HDTenEightyP/NetNews huggingface dataset:
From: smith@zeus.harvard.edu (Steven Smith)
Newsgroups: sci.math,sci.engr.control,sci.math.num-analysis
Subject: Re: Matrix Problem !
Date: 30 Sep 92 15:53:55 GMT
Article-I.D.: zeus.SMITH.92Sep30105355
Distribution: sci.math,sci.engr.control,sci.math.num-analysis
Organization: Harvard Robotics Lab, Harvard University

rairan@ecf.toronto.edu (RAI Ranjan) writes:
> 
>                               A     kBB'
> Hi.  I have a matrix H(k) =              where ' means transpose
>                              -kC'C  -A'
> and k is a constant.
> A, B , and C are nxn matrices.  So H(k) is a 2nx2n matrix.  
> 
> I have to compute the eigenvalues of H(k) for various values of 
> k that differ by a factor of 2.  ie H(k) then H(2k) then H(4k) ...
> 
> The question is:  Is there an elegant way of doing this.  A method
> that makes use of the symmytries of the original matrix, or uses
> previous results to make each H(k) computation more efficient would
> be appreciated.

This class of matrices is called infinitesimally symplectic or
Hamiltonian.  The corresponding transition matrix is called
symplectic.

To compute the eigenvalues, see C. F. Van Loan (1984), A symplectic
method for approximating all the eigenvalues of a Hamiltonian matrix,
Lin. Alg. Appl., 61, 233-252, and the references therein.  If you're
lucky, you'll be able to track down a program in ACM Trans. Math.
Softw.  (Please let me know if you find one.)

You haven't supplied enough information to determine if updates may be
computed efficiently from previous decompositions.

For a thorough control theoretic background of this type of problem,
see Brockett's _Finite Dimensional Linear Systems_.  For a mechanics
background, see Goldstein's _Classical Mechanics_, or Abraham and
Marsden's _Foundations of Mechanics_ for a modern treatment.

Steven Smith
From: crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass)
Newsgroups: sci.math
Subject: Re: Mattel says "Math is tough."
Date: 7 Oct 92 00:54:39 GMT
Organization: University of Virginia

In article <1at131INNc50@roundup.crhc.uiuc.edu> hougen@vision.csl.uiuc.edu (Darrell Roy Hougen) writes:
>
>In summary, I don't believe that math is hard.  Thinking is hard, but
>who would want to discourage that?

     Try teaching multiplication to a seven-year-old.  That way, 
     you get to see how 'hard' it is from both sides.

                         dale bass
-- 
C. R. Bass                                           crb7q@virginia.edu
Department of Mechanical and Aerospace Engineering
University of Virginia
Charlottesville, Virginia                            (804) 924-7926
From: robert@cs.caltech.edu (Robert J Harley)
Newsgroups: sci.math
Subject: Re: Most important event in the history of mathematics
Date: 29 Sep 1992 17:20:33 GMT
Organization: California Institute of Technology
NNTP-Posting-Host: flora.cs.caltech.edu

     Easy.  That has to be when some prehistoric dude started counting
on his fingers.
    __                                                      '. .`        __
 __/_/\___________________________________________________oOo_U_oOo_____/\_\__
/_/\_\/  B-) :o) :-b    I don't vote---                _|___|___|___|_  \/_/\_\
\_\/_/\  H a r l e y         it only encourages them.    _|___|___|_    /\_\/_/
/_/\_\/                                                    _|___|_      \/_/\_\
\_\/_/\__robert@vlsi.cs.caltech.edu_____________________________________/\_\/_/
   \_\/                                                                 \/_/
Xref: sparky sci.math:12780 sci.math.stat:2072
From: peterg@stat.ufl.edu (Pete Gieser)
Newsgroups: sci.math,sci.math.stat
Subject: Re: Stat problem...
Date: 6 Oct 92 15:26:28 GMT
Article-I.D.: papaya.PETERG.92Oct6082628
Organization: University of Fl, Department of Statistics

>>>>> On Tuesday, 6 Oct 1992 01:14:10 EDT, <ROCHC@CUNYVM.BITNET> said:

>      I'm studying for the GRE Subject Test in Mathematics and I'm having
> trouble with the following 2 statistics questions that I encountered in a
> practice exam:

>       1) In a game, two players take turns tossing a fair coin; the winner
> is the first one to toss a head.  What is the probability that the player who
> makes the first toss is going to win?

