HDTenEightyP/NetNews huggingface dataset:
From: jac@ds8.scri.fsu.edu (Jim Carr)
Newsgroups: sci.math,sci.physics
Subject: Re: Help me deal w/ infinity
Date: 11 Jan 93 14:54:06 GMT
Reply-To: jac@ds8.scri.fsu.edu (Jim Carr)
Followup-To: sci.math
Organization: SCRI, Florida State University

In article <1992Dec23.030309.125@front.se> samuel@front.se writes:
>
>If this argument doesn't help, why don't ask your friends exactly how much 
>they think that 0.999999... differs from 1.

Good suggestion.  I think this will help these poor souls examine the 
unexamined assumption that are leading them to have trouble with the 
proof, which is a very real difficulty with the fact that multiplying 
.999.... by 10 does *not* change the number of 9s after the decimal 
point!  I would love to overhear their conversation: 

The difference is 1 times 10 to the something power, lets see... hmm, 
it would seem that whatever power of 10 I choose, there is a larger 
power I could use.... how many 9s are there again? 

--
J. A. Carr                                    |  "The New Frontier of which I  
jac@gw.scri.fsu.edu                           |  speak is not a set of promises
Florida State University  B-186               |  -- it is a set of challenges."
Supercomputer Computations Research Institute |   John F. Kennedy (15 July 60)
From: dak@rama.informatik.rwth-aachen.de (David Kastrup)
Newsgroups: sci.math
Subject: Re: Rounding Rules
Date: 5 Jan 93 14:05:39 GMT
Organization: Rechnerbetrieb Informatik - RWTH Aachen
NNTP-Posting-Host: rama.informatik.rwth-aachen.de

kraai4712@iscsvax.uni.edu writes:

>In article <1992Dec23.140148.21009@hubcap.clemson.edu>, steve@hubcap.clemson.edu ("Steve" Stevenson) writes:
>> In article <1992Dec20.003018.14325@sol.ctr.columbia.edu> shaw@toadflax.UCDavis.EDU (Rob Shaw) writes:
>>>What is the rationale behind the following rounding rule?
>>>
>>>when dealing with 5's followed by all zero's, check the
>>>next digit to the left. If it's even, round down; odd,
>>>round up.
>>>
>>>For example both 1.13500 and 1.14500 are 1.14 to 3 places.

>My personal favorite rounding rule is to round anything that has {0,1,2,3,4} in
>the "rounding place" "down" and anything that has {5,6,7,8,9} "up".  So as in
>the previous example, 1.13500 would be rounded to 1.14 and 1.14500 would be
>rounded to 1.15.

>To this my teachers always gasped that this method was biased, and no amount of
>pursuasion using the above-mentioned sets could pursuade them.

>I have come to believe that the people who thought this was biased believed
>that anything that had a zero digit in the place to be rounded couldn't be
>rounded or didn't need to be rounded or some other mental block.

One problem with your rounding method is that rounding errors might add up.
So, successive rounding of 1.44445 yields 1.4445, 1.445, 1.45, 1.5, 2.0.
Rounding to nearest even will, when doing successive rounding, never
have an error more than half of the then LSB. Also, there are SOME
more properties of the real group that hold valid, making numerical
computations slightly more reliable. See Knuth, Seminumerical Algorithms
(Art of comp. progr., Vol 2) for reasons and rationalizations with proofs.
Newsgroups: sci.math
From: eng10524@nusunix1.nus.sg (RAMASWAMI VISHWANATH)
Subject: simultaneous equations...solutions
Organization: National University of Singapore
X-Newsreader: TIN [version 1.1 PL6]
Date: Mon, 11 Jan 1993 23:46:11 GMT

[ Article crossposted from comp.lang.fortran ]
[ Author was RAMASWAMI VISHWANATH ]
[ Posted on Sun, 10 Jan 1993 19:19:52 GMT ]



