HDTenEightyP/NetNews huggingface dataset:
From: walsteyn@fys.ruu.nl (Fred Walsteijn)
Subject: NAG routine D02BAF uses runge-kutta-MERSON ??
Summary: is it the Merson routine mentioned in the textbooks ?
Keywords: Merson, nonlinear problems
Organization: Physics Department, University of Utrecht, The Netherlands
Date: Mon, 4 Jan 1993 14:13:52 GMT

I have just read that the NAG routine D02BAF is based on
a Runge-Kutta-Merson embedded formula.
Is it the same formula as mentioned in the books of
Lambert (1991) and Butcher (1987) ?

If it is, does that mean that its error truncation estimate
is ``easily defeated'' (cite, as I remember it from one of
the abovementioned books) ?
The reason is that the ``high order'' component has a high
(fifth) order of accuracy only for linear problems.
It cannot have fifth order of accuracy for all (e.g. nonlinear) problems
as it has only five stages (Butcher, 1987).

Thanks for any clarifying remarks...
-----------------------------------------------------------------------------
Fred Walsteijn                                | Internet: walsteyn@fys.ruu.nl
Institute for Marine and Atmospheric Research | FAX:      31-30-543163
Utrecht University, The Netherlands           | Phone:    31-30-533169
Newsgroups: sci.math.num-analysis
From: walsteyn@fys.ruu.nl (Fred Walsteijn)
Subject: Re: Condition Number
Organization: Physics Department, University of Utrecht, The Netherlands
Date: Mon, 11 Jan 1993 14:48:01 GMT

In <1993Jan11.083253.9521@dutrun2.tudelft.nl> rcpshdb@dutrun2.tudelft.nl (Han de Bruijn) writes:

>The condition number of a matrix  A  is defined as the absolute value of
>its largest eigenvalue divided by its smallest eigenvalue. Right?

>I'm at loss how this is related to the loss of decimals when solving the
>equations system:
>                      A.x = b

>Can someone out there provide a simple argument?


A perturbation "db" in the right hand side (due to rounding errors for
example) results in a change "dx" of the solution vector.  
They are related by:

                |dx| / |x|  <=  cond(A)  |db| / |b|

The proof I am looking at right now assumes that A is symmetric...
-----------------------------------------------------------------------------
Fred Walsteijn                                | Internet: walsteyn@fys.ruu.nl
Institute for Marine and Atmospheric Research | FAX:      31-30-543163
Utrecht University, The Netherlands           | Phone:    31-30-533169
Newsgroups: sci.math.num-analysis
From: sanjay@eng.umd.edu (Kumarasamy Sanjay)
Subject: Re: Num Recipes errata?
Date: Mon, 11 Jan 93 14:20:49 GMT
Organization: Project GLUE, University of Maryland, College Park
Distribution: usa

 Thanks for all who responded to my query. Thanks to Stuart,Hanche,Steven.

 I guess I was naive to think that I can  find the code in the
 public domain.

 Well, thanks anyway.


Have fun

-sanjay
________________________________________________________________________
Sanjay Kumarasamy                |   
sanjay@eng.umd.edu               |                       
yajnas@wam.umd.edu               |    Thou art That
Voice:(H)301-345-0628            |
......(O)301-405-6872            |
------------------------------------------------------------------------
From: neilfp@astro.ocis.temple.edu (Neil F. Palumbo)
Newsgroups: sci.math.num-analysis
Subject: OOPS on HELP Quadratic Eqns
Date: 10 Jan 93 20:06:23 GMT
Organization: Temple University
X-Newsreader: TIN [version 1.1 PL8]

