HDTenEightyP/NetNews huggingface dataset:
From: dkrain@math.duke.edu (David Kraines)
Newsgroups: sci.math
Subject: Re: 1992 Putnam problems and unofficial solutions
Summary: Explicit solution
Date: 19 Dec 92 18:21:13 GMT

In article <1992Dec18.142423.18674@husc3.harvard.edu>, elkies@ramanujan.harvard.edu (Noam Elkies) writes:
> In article <a_rubin.723836042@dn66>
> a_rubin@dsg4.dse.beckman.com (Arthur Rubin) writes:
> ">Problem B6
> "
> ">Let M be a set of real n by n matrices such that
> ">(i) I \in M, where I is the n by n identity matrix;
> ">(ii) if A \in M and B \in M, then either AB \in M or -AB \in M, but not both;
> ">(iii) if A \in M and B \in M, then either AB = BA or AB = -BA;
> ">(iv) if A \in M and A \noteq I, there is at least one B \in M such that
> "
> "But can it actually contain n^2 matrices?
> "
> Yes it can: let n be a power of 2; let G be the extraspecial group of
> order 2n^2 which has a *real* (even rational) n-dimensional representation
> 
> --Noam D. Elkies (elkies@zariski.harvard.edu)
>   Dept. of Mathematics, Harvard University

One can easily construct an explicit set of matrices M for n = 2^k as
follows:

For n=2, let I=[1 0;0 1], A=[1 0;0 -1], B=[0 1;1 0], and C=[0 -1;1 0]
Observe that  AB=-BA=-C, AC=-CA=-B, BC=-CB=-A, and the square of each
is +-I.  Thus these 2^2 matrices satify the conditions.  

Inductively build up matrices of order 2^k by taking block matrices
of the above type with entries like the above.
For example for n = 4, consider matrices such as A(B)=[B 0;0 -B].
Only the notational problems prevent me from giving the general terms.
It is trivial to show that this gives a system closed under the
operations.  For example  A(B)*C(A) =-B(C).

As noted in previous solutions, one can show that if A in M then
A^2 = +-I.  In particular all matrices in M are non singular. For
n odd, AB=-BA implies det(A)det(B)=-det(B)det(A) so A or B must
be singular.  Thus no nontrivial system exists for n odd.  A slightly
more subtle argument shows that the max n^2 can be realized only
for 2=2^k.

David Kraines, Duke University, dkrain@math.duke.edu
From: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
Newsgroups: sci.math
Subject: Re: Factor 69 digit integer
Date: 16 Dec 1992 23:18:34 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
NNTP-Posting-Host: g210b-1.nextwork.rose-hulman.edu

In article <1992Dec10.132040.1186@walter.cray.com> slow@ferrari.cray.com (David  
Slowinski) writes:
> > Please help me.  I need the prime factors of 
> >  132686104398972053177608575506090561429353935989033525802891469459697

> >  Linda Bonanno - APPC Market Enablement, IBM, Research Triangle Park, NC

That's easy enough.  Using Mma,

In[1]:=
FactorInteger[13268610439897205317760857550609056142935393598903352580289146945 
9697]
Out[1]=
{{178230287214063289511, 1}, {61676882198695257501367, 1},  
{12070396178249893039969681, 1}}

;-)
--
Bradley W. Brock, Department of Mathematics
Rose-Hulman Institute of Technology  | "Resist not evil.... Love your
brock@nextwork.rose-hulman.edu       |  enemies."--Jesus of Nazareth
From: jeremy@atlantis.CS.ORST.EDU ((-| Jeremy |-) Smith)
Newsgroups: sci.math
Subject: Negative Zero
Date: 12 Dec 92 01:07:11 GMT
Article-I.D.: leela.1992Dec12.010711.15778
Organization: Computer Science Outreach Services - Oregon State University


      Some guy in Southern California proposed a method of naming multiples 
of ten which included a `logical' system for naming very large numbers 
(the largest being milli-decilli-fiveillionillion).  Does anyone have a 
reference for this.

