HDTenEightyP/NetNews huggingface dataset:
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.math
Subject: Funding of research
Date: 15 Aug 92 15:11:45 GMT
Organization: Purdue University Statistics Department

In article <1992Aug11.160727.27151@galois.mit.edu> jbaez@nevanlinna.mit.edu (John C. Baez) writes:
>In article <1165@kepler1.rentec.com> andrew@rentec.com (Andrew Mullhaupt) writes:

			....................

>>When I was at U.B. the NSF decided to cut down the funding of the category
>>theory group because it was 'useless'. But those guys were quite good at it.
>>Now we hear John Baez trying to drum up interest in the subject for the sake
>>of physics. I don't know whether to laugh or cry. 

>A cynical snicker will suffice.

			....................

I missed the original article; probably it was in the mass that came in
when I was gone for 6 days.  But the real problem is the existence of what
is effectively a government monopoly on funding mathematical research.  

There is no legal monopoly, but universities no longer budget funds for
research, and the researcher is told to get the money from some granting
agencies, which do work together (this is quite public information).  As
all universities operate this way, if the government does not fund something,
it does not get funded.

Now NSF was specifically set up to fund PURE research.  But they are using
more and more of their funds for "practical" problems, and have made funding
decisions opposed by almost the entire mathematical community about methods
of funding.  This last statement is not about what to fund, but how.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)
Newsgroups: sci.math
From: jbaez@nevanlinna.mit.edu (John C. Baez)
Subject: Re: Help - non-integral power of a matrix?
Keywords: matrix
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Wed, 12 Aug 92 23:17:08 GMT

In article <a_rubin.713653963@dn66> a_rubin@dsg4.dse.beckman.com (Arthur Rubin) writes:
>In <carle.713599691@vex> carle@vex.ugcs.caltech.edu (Matthew Thomas Carle) writes:
>
>>gonzalez@clam.rutgers.edu (Ralph Gonzalez) writes:
>
>
>>>Hi.  Does anyone know of an algorithm to find a non-integral
>>>power of a matrix, e.g. A^.5 or A^1.3? Thus, A^2 is the same
>>>as AxA and A^0 is the identity.
>
>>>I imagine if such a thing is defined, then there are conditions
>>>on A...

>log "obviously" converges if all eigenvalues of A are strictly within 1 of 1,

To clarify, perhaps, let me add that this is not only "obvious", it's
true, at least if A is diagonalizable.  If A is a
not-necessarily-diagonalizable matrix log A is defined if ||A - 1|| < 1;
I don't think the eigenvalue condition above is sufficient.

Gonzalez was interested one-parameter groups of matrices.  Well, that's
not how he phrased it, but he was looking for matrix-valued functions of
t such that A(t)A(s) = A(t+s).  A^t is a nice way to think about these
heuristically but it's sort of a nuisance because fractional powers of
matrices are even more multivalued and branchy than fractional powers of
numbers.  If A is close enough to 1 (as made precise above), there is
a unique "best" definition of log A, namely

(A-1) - (A-1)^2/2 + (A-1)^3/3 - ...

the usual power series.  One can see that this satisfies exp(log A) = A
and that exp(t log A) is good way of defining A^t, that is, it's a
one-parameter group.

In general, though, it is best to specify one-parameter groups by their
generators.  That is, any (continuous) 1-parameter group of matrices is
of the form exp(t C) for some matrix C.  If the 1-parameter group is a
rotations then C is an "infinitesimal rotation" (a skew-adjoint matrix)
and so on... huge amounts of stuff are known about this, so that's how I
would advise Gonzalez to proceed.
From: proberts@informix.com (Paul Roberts)
Newsgroups: sci.math
Subject: Re: Is Card(R)=Card(R^2)?
Date: 13 Aug 92 23:06:06 GMT
Organization: Informix Software, Inc.

