HDTenEightyP/NetNews huggingface dataset:
From: perlman@cis.ohio-state.edu (Gary Perlman)
Subject: |STAT now available via anonymous ftp
Originator: perlman@moose.cis.ohio-state.edu
Organization: Computer & Info Sci  Ohio State Univ  Columbus, OH 43210
Date: Thu, 13 Aug 1992 06:12:50 GMT

By popular demand, my |STAT package is now available on the internet.
|STAT runs on UNIX and DOS systems and provides about 30 programs
for data manipulation and analysis.  Further information is available
directly from me.

|STAT is available via anonymous ftp in pub/stat at:
	ftp.cis.ohio-state.edu (128.146.8.52)
The file:
	stat.tar.Z.crypt.uu
is the uuencoded, encrypted, compressed, tar archive of the package.
To unpack the archive, you need uudecode, crypt, uncompress, and tar.
To ensure that the distribution restrictions on |STAT are maintained,
a password has been attached to the archive.
To obtain the password from me, you must send me a message with:
	I AGREE TO ADHERE TO THE CONDITIONS OF USING |STAT.
	I AGREE THAT I WILL NOT SHARE THE |STAT PASSWORD WITH OTHERS.
After obtaining the file, which you can also request from me via email,
you should run the following commands:
	uudecode < stat.tar.Z.crypt.uu
	crypt < stat.tar.Z.crypt > stat.tar.Z
	uncompress stat.tar.Z
	tar xvf stat.tar
You should then have a "stat" directory that will take up about a megabyte.
In the stat/src directory, you should make any necessary changes
to the "makefile" and then run "make" to build the package.
In addition to the online manuals, the file handbook.txt contains
a lineprinter version of the |STAT handbook.  The troff source to
the handbook is not yet structured enough for ftp distribution.
-- 
Name:  Gary Perlman               | Computer and Information Science Department
Email: perlman@cis.ohio-state.edu | Ohio State University, 228 Bolz Hall
Phone: 614-292-2566               | 2036 Neil Avenue Mall
Fax:   614-785-9837 or 292-9021   | Columbus, OH 43210-1277  USA
From: rmverma@cs.uh.edu (Dr. R.M. Verma)
Newsgroups: sci.math
Subject: Re: Binomial like recurrence
Date: 12 Aug 92 17:15:16 GMT
Organization: Computer Science dept.,  Univ. of Houston (Main Campus)

In article <1992Aug12.100933.13400@aifh.ed.ac.uk> tw@aisb.ed.ac.uk (Toby Walsh) writes:
>
>The binomial recurrence,
>
>    c(n,k) = c(n-1,k-1) + c(n-1,k)
>
>is well known. Has the related recurrence,
>
>    u(n,k) = 2.u(n-1,k-1) + u(n-1,k)
>
>been studied? Does it have a closed form?
>What is its asymptotic behaviour?
>
>And more generally, how about,
>
>    v(n,k) = a.v(n-1,k-1) + b.v(n-1,k)
>
>for integer a and b?
>
>toby

Yes, they have been studied and there are answers to some of your
questions in the literature. 

See the paper by Monier in Journal of ALgorithms 1980, and
Ch. 8 of The Analysis of Algorithms by Purdom and Brown (more references
can be found here).

I would like to know your reason for studying them.

R.M. Verma
Newsgroups: sci.math
From: mab@wdl39.wdl.loral.com (Mark A Biggar)
Subject: Re: Prime conjecture
Organization: Loral Western Development Labs
Date: Wed, 12 Aug 1992 21:43:11 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.
>Related questions: Now that we know that there exists a k, are there
>other k's that satisfy this condition? If so, is there a largest k
>that satisfies this condition?

Please give a reference for this.  I thought that the twin primes
conjecture was still open.

--
Mark Biggar
mab@wdl1.wdl.loral.com

Newsgroups: sci.math
From: unidemo@FRD.AC.ZA
Subject: Re: Fundamental Theorem of Geometry (and others)
Reply-To: unidemo@FRD.AC.ZA
Organization: FRD Pretoria
Date: Thu, 13 Aug 1992 09:36:03 GMT