[OBtrivia: this is one of my plan files.  Amendments welcome]
         n
        --- = I (infinity) (n>0)
         0
 
 
         n
        --- = -I (probably) (n>0)
        -0
 
        Numbers greater than infinity, and less than negative infinity
include gadzillion, squillion, and zillion, and are possibly in
the class NaN (not a number).
 
        My favourite is -0, which I intend to
understand, in the same way that 0 was discovered,
understood, and used.
 
        For reference here is a number scale:
 
 I              infinity
 .              .
 .              .
 .              .
 10^google      googleplex
 10^?           milli-decilli-fiveillionillion
 10^303         centillion      
 10^140         asankheyya      
 10^100         google 
 10^87          #electrons in known universe
 10^63          vigintillion
 10^15          quadrillion
 10^12          trillion
 10^9           billion
 10^6           million
 .              .
 .              .
 .              .
 3              three
 2              two
 1              one
 0              zero
-0              negative zero
-1              negative one
-2              negative two
-3              negative three
 .              .
 .              .
 .              .
-I              negative infinity
From: hubert@ucsb.edu (Hung-Hsien Chang)
Newsgroups: sci.math
Subject: Names and pictures
Date: 14 Dec 92 01:43:29 GMT
Organization: University of California, Santa Barbara

From: hubert@ucsb.edu (Hung-Hsien Chang)
Newsgroups: sci.math
Subject: Names and pictures
Summary: 
Followup-To: 
Distribution: world
Organization: University of California, Santa Barbara
Keywords: 

I think it would be nice if the mathematical papers  published on 
journals contain the pictures of the authors as well. So people 
will know the authors not just by name.

Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
From: crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass)
Subject: Re: TIME HAS INERTIA - NewScientist Article
Organization: University of Virginia
Date: Sat, 12 Dec 1992 19:56:54 GMT

In article <1992Dec11.024139.12143@dmp.csiro.au> lachlan@dmp.csiro.au (Lachlan Cranswick) writes:
>
>I just read got this weeks New Scientist.  In the Feedback
>section on the second last page they mention this TIME
>HAS INERTIA thing on the Internet but also mention
>there is now a scale called the CRACKPOT INDEX.

     Just what we need, validation for Abian.  Why couldn't
     the mention have appeared in the American Journal of 
     Psychiatry?

     Of course, that would probably have been validation too.

>Which groups are these appearing in and are they being saved
>for posterity?  I would appreciate anyone who could email 
>me the spoof posts or tell me of an ftp site where
>they are stored.

     God forbid.  'Posterity' would think us quite batty.s

>Back to this INERTIA thing, I forgot most of my physics
>after my last 1st year Physics exam so I cannot add anything
>technical to the dabate. But I do have a few questions:-
>
>But is it coincidence or fate
>that this theory has come soon after the decision by the Vatican
>to admit that Galelao? (I forgot most of my spelling after my last
>high school English exam)  was right that the EARTH revolves
>around the SUN.  It only took them 500 or so years to realize
>their mistake.

     Let's get one thing straight;  Abian is spouting vacuous
     irrelevancies.  It has nothing to do with 1) nature 2) fate
     3) coincidence 4) galileo.  His repeated statements, when
     they even make sense, boil down to 'THINGS CHANGE UNLESS
     THEY DON'T' (using his idiom).  I think you can see
     that this is not exactly stunning news.  Crackpots are also
     not new, but usually they at least have charm enough to 
     provide physical predictions.

     Also, he continually misuses the term 'inertia'.

>Also what was the name of that "CRACKPOT" who suggested in the 
>1950's that the continents are moving, partly based on how you
>could fit part of Africa onto South America? like a jigsaw 
>puzzle?  It is a pity the internet did not exist then
>because it could have been a pretty good flame-war.