>             Answer: 2/3


P(player 1 wins) = P(H)  + P(TTH)  + P(TTTTH) + ...
                 = (1/2) + (1/2)^3 + (1/2)^5  + ...
                 = 2(1/4)/(1-(1/4))
                 = 2/3


>       2) Alternately a coin is tossed and a die is thrown, beginning with
> the coin.  What is the probability that the coin will register a "head"
> before the die registers a "5" or a "6"?

>             Answer: 3/4


Think of this as the same game as above only with the 2 players
now having different probabilities of success.

Let F = no 5 or 6
P(Player 1 wins) = P(H)  + P(TFH)          + P(TFTFH)                  + ...
                 = (1/2) + (1/2)(2/3)(1/2) + (1/2)(2/3)(1/2)(2/3)(1/2) + ...
                 = (1/2) + (1/2)^2 (2/3)   + (1/2)^3 (2/3)^2           + ...
                 = (3/2)(1/3)/(1-(1/3))
                 = 3/4


--
+--------------------------------------------------------------------+
|             No matter where you go...there you are.                |
|                                                                    |
| Remember, you can ALWAYS lie on a                                  |
| set of measure zero.  (Andrew Rosalsky)        peterg@stat.ufl.edu |
+--------------------------------------------------------------------+
From: tsen+@EDRC.CMU.EDU (Chung Kang Tsen)
Newsgroups: sci.math
Subject: Posets and Disjunctive graphs.
Date: 28 Sep 92 17:15:36 GMT
Article-I.D.: cs.BvAtA0.DDn.2
Organization: Carnegie Mellon University


I am working with Job-Shop scheduling and I want references about
properties of Disjunctive graphs on Posets.

Thanks in advance,

    Tsen
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: Re: Hyperbolic space?
Date: 29 Sep 92 22:32:15 GMT
Article-I.D.: camelot.ARA.92Sep29173215
	<1992Sep29.183907.6934@sun0.urz.uni-heidelberg.de>
Organization: M.I.T. Artificial Intelligence Lab.


I think that because of a problem with this editor, I wrote:
"with out cyclopean vision" instead of what I meant to write, which
was "with our cyclopean vision".

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math
From: ara@zurich.ai.mit.edu (Allan Adler)
Subject: classical analysis
Organization: M.I.T. Artificial Intelligence Lab.
Distribution: sci
Date: Tue, 29 Sep 1992 05:46:54 GMT


Does the term "classical analysis" have a definite meaning? If so,
what is it?

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math
From: tao@ginger.princeton.edu (Terry Tao)
Subject: Re: Hawking's portrayal of Newton and Einstien
Originator: news@nimaster
Organization: Princeton University
Date: Mon, 5 Oct 1992 14:29:05 GMT

Hawking, a Cambridge man, seems to have had some rivalry with Newton and
 Eddington.  He does seem unnecessarily critical of both of them.
From: maj@waikato.ac.nz
Newsgroups: sci.math
Subject: Re: Opinions Sought (Why major in math?)
Date: 1 Oct 92 17:03:45 +1200
Organization: University of Waikato, Hamilton, New Zealand

In article <stephen.717902097@mont>, stephen@mont.cs.missouri.edu (Stephen Montgomery-Smith) writes:
> In <1992Sep30.231548.1282@ncsu.edu> kbanerje@grad09.math.ncsu.edu (Kaushik Banerjee) writes:
> 
> 
> 
>>Why should one earn a math degree?
> 
>>Assume that you do not want to teach or conduct research.
>>What types of jobs are available for an individuals with
>>a math degree (at any level)?
> 
> I have interested in what careers there are for math majors, mainly
> so that I can provide information for students.  It seems that there
> are very few jobs out there that make use of the mathematics one has
> learned.
> 
> A while ago, I phoned up alumni from our math dept, asking people
[stuff deleted]

Let me make a prediction:

if or when there develops an area of Mathematics with 
significant employment opportunities other than teaching
or research, then that area will develop into a discipline
of its own, just as Computer Science and Statistics have.