In article <1992Aug6.163943.10934@galois.mit.edu>, jbaez@nevanlinna.mit.edu (John C. Baez) writes:
>In article <COLUMBUS.92Aug5160636@strident.think.com> columbus@strident.think.com (Michael Weiss) writes:
>>In article <1992Aug5.130502.28754@galois.mit.edu> jbaez@riesz.mit.edu (John
hhhhhhhhhhh>>C. Baez) writes: 
>>
>>   I may not have been clear enough.  The theorem I am referring to is
>>   1 \= 0.  
>es of this theorem are many. [...]
>>
>>I'm curious.  Have you actually had occasion to use this theorem, as
>>stated?  (No fair saying "Yes, any time I do a proof by contradiction!"
>>That would count only if the contradiction naturally fell out as
>>"1=0".)
>
>Well, I was sort of joking, and I was referring to proof by
>contradiction, but it is generally handy to know that 1 is not equal to
>0.  For example, "I would be happy only if I had 1 ice cream cone.  I have 0
>ice cream cones.  By the fundamental theorem of mathematics, 1 is not
>equal to 0.  Therefore I am not happy."
>
>
Newsgroups: sci.math
From: andyc@eliot.uucp (Andy Collins)
Subject:  Re: mathematician's marrying ages.
Keywords: Abel, Galois
 
Organization: Systems Center, Inc., Reston, VA, USA
Distribution: na
Date: Thu, 13 Aug 1992 18:49:58 GMT

>>My friend (yu@math.harvard.edu) keep advocating that marrying
>>early is good for mathematician.  He gave several examples
>>( most of them are number theorist, according to his statemnet)
>>Examples he gave are Delinge, Gauss, Milnor, Serre, Zariski.
>>He told me that he got these information from bibliography
>>(maybe from introduction to authors...etc)

>If he uses four examples to prove his statement - tell him to quit math!

>>Any counterexample? ( Marry late and have quite an achievement )

>Galois and Abel never married. So there.

Yes, it is true that these brillant mathematicians didn't marry.
This doesn't mean much though. Galois had more important things to
worry about, his mathematics, and his life. Galois got shot in a
duel as I recall. The night before the duel he scribbled all of his
theory down on paper and handed them to a friend (Who was it?...)
just before the duel.
Abel also had to worry about other things besides getting married,
namely having food to eat and shelter. His entire family was very
poor, and Abel had one chance to get into main-stream continental
Europe mathematics, but to no avail. He died in poverty, just after
returning to his "home" in Scandinavia.

As another example Euler married early enough to have a
considerable number of children (How many, two digit decimal?...)
and was noted as spending many hours of time with them.

Marriage is a personal matter anyway, but just know that you have
fewer life-threatening obstacles to overcome.

Andy Collins

Continue to post responses, mail is still rankled here.
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.math
Subject: Re: Power series solution to ordinary differential equation
Date: 17 Aug 92 14:40:35 GMT
Organization: Purdue University Statistics Department

In article <1992Aug16.231044.4401@pellns.alleg.edu> frisinv@alleg.edu (Vincent Frisina) writes:
>To anyone who has had differential equations:
>   I tried this once before but no one responded. I'm trying to learn  
>differential equations. The book I'm using has a great discussion of  
>everythinmg but power series solutions. My problem isn't with the series  
>themselves (I do remember calc two) but with the method. Could someone  
>please send me a summery of how and when to use this method of solution.  

The method of power series is actually the oldest method of numerical
solution of differential equations, but is now usually considered "not
in style."  There ARE many cases in which it is far better than the
usual ones, and of course many where it is not.  HOW is not much of
a problem; as to WHEN, this is a matter of art, not science.

Power series are also used for theoretical reasons.  Old DE books
spend some time on the topic.
-- 
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: dzk@cs.brown.edu (Danny Keren)
Subject: Re: Is Card(R)=Card(R^2)?
Organization: Brown University Department of Computer Science
Date: Thu, 13 Aug 1992 16:24:06 GMT

proberts@informix.com (Paul Roberts) writes:

#I believe that there is even an everywhere-continuous 
#bijective mapping from the unit line to the unit square.

That is not possible, since it would imply the unit interval is
homeomorphic to the unit square. This is because the inverse of
such a map is also contiuous. Since, take a closed subset of
the interval. It is compact; hence its image is compact, but
every compact subset of the unit square is closed. 

There is a continuous map from the interval *onto* the square; 
Peano constructed the first such map, and it is quite easy to
give a proof such a map exists using simple convergence properties
of functions.