Dear nettors , 
	writing a program for  a fortran77 project , i have run into a
bad spot . the prg requires a matrix subroutine to calculate values for
a set of equations . but the equations are not in a square matrix form .
most books i have referred to give solutions to n x n matrices only . 
this prg of mine ,( to calcualte deflections of beams under different
loading conditions) uses finite differentiaiton to get a set of
equations . thus the equations are of the form 
		k = x + y + z

and so on giving me a n x 3 matrix .
	however i justrealised that this is a tri-diagonal matrix 
since the equations are derived from finite differentiation .
thus the matrix looks like :
		0  -2  1  0 .....
		0  1  -2  1  0  ...
		0  0  1  -2  1  0 ....

since gaussian ,i believe is nottheleast cumbersome way to go about this
could someone suggest a good method ? are there any ideas for a fortran
prog. or sub-routine ?


thanx

Vishwa
Newsgroups: sci.math
From: ghica@fig.citib.com (Renato Ghica)
Subject: matrix manip. info
Originator: ghica@duck
Organization: Citibank IBISM
Date: Mon, 4 Jan 1993 14:31:16 GMT



Anyone know (or have available) public domain software
(C/C++ source preferred) that deals with matrix manipulation ?

Specifically, I'm looking for functions that return the determinant
and rank of an M x N matrix.


thanks to all replies
-- 

"delete *this"

"These views are my own. / Mail me or Flame me"
Newsgroups: sci.math
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Re: I imagine this comes up all the time...
Keywords: unique factors
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Tue, 5 Jan 1993 00:36:42 GMT

In article <1993Jan3.003521.26610@tessi.com> ronl@tessi.com (Ron Lunde) writes:
>I'm not a mathematician, so I'd appreciate it if anyone could point me to
>any references on this topic (that I might be able to understand :-)).
>
>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 unique factors (I guess I'm probably using "factor" in a funny way here,
 
Mathematicians usually include 1 and M as factors. Let 

N = p1^a1 * p2^a2 * p3^a3 * ....

be the canonical prime factorization of N. Then, the number of
factors is (a1+1) * (a2+1) * ....

If you don't want to include 1 and N, then subtract 2.

For your problem, we want (a1+1)(a2+1)... - 2 = 15,  so (a1+1)(a2+1) ... = 17
This leads to a1+1 = 17, or a1 = 16.

The smallest such N is 2^16. Indeed, 2 through 2^15 are the factors.
 
If you allow 1 and N as factors, we have (a1+1)(a2+1) = 15;
so either a1 =2 and a2 = 4, giving 2^2 * 3^4 = 324  or  a1 = 14 giving
2^14.  

It is easy to verify that 324 has 15 distinct factors. Note that for
ANY number to have an odd number of distinct factors it must be a 
square.


>since I'm not referring to primes, necessarily).  Obviously there *is* such
>a number, since we can construct at least one by multiplying the first N
>primes.  It seems odd that the first ones are all fairly small, but I can't
>find the 15th (at least nothing smaller than 614889782588491410):
>
 
rest deleted....
--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: sum of eigenvalues of a covariance matrix = trace ?
Date: 10 Jan 93 15:37:44 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <1993Jan9.194845.8567@noose.ecn.purdue.edu> kavuri@lips1.ecn.purdue.edu (Surya N Kavuri ) writes:
>  Is the sum of the eigenvalues of a covariance matrix equal to 
>   its trace ?


Yes. The sum of the eigenvalues _is_ the trace for any square matrix. I would
go so far as to define the trace of a nonsquare matrix as the sum of the
eigenvalues, but I have never run across a need for this item.

