HDTenEightyP/NetNews huggingface dataset:
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Re: New Mersenne Prime
Keywords: Mersenne, prime, primitive root, quadratic residue, reciprocity
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Thu, 9 Apr 1992 13:40:02 GMT

In article <1992Apr6.230422.10785@husc3.harvard.edu> elkies@ramanujan.harvard.edu (Noam Elkies) writes:
:In article <1992Apr1.182446.21988@linus.mitre.org>
:bs@gauss.mitre.org (Robert D. Silverman) writes:
:
:>The theorem [any prime factor of 2^p-1 is congruent 1 or -1 mod 8]
:>works because 2 is a primitive root. Any prime that has 2 as a
:>primitive root must be congruent to 1 or -1 mod 8. Here, we have 2p+1 = 8n+7.
:
:Um, for "primitive root" read "quadratic residue"; 2 is not a
 
Uh, yes! Absolutely. Very sloppy of me. I was thinking about primitive
roots at the time because Heath-Brown's recent work on primitive roots
can be applied to this problem.

--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"
From: gindrup@math.okstate.edu (Eric `'d'kidd' G..)
Newsgroups: sci.math
Subject: Re: fun with primes
Keywords: prime numbers
Date: 8 Apr 92 16:27:48 GMT
Organization: Oklahoma State University, Math Department

In article <1992Apr6.085801.16293@uniwa.uwa.oz.au> hartley@maths.uwa.oz.au (Mike Hartley) writes:
>gindrup@math.okstate.edu (Eric `'d'kidd' G..) writes:
>
>>As the earlier proofs have shown,
>>(1)  p is assumed to be the largest prime,
>
>But what if there IS no largest prime, because we've just thrown away
>the relation '<' ? Can we still do the proof? NB you aren't allowed to
>use p! anymore, because p! is the product of all "positive" integers
>"less than" or equal to p. 
[good questions deleted...]

Well, if we define p! as 

        p/||p||
       ---------
         |   |    j*p
p!  =    |   |   -----  ,  then we haven't really used the "<" relation and
         |   |   ||p||
          j=1

as long as we can norm over our space, then we don't have any problems 
writing p!.  Whether or not it's relevant is another matter.

-Eric Gindrup ! gindrup@hardy.math.okstate.edu
Newsgroups: sci.math
From: carabalo@phoenix.Princeton.EDU (David G. Caraballo)
Subject: Complex vs. Real
Originator: news@ernie.Princeton.EDU
Organization: Princeton University
Date: Fri, 10 Apr 1992 07:11:00 GMT

During a discussion about my previous post (no complete replies yet!), I was
asked (in an aside) if I could think of any major differences between functions
of complex variables and functions of real variables.  There are too many to
post, the most notable perhaps being the fact that all analytic functions (on
some domain) are infinitely differentiable.  I happened to mention another
striking difference, and he said it helped him, so I will share it with the
net.  It is less obvious than many of the other differences that come to mind.

There exist continuous, real-valued functions f (on R) that are nowhere
differentiable.  By a theorem of Weierstrass, one can find a sequence {P_n} of
real-valued polynomials such that these converge almost uniformly (on compact
sets) to f.  These polynomials are all infinitely differentiable (of course),
yet their almost uniform limit can be nowhere differentiable.  By contrast, the
almost uniform limit of any sequence of analytic functions (on some domain)
is analytic (throughout the domain).

David G. Caraballo
Newsgroups: sci.math
From: gindrup@math.okstate.edu (Eric `'d'kidd' G..)
Subject: Re: closed form solution to d.e.
Organization: Oklahoma State University, Math Department
Date: Tue, 14 Apr 1992 16:16:46 GMT

In article <1992Apr9.042657.3710@nuscc.nus.sg> fbagohkh@nuscc.nus.sg (Mark Goh (Dr)) writes:
>Is there a closed form solution for this d.e.
>
>y' + a(y)^b=1, 0<a,b<1 ?

e-1 + e*b = 0.  Then e = 1/(b+1)
y = x^[1/(b+1)]
y'= [1/(b+1)]x^[b/(b+1)]
y' + a(y)^b = {[1/(b+1)] + a}x^[b/(b+1)] = 1.
For this to be true, x^[b/(b+1)] must be constant.  I.e. b=0.  Then, a=0, also.
So, y=x is a solution provided that a=b=0 and I'm pretty sure that that's the
only polynomial solution for any a and b.

