HDTenEightyP/NetNews huggingface dataset:
Newsgroups: sci.math
Subject: Patents
From: <JOEYC@CUNYVM.BITNET>
Date: Friday, 25 Dec 1992 21:58:24 EST
Organization: City University of New York/ University Computer Center

Is there some convenient way of looking for patents that have a mathematical
  or computer science theme?   Is there an index of patents of some kind?
-------
JOE MALKEVITCH  DEPT. OF MATH. YORK COLLEGE (CUNY) JAMAICA, NY  11451
EMAIL: JOEYC@CUNYVM OR JOEYC@CUNYVM.CUNY.EDU  PHONE: 718-262-2550 (2551)
Newsgroups: sci.math,alt.books.technical
From: cjp8b@dayhoff.med.Virginia.EDU (Chris Penington)
Subject: Re: High Prices of Math Books. I am pissed.
Organization: University of Virginia
Date: Fri, 25 Dec 1992 19:29:24 GMT

In article <ng4.725269975@husc.harvard.edu> ng4@husc10.harvard.edu (Ho Leung Ng) writes:
>
>   Dover manages to put out lots of fairly specialized books in math
>and physics and sell them in paperback editions for <$15.  How is it that
>they can stay in business?

Primarily because they don't take any risks. They don't sell cutting
edge books in controversial areas or in areas where the subject matter
evolves so rapidly that a new book will be out of date in 5 years
time. The books they sell are books with a slow but steady demand over
a long period. They're usually books which have gone out of print and
are not likely to be reissued by the original publisher. Since the
authors are unlikely to realise any further royalties Dover is able to
pay a small up front fee and no subsequent royalties. They spend very
little on advertising and promotion, they're also careful to keep the
costs of printing and binding down and they're very good at what they
do. 

	Chris
-- 
Chris Penington (cjp8b@virginia.edu)   
Biochemistry Dept., Box 440             I'm not really a physical biochemist
UVa Health Sciences Ctr,                     but I play one in the lab... 
Charlottesville, Va 22908   (804)924-8210   
Newsgroups: sci.math
From: NAHAJ@CC.UTAH.EDU (John B 'Nahaj' Halleck, UUCC)
Subject: What is this factoring method called??
Organization: UNIVERSITY OF UTAH COMPUTER CENTER
Date: Thu, 31 Dec 92 22:13:29 GMT
X-News-Reader: VMS NEWS 1.24

What is this factoring method called?  Where can I read up on it?
(email me and I'll post a summary)

 p = isqrt(n);
 q = p; 
 quess = p*q;

 while guess <> n do
   if guess > n then
      guess = guess - p;
      q = q - 1;
   else
      guess = guess + q;
      p = p + 1;
   endif
 end while
 
 print ("The factors are: ", p, q );
Xref: sparky sci.math:17543 sci.physics:21942
From: allenk@ugcs.caltech.edu (Allen Knutson)
Newsgroups: sci.math,sci.physics
Subject: Banach-Tarski (_NOT_ Re: Bayes' theorem and QM)
Date: 31 Dec 1992 07:43:58 GMT
Organization: California Institute of Technology, Pasadena
NNTP-Posting-Host: torment.ugcs.caltech.edu

charlie@umnstat.stat.umn.edu (Charles Geyer) writes, under a wholly
inappropriate subject line:

>If you think that every "real world" set should be measurable, and hence
>Lebesgue theory is a waste of time, then you object to more of classical
>mathematics than just the axiom of choice.

>Not so?

Not so. Solovay proved in 1970 that the axiom "All subsets of the reals are
measurable" is consistent with ZF (obviously not with ZFC), under some
standard large cardinal assumption. I think I have this right... Allen K.
Newsgroups: sci.math
From: deghare@daisy.uwaterloo.ca (Dave Hare)
Subject: Re: TO ALL !!! -- End of Discussion, I hope
Organization: University of Waterloo
Date: Mon, 21 Dec 1992 12:49:17 GMT

In article <1h323mINN1rt@usenet.INS.CWRU.Edu> ak005@cleveland.Freenet.Edu (Yona Webb) writes:
>
>My posting (Dec. 18) has offended many netters.  Several people
>expressed quite vocally their anger and displeasure, both publicly and in
>E-Mail. There was no need for flames however, just to let me know that
>I have made a mistake.