     There is a difference, Wegener at least had
     a physical theory that made predictions.  Abian has
     a bunch of words that have no scientific meaning.
     (By the way, Wegener died in 1930).
>
>I'm sorry if this has come up before but I lost news for 55
>hours because of a dodgy computer on the other end of the wire.
>
>"Stay Cool, Whats going to happen in 55 hours?" I was asked.
>
>Nothing, EXCEPT THE LAWS OF PHYSICS AND CHEMISTRY ARE BEING
>REWRITTEN AND I AM THE LAST TO FIND OUT ABOUT IT!!!!

      This has been going on for probably 55 days.  I don't
      see any end to it.

                             dale bass
-- 
C. R. Bass                                          crb7q@virginia.edu        
Department of Mechanical, 
     Aerospace and Nuclear Engineering
University of Virginia                              (804) 924-7926
Newsgroups: sci.math
Subject: Re: Properties of Illumination Functions?
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 17 Dec 92 18:31:17 GMT
Organization: Beckman Instruments, Inc.

In <1992Dec16.225253.25173@jarvis.csri.toronto.edu> dret@dgp.toronto.edu (George Drettakis) writes:

>I sent this to sci.math.research, but I have a suspicion the big
>black net hole ate it. I apologize if you see this twice.
>-----------------------

>I have the following problem in computer graphics. Assume a rectangular 
>area in the plane z=d, with -xa1 < x1 < xa1 and -ya1 < y1 < ya1.
>This area is assumed to be a diffuse rectangular light source,
>with the surface normal 0, 0, -1.
>Assume also the receiving plane z=0, and the function I(x,y) defined on 
>this plane. The function I(x,y) expresses the illumination at this point:

>                       ya1    xa1
>                        /      /
>                       |      |                 1
>        I(x, y) :=     |      |   ----------------------------- dx1 dy1
>                       |      |            2           2    2 2
>                      /      /    ((x - x1)  + (y - y1)  + d )
>                    - ya1  - xa1


...

>What I want to show is that the function I(x,y) has only one maximum, and is
>(radially around 0, 0, 0 ) decreasing everywhere else.
>Ideally I want to show this for more general sources, but just the rectangle
>is a good start.

It is easy to show that I(x,y) has only one relative maximum; just
differentiated under the integral and estimate.  I don't think it's as easy
to show it's radially decreasing elsewhere, but that would be a good start.

--
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; please mail anything important.
Newsgroups: sci.math
From: phil@medici.trl.OZ.AU (Phil Nicholson)
Subject: Re: Marilyn vos Savant and Pancakes??
Organization: Telecom Research Labs, Melbourne, Australia
Date: Wed, 16 Dec 1992 23:41:16 GMT

->I ask the net Gods: Can this be correct??
->From ``Ask Marilyn'' by Marilyn Vos Savant, Parade magazine, December
-> 13, 1992.
-> 
->You have a hat in which there are three pancakes.  One is golden on
->both sides, one is brown on both sides, and one is golden on one side
->and brown on the other.  You withdraw one pancake and see that one side
->is brown.  What is the probability that the other side is brown?
-> 
->---Robert H. Batts, Acton, Mass.

It's about time the three card trick was discussed again. It's been months.

And then Monty Hall walks into the room, looks into the hat and withdraws and
eats a pancake that's gold on both sides. You of course like pancakes that are
brown on one side and gold on the other.

So should you switch doors, pancakes or hats?
Phillip Nicholson			Internet: p.nicholson@trl.OZ.AU
Telecom Australia Research Labs		AI Systems  
Phone: +61 3 253 6245			Fax: +61 3 253 6173 
x400: g=phil s=nicholson ou=trl o=telecom prmd=telecom006 admd=telememo c=au
Newsgroups: sci.math
From: kosowsky@minerva.harvard.edu (Jeffrey J. Kosowsky)
Subject: Re: Calculus Puzzle
Organization: Harvard Robotics Lab, Harvard University
Date: Fri, 18 Dec 1992 15:33:05 GMT

In article <BzFoLp.EHs@unccsun.uncc.edu> sbardhan@uncc.edu (Soumendu Bardhan) writes:
>   X + X + X + X +X.... X times = X^2
>   Differtiating both sides w.r.t X we get
>
>   1 + 1 + 1 + .....X times = 2X
>   or , X = 2X
>    as X may not be Zero
>   1 = 2.
>
>
>   --Soumendu, UNCC

This is an *old*, *stale* crackpot "proof". It is neither clever nor
original.  Please have the courtesy not to waste the time and
resources of other net users with more silly "proofs" of "1=2".  We
are all sick and tired of endless "1=2" threads. If you really have a
question, then pose a question. "Puzzles" belong on rec.puzzles.

