HDTenEightyP/NetNews huggingface dataset:
From: mjohnson@netcom.Netcom.COM (Mark Johnson)
Subject: Very challenging optimization problem
Date: Thu, 20 Aug 92 15:01:37 GMT
Organization: Netcom Online Communications Service

In article <cscoging.66@unpcs1.cs.unp.ac.za> cscoging@unpcs1.cs.unp.ac.za (Chris Scogings) writes:
   > I am testing various optimization methods and I need some
   > problems to test them out on.  These problems must not be
   > too simple (I have already used Rosenbrock's function, etc.) ...
   > Ideally, I need a moderately complex function of 3 to 8
   > variables.  It is not necessary for the function to be
   > differentiable.

The objective function below appeared in the ACM Transactions
on Mathematical Software.  I find it remarkably difficult;
perhaps you will have better success.  The number of variables
to be optimized (the dimensionality of the domain) is
user selectable; I find it difficult for n=4 and incredibly
difficult for n=9.  The function is not differentiable.
Code is in the "C" language.  Good luck!






#define		VECTLEN	(50)	/* max dimensionality of function */


/* Objective function of Corana et al  ACM Trans on Mathematical */
/*                                     Software V13 No3 p272     */

/* Like the Chebyquad function, this one lets the user select    */
/* the dimensionality of the domain ("nvars").                   */
/* However, it is a very difficult function even when nvars=4.   */

/* Starting point is:  even numbered coordinates have x[j] = 999 */
/*                     odd numbered coordinates have x[j] = -999 */
/*                     { x[2i]=999 , x[2i+1]=-999 }              */

/* Minimum is at x[j] = 0.00 , for all j                         */
double	f(x,nvars)
	double	x[VECTLEN] ;
	int	nvars ;
{
	double	s[VECTLEN], t[VECTLEN], d[VECTLEN] ;
	double	term, summ, dj, c, deviate ;
	int	i, j, k;

	funevals++;

	for(i=0; i<VECTLEN; i++) { s[i]=0.2 ; t[i]=0.05; d[i]=10.0 ; }
	d[0] = 1.0 ;      d[1] = 1000.0 ;
	d[2] = 10.0 ;     d[3] = 100.0 ;
	d[4] = 1.0 ;      d[5] = 10.0 ;
	d[6] = 100.0 ;    d[7] = 1000.0 ;
	d[8] = 1.0 ;      d[9] = 10.0 ;
	c = 0.15 ;

	summ = 0.0;
	for(i=0; i<nvars; i++)
	{
		dj = floor(  fabs(x[i] / s[i]) + 0.49999999 ) ;
		if(x[i] < 0.0) dj = 0.0 - dj ;
		dj *= s[i] ;
		deviate = fabs(x[i] - dj) ;
		if( deviate < fabs(t[i]) )
		{
			term = 0.0 ;
			if(dj < 0.0) term = t[i] ;
			if(dj > 0.0) term = (0.0 - t[i]);
			term += dj ;
			term = term * term * c * d[i] ;
		}
		else term = d[i] * (x[i] * x[i]) ;
		summ += term ;
	}
	return(summ) ;
}

-------------------
  -- Mark Johnson
Newsgroups: sci.math.num-analysis,comp.parallel
From: qliu@shape.mps.ohio-state.edu (Quan Liu)
Subject: Domain Decomposition code on CM-2 Needed
Organization: Department of Mathematics, The Ohio State University
Date: 13 Aug 1992 16:59:55 -0400

        As stated in the subject,I try to use domain decomposition method to
solve some simple problems in CM-2. I will appreciate it if someone could send me
code in CM Fortran, or even Fortran 77.

        Thanks a  lot!


      Quan



-- 
  Quan  Liu                   Dept. of Mathematics
  Email: qliu@shape.mps.ohio-state.edu     Ohio State University
  Phone: work: (614) 292-3532         204 Cockins Hall
From: tfrey@rp.CSIRO.AU (Thierry Frey)
Newsgroups: sci.math.num-analysis
Subject: function graphs display
Date: 21 Aug 92 11:24:18 GMT
Organization: CSIRO Division of Radiophysics/Australia Telescope National Facility

I am looking for a C program that displays the graph of a given function of one
or two variables, y=f(x), z=f(x,y), as well an in polar coordinates r=f(theta)

Has anybody got that?

