular, though, I need a solution to

	y - m/y - n*LN(y) = l - p*LN(x)		(4)

where m,n,l,p are all positive real numbers in the range 0 to 10.

Is there an established computation routine for this kind problem? 

E-mail to either of my e-mail address is fine. 

Thanks a lot.

James Pan


-- 
===========================================================================
James Jun Pan			E-mail:  JJPAN@unixg.ubc.ca
UBC & TRIUMF				 JJPAN@erich.triumf.ca	
Vancouver, BC			Phone:   (604)- 222-1047 (o)
Newsgroups: sci.math
From: rickert@mp.cs.niu.edu (Neil Rickert)
Subject: Re: computable reals
Organization: Northern Illinois University
Date: Sat, 12 Sep 1992 05:05:41 GMT

In article <9209120452.AA03328@ucbvax.Berkeley.EDU> lucas@WATSON.IBM.COM ("Bruce Lucas") writes:
>So, suppose we decided to limit the discussion to the set of "computable"
>reals.
>...
>This gives us a countable set that forms a field and contains all the
>"useful" reals (pi, e, sqrt(2), ...

>My question is is this in any way an interesting thing to do?  For example,
>what properties of the reals does this set have and which does it lack?

All you would lose would be the properties of reals useful to analysts,
physicists, and others.  Properties such as completeness, local
compactness, etc.  You would have to start worrying that perhaps the
solution f of an important differential equation might be such that
whenever x was computable, f(x) is not computable.  Presumably if this
could happen you would have to say that the equation was not solvable.

Newsgroups: sci.math
From: holmes@opal.idbsu.edu (Randall Holmes)
Subject: Re: Proof of God's Existence
Organization: Boise State University Math Dept.
Date: Tue, 8 Sep 1992 20:41:28 GMT



Please note that the existence of the set of all natural numbers is
sanctioned by one of the Fathers of the Church.  Note the use of
theological concepts to attack a set-theoretic problem.  But,
seriously, Augustine says some very modern things in this passage if
you think about it.  From St. Augustine, _the City of God_:


19.  The answer to the allegation that even God's knowledge cannot
embrace an infinity of things.

Then there is the assertion that even God's foreknowledge annot
embrace things which are infinite.  If men say this, it only remains
for them to plunge into the depths of blasphemy by daring to allege
that God does not know all numbers.  It is certainly true that numbers
are infinite.  If you think to make an end with any number, then that
number can be increased by the addition of one.  More than that,
however large it is, however great the quantity it expresses, it can
be doubled; in fact, it can be multiplied by any number, according to
the very principle and science of numbers.

Every number is defined by its own unique character, so that no number
is equal to any other.  They are all unequal to one another and
different, and the individual numbers are finite, but as a class they
are infinite.  Does that mean that God does not know all numbers,
because of their infinity?  Does God's knowledge extend as far as a
certain sum, and end there?  No one could be insane enough to say
that.

Now those philosophers who revere the authority of Plato will not dare
to despise numbers and say that they are irrelevant to God's
knowledge.  For Plato emphasizes that God constructed the world by the
use of numbers, while we have the authority of Scripture, where God is
thus addressed, "You have set in order all things by number, measure,
and weight".  And the prophet says of God "He produces the world
according to number"; and the Saviour says in the Gospel, "Your hairs
are all numbered".

Never let us doubt, then, that every number is known to him 'whose
understanding cannot be numbered'.  Although the infinite series of
numbers cannot be numbered, this infinity of numbers is not outside
the comprehension of him 'whose understanding cannot be numbered'.
And so, if what is comprehended in knowledge is bounded within the
embrace of that knowledge, and thus is finite, it must follow that
every infinity is, in a way we cannot express, made finite to God,
because it cannot be beyond the embrace of his knowledge.

				St. Augustine,
				_the City of God_,
				Book XII, ch. 19,
				pp. 496-7 (Pelican paperback)
-- 
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
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Lebesgue integral (was: Couple of questions
Date: 10 Sep 1992 08:26:46 -0400
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu


I have been told that the Lebesgue integral is not needed in physics--
presumably Riemann integral is enough.  Do you agree?
-- 
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
Newsgroups: sci.math
From: kyee@bnlux1.bnl.gov (kenton yee)
Subject: help me, please
Organization: Brookhaven National Laboratory, Upton, NY 11973
Date: Wed, 9 Sep 1992 13:57:41 GMT

I need to figure out what the following integral is:

  int dx_1 dx_2 ... dx_N  1    =   ??

where  0 < x_i < 1    subject to the condition  
   
  x_1 + x_2 + ... + x_N  is less than or equal to 1.  