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

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

				Neil
Xref: sparky sci.math.num-analysis:3725 sci.engr:2453 sci.engr.mech:713 um.general:248
From: geidel@wior360.wiwi.uni-karlsruhe.de (Joachim Geidel)
Newsgroups: sci.math,sci.math.symbolic,comp.graphics
Subject: Re: Help find optimum display of directed graphs
Date: 8 Jan 93 09:52:17 GMT
Organization: WIOR, Universitaet Karlsruhe (Germany)
NNTP-Posting-Host: wiormac5.wiwi.uni-karlsruhe.de
X-UserAgent: Nuntius v1.1.1d16
X-XXMessage-ID: <A7730D95AB017B07@wiormac5.wiwi.uni-karlsruhe.de>
X-XXDate: Fri, 8 Jan 93 09:53:09 GMT

In article <103943@netnews.upenn.edu> Bill Tozier, bill@amy.med.upenn.edu
writes:
>  I need some help with a problem in visualizing mathematical graphs.

I have compiled a little bibliography on this topic from recent postings
in some other newsgroups and from some articles. I have not (yet) merged
it
with the famous bibliography by Eades/Tamassia (which appears in my list,
complete with ordering information). If anyone is interested, just drop me
a message, I will send you the list by email.

-----------------------------------------------------------------------
---
Joachim Geidel                            Tel:  (+49)721/608-3226
Institut fuer Wirtschaftstheorie und OR   Fax:  (+49)721/608-4290
Universitaet Karlsruhe                    Internet:
Kaiserstrasse 12                         
geidel@wior360.wiwi.uni-karlsruhe.de
D-7500 Karlsruhe 1, Germany               BITNET: lc03@DKAUNI2
Newsgroups: sci.math
From: ger@cv.ruu.nl (Ger Timmens)
Subject: Re: What is the 'sinc' function?
Date: Tue, 12 Jan 1993 09:34:39 GMT
Organization: University of Utrecht, 3D Computer Vision Research Group
Keywords: sinc

In <1itehhINN8v1@roundup.crhc.uiuc.edu> hougen@focus.csl.uiuc.edu (Darrell Roy Hougen) writes:

>I came accross it in a paper about the scattering of electromagnetic
>radiation. 

          sin(Pi * x)
sinc(x) = -----------,
           (Pi * x)

So it's 0 at {...,-2,-1,0,1,2,...}. It's the Fourier transform of an ideal
lowpass filter.

Hope this helps,
-- 
|I|        Ger Timmens         |I| If you're not part of the solution, |I|
|M|  3D Computer Vision Group  |M| you're part of the problem!         |M|
|H|    e-mail ger@cv.ruu.nl    |H+-------------------------------------+H|
|O|   or  timmens@cs.unc.edu   |O| Album by Joe Henderson (best tenor) |O|
Newsgroups: sci.math,alt.books.technical
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Subject: Re: High Prices of Math Books. I am pissed.
Organization: Purdue University Statistics Department
Date: Sun, 10 Jan 1993 18:31:31 GMT

In article <1993Jan10.071945.1756@pegasus.com> tleylan@pegasus.com (Tom Leylan) writes:
>bathurst@phoenix.Princeton.EDU (Bruce Bathurst) writes:

>>The defending of American book prices as reasonable because they are
>>expensive to produce misses the point that students can't buy them.

>Some of us didn't get to attend Princeton and I didn't get to attend 
>a university at all... now I'm writing a technical book and you think
>the price should be based upon the income of a student ?

>It's those darn people who work at publishing companies and those guys
>who run presses and produce paper and those book store owners why don't
>they learn that their sons and daughters don't get to go to Princeton
>and just work for less.

>Why don't I uhhhh just give it away ?

When it comes to quality books, the author usually makes little enough.
I am co-author of two research monographs, and my wife is author of two
textbooks.  The amount we have made does not even come close to covering
a small part of the costs in time to write them.

The cost in time to produce a good textbook where one does not already
exist is likely to exceed $50,000.  If this is for a good course, not
the typical calculus garbage, it might not make anywhere near this 
before it becomes obsolete.  Meanwhile, those who grind out the typical
books produce a new edition every few years so that they will continue
to get royalties, which they do not get on resales of used books.