-- 
Murray A. Jorgensen [ maj@waikato.ac.nz ]    University of Waikato
Department of Mathematics and Statistics     Hamilton, New Zealand      
__________________________________________________________________
'Tis the song of the Jubjub! the proof is complete,
if only I've stated it thrice.'
Newsgroups: sci.math
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: Mattel says "Math is tough."
Organization: Department of Chemistry, University of Toronto
Date: Mon, 5 Oct 1992 14:53:14 GMT

In article <5805@tuegate.tue.nl> wsadjw@urc.tue.nl writes:
>Would people get upset if barbie said "Running marathons is tough"?
>Or "relativity is tough"?  Or "Homer is tough"?

No, maybe and yes.  The whole point of a marathon is that it is hard.
The problem with Barbie saying that math is hard is that this doll will
be not be given to college-aged women but to young girls.  There is
nothing intrinsically difficult about elementary school mathematics but
the attitudes developed at this age will last a lifetime.  If a young
girl starts to believe early on that math is hard, she will not later
pursue a career in science or engineering because these require
mathematics.  Barbie alone can't cement such attitudes, but it can
contribute to a barrage of negative social associations between
mathematics and women.
     I'm not sure about relativity; the message there is mixed.  On the
one hand, to say "relativity is tough" you have to have studied it
(which implies a certain level of achievement) but on the other hand,
the message is propagated that there might be upper limits to a woman's
achievement in science.  "Homer is tough" is just another swipe at the
nation's literacy; I would be quite unhappy at that one too, although
for different reasons.
     Children require encouragement to succeed, not negative comments.
Women, who face all manner of subtle disincentives in the sciences, must
be given as good a chance to develop their talents as possible.  A doll
aimed at young girls that reinforces negative attitudes toward
mathematics is a gigantic step backward.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
Xref: sparky sci.math:12501 sci.physics:15691
From: jac@ds8.scri.fsu.edu (Jim Carr)
Newsgroups: sci.math,sci.physics
Subject: Re: Lebesgue integral (was: Couple of questions
Date: 13 Sep 92 18:43:39 GMT
Reply-To: jac@ds8.scri.fsu.edu (Jim Carr)
Followup-To: sci.math
Organization: SCRI, Florida State University

In article <18q2s0INNmb5@function.mps.ohio-state.edu> edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:
>
>Now all you have to do is convince the physicists that their
>Ph.D. students (at least) should study the Lebesgue theory.

Good luck with the "up to their elbows in pump oil" crowd! 

Theoretical students should definitely have a grounding in more than the 
usual advanced calc and complex variables courses.  Or is the problem 
that Lebesgue measure theory is not taught in the advanced calc courses 
taken by many undergrad physics majors? 

--
J. A. Carr                                    |  "The New Frontier of which I  
jac@gw.scri.fsu.edu                           |  speak is not a set of promises
Florida State University  B-186               |  -- it is a set of challenges."
Supercomputer Computations Research Institute |   John F. Kennedy (15 July 60)
From: hoey@AIC.NRL.Navy.Mil (Dan Hoey)
Newsgroups: sci.math
Subject: Re: 1, 2, 4, 8, 13...where have I seen it before?
Date: 1 Oct 92 14:49:12 GMT
Organization: Naval Research Laboratory, Washington, DC

chrisman@herb-ox.berkeley.edu (chrisman) writes:

> I don't know if this sequence has anything to do with
> yours, but here it is (an example of a sequence whose
> first few terms are misleading):

> Let A(n) be the maximum number of regions into which
> a circle can be divided by drawing segments between
> n points on the circle.                      

