HDTenEightyP/NetNews huggingface dataset:
From: agw@cs.columbia.edu (Art Werschulz)
Subject: Daniel Gorenstein (1923-1992)
Reply-To: agw@cs.columbia.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Columbia University Department of Computer Science
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Thu, 27 Aug 1992 15:38:08 GMT


Daniel Gorenstein, founding director of the Rutgers University DIMACS
consortium, passed away yesterday, Wednesday 26 August, at the age of
69. 

He was famous for his development of a 16-step master plan for the
classification of finite simple groups.

--
      Art Werschulz
      InterNet:  agw@cs.columbia.edu
      ATTnet:    Columbia University (212) 939-7061
                 Fordham University  (212) 636-6325
From: klein@math205.mathematik.uni-bielefeld.de (john klein)
Newsgroups: sci.math.research
Subject: Re: Union of locally flat cells.
Date: 28 Aug 92 14:01:24 GMT
Organization: Universitaet Bielefeld
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu

In article <BtowMx.M9p@fuhainf.fernuni-hagen.de> le@tinosfernuni-hagen.de  
writes:
> 
> 1. Can anyone give information about the current status
> of the "annulus conjecture" ?
> Rushing stated in his book "Topological Embeddings, AP 1973"
> that "it is still unknown for n=4".
> 
> 2. Is the \beta-statement \beta(n,n-1,n-1,n-2) true for n=3 ?
> If not, under what additional conditions it it true ?
> Rushing states in his book that it is true for n > 3.
> 
> Any suggestions, hints are welcome.
> 
> Thanks in advance.

I believe that Quinn proved the 4-dimensional annulus conjecture.
The paper was published in the Journal of Differential Geometry
(1984?). The precise reference is in the Freedman-Quinn  book
"Topology of 4-manifolds" (Princeton , 1991)
Andrew Ranicki
Newsgroups: sci.math.research
From: israel@unixg.ubc.ca (Robert B. Israel)
Subject: Re: Borel measure question
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of British Columbia, Vancouver, B.C., Canada
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Tue, 25 Aug 1992 17:51:53 GMT

In <17dh96INN35s@function.mps.ohio-state.edu> edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:


>(I seem to remember seeing this, but can't remember for sure.)

>Let S be a metric space.  Write B(x,r) for the open ball with center
>x and radius r.  Let mu be a finite Borel measure on S.  For fixed
>r>0, does it follow that the function

>   x --->  mu(B(x,r))

>(from S to R) is a Borel function of x ?

Without loss of generality, assume that mu is a positive measure
(for a signed measure, use the Hahn decomposition).  Then your function
is not only Borel, it is lower semicontinuous, i.e. for any t,
{x: mu(B(x,r) > t} is open.

Suppose mu(B(x,r)) > t.  Since B(x,r) = union{B(x,r-1/n): n in positive 
integers}, mu(B(x,r-1/n)) > t for some positive integer n.  If d(x,y) < 1/n,
then B(x,r-1/n) is contained in B(y,r), so mu(B(y,r)) > t.

>Assume, if necessary, that S is separable.
>-- 
>  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)

-- 
Robert Israel                            israel@math.ubc.ca
Department of Mathematics             or israel@unixg.ubc.ca
University of British Columbia
Vancouver, BC, Canada V6T 1Y4


Newsgroups: sci.math.research
From: le@fuhainf.fernuni-hagen.de
Subject: PL Schoenflies Conjecture.
X-Submissions-To: sci-math-research@uiuc.edu
Organization: FernUniversitaet Hagen
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Mon, 31 Aug 1992 11:02:59 GMT


Could anyone give information about the PL Schoenflies Conjecture
as stated in Rushing: Topological Embeddings, AP 1973. He
stated that "it is still unknown".

Let \bigsigma^{n-1} be a PL (n-1)-sphere in S^n. Then,
the closures of the complementary domains of \bigsigma^{n-1}
are PL n-balls.