I disagree that you made a mistake in any way.  "Merry Christmas" and 
"Happy Hanukkah" are perfectly acceptable sentiments to wish upon the
world at this time of year, and people who object to them have problems
sufficient unto themselves.  There are many things to take issue with at
this time of year, and I am one of the more vocal to do so, but someone
wishing others well, in whatever form, is not one of them.

My previous posting on this matter was intended to be a sarcastic rejoinder
to the original flame, and was no doubt misunderstood by some (that's a 
given in newsgroup postings).

Season's greetings.

(And, in case I forget, Happy Groundhog Day, too.)

Dave Hare  
Newsgroups: sci.math,alt.books.technical
From: mkrogers@unix.amherst.edu (Michael Rogers)
Subject: Re: High Prices of Math Books. I am pissed.
Followup-To: sci.math,alt.books.technical
Organization: Amherst College
X-Newsreader: TIN [version 1.1 PL7]
Date: Fri, 25 Dec 1992 04:07:49 GMT

I agree that the "average price" of mathematics books is
justified, but there are a few prices which still seem
unjustified.  The reprints of classics in which no new
typesetting seems to be involved still cost the same as new
books.  For example _Commutative Algebra_ by Zariski/Samuel
published by Springer.  Compare this with Chelsea's prices.

Books published by Academic Press seem to cost more
than average (I'm probably wrong).  The most egregious
example is _Algebraic Number Fields_, Froehlich, ed.
which consists of photoreproductions of 600 pages of
typewritten (not typeset) pages and was first published
in 1976.  Four years ago, the list price was $120.
Admittedly it is a very specialized book.
I'm not sure I understand why the price of a book
doesn't approach the marginal price as the years go
by.  If the cost of the book is not recouped by the
time the libraries are done buying them, I would think
that the chances of making a substantial profit are
small.  (This is my own unsubstantiated intuitive guess.)
Do publishers count on it taking 10 years to make
a profit on the book?  Or perhaps they just feel entitled
to the money.  Perhaps they are.

Anyway it seems like the prices of the textbooks I bought
when I was starting graduate school have increased at
a rate far exceeding inflation.  The cost of producing
one more copy of a book may have outpaced inflation.
If most of the price is due to the initial investment
whose cost would increase at roughly the prime lending
rate (usually approx. = rate of inflation), you wouldn't
think that the price of a book should increase as rapidly
as it has.  I'm sure I don't understand fully the costs
involved in the publishing business, and perhaps my
analysis is too naive.  I would like to find out more.
From: dario@cns.nyu.edu (Dario Ringach, x3941)
Newsgroups: sci.math
Subject: Zariski tangent space
Date: 26 Dec 92 22:26:38 GMT
Reply-To: dario@cns.nyu.edu
Organization: Center for Neural Science, New York University.

I would be grateful for a reference to any basic textbook
explaining the concept.  Please email to me.  Thanks a lot.

---
Dario Ringach                           office: (212) 998-3941
Center for Neural Science               home:   (212) 727-9346
New York University                     e-mail: dario@cns.nyu.edu
Xref: sparky sci.math:17464 sci.physics:21819
From: samuel@front.se
Newsgroups: sci.math,sci.physics
Subject: Re: Help me deal w/ infinity
Date: 23 Dec 92 02:03:09 GMT
Organization: Samuel Gustaf Siren

In article <BzL73K.9xr@usenet.ucs.indiana.edu>, 
mkohlhaa@silver.ucs.indiana.edu (mike) writes:

> A core of our disagreement has been about .9(r) --that means .9repeating
> but I can't make a little bar over the 9.  Anyhow, its been documented that
> .9(r) is equal to 1.  Some of my friends think that this is some kind of 
> a mathematical trick, given the following equation (keep in mind that (r) 
> equals .9repeating):
> 
> 			N=.9(r)
> 		      10N=9.9(r)   Multiply both sides by 10
> 	               9N=9        Subtract N from both sides
> 		        N=1
> 
> My skeptical friends point out the "subract N from both sides" lines as
> the problem with the equation.  They think that it's bogus that I am 
> litterally subrtracting an N from one side, but subtracting it's equivalent,
> namely a .9(r) from the other side.