If we expect b<0, then y=e^x looks like
e^x + ae^(-Bx) = 1, B=-b, which looks a bit like a trigonometric function.
(Of course many things look *like* a trigonometric function... :-)

I'm out of ideas for today (I've used up my ration of clues, so I'm clueless
now...) so I guess some other bright person will have to answer this question
more fully.

-Eric Gindrup ! gindrup@hardy.math.okstate.edu
From: lipscomb@lonestar.utsa.edu (David S. Lipscomb)
Newsgroups: sci.math
Subject: decimal prefixes
Summary: help me I am desperate
Keywords: metric
Date: 13 Apr 92 15:38:48 GMT
Distribution: usa
Organization: University of Texas at San Antonio


        I have been trying to find out this information for weeks now
    and have little if any help.  If anyone can help please fill in the
    chart and email me.  Thankyou.


    ten                      deka
    hundred                  hecto
    thousand                 kilo
    ten thousand             myria
    hundred thousand         ?
    million                  mega
    ten million              ?
    hundred million          ?
    billion                  giga
    ten billion              ?
    hundred billion          ?
    trillion                 tera
    ten trillion             ?
    hundred trillion         ?
    quadrillion              ?
    ten quadrillion          ?
    hundred quadrillion      ?
    quintillion              ?
    ten quintillion          ?
    hundred quintillion      ?
    sextillion               ?


    I also have need for a listing for the first 20,000 prime numbers.  Is
-- 
FALCON,  THE MASTER OF TIME AND THE LORD OF THE FLAME

"LIVE LONG AND MAY THE FORCE BE WITH YOU"
From: flajolet@margaux.inria.fr (Philippe Flajolet)
Newsgroups: sci.math
Subject: exp(Pi)-Pi = 19.9990999...
Date: 11 Apr 92 10:10:35 GMT
Reply-To: flajolet@margaux.inria.fr (Philippe Flajolet)
Organization: INRIA Rocquencourt France

Simon Plouffe from UQAM at Montreal [plouffe@mipsmath.math.uqam.ca]
discovered the following fact:

        exp(Pi)-Pi = 19.9990999....

Does anybody have an explanation?

Note: We are aware of 
                        1/2
              exp(Pi 163   ) = 262537412640768743.999999999999...
and its implications that have already been extensively discusssed on
the net.

	Philippe Flajolet
Newsgroups: sci.math
From: poag@blues.rtp.dg.com (Coleman Poag)
Subject: Re: distribution of wealth
Date: Tue, 7 Apr 92 12:15:22 GMT
Organization: Data General Corporation, Research Triangle Park, NC

> If you added up everbody's bank balances, in the world, and then
> divided by the world population, what would we all get??
>
> A lot or a little?

Now that would depend on your point of view, wouldn't it?  Most of the 
world would think that they got a lot, but I imagine most of us would 
be very disappointed.
-- 

Coleman Poag                     Internet: poag@dg-rtp.dg.com
ECLIPSE Commercial Software      UUCP:     {world}!mcnc!rti!dg-rtp!poag
Data General Corporation
62 T.W. Alexander Drive
RTP, NC. 27709                   Phone:    919-248-5974
Newsgroups: sci.math
From: obryankw@NeXTwork.Rose-Hulman.Edu (Kevin W. Obryant)
Subject: Re: Paul Erdos [correction]
Reply-To: obryankw@NeXTwork.Rose-Hulman.Edu (Kevin W. Obryant)
Organization: Rose-Hulman Institute of Technology
Date: Wed, 15 Apr 1992 21:07:32 GMT

In article <ARNDT.92Apr14122042@julius.c3consult.comm.se>  
arndt@c3consult.comm.se (Arndt Jonasson) writes:
> 
> 
> I recently posted a piece of misinformation in stating that Paul
> Erdos's name is rightly spelled with "two grave accents". It should
> have been "two acute accents", i.e. the picture below is correct.
> Thanks to John Harper for pointing out the discrepancy.
> 
>                //
>          E R D O S
> 
> [... Second rule of fast proofreading: only read through the parts
> which you know you got right - that's where the mistakes are ...]
> --
> Arndt Jonasson				Communicator C3Consult AB
> arndt@c3consult.comm.se

Actually, the slant on the accents is irrelevant.  Hungarian typewriters  
give them a negative slope, but I know many people (Hungarians) whose  
handwritten version of the letter gives them a positive slope.  Either way  
is correct.