For what n is the PL Schoenflies Conjecture valid ?

Thanks in advance.


le@fuhainf.fernuni-hagen.de

Newsgroups: sci.math.research
From: agw@cs.columbia.edu (Art Werschulz)
Subject: Science reporting
Reply-To: agw@cs.columbia.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Illinois at Urbana
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Thu, 27 Aug 1992 15:42:16 GMT


In a previous posting, I mentioned the passing yesterday of Daniel
Gorenstein.  

His obituary appeared in the Newark (NJ) Star-Ledger for today
(Thursday 27 August).  The obituary describes Gorenstein as "an
international leader in the field of group therapy", and says that his
"work made Rutgers a major center for group therapy study".

Sigh.








--
      Art Werschulz
      InterNet:  agw@cs.columbia.edu
      ATTnet:    Columbia University (212) 939-7061
                 Fordham University  (212) 636-6325

Newsgroups: sci.math.research
From: moon@moon.ee.usu.edu (Todd Moon)
Subject: mixed-field arithmetic problems
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Utah State University Dept EE Logan, Utah
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Tue, 1 Sep 1992 16:01:58 GMT


Here is a problem in mixed field arithmetic.  In what follows, + will
denote addition over the field of reals, and | will denote addition
over GF(2).  Multiplication is over the reals.

consider a system of equations such as

a_1 c_0               + a_2 c_3               = s_0
a_1 c_1               + a_2 c_4               = s_1
a_1 c_2               + a_2 c_5               = s_2
a_1 (c_0 | c_1)       + a_2 (c_3 | c_5)       = s_3
a_1 (c_1 | c_2)       + a_2 (c_3 | c_4 | c_5) = s_4
a_1 (c_0 | c_1 | c_2) + a_2 (c_3 | c_5)       = s_5
a_1 (c_0 | c_2)       + a_2 (c_4 | c_5)       = s_6

where a_1 and a_2 are real and known, the s_i are real and known, and
the unknowns c_i are in GF(2) (that is, either 0 or 1).  Although the
problem has been written similar to a set of linear equations, it is
easy to verify that this is not a linear set of equations.

1) Find the set of c_i that satisfy this set of equations.  For this
problem, it can be accomplished simply by combinatorial search
techniques.  However, there are larger problems of interest similar to
for which searching is impractical.

2) Now consider the case of finding the "best" solution to the set of
equations where the equality does not hold -- there is unknown "noise"
in the equations:

a_1 c_0               + a_2 c_3               = s_0 + n_0
a_1 c_1               + a_2 c_4               = s_1 + n_1
a_1 c_2               + a_2 c_5               = s_2 + n_2
a_1 (c_0 | c_1)       + a_2 (c_3 | c_5)       = s_3 + n_3
a_1 (c_1 | c_2)       + a_2 (c_3 | c_4 | c_5) = s_4 + n_4
a_1 (c_0 | c_1 | c_2) + a_2 (c_3 | c_5)       = s_5 + n_5
a_1 (c_0 | c_2)       + a_2 (c_4 | c_5)       = s_6 + n_6

As before, a_i and s_i are known, but the noise n_i is not known.
Find the best (perhaps in least squares sense) set of c_i in GF(2).

What would be nice would be to have an algebra for these mixed field
problems, from which exact and pseudo-inverse solutions coulde be
obtained.

Any suggestions, comments, references, etc. would be greatly
appreciated.