It would be nice to learn a trick for doing such integrals
for arbitrary N in an elegant way.   AND...
 No, this is not a homework problem!


Newsgroups: sci.math
From: djoyce@black.clarku.edu (Dave Joyce)
Subject: Horus-eye numerals
Organization: Clark University (Worcester, MA)
Date: 10 Sep 92 08:01:47 GMT

Does anyone know a reference to Egyptian Horus-eye numerals besides Ifrah's
_From One to Zero_ (translation from _Histoire Univrselle des Chiffres_)?

He explains them pretty well, but gives G. Lefebvre's _Grammaire de l'egyptien
classique_ as his only named source (which I don't have access to), and
there must be something else.  In particular, I'd like an example of their
use.

The Horus-eye had six parts: the iris, the two sides of the white to the left
and right of the iris, the eyebrow, and two colored marks characteristic of
the peregrine falcon.  Each part represented a fraction 1/2, 1/4,..., 1/64,
for measuring volumes of grain.  It's a nice binary notation, and I've never
seen anything like it.




-- 
David E. Joyce				Dept. Math. & Comp. Sci.
Internet:  djoyce@black.clarku.edu	Clark University
BITnet:    djoyce@clarku		Worcester, MA 01610-1477
Newsgroups: sci.math
From: dak@tabaqui.informatik.rwth-aachen.de (David Kastrup)
Subject: Re: Chess Problem
Organization: Rechnerbetrieb Informatik  /  RWTH Aachen
Date: 12 Sep 92 18:55:01 GMT

rairan@ecf.toronto.edu (RAI Ranjan) writes:

>In celebration(?) of the Fischer-Spasky rematch in Yugoslavia, I thought I'd post
>a little chess problem I encountered in high school.
> 
>Chess Problem:
>     Eight rooks are placed at random on a chessboard.  What is the probability that
>   no two rooks can attack one another?
There are {64\over8} valid configurations, of which 8! configurations
have the desired property (in first column, 8 places to choose,
in second 7...)
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Interesting books
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Mon, 7 Sep 92 04:51:11 GMT

Here's a new book from the UC Press series "California Studies in the
History of Science."  I guess it's not out yet 'cause the ad says
"December" on it.  It might be interesting.

From c-Numbers to q-Numbers
The Classical Analogy in the History of Quantum Theory
Olivier Darrigol
ISBN 0-520-07822-5

...Darrigol illuminates not only the history of quantum theory but also
the role of analgoies in sicentific thinking and theory change.
Unlike previous works, which have tended to focurs on qualitative,
global arguments, Darrigols' study follows the lines of mathematical
reasoning and symbolizing and so is able to show the motivations of
early quantum theorists more precisely - and provocatively - than ever
before.  

Here's one from World Scientific that caught my eye.  It's been out a
while - anyone read it?  Care to write a review?

Mathematics and Science
ed. Ronald E. Mickens
ISBN 981-0234-2 (pbk)

The purpose of this review volume is to present the opinions of a
nubmer of distinguished individuals who have given careful thought as
to why mathematics is so "unreasonably effective" when applied to the
analysis of the natural sciences.

---
... which gives me a chance to give my own definition of physics: "the
study of those aspects of nature to which mathematics can most
fruitfully be applied."
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: Jokes in papers (was Re: Einstein's Erdos number)
Date: 10 Sep 92 01:44:30 GMT
Organization: U of Cambridge, England

Hmm. Lots of replies about the alpha-beta-gamma paper. Exactly one has the
names right. Just to confirm: It was Alpher, Bethe and Gamow. The article
was indeed published on April Fool's Day. Bethe did not contribute to the
paper, and the manuscript as submitted had a footnote to his name on the
title page: "(In absentia)". [Un]fortunately, in the version that was
finally printed this footnote was omitted. I believe many people refused
to believe that it was a serious paper.
-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
From: trh@ukc.ac.uk (T.R.Hopkins)
Newsgroups: sci.math.num-analysis
Subject: Re: public domain libs lapack etc?
Date: 14 Sep 92 15:05:37 GMT
Reply-To: trh@ukc.ac.uk (T.R.Hopkins)
Organization: Computing Lab, University of Kent at Canterbury, UK.