In article <16dihrINNpet@function.mps.ohio-state.edu> edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:
>
>>I believe that there is even an everywhere-continuous 
>>bijective mapping from the unit line to the unit square.
>
>No, there is not.  The interval and the square are not homeomorphic.
>Such a continuous bijective map would be a homeomorphism,
>since the two spaces are compact Hausdorff spaces.
>

How about the unit line minus the end points, and the interior of
the unit square? I am sure I saw the construction once, it stuck in
my mind because the conclusion seemed so counter-intuitive.

I am pretty sure that it was nowhere-differentiable, but everywhere-
continuous.

Paul
Newsgroups: sci.math
From: kurtles@momth3.maths.monash.edu.au (Mr K.A. Brinschwitz)
Subject: Re: Linaer Programming software sought
Keywords: linear programming
Organization: Monash University
Date: Wed, 19 Aug 1992 00:48:21 GMT

	I would recommend the G.A.M.S package (General Algebraic Modelling System).
This is a commercially available optimization modelling package which handles linear,
 non-linear, integer, mixed-integer and zero-one integer programming. The software 
uses MINOS and ZOOM routines, and the package is available on a wide variety of 
operating systems.

	GAMS uses its own language, which is based on FORTRAN, that is quite easy to 
use, and has various 'nice' features, such as allowing direct array manipulations. 
The language is set up in such a way that any program run in GAMS more or less reads 
as it would in the mathematical terminology. There is a comprehensive users guide, 
and a library of 100 or so example problems (some of which are very large)

	I am not sure where you can purchase the package itself, but the publishers
of the user guide are:

	THE SCIENTIFIC PRESS
	507 Seaport Court
	Redwood City, 
	CA 94063-2731

	Phone (415) 366-2577	

	Maybe they can point you in the right direction.

	Cheers,

	Kurt Brinschwitz
	kurtles@momth0.maths.monash.edu.au

	Monash University, Australia
Newsgroups: sci.math
From: tlee@poppy.uwaterloo.ca (Therese Lee)
Subject: Hasse-Teichmuller derivative
Organization: University of Waterloo
Date: Wed, 12 Aug 1992 19:02:59 GMT

Hi!
Have anyone seen the Hasse-Teichmuller derivative before?   
If yes, please let me know where I can find a description of this
derivative.  
Thanks.



-Therese
Newsgroups: sci.math
From: israel@unixg.ubc.ca (Robert B. Israel)
Subject: Re: Puzzles
Organization: University of British Columbia, Vancouver, B.C., Canada
Date: Thu, 13 Aug 1992 22:53:43 GMT

In <1992Aug13.172531.10744@galois.mit.edu> jbaez@nevanlinna.mit.edu 
(John C. Baez)writes:

>Some kind soul pointed out that one needn't write a program in C that
>can accept and run C programs to get the job done. Let me give away the
>answer to the problem (how to prove the "almost-paradox" A-P above).
  
>One need only write
>a program that looks through statements in ZFC to find those of the form
>"N cannot be printed by a program in C of length < E", and check
>which are provable in ZFC.  If it finds one, the program should print
>out the number N.

Well, if you can write a program that checks whether a statement is
_provable_ (and terminates in finite time if it isn't), then by Godel's
Theorem ZFC is inconsistent!  What you want your program to do is look
through all strings until it finds a _proof_ in ZFC that ends with
a statement of the form "N cannot be printed by a program in C of length < E",
and then print N.  If this program prints out N, then it is a counterexample
to the proof.  I might point out that, in concluding that no such proof
exists, we are using the consistency of ZFC, which is not part of ZFC itself.
If ZFC were inconsistent, every statement would be provable in it.

Your _program_ needn't be able to run C programs, but your statement
"N cannot be printed by a program in C of length < E" is really an abbreviation
for a very long formal statement in ZFC, which must contain a description of
the C language and how programs will be run.