-Danny Keren.
From: kosowsky@minerva.harvard.edu (Jeffrey J. Kosowsky)
Newsgroups: sci.math
Subject: Re: Help - non-integral power of a matrix?
Date: 17 Aug 92 21:31:40 GMT
Article-I.D.: minerva.KOSOWSKY.92Aug17163140
	<KOSOWSKY.92Aug14122403@schottky.harvard.edu>
	<1992Aug14.204404.23279@galois.mit.edu>
Organization: Harvard Robotics Lab, Harvard University

In article <1992Aug14.204404.23279@galois.mit.edu> jbaez@zermelo.mit.edu (John C. Baez) writes:

>   I'm particularly worried about the non-normal case, of course.  You are
>   right about the holomorphic functional calculus so we are free to say
>   that my series 
>
>   ln A = (A - 1) - (A - 1)^2/2 + ....
>
>   converges when the spectral radius of A - 1 is < 1. If our space is
>   finite-dimensional this just means that all eigenvalues of A have
>   |lambda - 1| < 1.   If A is normal the spectral radius equals the norm
>   so we may equivalently demand ||A - 1|| less than 1.   (In the
>   finite-dim case "normal" just means "diagonalizable".)
>

Just for clarification, the two mentions of finite-dimensionality above
can be extended to compact operators on any Banach space. In the
compact infinite dimensional case:
	a] spectrum = closure of set of eigenvalues
			  = {eigenvalues} U {0}
	 so, it is still sufficient check the size of the eigenvalues
	 plus the limit point 0. 
	In the case of the logarithm, 0 does not lie in the radius of
	convergence about 1. So, the Riesz functional calculus won't work
	here. Actually, the Borel functional calculus won't work either
	since the logarithm is not defined at 0.

	So, is there any way to define the logarithm of a (compact)
	operator on an infinite dimensional space that avoids this
	problem of 0 being in the spectrum?

	b]It is still true that normal iff diagonalizable
	


Jeff Kosowsky
From: 6500lem@ucsbuxa.ucsb.edu (Laurence Mailaender)
Newsgroups: sci.math
Subject: Re: Evaluation of an integral
Keywords: exponential
Date: 22 Aug 92 01:25:56 GMT

In article <BtACnF.CxK@news.cso.uiuc.edu> magdi@uxh.cso.uiuc.edu (Magdi N Azer) writes:

>Can anyone tell me if there is an analytical expression one can obtain
>]for exp[exp(x)].  I've done a Taylor Series expansion to fourth order,
>but I don't know if I am missing something obvious about this. 

>Second, can this be integrated(other than numerically)
>The limits of the integral are 0 and 0.5
>thank you

>Magdi N Azer
>magdi@uxh.cso.uiuc.edu

Magdi-

I haven't thought about it too much, 	but a simple way to look 
at this is:

exp(y) = 1 + y + (y**2)/2! + (y**3)/3! + etc.

substituting y= exp(x)

exp(exp(x)) = 1 + exp(x) + exp(2x)/2! + exp(3x)/3! + etc.

using the "ratio test" it is very easy to see that this is
a convergent series, therefore it is the function you want.
Since exp(x) itself is a transendental function, one should
not expect to find a closed-form expression for your function.

The expansion above is easily integrated term-by-term, although
you may need many terms for satisfactory precision.

	Laurence Mailaender
	Dept. of Electrical Engineering
	U. C. Santa Barbara
Newsgroups: sci.math
From: bx304@cleveland.Freenet.Edu (Jeff Epler)
Subject: Re: More than one 8 x 8 Magick Square?
Reply-To: bx304@cleveland.Freenet.Edu (Jeff Epler)
Organization: Case Western Reserve University, Cleveland, OH (USA)
Date: Wed, 19 Aug 92 01:38:28 GMT


In a previous article, Tagi@cup.portal.com (Tagi Mordred Nagashiva) says:

>Is there more than one major solution (aside from rotation) for the
>8 x 8 Magick Square?  What are the other possibilities?  Is there
>a method to generate even-numbered Squares aside from the 4 x 4?
>
>Below is the solution I know of for the 8 x 8.  Alternatives would
>be welcomed via email or post.  Thanks!

To any magic square you can do the following:
 
Scale each element by a constant
Exchange two rows
Exchange two columns

and the square will still work.

Now suppose you have a magic square AxA and an algorythm to construct a
magic square of BxB with an arbitrary sum.

To construct a square (A*B) on a side, construct A*A squares BxB, with
sums that correspond to each square in A.  Then arrange them (Replace
17 with the square that totals 17, etc) into one larger square.

There seems to be an algorythm for both odd x odd squares, and
multiple_of_four x multiple_of_four squares, but I don't know what it
is...