Jeff Kosowsky
From: cet1@cus.cam.ac.uk (C.E. Thompson)
Newsgroups: sci.math
Subject: Re: Tiling problem
Date: 20 Dec 92 22:53:30 GMT
Organization: U of Cambridge, England

In article <israel.724843610@unixg.ubc.ca>, israel@unixg.ubc.ca
(Robert B. Israel) writes:
|> 
|> As a matter of fact, there *is* something odd going on.  A close look at
|> this solution shows that all the rows are cyclic permutations of 
|> 001101a101100, where "a" is either 0 or 1, each row being displaced 5
|> places to the left from the previous one.  If you write one of these
|> 13-tuples as <c_i>_{i=0..12}, it satisfies the condition that for all
|> i and 1 <= j <= 12, c_i, c_{i+j}, c_{i+5j} and c_{i+6j} are not all the
|> same (considering the subscripts mod 13).  Thus such a 13-tuple generates
|> a square that works (with periodic boundary condition).  The only 13-tuples
|> for which this works are these two and those obtained from them by cyclic
|> permutation and interchanging 1 and 0.  I also tried shifts other than 5
|> (so for some b, 1<=b<=12, you want c_i,c_{i+j},c_{i+bj} and c_{i+(b+1)j}
|> never to be all the same).  No more examples except for b=8 (which is
|> equivalent to b=5 by left<->right symmetry).  Unfortunately, there are no
|> 14-, 15-, 16- or 17-tuples with the analogous properties either.

It really looks as thought there ought to be some significance in the fact
that 001101a101100 is the pattern of quadratic residues mod 13 (a at the
point 0 mod 13), and in the fact that 5 and 8 are the square roots of -1
mod 13. But naive attempts to use the same rules for larger primes don't
work. (They do work for N=5, 01a10 shifted 2 for each new row.)

|> I don't think that my search strategy has any inherent bias towards 
|> solutions with any particular regularity or periodicity.  I tried running
|> the 13 x 13 square again, with the following result:
|> 
|> 1011010011010
|> 0001111010110
|> 0111001000011
|> 1100011101010
|> 1001010100111
|> 0101110001101
|> 0000100111011
|> 1010111100001
|> 0110010110101
|> 0011001101100
|> 111010*000110
|> 1000001011101
|> 1101100110000
|> 
|> If there's structure here, it's certainly more subtle than last time.  
|> I haven't checked whether this satisfies the periodic boundary condition.

Not quite. But if the 1 at the point which I have taken the liberty of 
marking with a * is replaced by a 0, then it does satisfy the stronger
periodic constraints. This rather suggests that most (all?) 13x13 solutions
of the weaker problem are "not far" from a solution of the stronger one.

Chris Thompson
JANET:    cet1@uk.ac.cam.phx
Internet: cet1@phx.cam.ac.uk
Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
From: ak005@cleveland.Freenet.Edu (Yona Webb)
Newsgroups: sci.math
Subject: TO ALL !!!
Date: 19 Dec 1992 01:43:16 GMT
Organization: Case Western Reserve University, Cleveland, Ohio (USA)
NNTP-Posting-Host: slc4.ins.cwru.edu