It is not that uncommon that I would like to use as a text a book which
is out of print.  It used to be that a copyright was for 44 years; I
believe it is now lasts until 50 years after the death of the author.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@snap.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!snap.stat!hrubin(UUCP)
Newsgroups: sci.math
From: ags@seaman.cc.purdue.edu (Dave Seaman)
Subject: Re: Bayes' theorem and QM
Organization: Purdue University
Date: Tue, 5 Jan 1993 15:14:23 GMT

In article <5915@osc.COM> jgk@osc.COM (Joe Keane) writes:
> Banach-Tarski is a good demonstration of the tricks you can play if you  
have
> axioms which claim the existence of objects with infinite information,  
or
> however you want to interpret the non-constructible things that you can  
get
> only with the Axiom of Choice.  But does anyone think this has any  
relation to
> reality?

About as much as ideal points and lines have to do with reality.
 
> If you think so, please show me some pieces that you could make out of
> something real like wood, such that that they almost fit together into  
either
> one sphere or two.  Also please show me a computer chip that can store  
an
> infinite amount of information.  In fact i'll be generous, you only have  
to
> store an arbitrarily large amount of information.

What has any of this to do with Banach-Tarski? You can't make even one  
point out of wood (because anything made out of wood has non-zero  
thickness) and therefore it should not be surprising that you can't make  
infinitely many points out of wood. Even if you could manage that, there  
would be no way to hold it together, since the structure would be full of  
air.

The only way I can see any "infinite amount of information" in the sets  
involved is in the precise coordinates of all the points belonging to the  
set. By that criterion, any ordinary infinite point-set (including any  
ordinary computer chip) already contains an infinite amount of  
information.

--
Dave Seaman
ags@seaman.cc.purdue.edu
From: israel@unixg.ubc.ca (Robert B. Israel)
Newsgroups: sci.math
Subject: Re: Cantor set problem
Date: 6 Jan 93 00:18:58 GMT
Organization: The University of British Columbia
NNTP-Posting-Host: unixg.ubc.ca

In <C0EB3o.Kzy@undergrad.math.waterloo.edu> cmspring@undergrad.math.waterloo.edu (Colin Springer) writes:


>I'd be interested in any solutions or references anyone might find for the
>following problem which I've been thinking about recently.

>Problem:  Consider the subset of the plane formed by starting with the Cantor
>set placed on the interval [0,1], and for any two points a, b in this set
>we construct the circle centered at a passing through b.  Does this set have
>measure zero?

Almost certainly it doesn't.  If E is the Cantor set, this set is the
image of E x E x [0,2pi) under the map (x,y,t) -> x + (y-x)exp(it)
(considering the plane as the complex numbers).  E x E x [0,2pi] has
Hausdorff dimension greater than 2, so it's likely that the image
has positive 2-dimensional measure.  I don't have a proof, though.
What I can say is that the interval [-1,2] is contained in your set
(for t = pi, (2E) - E = [-1,2]). 
 
>If this were the case we could use this set as a "blanket" which could be
>translated to cover any given circle of radius at most 1, and was of measure
>zero.  Such a "blanket" can be formed to cover rectangles of arbitrary
>dimensions, but I'm not sure if it's possible.  The above construction is my
>best guess: if it doesn't work, I'd be interested in any other possible
>construction, with proof if possible.

I.e. (E x [0,1]) union ([0,1] x E) is a set of 2-dimensional measure 0 
containing rectangles of arbitrary dimensions <= 1.

>Have fun with it!

>Colin

-- 
Robert Israel                            israel@math.ubc.ca
Department of Mathematics             or israel@unixg.ubc.ca
University of British Columbia
Vancouver, BC, Canada V6T 1Y4
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: .articleask
Date: 8 Jan 93 16:18:51 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <86260@ut-emx.uucp> kingshu@ccwf.cc.utexas.edu (King Cheung SHU) writes:
>1. How many methods can be employed to find the solution of a integral
>function on computer ?

A lot.

>2. What are the methods about ?

All sorts of different things.