Todd Moon
Electrical Engineering Dept., UMC 4120
Utah State University
Logan, UT  84322
801 750 2970
moon@moon.ee.usu.edu

Newsgroups: sci.math.research
From: bs@fatima.mitre.org (Robert D. Silverman)
Subject: Re: Science reporting
Posted-Date: Thu, 27 Aug 1992 17:15:48 GMT
X-Submissions-To: sci-math-research@uiuc.edu
Old-Return-Path: <news@linus.mitre.org>
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Thu, 27 Aug 1992 17:15:48 GMT

In article <AGW.92Aug27104216@ibc.cs.columbia.edu> agw@cs.columbia.edu writes:
:
:In a previous posting, I mentioned the passing yesterday of Daniel
:Gorenstein.  
:
:His obituary appeared in the Newark (NJ) Star-Ledger for today
:(Thursday 27 August).  The obituary describes Gorenstein as "an
:international leader in the field of group therapy", and says that his
:"work made Rutgers a major center for group therapy study".
:
:Sigh.
 
I guess it gives new meaning to the term 'ask an analyst'.

--
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"

Newsgroups: sci.math.research
From: israel@unixg.ubc.ca (Robert B. Israel)
Subject: Re: convex functions on L_1 spaces
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of British Columbia, Vancouver, B.C., Canada
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Mon, 31 Aug 1992 17:00:19 GMT
Keywords: convex, L_1

In <fernand.715217944@acf9> Indrajit, using the account of 
   fernand@acf9.nyu.edu (Chris Fernandes) writes:

>I have a question regarding convex functions on L_1 spaces.

>Consider the space L_1.
>Let U: L_1->R  be a strictly convex function.
>Let G be a closed convex and bounded set in L_1.

>Is it then true that the function U achieves its minimum on the set G?

Not true in l_1: let G = { x: x_i >= 0, sum_i x_i = 1 } and U(x) = sum_i x_i^2.
The infimum is 0 (consider U(x) where x_i = 1/n for 1 <= i <= n, 0
otherwise), but it is not achieved.  I don't have an example for other
L_1 spaces, but it probably wouldn't be hard to construct.

>I have not been able to find this result in any reference book.  Intuitively,
> the result seems to be true, but I cannot come up with a clean proof.

>I do know that the set G is compact in the weak* topology, but on L_1
>the weak* and the weak do not coincide.

What weak* topology?  L_1 spaces (except for l_1) are generally not dual
spaces.

>  For example, in L_2, the set
>is weakly compact and thus the minimum is achieved.

>Hopefully  yours,

>Indrajit, mailing from friend's account.

-- 
Robert Israel                            israel@math.ubc.ca
Department of Mathematics             or israel@unixg.ubc.ca
University of British Columbia
Vancouver, BC, Canada V6T 1Y4


Newsgroups: sci.math.research
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Subject: Re: mixed-field arithmetic problems
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Illinois at Urbana
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Tue, 1 Sep 1992 19:51:58 GMT

In <MOON.92Sep1110158@moon.ee.usu.edu> moon@moon.ee.usu.edu (Todd Moon) writes:


>Here is a problem in mixed field arithmetic.  In what follows, + will
>denote addition over the field of reals, and | will denote addition
>over GF(2).  Multiplication is over the reals.

>consider a system of equations such as

>a_1 c_0               + a_2 c_3               = s_0
>a_1 c_1               + a_2 c_4               = s_1
>a_1 c_2               + a_2 c_5               = s_2
>a_1 (c_0 | c_1)       + a_2 (c_3 | c_5)       = s_3
>a_1 (c_1 | c_2)       + a_2 (c_3 | c_4 | c_5) = s_4
>a_1 (c_0 | c_1 | c_2) + a_2 (c_3 | c_5)       = s_5
>a_1 (c_0 | c_2)       + a_2 (c_4 | c_5)       = s_6

>where a_1 and a_2 are real and known, the s_i are real and known, and
>the unknowns c_i are in GF(2) (that is, either 0 or 1).  Although the
>problem has been written similar to a set of linear equations, it is
>easy to verify that this is not a linear set of equations.

>1) Find the set of c_i that satisfy this set of equations.  For this
>problem, it can be accomplished simply by combinatorial search
>techniques.  However, there are larger problems of interest similar to
>for which searching is impractical.