Thanks in advance,

	-Thierry
Newsgroups: sci.math.num-analysis,comp.parallel
From: nagrwb@vax.oxford.ac.uk
Subject: quadrature and parallelism
News-Moderator: Approval required for posting to comp.parallel
Organization: Oxford University VAX 6620
Date: 21 Aug 92 08:50:30 BST

I'm looking for references on parallel techniques for quadrature problems.
Even better, does anybody have a bibliography on the subject? Post to
the net or e-mail direct and I'll summarize.

TIA - Richard.
-- 
** R.W. Brankin -- nagrwb@vax.ox.ac.uk **
From: whart@cs.ucsd.edu (Bill Hart)
Newsgroups: sci.math.num-analysis
Subject: Re: WANTED: Optimization problem
Date: 20 Aug 92 15:18:44 GMT

cscoging@unpcs1.cs.unp.ac.za (Chris Scogings) writes:

>I am testing various optimization methods and I need some problems to test 
>them out on.  These problems must not be too simple (I have already used 
>Rosenbrock's function, etc.) but must not be so complicated that I spend all 
>my time setting up the function and not optimising it.

>Ideally, I need a moderately complex function of 3 to 8 variables.  It is 
>not necessary for the function to be differentiable.  Results of the 
>optimization and comparisons between various methods will be posted if 
>anyone is interested.

If you are working on global optimization approaches, you should
check out the problem sets described in the following two books:

Aimo Torn, Antanas Zilinskas.
Global optimization 
Berlin ; New York : Springer-Verlag, c1989

C.A. Floudas, P.M. Pardalos.
A collection of test problems for constrained global optimization algorithms
Berlin ; New York : Springer-Verlag, 1990


--Bill
Newsgroups: sci.math
From: sullivan@teal.csn.org (Steve Sullivan)
Subject: Re: Linaer Programming software sought
Keywords: linear programming
Organization: Colorado SuperNet, Inc.
Date: Wed, 19 Aug 1992 00:41:18 GMT

In article <893@unidoct.chemietechnik.uni-dortmund.de> pape@plato.chemietechnik.uni-dortmund.de (David Pape) writes:
>We are looking for programming packages/libraries/toolkits and the like
>to solve large linear and integer programming problems, preferably
>using the Dual-Simplex, Branch and Bound or Balas Zero-one algorithms.


I'm aware of several packages, though I've not used
any of them:

- Recently a PD package for mixed integer LP
  was posted to comp.sources.reviewed.  Called "lp_solve".
- Mathematica and Maple both have LP packages
- My Uniforum Products Directory lists LP packages by:
   Cplex Optimization, Inc.
   Haverly Systems, Inc
   MathWorks, Inc.
   SD Scicon UK Ltd
   Dash Associates Ltd
- In addition, IBM offers MPS/X, and no doubt other
  manufacturers (DEC? CRAY? etc) offer similar products.


=========================================================================
Oh!  This isn't as simple as it appears ...

Steve Sullivan    sullivan@csn.org

Any opinions expressed may represent my own views only, and
are not intended to represent those of any associated organization.
Information herein is simply my opinion or proposals for rumination;
no guarantees of accuracy are made.
=========================================================================

Newsgroups: sci.math
From: dak@messua.informatik.rwth-aachen.de (David Kastrup)
Subject: Re: You know, the integers (was: Re: Stupid question about FLT)
Organization: Rechnerbetrieb Informatik  /  RWTH Aachen
Date: 17 Aug 92 12:11:38 GMT

torkel@sics.se (Torkel Franzen) writes:


>  What is PA? My explanation of the integers is simple: the integers
>are 0, s(0), s(s(0)) and so on. Any obscurity or ambiguity that you
>find in this explanation carries over to any explanation of what is
>meant by "PA".