> The first few terms are (starting with n=1)

>       1, 2, 4, 8, 16, 31 (!).

Well, the reason that sequence is so misleading is that

    A(n)=C(n,0)+C(n,2)+C(n,4),

where C(n,k) is the binomial coefficient.  It is not hard to prove
that A(n) is one (C(n,0)) plus the number of segments (C(n,2)) plus
the number of intersecting pairs of segments (C(n,4)).  And when you
add up alternate pairs of coefficients, you get

    A[k](n) = C(n,0)+C(n,2)+C(n,4)+...+C(n,2k) = 2^(n-1) for n<=2k,

                                             but 2^(n-1)-1 for n=2k+1.

Note that Bill Hery's sequence is not of this type.

What I found fascinating is that A(10)=256=2^(n-2) (though it turns
out that's no coincidence).  Are there any other powers of two in the
sequence?  In any A[k]?

Dan Hoey
Hoey@AIC.NRL.Navy.Mil
Organisation: ECP-Paris France
Date: Wednesday, 30 Sep 1992 23:52:53 EDT
From: <COMTET@FRECP12.BITNET>
Newsgroups: sci.math
Subject: Samples of Gaussian-Markov chains

I would like to know if I can find articles or books talking about applications

of Gaussian-Markov chains . I would be especially interested about applications

in the field of statistical physics or theoretical physics.

Thank you by adavnces for sending me references.

Gilles Comtet-Varga

Ecole Centrale Paris

& Universite Pierre et Marie Curie (Paris 6)

COMTET at FRECP12.BITNET
Newsgroups: sci.math
Subject: <none>
From: broggi@prsun0in.cineca.it (Alberto Broggi)
Date: 6 Oct 92 19:26:42 +0100
Distribution: world

	I'm desperately seeking an article about mathematics
	for a friend of mine.
	I definitely do not know what it is about, but I do know the 
	complete reference:

	The actual name of the magazine is:

		'Acta Scientiarum Szegedensis'

	It was: 

	T.RADO`,   'Uber der Begriff den Riemanschan Flache'
		   Acta Litt. Scie. Szeged, 1925, 2, pag.101-121


	IF ANYBODY HAS ACCESS TO THIS MAGAZINE, PLEASE LET ME KNOW.

	Thanks in advance, 
			
					A.Broggi



-- 
  Alberto Broggi    
  Dipartimento di Ingegneria dell'Informazione   phone: +39 (521) 580707
  Universita` degli Studi di Parma                 fax: +39 (521) 580723
  43100 Parma - Italy                    E-Mail broggi@prsun02.cineca.it
Newsgroups: sci.math
From: martin@lyra.cis.umassd.edu (Gary Martin)
Subject: Re: Infinity
Organization: University of Massachusetts Dartmouth
	<1371.2acabc99@atlas.nafb.trw.com>
Date: Thu, 1 Oct 1992 20:52:32 GMT

In article <1371.2acabc99@atlas.nafb.trw.com> dsimon@atlas.nafb.trw.com writes:

   I am looking for an infinity of physical things.  There are a finite 
   number of atoms (or electrons or quarks) between Lincoln and Terre Haute. 
   You can say that each atom has an infinite number of "points", but a 
   "point" is a mathematical abstraction - it doesn't really exist.  

   True, there are an infinite number of possible times each rest can last,
   but I'm looking for an infinity of physical things.