-- 
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
From: wjcastre@magnus.acs.ohio-state.edu (W.Jose Castrellon G.)
Subject: Re: A Non-Cantorian Set Theory question
Organization: The Ohio State University,Math.Dept.(studnt)
Date: Mon, 17 Aug 1992 01:58:04 GMT

In article <1992Aug16.213657.4773@magnus.acs.ohio-state.edu> I write:

In article <1992Aug12.113415.1648@gacvx2.gac.edu> kiran@gacvx2.gac.edu writes:

>>Quite a while ago, I read Martin Gardner write in one of his _Mathematical 
>>Games_ column in _Scientific American_ that on a plane, a letter like _O_ can
>>be written--allowing smaller O's to be written inside larger O's-- _c_ 
>>times where _c_ is the cardinality of the continuum. On the other hand, he
>>pointed out, letters like _T_ can only be written aleph-nought times.
>>
>>A question that has remained in my mind for a long time since is the followin
>>
>>Since we know that non-Cantorian set theories are possible, is there a
>>one-dimensional shape which can be written some aleph times where that aleph
>>is between aleph-nought and _c_? If so, what would the shape be?
>>
>>I have once asked my mathematics teacher about it, and he remarked that that
>>shape might be a fractal!
>>
>>Does anyone have any idea on this?
>
>Nice question. If you allow disconnected spaces, the answer is yes:
>Let A be a subset of reals of cardinality  K  and call G the set obtained by
>taking all finite sums of elements in A and their negatives, then G also has
>cardinality K. Now partition the reals into equivalence classes, such that
>two elements belong to the same equivalence class iff their difference is an
>element of G. If we form a set S by picking one element from each equivalence
>class, then the real line is the disjoint union of K-many sets, each congruent
>to S  (Just take S_u = {s+u : s belongs to S}, for each u in G). Now by using
>Zorn's lemma, S can be constructed such that no more than K-many sets similar
>(i.e. homotetic) to  S can be disjoint in the real line. To get the final sub-
>set of the plane, it is enough to give  S some thickness, i.e. make P equal to
>the cartesian product of  S  and the interval [0,1], for example (though 
>lengthy to include in here, all details are easy to handle, just as for the T)

>I believe it is possible to construct a connected set P too, but I havent
>found a proof of that yet.

I've just found the connected set  P  and the proof involves no ideas different
from the above. (IMO it makes a nice exercise in plane analysis).
WJCG
Newsgroups: sci.math
Subject: Re: int(x*log(x)*((1-x)^n), x=0..1)
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 20 Aug 92 16:45:52 GMT
Keywords: Hairy integral, Beta function

In <dld.714296391@bruce.cs.monash.edu.au> dld@cs.monash.edu.au (David L Dowe) writes:

>Let  I(n) = int(x*log(x)*((1-x)^n), x=0..1);
>to use Maple's notation.        n is a positive integer.     log is ln  .

>I seek as simple an expression as possible or, that failing, as rapidly
>converging an expression as possible for I(n).

>Before you respond (to me rather than the newsgroup, please), let me tell
>you what I do know:
>By parts,  int((x^n)*log(x), x=0..1) = -1/((n+1)^2)          (1)

>Expanding (1-x)^n binomially and using (1)  enables us to get a
>fairly simple expression for I(n).   But, I would like (if possible) a simpler
>or more rapidly converging expression.

>o   I also know that, re-writing  I(n)  as  int((1-x)*log(1-x)*(x^n)),x=0..1);
>  Taylor expanding  log(x)  =  Sum(i=1,infinity) -(x^i)/i     gives
>  I(n)  =  int(-(x^(n+1)) + Sum(i=2,infinity) (x^(n+i))/((i-1)*i) , x=0..1)  ;
>and so     I(n)  =  -1/(n+2)  +  Sum(i=2,infinity) 1/((i-1)*i*(n+i+1)) .
>  This also converges more slowly than I would like it to.

>o   I also "know" that I(n) is rational.   I(0) = -1/4,  I(1) = -5/36,
>  I(2) = -13/144,  I(3) = -77/1200,  I(4) = -29/600,  I(5) = -223/5880,
>  I(6) = -481/15680,   and Maple Vn4.3 gave me a mammoth expression for
>  I(50) in 15 seconds.
>    When I gave Maple 4.3 the integral I(n)  (n unspecified), it merely
> returned some seconds later with the same initial expression I had given it.