>3. Are there any books that summarized all the methods ( at least some of
>them ) ?


You will probably be totally happy to look in Zwillinger's _Handbook of
Integration_ and Davis and Rabinowitz's excellent monograph on numerical
integration. For other, closely related themes you can consult Delves
and Mohammed's book on numerical solution of integral equations, etc.

Later,
Andrew Mullhaupt


Newsgroups: sci.math
From: myrberger@e.kth.se
Subject: New 3x3x3 cube puzzle list
Reply-To: myrberger@e.kth.se
Organization: KTH, Royal Institute of Technology, School of Electrical Engineering
Date: Thu, 7 Jan 1993 15:25:15 GMT

A new version of my list with puzzles that in their final state are
a 3x3x3 cube is ready.

If you'd like a copy just send me a MAIL.

Enjoy,

Johan Myrberger

MAIL: myrberger@e.kth.se
From: erwin@trwacs.fp.trw.com (Harry Erwin)
Subject: Fields Medal Winners
Organization: TRW Systems Division, Fairfax VA
Date: Fri, 8 Jan 1993 14:42:25 GMT

At one time, I was under the impression that Bott and Artin had won the
Fields Medal. It seems I'm wrong. Can someone confirm or deny? 

This impression is associated with one of those stories. I understand
Artin, Atiyah, and Bott were the first three at the math tripos one year
at Oxford (1950?). Apparently it made quite an impression.

Cheers,
-- 
Harry Erwin
Internet: erwin@trwacs.fp.trw.com

Newsgroups: sci.math
From: yeomans@austin.onu.edu (Charles Yeomans)
Subject: Re: Why no Nobel Prize in Math?
Date: Tue, 5 Jan 1993 16:14:40 GMT
Distribution: na
Organization: Ohio Northern University

In article <C06xJo.Grn@news.cso.uiuc.edu>, levine@symcom.math.uiuc.edu (Lenore Levine) writes:
> 
> dbriggs@zia.aoc.nrao.edu (Daniel Briggs) writes:
> 
> >In article <1992Dec31.145732.19319@cbnewsl.cb.att.com>
> >  wjh@cbnewsl.cb.att.com (william.j.hery) writes:
> >>hausner@qucis.queensu.ca (Alejo Hausner) writes:
> >>>       It seemed unlikely to me at the time that a mathematician
> >>>would have a love life, much less an adulterous one, but I've
> >>>since realized they're human too.
> >>
> >>?????? Is that because you think that all mahtematicians are 1) asexual,
> >>2) homosexual, 3) perfect moral speicmens according to some moral
> >>code that you recognize, 4) prudes, or 5) just don't have the time
> >>because they spend so much time doing mathematics?????
> 
> >Well, I can add a mildly amusing bit of annecdotal evidence which suggests
> >that there might be a grain of truth to the above.  (Take the implications
> >with a few smileys, but the story *is* true, albeit more than a decade
> >old.)
> 
> >A friend of the household, before I moved in, was active with COYOTE in the
> >SF Bay Area.  I can't remember the acronym expansion, but it is (was?) an
> >organization to promote legalized prostitution.  Among other things, COYOTE
> >kept summary statistics of the sales activities of all their members, as
> >ammunition for their lobbying battles.  There was always a big correlation
> >between sales and a major convention in San Francisco.  Until the AMS had
> >a major meeting there, that is.  COYOTE had its worst weekly sales ever!
> 
> Does that really mean that male mathematicians are less sexual? Or
> merely less interested in women who have no sincere romantic interest in
> them? 
> 
> 
Or perhaps it means that mathematicians are cheap.
Newsgroups: sci.math
From: dzk@cs.brown.edu (Danny Keren)
Subject: Re: proof wanted 2
Organization: Brown University Department of Computer Science
Date: Sun, 10 Jan 1993 05:45:10 GMT

cazelaig@ERE.UMontreal.CA (Cazelais Gilles) writes:
#                                                       n
#Is it true that if  C  is a nonempty closed subset of R  and x is a point not
#in  C  that there exists a point c in C that is closest in C to x.
# 
#i.e. such that:   |x-c'| >= |x-c| for all c' in C.