Wow, quite a few less features (axioms) than I need.
At least cyclelessness would be desirable, or else you end up with
a finite set. And some other things would be nice too, as someone
called Peano has figured out quite a while ago.

The above corresponds more or less to the axiom justifying
proofs by complete induction.
Organization: Queen's University at Kingston
Date: Tuesday, 18 Aug 1992 13:14:02 EDT
From: Peter Gogolek <GOGOLEKP@QUCDN.QueensU.CA>
Newsgroups: sci.math
Subject: Re: Did Gauss ever say ...
 <1992Aug17.203632.21234@kth.se>

A different quotation attributed to Gauss, this time by
R.W. Bilger (don't worry if you don't recognise the name)
   The great Physicist (sic :-)), Gauss, is reported to have
   said that with seven adjustable constants, he could
   produce an elephant on a tight rope and with nine he
   could make it dance.

Any chance this is correct?  Any pointers on context or a
reference?

Peter Gogolek
Kingston, Ontario, Canada
From: sichase@csa2.lbl.gov (SCOTT I CHASE)
Newsgroups: sci.math
Subject: Re: mathematician's marrying ages.
Date: 13 Aug 92 19:25:29 GMT
Organization: Lawrence Berkeley Laboratory - Berkeley, CA, USA
Distribution: na
Reply-To: sichase@csa2.lbl.gov
NNTP-Posting-Host: 128.3.254.197
News-Software: VAX/VMS VNEWS 1.3-4   

In article <1172@kepler1.rentec.com>, andrew@rentec.com (Andrew Mullhaupt) writes...
>In article <hubert.713379330@spica> hubert@spica.ucsb.edu (Chang;Hung-Hsien;H.;;;COMS;Graduate;930630;;;8-402525-19906-7;500) writes:
>>Any counterexample? ( Marry late and have quite an achievement )
> 
>Erdos.

Erdos seems to be a counterexample to almost every theorem one could think of.

-Scott
--------------------
Scott I. Chase			"The question seems to be of such a character
SICHASE@CSA2.LBL.GOV		that if I should come to life after my death
				and some mathematician were to tell me that it
				had been definitely settled, I think I would
				immediately drop dead again."      - Vandiver
From: mapsj@gdr.bath.ac.uk (Simon Juden)
Newsgroups: sci.math
Subject: Re: Is Card(R)=Card(R^2)?
Date: 13 Aug 92 13:15:18 GMT
Organization: School of Mathematics, University of Bath, UK

In article <1992Aug13.011522.11161@informix.com> proberts@informix.com (Paul Roberts) writes:
>In article <1992Aug13.000928.12631@unidus.rz.uni-duesseldorf.de> heisen@convex.rz.uni-duesseldorf.de (Henner Eisen) writes:
>>In article <1992Aug12.102140.5231@nntp.hut.fi> samu@lammio.hut.fi writes:
>>>I have been wondering... It seems first that there are more pairs of
>>>real numbers than real numbers, but is it really so? And if not, I would
>>>like to see a bijective mapping f:R->R^2.     ...
>>
>>Such mappings exist! To construct a mapping f(x,y) = z  choose a
>>unique decimal representation of x and y and then merge the digits.
>>
>>i.E.:
>>x =  1 0 0 2. 7 1 8 2 8 2 . . . . . .
>>y =   3 0 3 .1 4 1 5 9 3 . . . . . . 
>> 
>>z =  1300032.174118529832............
>>
>>This will be bijective for non-negative real numbers. In order to obtain a
>>bijective mapping R <-> R^2 this has to be combined with a bijection
>>which maps real numbers to non-negative real numbers (right now, I
>>don't remeber by heart how this is done, but it is possible).
>
>I believe that there is even an everywhere-continuous 
>bijective mapping from the unit line to the unit square.


Indeed so - an elementary version of Peano's construction of such may be found
on page 283 of the American Mathematical Monthly, April 1983.