>o   I also "know" that  n*(n-1)*I(n) + log(n + 1/2)   converges to
>  (I forget whether it's + or - )  +/- 0.42... ,
>  the 0.42... possibly (a guess) being something to do with Euler's constant.

>   I would appreciate (a reference to)
>  a proof that I(n) is rational,
>  a proof of the convergence result, and the value of "0.42..." ,   and
>  (most importantly)  as simple an expression as possible for I(n) .
>__


Mathematica 2.0 for HP/Apollo Domain OS reports:
Integrate[(1-x) Log[1-x] x^n,{x,0,1}] = (n^3 -4 n -2)/(n (n+1)^2 (n+2)^2) -
           (EulerGamma + PolyGamma[n])/((n+1)(n+2))

(PolyGamma is the digamma function "psi", and EulerGamma is Euler's constant.)

(1) You "know" I(n) is rational by using your expansion (1).

(2) EulerGamma + PolyGammma[n] is Sum[1/m,{m,n-1}], which produces a fairly
simple (but not rapidly convergent) rational expression.

(3) PolyGamma[n] =  log(n) + 1/2/n - 1/12/n^2 + 1/120/n^4 - 1/252/n^6 +  
1/240/n^8 -1/132/n^10 + ..., at least as an asymtotic series, (which can be
used for rapid calculation given the value of gamma) so your constant limit
of n(n-1)I(n) + Log(n+1/2)  or (n+1)(n+2)I(n) + log(n) is 1 - EulerGamma.







--
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
From: roach@bikini.wri.com (Kelly Roach)
Subject: u(v^n)w prime puzzle
Organization: Wolfram Research, Inc.
Date: Tue, 18 Aug 1992 17:15:32 GMT




     Prove or disprove:  There are three non-empty
     strings of digits u,v,w such that all the
     numbers in
          L = {u(v^n)w | n is a natural number}
            = {uw, uvw, uvvw, uvvvw, uvvvvw, ...}
     are prime numbers.


     Time to say a few more words about my u(v^n)w prime
puzzle which I posted yesterday.  I am definitely not looking
for any solutions involving u=v="0".  Ordinary syntax only
please.  No leading zeros in u.
     Some interesting patterns:

     u="3",v="3",w="1"
     31, 331, 3331, 33331, 333331, 3333331, 33333331

     u="1",v="36",w="1"
     11, 1361, 136361, 13636361, 1363636361, 136363636361

     u="17",v="57",w="09"
     1709, 175709, 17575709, 1757575709, 175757575709,
     17575757575709, 1757575757575709, 175757575757575709

Below each line giving u,v,w values appear a lot of prime
numbers.  These patterns do eventually fail:

     333333331 = 17*19607843
     13636363636361 = 17*1321*5693*106661
     17575757575757575709 = 232433*75616446785773

The question is, are there any {u,v,w} examples which do
not fail?  That always give prime numbers?
     I know the solution to this puzzle.  I think the
solution can be understood fairly easily by anyone that
has had a first course in number theory.  See if you
can discover it.






Newsgroups: sci.math
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: Why are Some Journals so Expensive?
Organization: Department of Chemistry, University of Toronto
Date: Tue, 18 Aug 1992 19:12:31 GMT

In article <ARA.92Aug16231911@camelot.ai.mit.edu> ara@zurich.ai.mit.edu
(Allan Adler) writes:
>Jocelyn Paine is under the impression that the number of mathematicians who
>do not have access to email, LaTeX and other facilities that would make it
>possible for them to receive math journals electronically is not significant.
[note indicating that many lack access to such tools deleted]

     In fact, wouldn't this sort of high-tech publishing cut off most
everyone outside of North America and Western Europe?  I was under the
impression that email/LaTeX/PostScript were relatively rare elsewhere.
(Many places have one or the other, but not all three; LaTeX is probably
not an issue since it's free and runs on anything you have, but the
other two are more problematic, as I understand it.)