Take a closed ball around x that intersects C. Evidently, it is
enough to look for the closest point in the intersection of C
and that ball, but this intersection is closed and bounded in
R^n, hence compact, and so the function on it which is defined
as the distance to x has to attain its minimum. So the answer
to your question is yes.

-Danny Keren.
From: mbeattie@black.ox.ac.uk (Malcolm Beattie)
Newsgroups: sci.math
Subject: Re: homotopy groups for products of spheres into unitary groups
Date: 7 Jan 93 13:38:36 GMT
Distribution: sci.math
Organization: Oxford University Computing Service, 13 Banbury Rd, Oxford, U
Originator: mbeattie@black

In article <TRAHERN.93Jan6115340@telperion.ssc.gov> trahern@fremont.ssc.gov writes:
>
> I would like to know if there are results for the homotopy group for
>the following class of mappings:
>
> The map of the cartesian product of a two sphere and a three sphere
>(S2xS3) into the unitary groups U(N). 
>
> I know that the 5th homotopy group of U(N) is the set of integers, Z,
>for N > 2, but I do not know how to find the results (if they exist)
>for maps which are not just spheres. 
>
> An integral which I believe is a representative of this homotopy
>group arises in a physics problem I am thinking about, and if there
>are general results, I would appreciate knowing them. 
>
> Please send replies by email to trahern@fremont.ssc.gov (or to the net).
>

It is not clear to me exactly what you are after: information
about the mapping space itself from S^2 x S^3 to U(N) or about
classifying maps from S^2 x S^3 to U(N). I'll say something about
the latter. Ignoring a couple of minor technicalities, you can
consider the cofibre sequence
S^2 v S^3 ---> S^2 x S^3 ---> S^2 ^ S^3 ---> S(S^2 v S^3) --> ...
where `v' is wedge, `^' is smash
and this sequence can be written as
S^2 v S^3 ---> S^2 x S^3 ---> S^5 ---> S^3 v S^4 ---> ...
Now look at the long exact sequence obtained by applying
[-,U] (abbreviating U(N) to U) and you get an exact sequence of groups:
pi_3(U) x pi_4(U) ---> pi_5(U) ---> [S^2 x S^3,U] ---> pi_2(U) x pi_3(U)

If I could remember off-hand the homotopy groups of U(N) then
I could go a bit further but I can't so I won't.
If you post a bit more about what information you're after,
I'll try and help a bit more.

--Malcolm

> thanks, 
>
> garry trahern


-- 
Malcolm Beattie <mbeattie@black.ox.ac.uk> | I'm not a kernel hacker
Oxford University Computing Services      | I'm a kernel hacker's mate
13 Banbury Road, Oxford, OX2 6NN (U.K.)   | And I'm only hacking kernels
Tel: +44 865 273232 Fax: +44 865 273275   | 'Cos the kernel hacker's late
Newsgroups: sci.math
From: rivin@SAIL.Stanford.EDU (Igor Rivin)
Subject: Re: term for the "angle" of a complex number
Organization: Computer Science Department,  Stanford University.
Date: Tue, 12 Jan 1993 22:45:54 GMT

In article <C0rFC2.A8@smsc.sony.com> markc@smsc.sony.com (Mark Corscadden) writes:
>A complex number Z can be expressed in these ways:
>
>rectangular -   X + Yi         where X and Y are real
>polar -         R  exp(Ai)    where R>=0 and A are real (A is not unique)
>
>Terminology for these quantities:
>
>X - the real part of Z
>Y - the imaginary part of Z
>R - the magnitude of Z or the absolute value of Z
>A - ???  I have no idea ???
>
>What do you call "A"?  Ideally this would be a term that you could expect
>to be recognized in a discussion about quantum field theory, for example.