Simon
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: Category theory funded by DOD?
Date: 12 Aug 92 13:59:12 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <1992Aug11.160727.27151@galois.mit.edu> jbaez@nevanlinna.mit.edu (John C. Baez) writes:
>In article <1165@kepler1.rentec.com> andrew@rentec.com (Andrew Mullhaupt) writes:
>>One of the ones I expect to be answered sooner rather than later is the
>>explanation of the inertial range of fluid turbulence.
>
>What's that?

The problem is to explain the observed scaling of the energy in a turbulent
fluid with wavenumber. Heisenberg's scaling law governs small scales only.
There is (as one would expect) a vast literature on this subject, and there
are many possible explanations. (C. E. Leith pointed out that there were at
one point, dozens of different sets of assumptions which arrived at the
correct scaling law, but many of them were mutually exclusive...). A successful
explanation would not only reproduce Kolmogorov's scaling, but would determine
this behavior from something resembling first principles. The Yahot-Orszag
theory is the latest one I know of, but there is a general feeling that this
kind of explanation (renormalization group) is not the answer.

>>Now we hear John Baez trying to drum up interest in the subject for the sake
>>of physics. I don't know whether to laugh or cry. 

>A cynical snicker will suffice.

I have a better idea. If you're seriously interested in getting category theory
to do a job in physics, I can suggest some people you can try.

Later,
Andrew Mullhaupt
From: wjcastre@magnus.acs.ohio-state.edu (W.Jose Castrellon G.)
Newsgroups: sci.math
Subject: Dirichlet's theorem (was Re: Primes in x_{n+1} = ax_n+b)
Date: 21 Aug 92 16:22:41 GMT
Article-I.D.: magnus.1992Aug21.162241.7303
Organization: The Ohio State University,Math.Dept.(studnt)

In article <1992Aug21.103132.29967@ecrc.de> jeanmarc@ecrc.de writes:

>Let a,b be integers, and (x_n) be a sequence s.t. x_{n+1} = a x_n + b
>
>My question is: does it contain infinitely many primes ?
>
>There are trivial cases, where the answer is no:
>1/ if (a x_0 + b = x_0) the sequence is constant.
>2/ if (a = -1) the sequence alternates between two values x_0 and x_1.
>3/ if ((a,b) > 1 or (x_0,b) > 1) then the sequence clearly contains only
>composite numbers.
>
>What about the other cases ?
>
>I've seen a "theorem of Dirichlet" in Hardy&Wright which handles the case a=1.
>Can anyone give me a pointer to a proof of that theorem (Hardy&Wright don't
>give it and the only reference they give is in German).
>
>---

There is one in Ireland&Rosen's _A Classical Introduction to Modern Number 
Theory_. It uses only basic complex analysis (as in Knopp's dover books).

Dirichlet's Theorem: If a and b are relatively prime, then there are infinitely
many primes of the form  an+b. Even more, the density of primes is equally dis-
tributed among all b's  <a  which are relatively prime to  a.
Newsgroups: sci.math,comp.binaries.ibm.pc.wanted
From: lee@ms.uky.edu (Carl Lee)
Subject: DOS Traveling Salesman Programs
Keywords: wanted
Date: Thu, 13 Aug 1992 15:32:36 GMT
Organization: University Of Kentucky, Dept. of Math Sciences

I would like information on existing programs for DOS machines
to find good approximate solutions to the assymmetric traveling salesman 
problem.  Please email me your suggestions, if possible.

Carl Lee
Department of Mathematics
University of Kentucky
Lexington, KY 40506
lee@s.ms.uky.edu
lee@ukma.bitnet
Newsgroups: sci.math
From: achim@unibi.uni-bielefeld.de (Achim Flammenkamp)
Subject: non continious derivation wanted
Date: Fri, 14 Aug 92 14:02:20 GMT
Organization: Universitaet Bielefeld

I think everyone knows the example of a derivatable function which
is not continiously derivatively.
f(x) = x^2*sin(1/x)  for x != 0 and f(0) = 0

From this function one can construct another one
,without loose of generality on the closed interval [0,1],
which set of points in which the derivation is continious has lebeque measure
epsilon for each postive epsilon < 1. 