I would be interested in a post of C source code that could do the
job... (Or Pascal, I actually prefer that language.)
>
>Tagi
>
>--------------------------------
>
>01 56 48 25 33 24 16 57
>63 10 18 39 31 42 50 07
>62 11 19 38 30 43 51 06 
>04 53 45 28 36 21 13 60
>05 52 44 29 37 20 12 61
>59 14 22 35 27 46 54 03
>58 15 23 34 26 47 55 02
>08 49 41 32 40 17 09 64
>
>The one I know about.
>
>-------------------------------------
>

-- 
|Jeff Epler               Additions Welcome           c(-8 ;-) >{8-) |
| :) (=( =-] (-= Celebrating the variety of faces =-> :^) {-= |-) (: |
|                                                   Lincoln, Nebraska|
From: proberts@informix.com (Paul Roberts)
Newsgroups: sci.math
Subject: Re: Is Card(R)=Card(R^2)?
Date: 13 Aug 92 01:15:22 GMT
Organization: Informix Software, Inc.

In article <1992Aug13.000928.12631@unidus.rz.uni-duesseldorf.de> heisen@convex.rz.uni-duesseldorf.de (Henner Eisen) writes:
>In article <1992Aug12.102140.5231@nntp.hut.fi> samu@lammio.hut.fi writes:
>>I have been wondering... It seems first that there are more pairs of
>>real numbers than real numbers, but is it really so? And if not, I would
>>like to see a bijective mapping f:R->R^2.     ...
>
>Such mappings exist! To construct a mapping f(x,y) = z  choose a
>unique decimal representation of x and y and then merge the digits.
>
>i.E.:
>x =  1 0 0 2. 7 1 8 2 8 2 . . . . . .
>y =   3 0 3 .1 4 1 5 9 3 . . . . . . 
> 
>z =  1300032.174118529832............
>
>This will be bijective for non-negative real numbers. In order to obtain a
>bijective mapping R <-> R^2 this has to be combined with a bijection
>which maps real numbers to non-negative real numbers (right now, I
>don't remeber by heart how this is done, but it is possible).

I believe that there is even an everywhere-continuous 
bijective mapping from the unit line to the unit square.
Newsgroups: sci.math
From: orourke@sophia.smith.edu (Joseph O'Rourke)
Subject: Re: Mapping points in space to a plane
Organization: Smith College, Northampton, MA, US
Distribution: usa
Date: Thu, 20 Aug 1992 19:20:10 GMT

In article <BtAIpG.5pL@wpi.WPI.EDU> jac@cs.WPI.EDU (Jeffrey A Choate) writes:
 >One suggestion is to find the orthogonal projection 
 >of the point on the plane.  Another suggestion is to 
 >use the normal to the plane (1,1,1), and starting at 
 >the point follow the normal vector back until it 
 >intersects the plane, and use the intersection point.

I believe the second suggestion is equivalent to the first.

 >Are any of these ideas good?  

Depends on what properties you desire for your projection.

 >Is there an algorithmic way of doing this?

If your point is (a,b,c), you want (a,b,c) + t(1,1,1) to lie on
the plane.  So (a+t) + (b+t) + (c+t) = 1, which implies that
t = [1 - (a+b+c)]/3.  So, e.g., the point (a,b,c) = (2,3,5) leads 
to t = -3, mapping to (-1,0,2).
Newsgroups: sci.math
From: ramsay@unixg.ubc.ca (Keith Ramsay)
Subject: Re: mathematician's marrying ages.
Keywords: Abel, Galois 
Organization: University of British Columbia, Vancouver, B.C., Canada
Date: Fri, 14 Aug 1992 01:17:58 GMT

In article <1992Aug13.184958.4632@eliot.uucp> andyc@eliot.uucp 
(Andy Collins) writes:
|Galois got shot in a duel as I recall. 

This is true.

|The night before the duel he scribbled all of his
|theory down on paper and handed them to a friend (Who was it?...)
|just before the duel.

The story has been romanticized and exaggerated. For one thing, he
didn't write it all down the night before.

Keith Ramsay
ramsay@raven.math.ubc.ca
Newsgroups: sci.math
From: roach@bikini.wri.com (Kelly Roach)
Subject: Re: u(v^n)w prime puzzle (SPOILER)
Organization: Wolfram Research, Inc.
Date: Fri, 21 Aug 1992 17:32:20 GMT

In article <4796@balrog.ctron.com> wilson@web.ctron.com writes:

     Very nice.   Looks like the second correct proof.

				Kelly
From: crhodes@spam.ua.oz (Colin Rhodes)
Newsgroups: sci.math
Subject: e-mail
Keywords: simms, mckay
Date: 22 Aug 92 00:49:14 GMT
Organization: Stats Pure & Applied Maths, Uni of Adelaide, Australia

Hi.

I'm trying to get the e-mail addresses for the following two group theorists:

   Charles Simms  -   still at Rutgers?