Kevin O'Bryant
obryankw@hydra.rose-hulman.edu
From: jbarnett@nrtc.northrop.com (Jeff Barnett)
Newsgroups: sci.math
Subject: Question on Connectedness
Date: 14 Apr 92 20:53:23 GMT
Reply-To: jbarnett@nrtc.northrop.com (Jeff Barnett)
Keywords: Topology
Cc: jbarnett@nrtc.northrop.com

Is the following true in the topology of Euclidean n space:

P is a collection of non-empty (pairwise) disjoint closed sets.  P is
a partition of S.  Claim -- if S is connected, then the cardinality
of P is either 1 or uncountable.

Jeff

P.S. This is my 1st attempted to post with a version of XRN.  In case the
header is munged, my email address is jbarnett@nrtc.northrop.com 
Newsgroups: sci.math
From: orourke@sophia.smith.edu (Joseph O'Rourke)
Subject: Re: Interesting problem help!!
Organization: Smith College, Northampton, MA, US
Date: Fri, 17 Apr 1992 17:47:47 GMT

In article <1992Apr17.141404.24777@samba.oit.unc.edu> Jason.Breitweg@bbs.oit.unc.edu (Jason Breitweg) writes:
>Knowing that exp(i(a+b))=exp(ia)exp(ib) derive the relations for
>sin(a+b) and cos(a+b).

	Sounds like a homework problem.
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Newsgroups: sci.math
Subject: Re: On knowing who's who (was: Fermat's Last Theorem)
Date: 9 Apr 92 19:12:34 GMT
Distribution: na
Organization: Beckman Instruments, Inc.

In <22604@dog.ee.lbl.gov> sichase@csa2.lbl.gov (SCOTT I CHASE) writes:

>In article <a_rubin.702838383@dn66>, a_rubin@dsg4.dse.beckman.com (Arthur Rubin) writes...
>>In <COLUMBUS.92Apr9091341@strident.think.com> columbus@strident.think.com (Michael Weiss) writes:
>> 
>>>	<STROMME.92Apr6130830@jeeves.math.utah.edu> <3660@tuegate.tue.nl>
>>>	<1992Apr9.021905.20917@linus.mitre.org>
>>>NNTP-Posting-Host: strident.think.com
>>>In-reply-to: bs@gauss.mitre.org's message of Thu, 9 Apr 1992 02:19:05 GMT
>> 
>>>Our story so far:
>> 
>>>   Derek Abbott: "Who is this Erdos dude?"
>>>   Robert D. Silverman: "You're kidding, right? How could you not know one
>>>    	of the foremost mathematicians of this century?"  (approximate
>>>    	quotation)
>>>   Various posters: give the guy a break.
>>>   Other posters: give *us* a break.
>> 
>>>In an interview in Scientific American a few months back, then Chief of
>>>Staff John Sununu did not know (or professed not to know) who Leon Lederman
>>>is.  I leave it for the reader to decide which side of the debate (if
>>>either) this factlet supports.
>> 
>>OK, who IS Leon Lederman?
>> 

>Leon Lederman is probably the most famous and most uncannily successful
>experimental particle physicist of our generation.  He has so many big
>discoveries to his name that when he was awarded the Nobel Prize a few years
>ago he wasn't sure at first what it was for.

....

>Conclusion:  Lederman is as luminary a figure as Erdos, if not moreso in his
>respective field.   Derek probably didn't know who he is either. :)

Erdos is probably the best known active mathematician, possibly the best
known living mathematician.  I don't think Lederman is the best known
active physicist.

>But jeez, guys.  I lament the fact that more people don't know who Erdos, or
>Lederman, or Weinberg, etc., are.  But most people don't even know who
>Euler, Gauss, Maxwell, Faraday, Boltzmann, Bernoulli, Fermat, Laplace,
>Lagrange, and so forth... are.  