For equations of the form:

(E_i) a_1 f_i(C) + a_2 g_i(C) = s_i, we have:

If (1)  all of a_1, a_2, a_1+a_2, and a_1-a_2 are nonzero, then E_i
translates to f_i(C) = t_i_1 and g_i(C) = t_i_2.

If (2) a_2 = 0 , then E_i translates to f_i(C) = t_i

If (3) a_2 = a_1, then E_i translate to f_i(C) = 0 and g_i(C) = 0; or
f_i(C) | g_i(C) = 1; or f_i(C) = 1 and g_i(C) = 1

If (4) a_2 = -a_1, then E_i translates to f_i(C) = 0 and g_i(C) = 1; or
f_i(C) | g_i(C) = 0; or f_i(C) = 1 and g_i(C) = 0

If (5) a_1 = a_2 == 0 , then the equations do not depend upon the c's.

In any of these cases, the (E_i) reduce to a linear set of equations over
GF(2), which can be solved by the usual methods.

(This method fails if we have a_1, a_2, and a_3, and they are all equal. 
It works, for example, if the a_i's are "almost sum-distinct"; for any s
there are at most two sum(a_i c_i) equal to s.)


--
Arthur L. Rubin: a_rubin@dsg4.dse.beckman.com (work) Beckman Instruments/Brea
216-5888@mcimail.com 70707.453@compuserve.com arthur@pnet01.cts.com (personal)
My opinions are my own, and do not represent those of my employer.
My interaction with our news system is unstable; if you want to be sure I see a post, mail it.

Newsgroups: sci.math.research
From: robby@math.orst.edu (Robby Robson)
Subject: 1992 West Coast Number Theory Conference
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Oregon State University Math Department
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Mon, 24 Aug 1992 00:51:55 GMT
Keywords: Conference

The West Coast Number Theory conference (an informal but fun conference with
no outside support) will be held in Corvallis from December 18 to December 22.
If you would like to get a registration form, please send email to 

			robby@math.orst.edu

This will get you on the mailing list (if you are not already on it), and you
should get materials in the next few weeks.  There is no electronic
registration.
-- 
Robby Robson 			Phone: 503-737-5171
Department of Mathematics	Fax: 503-737-0517
Oregon State University		Email: robby@math.orst.edu
Corvallis, OR  97331-4605

Newsgroups: sci.math.research
From: jtrsmith@garnet.Berkeley.EDU ()
Subject: A question on Laplace eq.
Followup-To: poster
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of California, Berkeley
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Thu, 3 Sep 1992 17:29:59 GMT

Hi, Sirs,
I have a question about if a Laplace equation 

       div grad T = 0       in a smooth enough domain,

is well-posed under following boundary condition:

    - dT/dn = a ( T*T*T*T - c),  on the domain boundary, 

    (note: T*T*T*T means T to the fourth power.)
where n is in the direction of outward unit normal along the boundary,
a, c is constant, and  a>0.

This boundary is equivalent to a radiation along boundary; heat
conducted from the domain is radiated to out side environment.

Can anybody prove that the problem is well-posed? 

If possible, please reply to this account directly. Thanks.

JTR Smith

Newsgroups: sci.math.research
From: mills@redgum.bcae.oz.au (t.mills)
Subject: Series Expansion
Originator: mills@redgum.ucnv.edu.au
Followup-To: poster
X-Submissions-To: sci-math-research@uiuc.edu
Organization: UCNV, Bendigo, Victoria, Australia
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Thu, 27 Aug 1992 08:43:14 GMT


I need a series expansion for odd powers of cot(z)
such as (cot(z))^3, (cot(z))^5 etc.

Does anyone know a reference please ?

Newsgroups: sci.math.research
From: reus@klein.euromath.dk (Jens Peter Reus Christensen)
Subject: Re: Borel measure question
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Copenhagen, Dept. of Math.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Wed, 26 Aug 1992 15:36:19 GMT

In article <17dh96INN35s@function.mps.ohio-state.edu> edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:

   (I seem to remember seeing this, but can't remember for sure.)