Well, I hope you've got lots of time and patience, or can look awfully fast!
--
Gary A. Martin, Assistant Professor of Mathematics, UMass Dartmouth
Martin@cis.umassd.edu
Xref: sparky sci.math:12233 sci.image.processing:786
From: news@ibmarc.UUCP (news)
Newsgroups: sci.math,sci.image.processing
Subject: Re: fast chirp z-transform
Date: 26 Sep 92 06:47:38 GMT
Organization: IBM Almaden Research Center

In article <1992Sep23.191245.14560@mr.med.ge.com> carl@crazyman.med.ge.com (Carl Crawford) writes:
>does anyone have any PD software for performing a fast chirp z
>transform. thanks.
>--
From: flick@flick.almaden.ibm.com (Myron Flickner)
I believe there is a fast chirp z x-form in the IEEE programs
for digital signal processing.  Archie should be able to find
a ftp site. 

imaging away / M. Flick Flickner, IBM Almaden Research Center, San Jose, CA
VNET/BITNET: FLICK at ALMADEN  Internet: flick@almaden.ibm.com
From: guan@cs.monash.edu.au (NAME)
Subject: Graph isomorphism problem
Summary: Is the Graph Isomorphism Problem polynomial-time?
Keywords: graph, isomorphism, problem, NP-complete, complexity
Organization: Computer Science, Monash University, Australia
Date: Tue, 29 Sep 1992 14:16:02 GMT

   Hello.  I am working on an algorithm for a problem very similar to
the Graph Isomorphism Problem.  I have heard that it might not be possible
to solve the Graph Isomorphism Problem in Deterministic polynomial time.
Is this true?   Does anyone know of any (relevant) known lower (or upper)
time bounds (e.g. NP-completeness)?

Please direct responses to me rather than to the newsgroup.

Regards

Guan Xiaoxiang
From: zeleny@husc9.harvard.edu (Michael Zeleny)
Newsgroups: sci.math
Subject: Re: Most important event in the history of mathematic
Date: 29 Sep 92 01:29:24 GMT
Organization: Harvard University Science Center

In article <1992Sep28.174237.26784@Cookie.secapl.com>
frank@Cookie.secapl.com (Frank Adams) writes:

>In article <1992Sep28.145025.4059@guinness.idbsu.edu>
>holmes@opal.idbsu.edu (Randall Holmes) writes:

>>In article <1992Sep25.201622.40255@Cookie.secapl.com>
>>frank@Cookie.secapl.com (Frank Adams) writes:

FA:
>>>[the proof of the inconsistency of naive set theory]
>>>was nevertheless probably the most [important] event in the history of
>>>mathematics.

RH:
>> It was not the most important
>>event in the history of math by a long shot.

Getting pretty authoritative in your old age, aren't you?

FA:
>All right; what was the most important event in the history of mathematics?
>My vote is in; what do the rest of you think?

The discovery of zero by a swarthy individual whose name escapes me at the
moment, closely followed by Galileo's discovery of the paradoxes of the
infinite.

cordially,
mikhail zeleny@husc.harvard.edu
"Un de mes plus grands plaisirs est de jurer Dieu quand je bande."
From: marcos@iota.ece.ucsb.edu (Marcos Valerio)
Newsgroups: sci.math
Subject: a graph problem
Date: 5 Oct 92 21:58:28 GMT
Reply-To: marcos@nu.ece.ucsb.edu
Distribution: sci.math
Organization: /home/marcos/.organization


I came across this problem and I believe it must have been already solved
by someone. Please send me the solution and/or references if you know it.

What is the maximum number of nodes possible in a graph if all nodes have
degree at most d (in my case d=16) and the distance between any two nodes
is at most dist (i.m.c. dist=4) ??

I welcome (pleased) solutions both to the general case as well as solutions
to my instance (d=16, dist=4).

Thanks,

--
Marcos de Macedo Valerio
Center for Distributed Systems
Department of Computer Engineering
University of California, Santa Barbara
Phone : (805) 893-4461 office
        (805) 685-9677 home
email address : marcos@nu.ece.ucsb.edu
Newsgroups: sci.math
From: ara@zurich.ai.mit.edu (Allan Adler)
Subject: Nagata's embedding theorem
Organization: M.I.T. Artificial Intelligence Lab.
Distribution: sci
Date: Wed, 30 Sep 1992 23:26:33 GMT