*****************************************************************
*                                                               *
*         *                 M E R R Y                           *
*        <^>                                                    *
*        ***        CHRISTMAS   &   HANUKKAH                    *
*       *****                                        *          *
*      *******           HAPPY NEW YEAR      * * * * | * * * *  *
*     *********           - 1 9 9 3 -        | | | | | | | | |  *
*    ***********                              \|_|_|_|_|_|_|/   *
*   *************      May all your dreams     ~~~~~\|/~~~~~    *
*  ***************          come true                |          *
* *****************                                 _|_         *
*        ] [          Best wishes to all - Yona     ~~~         *
*****************************************************************
-- 
Newsgroups: sci.math
From: sbardhan@uncc.edu (Soumendu Bardhan)
Subject: Pi in beatiful form --lost
Reply-To: sbardhan@uncc.edu
Organization: University of NC at Charlotte
Date: Wed, 16 Dec 1992 00:27:25 GMT

I  hope Mathematicians especially  Pi'ans  could help me remember this beautiful form of pi.
I  can only faintly remember this beautiful form  invented by Ramanujam
pi = (1*2)/(3*4) +(5*6)/(6*7)....

All I remember is that it is very close to this representation ....it involved multiplication of two numbers
and divsion by two very close numbers .. it was indeed  one of the fascinating forms.

Thanks
--bardhan


Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
From: jarleb@athena.uio.no (Jarle Brinchmann)
Subject: Funny, Funny was Re: TIME HAS INERTIA - NewScientist Article
Followup-To: sci.physics
Reply-To: jarleb@athena.uio.no (Jarle Brinchmann)
Organization: Institute for Theoretical Astrophysics
Date: Tue, 15 Dec 1992 14:48:09 GMT


In article <Bz8nzF.Axo@well.sf.ca.us>, hluce@well.sf.ca.us (Hudson Hayes Luce) writes:
|>Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
|>From: hluce@well.sf.ca.us (Hudson Hayes Luce)
|>Subject: Re: TIME HAS INERTIA - NewScientist Article
|>
|>
|> Abian needs to submit his theory in an article to Physica D, the
|> appropriate journal for this kind of thing. This has no place in
|> sci.chem, it's a waste of bandwidth. Publications in the New Scientist
|> are OK, but he really needs to get into some sort of refereed journal,
|> and OUT OF THIS NEWSGROUP !!!!!
|>(he might also give Phys. Rev. Lett. a try......)
|>

This is absolutely the funniest thing I've read. I hope for your
own sake that you don't believe it ??
(If you had written MetaPhys.Rev.Lett. or something :-)

PS! Note followup, I just wish we'd get rid of it on sci.physics.

				Jarle.

      ---------------------------------------
       Internet: jarleb@medusa.uio.no         
       or        Jarle.Brinchmann@astro.uio.no
      ---------------------------------------

Newsgroups: sci.math
From: news@massey.ac.nz (USENET News System)
Subject: Re: Marilyn Vos Savant's error?
Organization: Massey University
Date: Tue, 15 Dec 92 20:47:31 GMT

In article <1992Dec15.012403.28006@news.cs.brandeis.edu>, palais@binah.cc.brandeis.edu writes:
> 
> You have a hat in which there are three pancakes.  One is golden on
> both sides, one is brown on both sides, and one is golden on one side
> and brown on the other.  You withdraw one pancake and see that one side
> is brown.  What is the probability that the other side is brown?
> 
> I think she is correct (as usual) [2/3]. It is clear that the pulling out of 
> the hat involved choosing one of SIX sides to look at---all equally likely. 
 If you don't believe it, test it experiment 
> experimentally a few dozen times and see if you come close to 66% 
> or 50%.

These questions are all easy if you draw a tree.

Newsgroups: sci.math
From: ags@seaman.cc.purdue.edu (Dave Seaman)
Subject: Re: What is the number
Organization: Purdue University
Date: Thu, 17 Dec 1992 22:51:52 GMT

In article <1gqm29INN9f@flop.ENGR.ORST.EDU> koc@rize.ECE.ORST.EDU (Cetin Kaya Koc) writes:
>>    Whose sum of the factorials of the digits is the number itself
>
>1, 145, 40585

and also 2.