   John McKay     -   "      " Concordia?

If you can help, thanks!


C. Rhodes
(Pure Maths Adelaide)
e-mail : crhodes@spam.maths.adelaide.edu.au
Newsgroups: sci.math
From: orourke@sophia.smith.edu (Joseph O'Rourke)
Subject: Re: min distace between a point and a polygon
Keywords: min distance
Organization: Smith College, Northampton, MA, US
Date: Tue, 18 Aug 1992 16:20:31 GMT

In article <1992Aug14.142300.18732@imada.ou.dk> hamid@imada.ou.dk (Hamid Sarabi) writes:
>I have a point and a convex polygon(set of ordered points). 
>How can I find the distance, if the projection of the point is outside of polygon.

	Unless you have a very large number n of polygon vertices,
the distance between the exterior point p and the polygon can best
be found with the straightforward O(n) algorithm:  Compute the
distance from p to each edge e of the polygon.  The distance from
p to e is either the length of the perpendicular from p to the
line containing e, if the foot of that perpendicular lies on e,
or the distance from p to the closest endpoint of e.
	If your n is very large, it might be worth implementing
a binary search on the edges to achieve O(log n) performance.
From: wilson@web.ctron.com (David Wilson)
Newsgroups: sci.math
Subject: Beloved Books + Request
Date: 19 Aug 92 14:03:58 GMT
Reply-To: wilson@web.ctron.com (David Wilson)
Organization: Cabletron Systems INc.
Originator: wilson@web


    I just felt compelled to mourn publically over a couple of dearly
    departed math texts.  One was Rudin's Analysis, which I lent to a
    classmate to peruse, which perusal has been going on now for about
    10 years.  The second was Spivak's Calculus, which I lent to a
    trusted precocious young friend.  This friend subsequently died in
    a tragic accident, and his parents would not part with the book.

    The moral is:  I learn the hard way.

    Anyway, I am now looking to acquire a text on set theory.  It
    should be somewhat advanced and fairly thorough.  It should contain
    an axiomatic development of a good set theory (preferably ZFC), and
    discussions of the recurrent topics (e.g., Russell's Paradox, AC,
    naive set theory, alternate set theories, etc).  You know, one of
    those books that will in future years become a good friend.

    Please email me with suggestions.


-- 
David W. Wilson (wilson@ctron.com)

Disclaimer: "Truth is just truth...You can't have opinions about truth."
- Peter Schikele, introduction to P.D.Q. Bach's oratorio "The Seasonings."
From: kiran@gacvx2.gac.edu
Newsgroups: sci.math
Subject: A Non-Cantorian Set Theory question
Date: 12 Aug 92 11:34:15 -0600
Organization: Gustavus Adolphus College, St. Peter, Minnesota

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 following:

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?
Newsgroups: sci.math
From: cc869@cleveland.Freenet.Edu (Udo Sprute)
Subject: Re: Ellipsoid formula wanted
Organization: Case Western Reserve University, Cleveland, Ohio, (USA)
Date: Wed, 12 Aug 92 12:09:02 GMT


A friend of mine was interested at this problem too. He found
some referrences from Carlsson in Duke Journal of Mathem. about
1960. He used Hypergeometrc series as I remember. Another
good articel is in Canadian Mathematical Journal of D.Lehmer in
1950. He compares different approx. formulaes. But he only assume
s that the excentricities are small :).
My friend Torsten want an approx. formula with minimize the rel.
error for all excentricities! BTW. If two of the axis of the
ellipsoid are equal you can solve the surface integral algebraic!
Good luck for research :)
From: clong@remus.rutgers.edu (Chris Long)
Newsgroups: sci.math
Subject: Re: Puzzles
Date: 14 Aug 92 06:31:41 GMT
Organization: Rutgers Univ., New Brunswick, N.J.

In article <1992Aug11.154417.26681@galois.mit.edu>, John C. Baez writes:

> Sorry you found it painful.  Of course I was not only saying this but
> proving it.  I was quoting the Mathematical Intelligencer's solution,
> which I think some might find easier to understand than the other
> approach, which is to note that {cm mod 1} must have a cluster point
> since the unit interval is compact.  Of course that approach is
> nonconstructive.   

But it can be made constructive (mirroring the same approach you gave).
For finding actual examples, it is also more important to know that
{c*m} is uniform modulo 1 than it would be to know this algorithm.
-- 
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_
Newsgroups: sci.math
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: Is Card(R)=Card(R^2)?
Date: 13 Aug 1992 07:54:35 -0400
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu


>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.

-- 
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
Newsgroups: sci.math,sci.physics