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
Newsgroups: sci.math
From: rose@fsu1.cc.fsu.edu (Kermit Rose)
Subject: Re: Primes
News-Software: VAX/VMS VNEWS 1.3-4   
Reply-To: rose@fsu1.cc.fsu.edu
Organization: Florida State University
Distribution:  world
Date: 21 AUG 92 23:59:30    

In article <1992Aug18.091619.10152@waikato.ac.nz>, bill@waikato.ac.nz writes...
>In article <9208171021.aa01492@Paris.ics.uci.edu>, kibler@turing.ICS.UCI.EDU (Dennis Kibler) writes:
>> In mathematica the number of primes less than n or equal to n
>> is given by PrimePi[n].
>> 
>> The following took about 1 second to compute.
>> 
>> 
>> 
>>  Do[Print[i," ",PrimePi[2^i]],{i,30}]
>> 1 1
>> 2 2
>> 3 4
>> 4 6
>> 5 11
>> ....
>> 28 14630843
>> 29 28192750
>> 30 54400028
>> 
> 
>Does anyone know how Mathematica stores its table of primes, and how efficient
>it is in terms of space and access time? What's the minimum space a table
>of primes can be compressed into if constant access time to find the nth prime
>is required?
> 
>Bill Teahan,
>Systems Programmer,
>University of Waikato,
>Hamilton, New Zealand.
>"I have never been lost, but I will admit to being confused for several weeks."
>-- Daniel Boone.

In general, one can use a bitmap to represent a prime number table.  Some 
compression can be obtained by representing only odd numbers, or only 
odd numbers not divisible by 3.  
Then the computer can count primes by using the count bits function of the 
hardware amazingly fast.  If the computer does not have a count bits 
function, then this technique is lost.

rose@fsu1.cc.fsu.edu          To be sure I see your response, use e-mail.
-----------------------------------------------------------------------
You may post, repost, or publish ANY communication received from me.
Be of good cheer, for it is much more fun than being depressed.
From: petry@pythagoras.math.washington.edu (David Petry)
Newsgroups: sci.math
Subject: Re: Still another problem.
Date: 19 Aug 92 23:09:28 GMT
Article-I.D.: u.1992Aug19.230928.17072
Organization: University of Washington, Mathematics, Seattle

>In article <1992Aug14.142149.16686@mcs.drexel.edu>, dmagagno@mcs.drexel.edu
>(David Magagnosc) wrote:
>> 
>> While we're at it, prove that the following sum is always an
>> integer:
>> 
>> 	 n    n    n    n
>> 	1    2    3    4
>> 	-- + -- + -- + -- + ...
>> 	 1    2    3    4
>> 	2    2    2    2
>> 
>> and find reasonable generalizations.


While we're at it, denote the sum with exponent n by f(n), and prove

f(n+p) = f(n+1)  (mod p),  for all n >= 0, and all primes p. 


For more fun, show that f(n) ~= n!/(log2)^(n+1)  for large n.


David Petry
 
Newsgroups: sci.math
From: N020BA@tamvm1.tamu.edu
Newsgroups: sci.math
Subject: Custom Wavelets-How do you make them?
Date: 21 Aug 92 01:57:04 GMT
Organization: Texas A&M University


 
    Hello! How to do take a waveform and make it into a wavelet? Can you
plot some data, get a waveform and use that for a wavelet?
    Please reply to N020BA or the net. I think many other people are inter-
ested, as I've had mnay people asking me. E-mail N020BA@tamvm1.tamu.edu
 
========================================================================
The truth may hurt, but lies hurt more.  | My opinions are mine and mine
The difference between left-wing incomp- | alone. I speak for myself and
etance and right-wing incompetance is    | no-one else.
the difference between cat #$!& and dog  |______________________________
#$!&. Reply to N020BA@tamvm1.tamu.edu.        Bill and Opus in '92!!
Newsgroups: sci.math
From: tycchow@riesz.mit.edu (Timothy Y. Chow)
Subject: Re: Prime conjecture
Organization: None.  This saves me from writing a disclaimer.
Date: Wed, 12 Aug 92 22:26:58 GMT

In article <18990@nntp_server.ems.cdc.com> mstemper@ems.cdc.com writes:
<In article <1992Aug11.162953.13961@uwm.edu>, radcliff@csd4.csd.uwm.edu (David G Radcliffe) writes:
<|> 
<|>    Conjecture:  There exists a k > 0 so that p + k is prime 
<|>                 for infinitely many primes p.
<|> 
<|> Does anybody know the status of the this conjecture?
<
<I believe that
<  There exist infinitely many primes p
<  Such that p+2 is prime
<has been proven, which would prove this conjecture by showing k=2.