Try this argument ('...' means 'repeating') :

  (A)      :     N = 0.999999...
  (B)      :   10N = 9.999999...

  (B)-(A)  : 10N-N = 9.999999...-0.999999...
                9N = 9
                 N = 1

It in NOT bogus to subtract N from one side and its equivalent from the other,
since N and its equivalent are equivalent (sic!).
Please note that I have subtracted EQUATION (A) from EQUATION (B) to get
the EQUATION "9N = 9". This in an appropriate mathematical method (which I 
think have been used for milleniums).
Example :
  (a)     :  1 + 2 = 3 
  (b)     :  5 + 8 = 13
  (b)-(a) :  5 + 8 - 1 - 2 = 13 - 3

If this argument doesn't help, why don't ask your friends exactly how much 
they think that 0.999999... differs from 1.


It's not my intention to disappoint your friends totally, so I supply this
BOGUS PROOF of that ANY NUMBER EQUALS ONE : 

  Imagine an arbitrary number a which equals to b :

  a = b   =>                   a - b  = 0    (1)

  a - b   =>  a^2 = ab  =>   a^2 - ab = 0    (2)

  (1) and (2) implies :
  a^2 - ab = a - b =>  a (a - b) = a - b =>  a (a - b) = 1 (a - b) =>  a = 1

which proves that any arbitrary number equals 1 ! Why don't you ask your
'skeptical friends' if they can find out what's erroneous with this bogus
proof !

/SS
-- 
+----------------------+--------------------------------------+
|                      |        / \                           |
| Samuel Gustaf Siren  |      __!_/_                          |
|                      |    / \ |  / \                        |
|                      |   |/  || | \__oW)----------          |
| All opinions and     |   !! / /\ \                          |
| questions are my     |     / /  \ \                         |
| own /SS              |    //    //                          |
|                      |   /|    ((                           |
+----------------------+--------------------------------------+
Newsgroups: sci.math,sci.physics
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Vertex Operator Algebras
Organization: MIT Department of Mathematics, Cambridge, MA
Distribution: sci
Date: Sun, 20 Dec 92 19:12:58 GMT

In article <ARA.92Dec20081838@camelot.ai.mit.edu> ara@zurich.ai.mit.edu (Allan Adler) writes:
>
>From time to time, I pick up the book on Vertex Operator Algebras and
>the Monster, by Frenkel, Lepowski and Meurman, and while the results
>are admirable, I am nevertheless repelled each time by the notation
>and the exposition. Apart from such discourtesies as changing their
>notation and conventions in the middle of a book whose  technical details
>would be hard enough to follow with consistent notation (something like
>Grothendieck changing the meaning of the word scheme in the middle of
>writing EGA), the authors often remind us that they are not giving
>us the general picture (suggesting that the carefully learned technical details
>will have to be unlearned later, either in the same book or in other sources).
>The overview is essentially lacking while instead
>the authors torture one kind of quadratic form after another, assuming that
>the reader will get the general idea of how to proceed without a general
>definition of the torturous procedure. Maybe it is the fate of books
>on such technical material to be like that but I am not convinced.

One key thing to note is that vertex operator algebras come from
physics, and can only be fully understood (in my opinion) if one takes
the time to learn a little quantum field theory.  The complicated definition
of a vertex operator algebra, for example, is an attempt to take the simpler
intuitive physical notion and make it rigorous while simultaneously (for
some reason) not using any analysis whatsoever - a tall order!  I had to
go through the definition of a VOA with Allen Knutson and say "what this
clause REALLY means is this... what this clause REALLY means is this..."
Once decoded, it made sense.