Later,
Andrew Mullhaupt
Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Combinatorical problem
Organization: Computer Science Department,  Stanford University.
Date: Wed, 13 Jan 1993 05:45:25 GMT

In article <1j04niINNe98@news.cerf.net> jcbhrb@nic.cerf.net (Jacob Hirbawi) writes:
>I know of a form that has a number of nice features. (I'm not sure how it
>relates to the two forms suggested by Vaughan Pratt but chances are good it's
>a close relative). I'll look at permutations of degree 4 but all the results
>are easily extended:
>
>First let the transpositions T(4)={a1,b1,b2,c1,c2,c3} be defined by:
>
>    a1 = (1,2),   b1 = (1,3),    c1 = (1,4),    ...
>                  b2 = (2,3),    c2 = (2,4),
>                                 c3 = (3,4),
>then every permutation can be written uniquely as
>
>     (ai^ri)(bj^rj)(ck^rk)  with     ri,rj,rk = 0 or 1
>                            and i=1,j=1 or 2,k=1,2, or 3, ...

This coicides with my first form, if both the permutation and the
string of generators are read in the opposite order to mine.  The ci's
correspond to the first transposition in my scheme, and rk=0 just when
A1=1 in my notation (A1 A2 ... An).  And so on with 0 or 1 instances of
bj, then 0 or 1 of ai.

Since posting my message it occurred to me that there is a universal
optimal algorithm: just keep transposing pairs from the same cycle as
long as there exist nontrivial cycles.  This is optimal since each
transposition breaks its cycle into two cycles.  Furthermore it is
universal in the sense that every optimal algorithm is a special case
of this, since every transposition of an optimal run must break a cycle
into two cycles at each transposition, the remaining distance being n-c
where c is the number of cycles remaining.

>There is a connection which is either superficial or very deep (sometimes it's
>hard to distinguish between the two ;-) ). These are also connected to 
>semi-simple Lie algebras.

Extremely interesting.  I'd been hoping to learn about Lie algebras,
now I have additional motivation *and* it suddenly looks a lot less
intimidating.  Thanks!
-- 
Vaughan Pratt				There's no safety in large cardinals
Newsgroups: sci.math
From: ledwards@leland.Stanford.EDU (Laurence James Edwards)
Subject: Re: High Prices of Math Books. I am pissed.
Organization: DSG, Stanford University, CA 94305, USA
Date: Sun, 10 Jan 93 12:39:35 GMT

In article <93008.053113DLVGC@CUNYVM.BITNET>, Dimitri Vulis <DLVGC@CUNYVM.BITNET> writes:
|> [...]
|>
|> 3. 'Most' publishers of math books pay the author either no royalty
|> or a symbolic royalty.  At the same time, they insist now that the
|> authors turn over either a camera-ready MS or a diskette with TeX
|> source.  In the pas, typesetting a math book by hand was a major cost;
|> now that the cost has shifted to the authors, the prices continue to
|> rise.
|> 
|> 4. A friend of mine, who runs a publishing business, claims that the
|> cost of printing 1,000 hard-bound 200-page books on good paper would
|> be about $4--6 a piece. The prohits the publishers rake in
|> are enormous.

Yes, a friend of mine had a book of his (computer science not math) published a
couple years back, the publisher told him that production costs would be about
50 cents a piece for paperback and about $1.50 a piece for hardback. If I
remember correctly the book was between 100-200 pages and I don't know how many
were printed. He gave them a tape with camera ready PostScript source. They
gave him 10k up front and some small royalties. Their only other direct cost
was to pay an artist to do the the cover artwork. In any case the paperback
version costs $35 at the book store. So these guys don't have to sell too many
books to cover their initial cash outlay (of course they do have some 
unknown overhead in doing business).

I don't know about everyone else but I was amazed that the difference in
production costs for paperbacks and hardbacks was so small given the price
differential seen in bookstores. Ahhh, the beauty of supply and demand!
Capitalism, ya gotta love it.

Larry Edwards
Newsgroups: sci.math
From: rivin@SAIL.Stanford.EDU (Igor Rivin)
Subject: Re: Zadachka: pro sifilitika
Organization: Computer Science Department,  Stanford University.
Date: Tue, 5 Jan 1993 04:17:13 GMT

In article <1993Jan3.134333.18958@husc3.harvard.edu> zeleny@husc10.harvard.edu (Michael Zeleny) writes:
>In article <C0AFDG.4xx.1@cs.cmu.edu> 
>smir+@CS.CMU.EDU (Yury Smirnov) writes:
>[...solution omitted...]
>I would like to see references to the generalized version of this problem.
>

See Ilan Vardi's book "Computational Recreations (in Mathematica)",
where a chapter is devoted to the "Condom Problem", and the sharpest
result is obtained.




Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: proof wanted 2
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Fri, 8 Jan 93 21:18:09 GMT

In article <1993Jan8.195646.1694@cc.umontreal.ca> cazelaig@ERE.UMontreal.CA (Cazelais Gilles) writes:
>
>                                                       n
>Is it true that if  C  is a nonempty closed subset of R  and x is a point not
>in  C  that there exists a point c in C that is closest in C to x.
> 
>i.e. such that:   |x-c'| >= |x-c| for all c' in C.
> 
>If it is true I would appreciate if someone could give me a proof
>of the result.

Sounds like a homework problem, but I'll give you a big hint, yes it's
true, and you get the point c by taking a limit.
From: aa783@cleveland.Freenet.Edu (Mark Spaeth)
Newsgroups: sci.math
Subject: A simple (?) integral
Date: 10 Jan 1993 07:37:40 GMT
Organization: Case Western Reserve University, Cleveland, OH (USA)
Reply-To: aa783@cleveland.Freenet.Edu (Mark Spaeth)
NNTP-Posting-Host: hela.ins.cwru.edu


Considering 1,000,000 minds are better than one, I thought I'd post this
wonderful problem...

  _    ______
 (    /
 _) `/ tan x   dx


Obviously the normal substution t=tan(x/2) won't work since this is no a
rational function of since and cosine, and integration by parts doesn't
look too promising...

Mail ranging from insight to a solution, a complete solution, or this is
not integrable in elementary functions because ________ would be greatly
appreciated...

Thank you.

Newsgroups: sci.math
From: yeomans@austin.onu.edu (Charles Yeomans)
Subject: Re: Frankly,my dear......was: Fermat's Last Theorem
Date: Fri, 8 Jan 1993 16:23:34 GMT
Distribution: usa
Organization: Ohio Northern University

In article <1993Jan7.171719.28657@infodev.cam.ac.uk>, gjm11@cus.cam.ac.uk (G.J. McCaughan) writes:
> [stuff omitted]

>  * Work on FLT was one of the big motivators for the theory of ideals. I don't
>    call that trivial, boring, or even "recreational".
> 
It's not so clear that this is historically accurate.  Kummer was
motivated to introduce ideal numbers - out of which came the theory of
ideals, etc. - as a consequence of his work on higher reciprocity laws-
a subject which was intensely studied in the 19th century, is largely
ignored today because these laws are now a part of class field theory.
I believe it was while studying reciprocity that Kummer was forced to
consider problems of nonunique factorization.  On the other hand, it 
was Lame who proposed the idea of factoring the Fermat equation over a
cyclotomic field, but who didn't see that there was a problem with
unique factorization.

Charles Yeomans


Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: wanted: diff. criterium for pureness of tensors.
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Mon, 11 Jan 93 20:33:44 GMT

In article <1993Jan11.115730.42655@urz.unibas.ch> kullmann@urz.unibas.ch (Peter Kullmann) writes:
>
>Is there a differentiable criterium for the pureness *) of tensors in the 
>outer tensor algebra over a real vector space? I.e. a function 
> 
> f:Alt(k,V) ---> R differentiable
>
>such that if s \in Alt(k,V): f(s) = 0 iff s is pure.
>
>This has of course to do with Grassmanians, and what I actually want is to
>have Grassmann (n,k) as a level surface in Alt(k,R^n). I doubt it very much
>that this is possible, so an argument for the contrary would be welcomed as
>well:-)

Such a function exists in the complex case (vector spaces over
the complex numbers) - I don't know if you are asking the real case to
be deliberately difficult, and I don't know if the real case is actually
harder, but I'll tell you how to do it for the complex case - from some
lecture notes by Guillemin.