Agreed.

>So I think that if someone asks, we who know are obliged to put on the best
>smile possible (no condescending allowed) and teach them.  Don't you want them
>to learn?

Agreed.



--
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.
Ich bin ein Virus.  Mach' mit und kopiere mich in Deine .signature.
Newsgroups: sci.math.num-analysis
From: hatay@spot.Colorado.EDU (Ferhat F. Hatay)
Subject: Re: Eigenvalue,Eigenvector
Organization: University of Colorado, Boulder
Date: Sun, 12 Apr 1992 18:41:51 GMT

In article <17229@sophia.inria.fr> falzon@sophia.inria.fr writes:
>
> Does anybody have the general forms of eigenvalues and eigenvectors of an NxN
> pseudo-tridiagonal matrix of the form :
> 
> For example with N=4;
> 
>
>	[(1+1/a) -1/a       0         0 ]
>  A = 	[-1/a    (1+2/a)  -1/a        0 ]
>	[ 0       -1/a    (1+2/a)  -1/a ]
>	[ 0         0      -1/a  (1+1/a)] 
>
> Thanks in advance.
>
>
>      Fred.
>-----------------------------------------------------------------------------------------


Let me take this moment to recommend one of those old books lying
on the hard-to reach shelves of your library. 1966 "A collection of 
Matrices for Testing Computational Algorithms" by Robert T. Gregory and
David L. Karney by Wiley-Interscience. The book is dedicated to
A. S. Householder and it lives up to its title. 

I am certain (100%) that you will find the eigenvalues and eigenfunctions
to the matrix which is apparently from a second order central difference
finite difference discretization. It is a circulant matrix and have eigen
solutions which can be expressed in terms of bunch of cosines and sines. 
Contact me if you are still at loss. 

Ferhat 

-- 
Ferhat F. Hatay                        || Disclamer: |||||||||||||||||
Aerospace Engineering Sciences         || I speak for myself unless || 
University of Colorado, Boulder        || otherwise indicated.      ||
e-mail: hatay@spot.colorado.edu        |||||||||||||||||||||||||||||||
From: ajayshah@alhena.usc.edu (Ajay Shah)
Newsgroups: sci.math.num-analysis
Subject: Re: Optimization Question Two
Date: 16 Apr 1992 22:28:54 -0700
Organization: University of Southern California, Los Angeles, CA
NNTP-Posting-Host: alhena.usc.edu

dow@nova2.stanford.edu (Keith Dow) writes:

>One last question.  It seems to me that nonlinear optimization
>is nonlinear optimization is nonlinear optimization.  So why
>are there different routines for fitting data to a nonlinear
>function and for optimizing a nonlinear function?

In the case of MLE, it turns out that we can exploit properties
of the objective function (the likelihood function) to gain
efficiency.  Esp. once you have "decent" seeds, there are ways
to get big gains.

I believe there are similar tricks for NLS.

It's sortof like matrix inversion.  Matrix inversion is matrix inversion
is matrix inversion.  But the name of the game is exploiting
structure and specail properties.

        -ans.
-- 

Ajay Shah, (213)749-8133, ajayshah@usc.edu
From: ronald@cs.kuleuven.ac.be (Ronald Cools)
Newsgroups: sci.math.num-analysis
Subject: Re: Numerical integration of squares,cubes etc.
Date: 14 Apr 92 08:56:46 GMT
Organization: dept. Computerwetenschappen (K.U.Leuven)

In article <4777@mccuts.uts.mcc.ac.uk>, mbgapdk@uts.mcc.ac.uk (Dr. D. Kidger) writes:
|> Does anyone have any references to integration formulae for 2d/3d 'squares' 
|> other than the 'standard' product Gauss rules.
|>  I have 6,14 and 15 point rules for cubes (range -1--> +1) and a 
|> 'better than 3x3x3 Gauss' 27 point rule for cubes.
|> 
|> In particular what are the optimal sampling points (and weights) for 9
|> integration points in 2d ?
|> 
|> --------- Dr. Dan Kidger ------ Dept. of Civ Eng. Manchester, UK ---------

Most integration formulae that were known in 1971 are listed in the book
   A.H. Stroud: Approximate calculation of multiple integrals,
   Prentice Hall, Englewood Cliffs, N.J., 1971

Since then a lot of new integration formulae were constructed. The report
   R. Cools and P. Rabinowitz:
   Monomial cubature rules since 'Stroud': a compilation,
   Report TW161, Dept. of Computer Science, K.U. Leuven, 1991.
contains now 99 references.