--
Dave Seaman
ags@seaman.cc.purdue.edu
Newsgroups: sci.math
From: joel@math.toronto.edu (Joel Chan)
Subject: Re: Marilyn Vos Savant's error?
Keywords: savant
Organization: Department of Mathematics, University of Toronto
Date: Tue, 15 Dec 92 05:00:47 GMT

In article <1gj5grINNk05@crcnis1.unl.edu> burchell@cse.unl.edu (David Burchell) writes:
>I ask the net Gods: Can this be correct??

Ouch.  I'm not a net god... but I'll give it my best shot! :-)

>From ``Ask Marilyn'' by Marilyn Vos Savant, Parade magazine, December
>13, 1992.
>
>You have a hat in which there are three pancakes.  One is golden on
>both sides, one is brown on both sides, and one is golden on one side
>and brown on the other.  You withdraw one pancake and see that one side
>is brown.  What is the probability that the other side is brown?
>
>---Robert H. Batts, Acton, Mass.
>
>It's two out of three.  The pancake you withdrew had to be one of only
>two of them: the brown/golden one or the brown/brown one.  And of the
>three brown sides you could be seeing, two of them also have brown on
>the other side.

This is either a really simple way of looking at it... or really confusing.
You pull out the pancake and the side you see is brown.  There are a total
of three brown sides and three golden sides.

Pancake     1         2         3
          -----     -----     -----
One side   B1        B3        G2
          -----     -----     -----
Other side B2        G3        G1
          -----     -----     -----

So by the question, the 'side' that you see is either B1, B2, or B3.

If you had B1, the other side is B2.  Bingo.
If you had B2, the other side is B1.  Bingo.
If you had B3, the other side is G3.  Nope.

Therefore the probability is 2/3.  QED and what not.
I'd have to agree with Marilyn on that one.

Hope it helps.

Joel
-- 
Joel Chan, Department of Mathematics	  	 joel@math.toronto.edu
Toronto Blue Jays: 1992 World Series Champions
"History: Those who ignore it are condemned to repeat it.  Math, too."
				    -From the comic strip "Betty"
Newsgroups: sci.math
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: Alleged shortage of mathematicians (was Re: M
Organization: Department of Chemistry, University of Toronto
Date: Thu, 17 Dec 1992 18:31:24 GMT

In article <1992Dec17.001527.18598@husc3.harvard.edu> kubo@boucher.harvard.edu
(Tal Kubo) writes:
>I should have said, chemistry done in industry, rather than chemical
>engineering (which as you point out is sufficiently different to vitiate
>the original analogy).  Although industry may be ahead in certain parts of
>that field, the situation is in general that new ideas are developed in
>academia and optimized in industry. (At least that's the consensus among
>chemists to whom I've spoken.)

     I think you had better drop this example and think up another one.
I'm about as pure a chemist as you're ever likely to meet, and even
I wouldn't make that statement.  As much new chemistry is done in
industrial laboratories as in academic ones.  The principal difference
is that the industrial chemists almost never publish, often because
their companies rightly expect to be able to patent and profit from the
discoveries of their employees.  Academic chemists are of course a
little more likely to pursue highly speculative ideas with no obvious
application, but chemistry is still in such a state that entirely new
chemistry can be explored even while trying to solve old problems in
industry.  I have no idea what it's like in other fields.

>Publications aside, I see this as part of a more general problem with
>private employment, where you miss out on a lot of opportunities to meet
>people outside your own backyard.  The mechanisms for doing so are much
>better developed in academia (visiting scholars, colloquia, sabbatical
>leave, conferences, travel grants, etc).  Employers are gradually becoming
>more enlightened in this respect, though.

     You must not go to the right conferences.  At SIAM conferences, a
large proportion of the participants and an even larger proportion of
the general attendance consists of industrial mathematicians.  This was
true even at the recent Conference on Dynamical Systems, a field which
shows much promise but is hardly a mainstay of industrial mathematics at
this point.
     Since I'm not a mathematician, it's difficult for me to comment
with any authority on this matter, but doesn't the very existence of
SIAM shed some doubt on this part of your argument?  SIAM is supported
in part by direct corporate sponsorships.  Some companies clearly
think that fostering contacts among industrial mathematicians is
important.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
Newsgroups: sci.math