What you call pure tensors he calls "decomposable."  Pick a basis e_i
for V and the dual basis e^i for V*, and let e^I for any multiindex I =
(i_1,...,i_k) be the exterior (or wedge, or outer) product e^{i_1} x ...
x e^{i_k}; here I'm using x for exterior product.  Then s is
decomposable iff for all I, iota(e^I)s x s = 0.  Here iota(v)s is the
interior product of v (in the exterior algebra over V*) and s (in the
exterior algebra over V).  

The conditions iota(e^I)s x s = 0 are a bunch of quadratic equations in
the components of s.  So we have found a *bunch* of functions that *all*
vanish precisely on the decomposable tensors.  If you really need *one*
function that vanishes precisely on the decomposable tensors, take all
these functions, take the squares of their absolute values, and add them
up.

Feel free to ask if some of the above doesn't make sense.  In
particular, the interior product of something in the exterior algebra
over V* with something in the exterior algebra over V is a notion that's
not very commonly used, though it's an obvious generalization of the
interior product of something in V* with something in the exterior
algebra over V.
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: Fields Medal Winners
Date: 9 Jan 93 17:00:37 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <erwin.726504145@trwacs> erwin@trwacs.fp.trw.com (Harry Erwin) writes:
>This impression is associated with one of those stories. I understand
>Artin, Atiyah, and Bott were the first three at the math tripos one year
>at Oxford (1950?). Apparently it made quite an impression.

I'm a bit surprised at the idea that the tripos still existed in 1950,
since Hardy successfully abolished them but did not see 1950. Can
anyone clear this up?

Later,
Andrew Mullhaupt
Newsgroups: sci.math
From: dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott)
Subject: Matlab question
Organization: Electrical and Electronic Eng., University of Adelaide
Date: Wed, 13 Jan 1993 01:43:32 GMT


Can a line in a .mat file be commented out?

I tried % and it didn't work.



BTW, how is the creation of the matlab newsgroup going?
What's the vote count so far?
From: wbs@vax.oxford.ac.uk
Newsgroups: sci.math
Subject: Re: factorization in commutative rings
Date: 6 Jan 93 12:52:03 GMT
Distribution: sci.math
Organization: Oxford University VAX 6620

In article <HAMMOND.93Jan3134111@annemarie.albany.edu>, hammond@csc.albany.edu (William F. Hammond) writes:
> In article <Jan.3.02.05.44.1993.24643@spade.rutgers.edu>
>    cadet@spade.rutgers.edu (Uniquely TiJean) writes:
[....]
 
>> Well, Given D an integral domain 
>> 
>> Then D = euclidean domain ==> D = principal ideal domain ==> D = factorial 
>> 								    domain.
>> 
>> I am looking for counterexamples 
>> 
>> B) D= princ. idl. domain doesn't imply D= euclidean domain.
>> 
>>    Well, I found in Hungerford ( Algebra ) 
>> 
>>    the following  Z( (1+sqrt(-19)) / 2 )
>> 
>> Question: How come? I have no cue as to why the above domain isn't euclidean.
> 
> Is there a standard definition of "Euclidean", i.e., of what it means to
> have a ring in which there is a division algorithm?  Anyway, that is not
> a problem here.
> 
> Let  w = (1+sqrt(-19))/2 ,  R = Z[w] = Z + Zw , and  K = Q(w) = Frac(R).
> In this context "Euclidean" means that given  a, b  in  R  with  b  not
> 0,  one can find  q, r  in  R  such that  (i)  a = qb + r   and
> (ii)  Nm(r) < Nm(b),  where  Nm(x)  is the product of  x  and its
> conjugate.  (Note:  Nm(x) > 0  for  x  not  0.)
> 
> "Euclidean" is equivalent to the statement that given an element  x  of
> K  there is an element  a  of  R  such that  Nm(x-a) < 1.
 