          R o n a l d

-----------------------------------------------------------------------------
| Name   : Ronald  Cools                                                    |
| Email  : ronald@cs.kuleuven.ac.be        Katholieke Universiteit Leuven   |
|          na.cools@na-net.stanford.edu    Department of Computer Science   |
|                                          Celestijnenlaan 200 A            |
|        :                                 B-3001 Leuven (Heverlee)         |
| Phone  : +(32) 16 20 10 15 x3562         BELGIUM                          |
-----------------------------------------------------------------------------
From: samuell@cis.uab.edu (Bobb Samuell)
Newsgroups: sci.math.num-analysis
Subject: RE: PI replies
Keywords: thanks, PI digits, C routine, computation
Date: 7 Apr 92 01:57:17 GMT
Organization: University of Alabama at Birmingham

TO:  All respondents to PI posting

Thank you all for your assistance in providing me with information and
references on the value of PI.  I have received sixteen responses 
providing values of PI from 100 to 2000 + digits.  I have also received 
several routines for computing the digits of PI in LISP and C.  The C 
routine which calculates the first 800 digits (in a compactly unfathomable 
way) was ideal as I was able to incorporate it directly into my project 
(after verifying its accuracy from the values of PI provided by other
respondents). 

Thanks again and I will always be

Numerically yours,


Bobb Samuell
Xref: sparky sci.math.num-analysis:1393 comp.lang.c:7260
From: purvis@mulab.physiol.upenn.edu (bedenbaugh)
Newsgroups: sci.math.num-analysis,comp.lang.c
Subject: Re: Digital-age counterpart for Abramowitz/Stegun?
Date: 6 Apr 92 15:15:46 GMT
Followup-To: sci.math.num-analysis
Organization: University of Pennsylvania

In article <ktvca3INNdta@alhena.usc.edu> ajayshah@alhena.usc.edu (Ajay Shah) writes:
>purvis@mulab.physiol.upenn.edu (bedenbaugh) writes:
>
>
>>A recent subroutine collection companion to Abramowitz and Stegun is
>
>>Louis Baker,
>>_C Mathematitcal Function Handbook_
>>McGraw-Hill
>>1992
>
>
>Just one question.  I saw a pair of books of C numanal some time ago.
>One of them is named something like "C toolchest" and on the cover is
>a vise, and the 2nd is the sequel.  I thought they are really terrible
>books.  Does this guy have anything to do with it?  (I was bothered by
>"other books": there aren't too many books of the sort or I would have
>heard of Mr. Baker).
>

Yes: the author seems to be the same.  The above book is not great
literature, though its routines are potentially useful.
 
>>The book comes with a floppy disk with programs for each function.  I have
>Is the source code in the public domain?  I.e., if I write a program
>which uses them, can I post functions used on the net?
>
>(The big screwup with Numerical Recipes is that unlike (say) Linpack
>it is not PD.  So if you plan to share your work with others you
>can't use NR).
>

The Numerical Recipes software has worse problems than its copywrite.
Do you really want to share NR code ? The NR people give anyone who
reads the book permission to have a machine readable copy.  Besides
their main goal is teaching programming, not publishing a subroutine
library. 

The Baker book is copywrited.  This is more of a problem for it since
it has little to recomend it beyond the code.  On P. 740 Baker writes,
in reference to an included cross referencing program

"Taking a cue from the Free Software Foundation, I should copyleft
this program. Having difficulty telling my right from my left, let me
introduce the concep of _copysideways_.  If you have read this far,
you are deemed to have implicitly agreed to any licensing agreement I
care to invent. (Just kidding. But remember, _all_ of this book and
the associated software is copywrited.)"

The accompanying disk says "Opening this disk package constitutes
acceptance of the terms on the opposit page...". The opposit page is
blank. 

Buying the book is 1-2 orders of magnitude cheaper than buying
Mathematica, though, depending on what you run Mathematica on. (It
doesn't do as much as Mathematica, of course.)