The two terms in wide use are "phase" (polar form is also known as
phase/magnitude) and "argument". "Phase" is more often used in applied
mathematics, "argument" in complex function theory.
From: johnsbra@tmlh (Havard Johnsbraten)
Newsgroups: sci.math
Subject: Re: Two (I think) interesting Problems
Date: 7 Jan 93 10:46:56 GMT
Organization: tmlh


In article <1992Dec23.134651.7759@neptune.inf.ethz.ch> 
yoparish@iiic.ethz.ch (Yoav Ilan Haim Parish) poses the problem
       
     How can I fold an approximate (regular) pentagon from a 
     quadratic sheet of paper easily ?

In addition to the nice constructions of G.J. McCaughan and Marvin Minsky 
(the man with the finite automata?) I have the following contribution:

One of my students once showed me this beautiful paper folding procedure, 
wondering whether or not it was exact:

Start with a square ABCD.  Fold along the diagonal BD, folding C to A.  
Find the midpoint E on AB (folding B to A and opening it again).  
Then fold D to E. 
By this last folding you get two new points: F on BD and G on AD.
The angle EFG is about twice the angle BFE.  
Bisect angle EFG by folding such that G will be lying on FE, and fold angle 
BFE to the backside.
Now you may use a scissor to cut out a regular pentagon (cut at right angle) 
or a nice star (cut more arbitrarily)!

The folding procedure above is not exact; the angle BFE being slightly less 
than 37 degrees, instead of the exact value of 36 degrees.  But when you are 
folding, you are not able to see the inaccuracy.  (The McCaughan folding 
from an A4-sheet wasn't exact either, but also very close.)  
But F divides BD in an exact rational ratio:  DF:FB = 5:7 !

 o            o
Havard Johnsbraten, Telemark College of Education, Notodden, Norway
E-mail  haavard.johnsbraaten@tmlh.no  or
G=haavard;S=johnsbraaten;O=tmlh;P=uninett;A= ;C=no
From: squash@math.ufl.edu (Jonathan King)
Newsgroups: sci.math
Subject: Re: Constant-sum table algorithm
Date: 8 Jan 93 21:31:08 GMT
Organization: University of Florida Department of Mathematics

In article <79483@hydra.gatech.EDU> np4@prism.gatech.EDU (Nick Pomponio) writes:

   I would like to generate an NxN table of positive integers such that
   any N entries chosen from the table, with the restriction that no
   two in are in the same row or column, add up to the same value, S.
   The only way I know to construct such a table is to choose 2N integers
   which sum to S, arrange N along the top of the table (one above each
   column), and N along the side (one beside each row), then fill in each
   entry as the sum of it's corresponding row and column heading numbers.

   Question: Is there an algorithm for choosing the 2N integers such that
   every resulting number in the NxN table is unique (no repetitions)?
   For my particular case, N^2 << S.

Yes.  Call such a set of N entries a "diagonal".
(NB.  Any board whose diagonal-sums are constant can be built by the
algorithm Mr. Pomponio describes.)

Consider the board

	1		2	 ...	N

	N+1		N+2		2N

	2N+1		2N+2	...	3N

	...

	(N-1)N+1	(N-1)N+2 ...	N^2 .


Every diagonal of this board sums to  

	S' :=   N(N+1)/2  +  N*(N-1)N/2   
	    =   N(N^2 + 1) / 2.

Moreover, no distinct-entry board consisting of positive integers could have a
smaller diagonal-sum.

	Now add a non-negative constant B to every entry in the bottommost row.
Certainly the entries in this new table are distinct, and the diagonal-sum for
this new table is

	S  :=   S' + B .

So using positive integers as entries, one can obtain a distinct-entry
[diagonal-sum = S] board iff  S is an integer which is
greater-equal  N(N^2 + 1) / 2.			-Jonathan
Newsgroups: sci.math
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: test again
Date: 4 Jan 1993 19:09:31 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu

yawn
Xref: sparky sci.math:17733 misc.books.technical:1871