Am I being very silly in not seeing why there are not other 
candidates for the Euclidean function? 
(If so please tell me why.)

[...]
 
> Good luck with your qual.
> ----------------------------------------------------------------------
> William F. Hammond                

B.
From: tanm@bio1.bst.rochester.edu (Martin Tanner)
Newsgroups: sci.math
Subject: postdoc positions
Date: 5 Jan 93 14:49:54 GMT
Organization: University of Rochester (Rochester, NY)


The Department of Biostatistics at the University of Rochester invites
applications for NIH funded postdoctoral positions, beginning 6/1/93.
Post-doctoral fellows will participate in the design and analysis of clinical
and epidemiological studies in cancer, AIDS and environmental health, as  
well as conduct their own independent research.  These positions require
permanent residence in the US or US citizenship.  Postdoctoral applicants
must possess a PhD or equivalent.  Contact:

Martin Tanner
Dept of Biostatistics - Box 630
University of Rochester Medical Center
60l Elmwood Ave
Rochester NY l4642
tanm@seneca.bst.rochester.edu
Newsgroups: sci.math
From: ara@zurich.ai.mit.edu (Allan Adler)
Subject: Re: Job Application Skills
Organization: M.I.T. Artificial Intelligence Lab.
	<1993Jan9.194557.10082@CSD-NewsHost.Stanford.EDU>
	<93011.175039U53644@uicvm.uic.edu>
Distribution: sci
Date: Tue, 12 Jan 1993 04:19:30 GMT


Joseph Dunphy has succeeded in astonishing me with his ability to fabricate
a complete fantasy about my problems and their solutions based on no
real information and then to believe in it enough to post it on the net.

I believe I am too astonished to be outraged, but I think I will get
over that.

Allan Adler
ara@altdorf.ai.mit.edu
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: Two (I think) interesting Problems
Date: 7 Jan 93 17:22:14 GMT
Organization: U of Cambridge, England

In article <johnsbra.2@tmlh> johnsbra@tmlh (Havard Johnsbraten) writes:
>
>In article <1992Dec23.134651.7759@neptune.inf.ethz.ch> 
>yoparish@iiic.ethz.ch (Yoav Ilan Haim Parish) poses the problem
>       
>     How can I fold an approximate (regular) pentagon from a 
>     quadratic sheet of paper easily ?
...
> (The McCaughan folding 
>from an A4-sheet wasn't exact either, but also very close.)  

1. It *is* exact, unless I've got my calculations wrong.
2. I don't think you should call it "the McCaughan folding"; I didn't
   discover it. (I don't know who did.)

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
From: cet1@cus.cam.ac.uk (C.E. Thompson)
Newsgroups: sci.math
Subject: Re: Looking for help
Date: 8 Jan 93 15:09:41 GMT
Organization: U of Cambridge, England

In article <1444@kepler1.rentec.com>, andrew@rentec.com (Andrew Mullhaupt) writes:
|> In article <1993Jan4.140128.20155@choate.edu> jburne@spock.uucp (John Burnette)
|> writes:
|> >"Give two numbers, x and y, whose sum is rational and whose product is 
|> >irrational."
|> 
|> >x = .10100100010000....
|> >y = .01011011101111....
|> 
|> >Obviously x+y=1/9 (and, please, let's not start that thread again...)
|> >but I've always been at a lost about x*y.
|> 
|> It isn't entirely clear but I suppose that x is a Liouville* number, in
|> which case it is transcendental.

It wasn't explicitly stated, but I took the chains of zeroes to be increasing
linearly in size, i.e. x = \sum_{n=1}^{\infty} 10^{-n(n+1)/2}. In which case
the gaps aren't big enough to make the rational approximations with denominator
10^{n(n+1)/2} convergents to x, let alone make it a Liouville number.

|> *Or a Thue-Siegel-Roth number, etc.

Same applies.

Chris Thompson
JANET:    cet1@uk.ac.cam.phx
Internet: cet1@phx.cam.ac.uk