>>The people at Quantum Books (an excellent technical bookstore)
>>in Philadelphia tell me that Baker's books have not sold well here or
>Could it just be poor publicity?  Or are the books poor?
>

Probably because the books are poor.  Check them out though if you
need special functions code for things in Abromowitz and Stegun.

Purvis
purvis@mulab.physiol.edu
Newsgroups: sci.math.num-analysis
From: mcgrant@isl.stanford.edu (Michael C. Grant)
Subject: Patents on interior-point methods
Organization: Information Systems Laboratory, Stanford University
Date: 16 Apr 92 17:25:18

We're developing some software here at Stanford which utilizes interior-
point methods for optimization. Karmarkar's famous LP algorithm is an
example of such methods, but it is not the one we use.

...however, I have heard that AT&T has a patent whose scope extends
over all interior-point methods; on the other hand, I know at least
some countries who specifically disallow patents on 'algorithms', such
as France. So I may not be correct on that. I do know that, after the
initial fervor over Karmarkar's algorithm in the press, AT&T quickly
squelched when the realized what a money-making tool was being given away
to/by the academic community!

Can anyone shed some light on this issue? It certainly would affect the
distribution of our work if AT&T breathes down our necks. It certainly
has enough new, original work that maybe we could escape from under the
patent, but a bunch of grad students/professors can't afford to go up
against a giant.

(Yes, I'm going today to the library to check out the patent).

(I posted to gnu.misc.discuss because of the League for Programming Freedom
announcements that occaisonally show up---so I thought this might coincide).

Thanks a lot,
Michael C. Grant
Newsgroups: sci.math.num-analysis
From: mece1uu@rosie.uh.edu (Singer, Jurgen Kurt)
Subject: Re: wavelet code?
News-Software: VAX/VMS VNEWS 1.41    
Organization: University of Houston
Distribution: na
Date: Tue, 14 Apr 1992 15:44:00 GMT

In article <32822@darkstar.ucsc.edu>, tomas@cats.ucsc.edu (Thomas Joseph Avila) writes...
> 
> 
>   Hi, does anyone know where I could find code (preferably in C) to
>perform wavelet analysis AND synthesis (reconstruction) on a time
>series.  I have been trying to code this myself but the reconstructions
>aren't correct, so I have a bug somewhere.  Actually code that
>just does wavelet analysis would be helpful also.
> 
>   Any help greatly appreciated.  
> 
> 
>   tomas@cats.ucsc.edu
Check out the latest issue of Dr. Dobbs Journal. It contains wavelet code in C
Their code is usually also available on CompuServe.
Hope this helps,
Jurgen

Xref: sparky sci.math.num-analysis:1454 sci.math.symbolic:1262
From: miller@cogsci.ucsd.EDU (Jeff Miller)
Newsgroups: sci.math.num-analysis,sci.math.stat
Subject: Search for minimum of function of INTEGER parameters?
Keywords: simplex, parameter, function minimization
Date: 12 Apr 92 17:47:46 GMT
Organization: University of California, San Diego


I have seen several general algorithms (eg Simplex) to search for
parameter settings that minimize functions of real-valued parameters.

Are there also algorithms to search for settings that minimize
functions of INTEGER-valued parameters?

Or, better yet, are there search algorithms for the case in which
functions take both integer and real parameters?

Or is there a good trick with which a real-valued search algorithm
(like Simplex) can be used with integer-valued parameters?

Any information relevant to this problem would be appreciated.

Jeff Miller
Professor of Psychology
UC San Diego
jomiller@ucsd.edu
From: tomas@cats.ucsc.edu (Thomas Joseph Avila)
Newsgroups: sci.math.num-analysis
Subject: wavelet code?
Date: 14 Apr 92 00:25:12 GMT
Distribution: na
Organization: University of California, Santa Cruz



   Hi, does anyone know where I could find code (preferably in C) to
perform wavelet analysis AND synthesis (reconstruction) on a time
series.  I have been trying to code this myself but the reconstructions
aren't correct, so I have a bug somewhere.  Actually code that
just does wavelet analysis would be helpful also.

   Any help greatly appreciated.  


   tomas@cats.ucsc.edu