   Let S be a metric space.  Write B(x,r) for the open ball with center
   x and radius r.  Let mu be a finite Borel measure on S.  For fixed
   r>0, does it follow that the function

      x --->  mu(B(x,r))

   (from S to R) is a Borel function of x ?

   Assume, if necessary, that S is separable.
   -- 
     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)

*****
I do think this function is lower semicontinuous! Thus always
measurable!

--
|--------------------------------------------------------------------------|
|  Jens Peter Reus Christensen   |                                         |
|  Associate professor, Dr. Phil.|                                         |
|  Department of mathematics     | e-mail:          reus@math.ku.dk        |
|  University of Copenhagen      |                                         |
|  Universitetsparken 5          | phone:           +45 3135 3133 ext. 458 |
|  DK-2100 Copenhagen            | fax:                      +45 3135 4254 |
|--------------------------------------------------------------------------|
|  Disclaimer: Except when explicitly stated otherwise any message         |
|  with this signature is the authors purely private responsibility.       | 
|--------------------------------------------------------------------------|
|  Motto : How can I curse those whom GOD has not cursed?                  |
|  How can I denounce those whom the LORD has not denounced?               |
|  Balaam's First Oracle , Numbers Ch 23,v 8.                              |
|--------------------------------------------------------------------------|






















































Newsgroups: sci.math.research
From: le@tinosfernuni-hagen.de
Subject: Union of locally flat cells.
X-Submissions-To: sci-math-research@uiuc.edu
Organization: FernUniversitaet Hagen
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 28 Aug 1992 10:47:21 GMT


1. Can anyone give information about the current status
of the "annulus conjecture" ?
Rushing stated in his book "Topological Embeddings, AP 1973"
that "it is still unknown for n=4".

2. Is the \beta-statement \beta(n,n-1,n-1,n-2) true for n=3 ?
If not, under what additional conditions it it true ?
Rushing states in his book that it is true for n > 3.

Any suggestions, hints are welcome.

Thanks in advance.

Newsgroups: sci.math.research
From: sullivan@pysgjb.physics.ncsu.edu (Dan Sullivan)
Subject: Re: Exponential of an arbitrary mapping f: R^n -> R^n
Posted-Date: Fri, 28 Aug 1992 20:40:54 GMT
Followup-To: sci.math.research
X-Submissions-To: sci-math-research@uiuc.edu
Organization: NCSU Physics, Condensed Matter Theory
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 28 Aug 1992 20:40:54 GMT

In article <1992Aug28.181224.14463@nas.nasa.gov> asimov@nas.nasa.gov (Daniel A. Asimov) writes:
>One way to generalize the exponential of a matrix to arbitrary

You may have these references already, but maybe not:

C.B. Moler and C.F. Van Loan (1978). "Nineteen Dubious Ways to
   Compute the Exponential of a Matrix," SIAM Review 20, 801.
Gene H. Golub and Charles F. Van Loan (1989). Matirx Computations,
   2nd ed., The Johns Hopkins University Press, Baltimore.  pp. 551-560.
B.W. Helton (1968). "Logarithms of Matrices," Proc. Amer. Math.
   Soc. 19, 733.

--Dan

---------------------------------------------------------------------------
Dan Sullivan | +1 919 515 7991 | Dan_Sullivan@ncsu.edu or sullivan@ncsuphys
---------------------------------------------------------------------------

Newsgroups: sci.math
From: dak@kaa.informatik.rwth-aachen.de (David Kastrup)
Subject: Re: x 2^x = 2^n ?
Organization: Rechnerbetrieb Informatik  /  RWTH Aachen
Date: 27 Aug 92 08:25:36 GMT

soeren@cse.ucsc.edu (Soren Soe) writes:

>Can anyone tell me what `x' is in this equation:

>	x 2^x = 2^n

>Is there a general solution, or do I have to approximate `x' to something like
>x = n - lg n + a_little_more ?
>In fact I can do with an approximation to x, iff 
>		floor(x) <= app(x) <= x

>I need the "floor" of `x' to solve the following summation, where k 
>would be equal to floor(x):

>	i=n-1
>	SUM   min(2^i, 2^2^(n-i))
>	i=0

>	i=k	     i=n-1
>    =   SUM  2^i  +  SUM   2^2^(n-i)
>	i=0	     i=k+1

>--soeren

>Soren Soe,
>soeren@ce.ucsc.edu
x = n - lg x
x = n - lg (n - lg x)
x = n - lg n - lg (1 - (lg x)/n)
Now lg (1-k) = lg e ln (1-k)  >= (lg e) (-k).
Setting k = (lg x)/n, you can see that an error of 1 can be achieved
easily for greater values of x.
From: jwd2@owlnet.rice.edu (Joseph William DeVincentis)
Newsgroups: sci.math
Subject: Re: Problematic smurfs!
Keywords: smurfs
Date: 31 Aug 92 00:06:08 GMT
Organization: Rice University

In article <94952@bu.edu>, spacefox@acs.bu.edu (Godfrey Degamo) writes:
|>      A group of 1000 smurfs wear either a red or blue hat on their head.
|> They can only wear one color. The color hat on their head is known to all, but
|> the wearer.  The wearer of the hat has no means whatsoever for obtaining the
|> color of his hat.  It is never the case that all 1000 smurfs will wear
|> the same color hat.
|>      One day the mayor, not apart of the 1000 smurfs, decides to call a
|> town meeting.  All 1000 smurfs are gathered into the town hall.  The mayor
|> is not wearing a hat.  During the meeting, the mayor asks that all the
|> smurfs wearing red hats to stand up.
|>      There is a bit of commotion in the crowd, but no one stands up.
|>      The mayor requests the same demand a bit more sternly.
|>      Again, commotion, but no one stands up.
|>      The mayor, irate, demands the red hatted smurfs to stand up.
|>      Then, a certain amount of smurfs rise.
|> 
|> find:
|>      The exact amount of smurfs that rise.  
|>          (Hint: This number will be greater than one.)
|>      The color of the hats of the smurfs that rise.
|> 
|> more importantly,
|>      Explain how you deduced your answer.

   First, I will assume that all the smurfs know all the information above,
and they know that all the other smurfs know all the information above,
ad infinitum, and I also assume that all the smurfs are perfect logicians.
(and that they know all the other smurfs are perfect logicians, etc., etc.)

   So, we begin by noting that there is at least one red-hatted (RH) smurf.
All the smurfs know this, so if there had been only one RH smurf, he would
have seen no other RH, and would know he had a RH, so he would stand up.
Since no smurf stood up the first time, there must be at least two RH smurfs.

   If there were exactly two RH smurfs, then on the mayor's second
command, each of them would have seen only one RH, and, noting that
this smurf did not stand up the first time, would deduce that he himself
also wore a RH.

   Similarly, on the third call, if any smurf stood up, he would only have
done so if he saw exactly two other red hats (noting that those smurfs didn't
stand up the previous time).  Since some smurfs stood up, there must be
exactly three of them, and all correctly deduced that they wore red hats.

It's a good thing there were only three red hatted smurfs, and not 997!



|> PS: please, no Delft University students' input! ;)

Delft University?  Where's that?  ;-)

-- 
----w-w--------------Joseph  De Vincentis--jwd2@owlnet.rice.edu----------------
   ( ^ )   Disclaimer: My opinions do not represent those of Owlnet.
   (O O)   Owlnet: George R. Brown School of Engineering Educational Network. 
    v-v    (Unauthorized use is prohibited.)  (Being uwop-ap!sdn is allowed.)
Newsgroups: sci.math