If one let oneself use analysis one might come up with something similar to the
Garding-Wightman axioms for quantum field theory, adapted to the case at
hand (in which conformal invariance rules).  But rather than use
distributions or hyperfunctions, the folks who defined vertex operator
algebras used formal power series.  If there was a good reason for doing
this other than a distaste for analysis (or ignorance of it), I wish
they would have told us what it is.  

In any event, I have no big problem with using algebra instead of analysis.  I
*do* think it would have been better to first give a simple heuristic
discussion of how physicists use these things before launching into the
formidable axiomatic framework.  For no mathematician would have ever
invented these ideas if they were not already popular in string theory,
and to a large extent the whole game is to legitimate what physicists do
in their own bold and sloppy manner.
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: more math puzzles
Date: 23 Dec 92 20:39:44 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: ara@zurich.ai.mit.edu (Allan Adler)

In article <ARA.92Dec23115312@camelot.ai.mit.edu>, ara@zurich (Allan Adler) writes:
>More generally, any map from L to a metric space is eventually
>constant. To prove this, note that L is sequentially compact [...]

L is of course not sequentially compact.  Since any metric space embeds
into a product of R's, the result follows from R's.

>it is proved in Singer and Thorpe, e.g. that the product of continuum
>many unit intervals is not metrizable. But using the long line, you can
>prove that the product of aleph-1 unit intervals is not metrizable: [...]

The product is separable yet not second countable, so not metrizable.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
From: allenk@ugcs.caltech.edu (Allen Knutson)
Newsgroups: sci.math
Subject: Re: I imagine this comes up all the time...
Date: 3 Jan 1993 01:03:55 GMT
Organization: California Institute of Technology, Pasadena
NNTP-Posting-Host: torment.ugcs.caltech.edu
Keywords: unique factors

ronl@tessi.com (Ron Lunde) writes:

>The question I was toying with last night was: Given a number N,
>what is the smallest number M such that aside from 1 and M, M has exactly
>N divisors.
...
>It seems odd that the first ones are all fairly small, but I can't
>find the 15th (at least nothing smaller than 614889782588491410):

Let's factor M as \product_i {p_i}^{n_i}. Then the number of divisors
including 1 and M is \product_i (1+n_i), because we can use each prime
to an exponent between 0 and n_i.

You want this product to be 17, which is prime, so you need just one
prime, and n_1=16. The smallest prime being 2, you appear to have overlooked
2^16 = 65536. I hope this is right...				Allen K.


Newsgroups: sci.math,sci.physics
From: dseeman@novell.com (Daniel Seeman)
Subject: Re: Help me deal w/ infinity
Organization: Novell Inc., San Jose, Califonia
Date: Mon, 21 Dec 1992 18:08:15 GMT

In article <BzL73K.9xr@usenet.ucs.indiana.edu> mkohlhaa@silver.ucs.indiana.edu (mike) writes:
>Some friends and I have recently been having some discussions/arguments 
>about infinity and its meaning in math.
>
>A core of our disagreement has been about .9(r) --that means .9repeating
>but I can't make a little bar over the 9.  Anyhow, its been documented that
>.9(r) is equal to 1.  Some of my friends think that this is some kind of 
>a mathematical trick, given the following equation (keep in mind that (r) 
>equals .9repeating):
>
>			N=.9(r)
>		      10N=9.9(r)   Multiply both sides by 10
>	               9N=9        Subtract N from both sides
>		        N=1
>
I too have some misgivings about your "subtrace N from both sides" operation.
When I do that, this is what I get:

	10N = 9.9(r) = 10(.9(r)) = 10(N)

	10N - N = 9.9(r) - N	(This is where I subtract N from both sides)

	N(10 - 1) = N (10 - 1)	(Replace .9(r) with N) 