In article <1992Sep11.190806.949@newton.ccs.tuns.ca> greene@newton.ccs.tuns.ca (Courtney Greene) writes:
>
>Could someone either foward to me or post the address and procedures for
>receiving the indicies for lapack, matlab and whatever other public domain
>num. anayl. libraries are out there.
>

If you're in the UK/Europe area try mailing netlib@unix.hensa.ac.uk the
message

send index
send index from lapack
send index from matlab

you can also connect to this m/c for anonymous ftp. lapack s/ware is in
pub/netlib/lapack etc. 

Tim
Newsgroups: sci.math.num-analysis
From: ppc1@cec1.wustl.edu (Peter Pui Tak Chiu)
Subject: two pairs
Organization: Washington University, St. Louis MO
Date: Tue, 15 Sep 1992 02:48:08 GMT



hi,

can anyone point out what is wrong with my calculation of getting a hand
of two pairs from a shuffled deck of cards?

    the probability i have is:

	(13 * 4C2) (12 * 4C2) (4 * 11)
	------------------------------ = 0.095078
		      52C5

which is exactly two times the correct value (0.047539).

pete
From: cohen@alioth.greco-prog.fr (Henri Cohen)
Newsgroups: sci.math.num-analysis
Subject: Re: multiple precision floating point arithmetic ?
Date: 5 Sep 92 10:40:29 GMT
Reply-To: cohen@alioth.greco-prog.fr (Henri Cohen)
Organization: GRECO Programmation du CNRS - Bordeaux,France

In article <1992Sep1.010903.23456@julian.uwo.ca>,
plenson@hi_presure_lab.gp.uwo.ca (Peter Lenson) writes:
|> Hi,
|> 
|> I need help in locating a package which does multiple precision floating  
|> point operations with a precision of up to 500 decimal digit accuracy.
|> 
|> thanx 
|> 
|> Peter.


For MS-DOS machines, get UBASIC at shape.mps.ohio-state.edu
For Unix and Mac machines, get Pari at math.ucla.edu

Pari is callable from C.
     
     Henri Cohen

cohen@alioth.greco-prog.fr
Newsgroups: sci.math.num-analysis
From: eln122b@fawlty3.eng.monash.edu.au (Ivan Chin)
Subject: Itpack for complex number
Organization: Monash University, Melb., Australia.
Date: Wed, 16 Sep 1992 01:54:32 GMT

I am looking for some iterative package like itpack
that solves Ax=b where A is a sparse slightly non symmetrical
diagonal complex matrix. As itpack is based on A being real.
If anyone who has such information please inform me through email
In fact anyone who knows about the iterative method 'Orthomin',
please inform me of the source (books , periodicals anything ).
Thanks
Ivan...
From: neilfp@astro.ocis.temple.edu (Neil F. Palumbo)
Newsgroups: sci.math.num-analysis
Subject: Re: XAY+XB+CY+D=0, HELP
Date: 11 Sep 92 16:48:03 GMT
Organization: Temple University
X-Newsreader: Tin 1.1 PL5

In the equation:
           
             XAY+XB+CY+D=0,

the dimensions are: A(nxn), B(nxm), C(mxn), D(mxm), X(mxn), Y(nxm), with
 n > m. Furthermore, there is a required structure for the solutions {X,Y}.
X must be of the structure:

		| xx xx .. xx 0  0 ..................................0 |
		| 0  0 ....0 .xx xx .. xx 0 .........................0 |
                | 0  0 ................0  xx xx .. xx 0 .............0 |
                | .................................................... |
                | .................................................... |
                | 0  0 ................................. 0 xx xx .. xx |

and Y must be of the structure X' (note Y not = X'). Any suggestions??
From: rush@pine.circa.ufl.edu (PANCHAPAKESAN)
Newsgroups: sci.math.num-analysis
Subject: Info needed on FEM package
Date: 13 Sep 92 22:42:01 GMT
Reply-To: rush@pine.circa.ufl.edu
Distribution: usa
Organization: University of Florida  (ufl.edu)
News-Software: VAX/VMS VNEWS 1.3-4

Hi,

I need some information about some heat transfer/fluid flow
slover packages, and in particular a package called FIDAP.
Can anyone tell me where to look?

Thanks in advance,

Raghu

Email to : rush@pine.circa.ufl.edu (internet)
           rush@ufpine  (bitnet)
From: st_waldman@zodiac.dsto.oz.au
Newsgroups: sci.math.num-analysis
Subject: Frequency-domain curve fitter wanted
Date: 7 Sep 92 21:39:09 GMT
Organization: D.S.T.O. Aeronautical Research Laboratory

Hi,

I am interested in curve-fitting sound pressure and impedance
response functions in the frequency domain using a rational
fraction polynomial formulation. Does anyone have any source
code to such a routine in Fortran, Pascal, or C?.