My question is : Exists a function on [0,1] with a derivation but the measure
of the set of points where this derivation is continious is zero ? 
If the answer is yes one can try to sharpen:
Can this set of points be countable?

achim
From: mstemper@ems.cdc.com (Michael Stemper)
Newsgroups: sci.math
Subject: Prime conjecture
Date: 12 Aug 92 17:17:35 GMT
Reply-To: mstemper@ems.cdc.com
Organization: Empros Systems International, a division of Ceridian

In article <1992Aug11.162953.13961@uwm.edu>, radcliff@csd4.csd.uwm.edu (David G Radcliffe) writes:
|> 
|>    Conjecture:  There exists a k > 0 so that p + k is prime 
|>                 for infinitely many primes p.
|> 
|> Does anybody know the status of the this conjecture?

I believe that
  There exist infinitely many primes p
  Such that p+2 is prime
has been proven, which would prove this conjecture by showing k=2.

Related questions: Now that we know that there exists a k, are there
other k's that satisfy this condition? If so, is there a largest k
that satisfies this condition?

-- 
#include <Standard_Disclaimer.h>
Michael F. Stemper
Power Systems Consultant
mstemper@ems.cdc.com
Newsgroups: sci.math,sci.physics
From: Tom Pierce <pierct@rpi.edu>
Subject: Re: tensors: How about 3rd, 4th rank?
Organization: Physics Dept.
X-Useragent: Nuntius v1.1b1
     <israel.714359708@unixg.ubc.ca> <5130@tuegate.tue.nl>
     <5134@tuegate.tue.nl>
Date: Fri, 21 Aug 1992 18:29:03 GMT

I know all about 1st and second order tensor, but what's a third order
tensor look like?  Also, aren't these the same mathematical critters as
"matrices", witha the added "square" criterion?
What would you use a third or highr order tensor for?  Any PHYSICAL
applications?
From: wilson@web.ctron.com
Newsgroups: sci.math
Subject: EATCS stands for...
Date: 18 Aug 92 15:00:09 GMT
Reply-To: wilson@web.ctron.com ()
Organization: Cabletron Systems INc.
Originator: wilson@web


    I post this in response to email (now lost) asking about the EATCS.

    From the generous dose of email responses I've recieved concerning
    the matter, it has come across fairly that EATCS stands for

	European Association for Theoretical Computer Science

    Disclaimer:  Despite having been published in the EATCS, I am not
    now, nor have I been at any time, European.


-- 
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."
Newsgroups: sci.math
Subject: An advertisement.   ;-)
From: wft@math.canterbury.ac.nz (Bill Taylor)
Date: 20 Aug 92 12:33:43 +1200
Distribution: world
Organization: Department of Mathematics, University of Canterbury

I warmly recommend a recent article that appeared in the "New Scientist".

Although it has more to do with science in general than math in particular,
a recommendation will not be out of place here, as the article concerns the
issue of how far science and math may go toward explaining "everything".

It is....
           "WILL SCIENCE EVER FAIL"
            ~~~~~~~~~~~~~~~~~~~~~~   by Peter Atkins; New Scientist, 8 Aug. '92

It is written partly in reply to a (slightly) anti-scientific article appearing
the week before by Mary Midgley. (I only read the first paragraph or so of
this earlier article, but I may go back and complete it now!)

IMHO,  Atkins' article is a must for all who are interested in the limits of
scientific endeavour, or in the ongoing conflict between science and religion.

Warning: those of a religious disposition may find the contents offensive !
=======     To whet your appetite I will offer a few quotes.

"There is room for ... fear, for those who seek to found their lives on the
 vapourous precepts so favoured by religion...."

"Religion claims total understanding, but fails to deliver anything but
 sweet words; science claims cautious progress, and is able to demonstrate
 success at every stage."