	N = N

It seems to me that N is not being applied consistantly in your original posting
but that may just point out my ignorace of the problem.  I will be on the look-
out for other responses.  I am interested in knowing others' understandings...:)

dks.
>My skeptical friends point out the "subract N from both sides" lines as
>the problem with the equation.  They think that it's bogus that I am 
>litterally subrtracting an N from one side, but subtracting it's equivalent,
>namely a .9(r) from the other side.
>
>I appeal to any math gurus out there to comment on the validity of .9(r)
>equals one, and anything else which may increase my understand of the
>concept of infinity and how putting an "infinite" amount of 9's after
>a decimal point can become 1.
>
>Thanks
>
>
>
>
>-- 
>					-- Mike
>-------------------------------------------------------------------------------
>| If the above information is incorrect, then I don't even speak for myself.  |
>|      mkohlhaa@silver.ucs.indiana.edu | mkohlhaa@amber.ucs.indiana.edu       |


Newsgroups: sci.math
From: tao@fine.princeton.edu (Terry Tao)
Subject: Re: need help in calculus problem.
Originator: news@nimaster
Organization: Princeton University
Date: Sun, 3 Jan 1993 16:06:53 GMT

In article <1i70mpINNcrj@news.umbc.edu> rouben@math9.math.umbc.edu (Rouben Rostamian) writes:
>In article <1i688pINNls9@usenet.INS.CWRU.Edu> cd187@cleveland.Freenet.Edu (Aye Naing) writes:
>>The following equations describe a curve parameterized by 't'
>>F(x,y,t)=0
>>G(x,z,t)=0
>>H(y,z,t)=0
>>Find the equation of the tangent line.
>
>Differentiate each equation wrt t, via the chain rule:
>F_x x' + F_y y' + F_t = 0,
>G_x x' + G_z y' + G_t = 0,
>H_y y' + H_z z' + H_t = 0,
>where F_x indicates the derivative of F wrt the x variable, etc.  (I know,
>it's a bad notation, but you know what I mean.)
>Solve this linear system of three equations for the three unknowns x', y', z'.
>The vector (x',y',z') is the desired tangent vector.
>
>To alleviate the concerns of another reader regarding the implicit
>form of these derivatives,  let's note that no differential
>equations are involved anywhere.  The solution vector is of the form:
>
>(x'(t), y'(t), z'(t) ) = an an explicit function of x(t), y(t), z(t).  (*)
>
>Rouben Rostamian

Yes, you're right.  Sorry about that.

Of course, doing things the other way around (knowing the tangents first
and then trying to work out the curve) requires a DE.. or shall I be
corrected a second time?

Terry
Newsgroups: sci.math,rec.puzzles
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Marilyn Vos Savant's error?
Keywords: savant
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Mon, 21 Dec 92 18:07:04 GMT

In article <1992Dec17.071340.3761@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>In article <1992Dec17.041022.29031@thunder.mcrcim.mcgill.edu> mouse@thunder.mcrcim.mcgill.edu (der Mouse) writes:
>>In article <1992Dec15.055832.26324@galois.mit.edu>, jbaez@riesz.mit.edu (John C. Baez) writes:
>>
>>> 1)  You draw 4 cards from a well-shuffled standard deck.  You turn
>>>     one over and it's an ace.  What's the probability that they are
>>>     all aces?
>>
>>There are 4! C(52,4) = 52!/48! = 6497400 sets of 4 cards you could
>>draw, counting different orders as different.  In one case in 13 you'll
>>turn up an ace, for a total of 499800, while in only 24 cases are they
>>all aces.  The answer to this question is therefore 24/499800, which is
>>1 in 20825, or, to 20 places from dc, .00004801920768307322.
>
>Ha!  This is right and I was wrong.  I just took this to be the problem
>where you look at your whole hand and observe at least one ace, and so
>figured there were 48*47*46*45 = 4669920 ways to get no aces, hence
>6497400-4669920 = 1827480 ways to get at least one ace, giving the
>estimate as 24/1827480 = .000013.  But the problem clearly states you
>just look at one card, for which the above calculation is correct.
>Ditto for the remaining calculations.  Oh well, at least we now have
>the numbers for both versions of the problem (look at whole hand/look
>at one card).