I have seen a paper titled "A Frequency Domain Curve Fitting
Algorithm With Improved Accuracy", by Jim Adcock (Hewlett-
Packard) and Ron Potter (Consultant) that was presented at a
modal analysis convention a few years ago.

The above algorithm can fit to data that is log-spaced in the
frequency domain, which is the common form for audio/acoustic
measurements as published in loudspeaker manufacturers data
sheets.

My application is related to modelling of loudspeaker systems so
that it will be possible to design crossover networks that take
into account each driver's natural response characteristics.

Any suggestions or pointers where I could obtain program source
code that implements this algorithm will be gratefully received.

Maybe even someone from Hewlett-Packard can help me?

Thank you.

-----------------------------------------------------------------------
 Witold Waldman
 Aeronautical Research Laboratory   Internet: witold@hotblk.dsto.gov.au
 Melbourne                          Fax     : +61 3 646 7771
 Australia                          Tel     : +61 3 647 7488
-----------------------------------------------------------------------
Newsgroups: sci.math.num-analysis
Newsgroups: sci.math.num-analysis
Subject: "Difficult" oscillatory integrations
From: campo@sunthpi3.difi.unipi.it (Massimo Campostrini)
Date: 5 Sep 92 09:46:13 +0100
Reply-To: campo@sunthpi3.difi.unipi.it
Distribution: world
Organization: Istituto Nazionale di Fisica Nucleare, Pisa, Italy
Keywords: numerical integration

   I often have to perform numerical integrals of the form


          /\ infinity
         / 
        /      f(x) dx
       /
     \/ 0

where f(x) is oscillating and the integral of |f(x)| diverges
[f(x) often behaves like sin(omega*x+phi)/sqrt(x) for large x].
Are there any really accurate numerical integration methods for
this class of problems (I need at least 7 digit precision),
apart from rotating the integration contour in the complex plane
to imaginary x?  (contour integration works very well, but takes
a lot of analytical effort: I have identify all poles and cuts
of f, which is a very complicated transcendent function,
depending on parameters...)

   Thanks in advance,

-- 
        Massimo Campostrini, 
Istituto Nazionale di Fisica Nucleare, Sezione di Pisa,
Piazza Torricelli 2, I-56126 Pisa, Italy  ||  Phone: (+39)(50)42093
Internet: campo@sunthpi3.difi.unipi.it    ||  Fax:   (+39)(50)48277
From: randalld@ctcvax.ccf.swri.edu
Newsgroups: sci.math.num-analysis
Subject: Re: Info needed on FEM package
Date: 14 Sep 92 18:45:55 GMT
Distribution: usa
Organization: Southwest Research Institute

In article <37029@uflorida.cis.ufl.edu>, rush@pine.circa.ufl.edu (PANCHAPAKESAN) writes:
> Hi,
> 
> I need some information about some heat transfer/fluid flow
> slover packages, and in particular a package called FIDAP.
> Can anyone tell me where to look?
> 
 FIDAP is marketed by:

  Fluid Dynamics International
  500 Davis Street, Suite 600
  Evanston, IL  60201
  (phone)  708-491-0200
  (fax)    708-869-6495
Newsgroups: sci.math.num-analysis
From: Scottl@mot.com (Scott Lindsey)
Subject: Re: Frequency-domain curve fitter wanted
Organization: Motorola Land Mobile Products Sector
Date: Wed, 9 Sep 1992 23:19:32 GMT

It is possible to take whatever function you are using to fit your response
curves and determine best-fit parameters using pretty much any minimization 
type program. If there is difficulty in writing the derivative analyitically,
you can still use the Simplex algorithm. This procedure has been used to fit
complex impedance data to model circuits. The trick is to modify the object
function to account for logarthmic behavior. For example, normally one uses
F(x,y,z)-F(x.,y.,z.)  and minimize this
(where x, y, and z are the calculated and x., y., and z. are the
data values.. The most simplistic way of accounting for large value changes
over a wide range of data is to simply divide the difference by the data value.
Of course, one can become much more creative.... The simplex algorithm works
with any function that you can write.. no need to differentiate.
See Marco Caceci, Wiliam Chacheris in an article "FItting Curves to Data"
in Byte, Mqy 1984, P 340-62 (best) or
William Press et. al in Numerical Recipes