Masayoshi Nagata published two papers in which he proved that if S is a
Noetherian scheme and M is a Noetherian S-scheme of finite type over S
then M is an open subscheme of a proper scheme over S. The references
are:
(1) Imbedding of an abstract variety in a complete variety, 
    J.Math.Kyoto Univ. 2 (1962) 1-10
(2) A generalization of the imbedding problem of an abstract variety in
    a complete variety, J.Math. Kyoto Univ. 3 (1963) 89-102

Paper (2) proves the result I mentioned by reducing it to the situation
treated in paper (1). However, paper (1) is based on Nagata's own
foundations for algebraic geometry over Dedekind domains, which has fallen
into disuse in favor of Grothendieck's  EGA. Nagata's foundations are in
his trilogy

(3) A general theory of algebraic geometry over Dedekind domains,I,II,III
    Amer.J.Math. 78 (1956) 78-116; 80 (1958) 382-420; 81 (1959) 401-435

Before I plunge into Nagata's (3) in order to read (1) and (2), I would
like to reassure myself that it is really necessary to do so. Has anyone
rewritten Nagata's result using only the foundations provided by EGA?

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math
From: pjt@newton.cs.jhu.edu (Paul Tanenbaum)
Subject: Re: set theory
Keywords: cardinality, Legesgue measure
Organization: Johns Hopkins Computer Science Department, Baltimore, MD
Date: Tue, 6 Oct 1992 13:49:44 GMT

In article <1992Oct6.021037.6554@math.utexas.edu> epstein@rene.ma.utexas.edu (Paul Epstein) writes:
>Let's not assume the continuum hypothesis.  Let S be a subset of the real
>numbers with cardinality less than that of the reals.
>Does S have Lebesgue measure zero?

     Is Paul Epstein's question nothing more than a rigorous version of the
following line of puzzlement (which occured independently to me during my
morning commute today):

	  Everybody knows that |Q| = \aleph^0 and |R| = 2^{\aleph^0}.
     I've frequently read/heard that there are scads of irrationals
     between any pair (r1, r2) of rationals, and I think I remember
     that one can define a function that is continuous precisely on
     the irrationals.  But surely for any real x and \epsilon one
     can find a rational q such that |x - \epsilon| < q, no?  On the
     other hand, if I'm clear enough about how cardinalities of infinite
     sets behave, then |R - Q| = |R| so there would have to be vast
     stretches of the real line that are devoid of rationals.  How fouled
     up have I gotten things here?  Sorry for the ill formed question.

     +++paul

Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: INTERESTING TOPOLOGY QUESTION
Keywords: Dense sets
Organization: MIT Department of Mathematics, Cambridge, MA
Distribution: usa
Date: Tue, 6 Oct 92 02:07:15 GMT

In article <4frzz5=@rpi.edu> sassoj@rs6412.ecs.rpi.edu (John J. Sasso Jr.) writes:
>QUESTION:  Given the interval [0,1], does there exist two sets A and B such
>           that A is dense in [0,1], B is dense in [0,1], and the Lebesgue
>           outer measure of A and B is |A| = |B| = 1/2 ? 

Nice question.  Simply take the interval [0,1] and, starting at the left
endpoint, color the first point red, the second point black, the third
point red, and so on; call all the red points A and all the black points
B.  :-)  

I suppose you want A and B disjoint?  As phrased, the answer to your
question is clearly yes, take A to be [0,1/2] union the rational numbers
in [0,1], and take B = A.  But I bet that's not what you MEANT.

In any event, here's what I know, which was enough to answer my own
questions along these lines.  Given a Lebesgue measurable set S of
positive measure, it has a "point of density," that is, a point x
such that as e -> 0 (from above), 

measure([x-e,x+e] intersect S)/2e -> 1.

This settled my question, which was: is there a measurable set S
such that the measure of S intersect any interval [a,b] is, say,
half the length of [a,b]?  I.e., is there a set of "uniform density
1/2"?  No.  Any measurable set must be "lumpy".


Newsgroups: sci.math