"Happily, science will continue despite the cantankerous efforts of
 philosophers to thwart its progress. As it does so philosophers will have
 to strike camp every few years and rush along to comment on what has been
 achieved by scientists working in the fray of discovery."


Needless to say, not all of the article is so feisty. Although not technical
in content, it is a thoughtful and authoritative account of the scientific
endeavour of humankind;  an optimistic review, and prognosis, of what has been
and may be achieved by science, backed by mathematics.

------------------------------------------------------------------------------
            Bill Taylor              wft@math.canterbury.ac.nz
------------------------------------------------------------------------------
 Free will - the result of chaotic amplification of quantum events in the brain.
Galaxies - the result of chaotic amplification of quantum events in the big bang.
--------------------------------------------------------------------------------


Newsgroups: sci.math
From: roach@bikini.wri.com (Kelly Roach)
Subject: Re: u(v^n)w prime puzzle
Organization: Wolfram Research, Inc.
Date: Wed, 19 Aug 1992 15:37:55 GMT

In article <l93702INNaq9@aludra.usc.edu> rmurphy@aludra.usc.edu (Bob  
Murphy) writes:
> If there were such values of u, v, and w, then one could construct
> arbitrarily large prime numbers.  Since I have often heard
> reference to "the largest known prime number", I would guess that
> there are no such values.  Now if only I had a proof.


     Not quite.  The largest known prime number is 2^756839-1.
But emphasize the word "known" here.  In 1985, 2^216091-1 was
the largest known prime number.  It takes a few years to
break each new "largest known prime number" record.
     There ARE infinitely many prime numbers and they do
get arbitrarily large.  A classic proof, due to Euclid is to
take

     P = p1*p2*p3*...*pN+1

where p1,p2,p3,...,pN are the primes you already know.
The number P is not divisible by any of p1,p2,p3,...,pN.
All the primes dividing P are new primes.  Example:
Suppose you know that 2,3,5,7,11,13 are prime.  Then

     P = 2*3*5*7*11*13+1 = 30031 = 59 * 509

gets you two new prime numbers 59 and 509.  The process
can be repeated ad infinitum.


> So far I have only been able to show that if a solution exists 
> then v must be a multiple of 3.


     This is a good observation.
Newsgroups: sci.math
Subject: Try this problem.
From: wft@math.canterbury.ac.nz (Bill Taylor)
Date: 20 Aug 92 11:57:38 +1200
Distribution: world
Organization: Department of Mathematics, University of Canterbury

An ellipse is fixed in a vertical plane  (but with neither axis vertical).

Various chords may be drawn from the highest point on the ellipse, to some
other point on the ellipse; a smooth segment of wire laid along the chord
and a frictionless bead allowed to slide (under gravity) from the top end 
of the chord down to the other end.

What are the directions of the maximum and minimum times of descent ?

-------------------------------------------------------------------------------
              Bill Taylor              wft@math.canterbury.ac.nz 
-------------------------------------------------------------------------------
 Free will - the result of chaotic amplification of quantum events in the brain.
Galaxies - the result of chaotic amplification of quantum events in the big bang.
--------------------------------------------------------------------------------

Newsgroups: sci.math
From: davidba@carmel.technion.ac.il (David Ben_Ami)
Subject: Topology Textbooks - beginner's level
Organization: Technion, Israel Inst. of Technology
Date: Sat, 15 Aug 1992 13:09:38 GMT

Hello all,

  I want to study a little topology on my own and wonder what 
  books are the best for self-instruction. My mathematical background
  is Comp. Sci. student near gradution.

  I would prefer books with relatively "user-friendly" tone since I
  do not major in theoretical mathematics.

  Please reply by email to: davidba@moav.technion.ac.il
  (I don't read sci.math regularly)

Thanks in advance for any information,

  David Ben-Ami.

-- 
=============================================================================
  David Ben-Ami (irc: bigdav)      |   "I can resist anything but Temptation"
  s2780369@Techst02.Technion.Ac.Il |       Oscar Wilde
  davidba@Carmel.Technion.Ac.Il  davidba@Moav.Techniona.Ac.Il