In article <1992Sep8.083909.1@zodiac.dsto.oz.au>, st_waldman@zodiac.dsto.oz.au writes:
> 
> Hi,
> 
> I am interested in curve-fitting sound pressure and impedance
> response functions in the frequency domain using a rational
> fraction polynomial formulation. Does anyone have any source
> code to such a routine in Fortran, Pascal, or C?.
> 
> I have seen a paper titled "A Frequency Domain Curve Fitting
> Algorithm With Improved Accuracy", by Jim Adcock (Hewlett-
> Packard) and Ron Potter (Consultant) that was presented at a
> modal analysis convention a few years ago.
> 
> The above algorithm can fit to data that is log-spaced in the
> frequency domain, which is the common form for audio/acoustic
> measurements as published in loudspeaker manufacturers data
> sheets.
> 
> My application is related to modelling of loudspeaker systems so
> that it will be possible to design crossover networks that take
> into account each driver's natural response characteristics.
> 
> Any suggestions or pointers where I could obtain program source
> code that implements this algorithm will be gratefully received.
> 
> Maybe even someone from Hewlett-Packard can help me?
> 
> Thank you.
> 
> -----------------------------------------------------------------------
>  Witold Waldman
>  Aeronautical Research Laboratory   Internet: witold@hotblk.dsto.gov.au
>  Melbourne                          Fax     : +61 3 646 7771
>  Australia                          Tel     : +61 3 647 7488
> -----------------------------------------------------------------------
> 
>
From: isaman@acsu.buffalo.edu (Fredric A. Isaman)
Newsgroups: sci.math.num-analysis
Subject: Re: Computing PI:
Date: 12 Sep 92 19:27:56 GMT
Organization: UB

I know some have asked for programs to generate pi.  I was wondering
if anyone knows where I could get a file containing pi out a few thousand
places without having to compute them myself?  Many thanks.
Newsgroups: sci.math.num-analysis
From: ppc1@cec1.wustl.edu (Peter Pui Tak Chiu)
Subject: FULL HOUSE (REVISED)
Organization: Washington University, St. Louis MO
Date: Sun, 13 Sep 1992 18:52:42 GMT



// this previous version of this program assumes that we are drawing from
// an infinite deck.  (which is a bug).

// now this version has no such problem...
// but still the probability is around 0.004...
// which is four times the theoretical value 0.001441

// what's wrong???!!!

#include <iostream.h>
#include <time.h>
#include <stdlib.h>
#include <math.h>

static int hand[5];
long COUNTER=0, GOOD=0;

int getRandom(){
int n,BAD=1;
while(BAD){
n=rand()%52+1;
for(int i=0;i<5;i++){
	int FLAG=0;
	if(n==hand[i])FLAG=1;
	if(!FLAG)BAD=0;
	}}
return(n);
}

void init(){
for(int i=0;i<5;i++)hand[i]=0;
for(i=0;i<5;i++)hand[i]=getRandom();
for(i=0;i<5;i++)hand[i]=hand[i]%13;
}

int fullhouse(){
int counter[13],flag2=0,flag3=0;
for(int i=0;i<13;i++)counter[i]=0;
for(i=0;i<5;i++)counter[hand[i]]++;
for(i=0;i<13;i++){
	if(counter[i]==2)flag2++;
	if(counter[i]==3)flag3++;
	}
return(flag2&&flag3);
}

main(){
randomize();
while(1){
COUNTER++;
init();
if(fullhouse())GOOD++;
if(!fmod(COUNTER,10000))cerr<<COUNTER<<double(GOOD)/COUNTER<<"\n";
}}
From: ags@seaman.cc.purdue.edu (Dave Seaman)
Newsgroups: sci.math.num-analysis
Subject: Re: FULL HOUSE
Date: 15 Sep 92 23:55:12 GMT
Organization: Purdue University

In article <1992Sep15.180943.1844@hpmcaa.mcm.hp.com> scotts@hpmcaa (Scott  
Scheirman) writes:
> Also srand() may repeat before you have run out of all possible card  
hands.

If you want to generate all possible card hands, you don't need a random  
number generator. The whole point of using a random number generator is to  
select a sample that is smaller than the entire space being considered,  
and yet to do the selection without bias.

--
Dave Seaman
ags@seaman.cc.purdue.edu
Newsgroups: sci.math.num-analysis
From: greene@newton.ccs.tuns.ca (Courtney Greene)
Subject: public domain libs lapack etc?
Organization: Technical University of Nova Scotia, Halifax, N.S.
Date: Fri, 11 Sep 1992 19:08:06 GMT

Hi,

Could someone either foward to me or post the address and procedures for
receiving the indicies for lapack, matlab and whatever other public domain
num. anayl. libraries are out there.

Thanks,
Courtney Greene
greene@tuns.ca