Gee, now I feel less dumb, at least relatively speaking.  I'm still
confused, and after a few strong cups of coffee I will look at these
calculations.  

Historical note: After posting my first version I realized I had meant to
post the second version.  I then drove back to my office and canceled
the first version.  (For both versions, see der Mouse's post.)  I also
replied apologetically to the rapidly growing piles of email from
people who said that they got the same answer to parts 1 and 2 of my
first version, telling them to check out the new version.  So all these
folks did the first version wrong?  Quite possible.  I'm just glad I
work on simple things like quantum field theory, where I don't need to
know how to count.


Newsgroups: sci.math
From: Chris.Fortin@launchpad.unc.edu (Chris Fortin)
Subject: multi-dimensional matricies
Followup-To: sci.math
Summary: how are they handled?
Organization: University of North Carolina Extended Bulletin Board Service
Date: Thu, 31 Dec 1992 03:29:51 GMT


Merry Christmas, everyone.

	Recentlly, i have come upon an expression x^{t}R^{-1}x in
which x is a n*n matrix and R is a rank 4 tensor, ir R = R_{ijkl}.
All the indecies are descrete. Could someone point me at a reference
for handling the inversion, determinant, and product for such a
group of objects? In particular, inverting R_{ijkl} appears to 
be non-trivial, in that i can not even find a discussion of the problem.

		Thank you for your help,
				Christopher Fortin

<fortin@orca.ele.uri.edu> or <fortin@tautog.npt.nuwc.navy.mil>

--
   The opinions expressed are not necessarily those of the University of
     North Carolina at Chapel Hill, the Campus Office for Information
        Technology, or the Experimental Bulletin Board Service.
           internet:  laUNChpad.unc.edu or 152.2.22.80
Xref: sparky sci.math:17558 sci.physics:21974
Newsgroups: sci.math,sci.physics
Subject: Lapl. Transf. of Product of Functions
From: <CCB104@psuvm.psu.edu>
Date: Thu, 31 Dec 1992 13:24:39 EST
Organization: Penn State University

Hello!
Does anyone know what the Laplace transform of a product of functions is,
please?
A math professor told me that there is some "rare" theorem on this,
but I hardly know where to look for it.
He also said that it would be "some kind of convolution."
Now of course the product of Laplace transforms of functions can be
expressed by means of the convolution (1st convolution?) theorem. But
what I am looking for is the Laplace transform of a product of (unknown)
functions! There are well known formulas for the Laplace transforms of
functions, of nth derivatives of functions, etc., in terms of values of
the functions and their derivatives at various points, but . . . what
about the Laplace transform of a product of functions?? Naturally, if
that were known, it should apply to the special case of the Laplace
transform of the second power of a function.
I realize that the functions may have to satisfy various auxiliary conditions.
Thanks!!! And, I hope I didn't ramble too much . . . .
Carey
ccb104@psuvm.psu.edu
ccb104@psuvm.BITNET
Xref: sparky sci.math:17383 comp.theory:2754
From: wbs@vax.oxford.ac.uk
Newsgroups: sci.math,comp.theory
Subject: Re: Cospectral Graphs (need references)
Date: 23 Dec 92 14:47:29 GMT
Organization: Oxford University VAX 6620

In article <BzoDsp.Dw4@ux1.cso.uiuc.edu>, sree@ux1.cso.uiuc.edu (sreenivas rama) writes: 
> I would like to get some pointers on a monograph or review article
> on Cospectral graphs, that is, graphs whose adjacency matrices have
> the same eigenvalues (with same multiplicities).  The only reference
> I have is a thesis from Belgrade in the 70's.


Is Cvetovic, Doob, Sachs : Spectra of graphs : Acad Press 1979
too ancient?

B.