No.  This is the Twin Prime Conjecture, which is still open.
-- 
Tim Chow     tycchow@math.mit.edu
Where a calculator on the ENIAC is equipped with 18,000 vacuum tubes and weighs
30 tons, computers in the future may have only 1,000 vacuum tubes and weigh
only 1 1/2 tons.                               ---Popular Mechanics, March 1949
Xref: sparky sci.math:10401 sci.psychology:3516
From: jk87377@cc.tut.fi (Juhana Kouhia)
Newsgroups: sci.math,sci.psychology
Subject: Re: mathematician's marrying ages.
Date: 19 Aug 92 12:02:00 GMT
Organization: Tampere University of Technology


In article <chepan.713715679@gsusgi1.gsu.edu> chepan@gsusgi1.gsu.edu
(Parthasarathy Nambi) writes:
>
>	What does marrying early and being a good mathematician
>	has anything to do with each other? I think this is nonsense.


It is researched that those who are not married does have more
mental, say, problems. Lonely people usually die more early than
non-lonely people.
You see, human is not meant to be lonely.

I don't have references, because my source is newspaper.
I have posted this to sci.psychology too, they may verify
this -- however, I expect that they will verify this from
the research results, instead of telling their guesses.

Juhana Kouhia
Xref: sparky sci.math:10474 sci.physics:13211
From: johan@blade.stack.urc.tue.nl (Johan Wevers)
Newsgroups: sci.math,sci.physics
Subject: Re: tensors
Keywords: Tensor
Date: 21 Aug 92 08:06:04 GMT
Followup-To: sci.math
Organization: MCGV Stack, Eindhoven University of Technology, the Netherlands.

schlegel@cwis.unomaha.edu (Mark Schlegel) writes:

[A lot about *matrix* and *vector* calculus]

You didn't get the point: as many people, you seem to think that a
tensor is ``something with an index''. That is *NOT TRUE*. Something
is a tensor when it obeys certain transformation rules under
coordinate transformation. For example, the Christoffel symbols
\Gamma^{a}_{bc}, often used in GR, are NO TENSORS. They don't
transform in the right way.

******************************************************************** 
* J.C.A. Wevers                *         u\  _\       /e+        2 * 
* johan@blade.stack.urc.tue.nl *     1 |   \ u \  X  /         |   * 
******************************** P = - |    >   >---<     + ...|   * 
*     The only nature of       *     N |   /   /     \         |   * 
*     reality is physics       *         u/   /d     u\            *
********************************************************************
Xref: sparky sci.math:10302 rec.puzzles:5677
From: clong@remus.rutgers.edu (Chris Long)
Newsgroups: sci.math,rec.puzzles
Subject: Re: Skittles commercial
Date: 15 Aug 92 16:38:23 GMT
Followup-To: sci.math
Organization: Rutgers Univ., New Brunswick, N.J.

In article <1992Aug10.163022.12987@dg-rtp.dg.com>,
banksd@hydra.rtp.dg.com writes:

> I saw a commercial for Skittles candies, where they are
> trying to figure out the number of "different combinations"
> of Skittles. Their final answer is remarkably small -- only
> six digits -- for a combinatorial property of a bag full of
> candy. And as I recall, it wasn't very divisor-rich either.

A friend of mine claims that the number is 371,292.  Now, how did
they arrive at it?
-- 
Chris Long, 265 Old York Rd., Bridgewater, NJ  08807-2618

"In a study of schoolboys, an educator discovered a correlation between size
 of feet and quality of handwriting.  The boys with the larger feet were,
 on the average, older."        Wallis & Roberts, _The Nature of Statistics_