HDTenEightyP/NetNews huggingface dataset:
From: tycchow@riesz.mit.edu (Timothy Y. Chow)
Subject: Re: An interesting limit problem.
Organization: None.  This saves me from writing a disclaimer.
Distribution: na
Date: Sun, 26 Jul 92 21:02:41 GMT

In article <24912@dog.ee.lbl.gov> sichase@csa2.lbl.gov writes:

>Then I am disappointed in Arnol'd who should know better about what the
>phrase "the exception proves the rule" means.

Yes, I used to get bent out of shape about this, but I think that from
sheer force of mass misusage the phrase "the exception proves the rule"
has now changed its meaning, and means what everybody thinks it means
(as opposed to what it originally meant).  Personally I think the original
makes a lot more sense, but the new meaning has become so dominant that
the original meaning has practically become a piece of trivia.
-- 
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
Newsgroups: sci.math
Subject: Re: Homeomorphism
From: wft@math.canterbury.ac.nz (Bill Taylor)
Date: 27 Jul 92 11:33:05 +1200
Distribution: world
Organization: Department of Mathematics, University of Canterbury
Keywords: glitch, bicontinuous, hmmm?

In article <_1gmcfj@lynx.unm.edu>, weishaup@vesta.unm.edu writes:
|> I was looking at Gelbaum's book of problems in Analysis (Springer, ~1990),
|> and i found a problem that I don't understand:
|> 
|> 1.)Show that the set [0,1) is homeomorphic to the Real Line...

I checked this out and found the Gelbaum book's problem, (number 8), does
NOT ask for a homeomorphism, but for a continuous map from [0,1) onto  R.
                                       ``````````                ````
This falls just short of being a homeomorphism, of course, as it need not be 1-1.

The solution given stretches out [0,1) increasingly, and folds it to and fro 
onto R in ever-widening zig-zag fashion.  
Every point in R has infinitely many preimage points.
Newsgroups: sci.math
From: sethb@fid.morgan.com (Seth Breidbart)
Subject: Re: What more do you want?
Organization: Morgan Stanley & Co., New York, NY
Date: Wed, 22 Jul 1992 21:35:01 GMT

In article <1992Jul21.190243.16846@galois.mit.edu>
tycchow@riesz.mit.edu (Timothy Y. Chow) writes:
>For a change of pace, here's a dramatization of the frustration that
>existence proofs can sometimes cause.
:
;
>    but I don't have any idea how
>   big C is.  On the other hand, that's not a big problem, because
>   C is computable.
>B: You mean there's an algorithm that will give you the value of C
>   explicitly?
>A: Exactly.

All integers are computable.

Nice post, though.  It does illustrate some concepts that some people
have trouble with.

Seth		sethb@fid.morgan.com
From: weishaup@vesta.unm.edu
Newsgroups: sci.math
Subject: Homeomorphism
Summary: problem from analysis book I don't get
Keywords: glitch, bicontinuous, hmmm?
Date: 23 Jul 92 17:02:50 GMT
Organization: University of New Mexico, Albuquerque

I was looking at Gelbaum's book of problems in Analysis (Springer, ~1990),
and i found a problem that I don't understand:

1.)Show that the set [0,1) is homeomorphic to the Real Line...
At first I thought that this was impossible (The real line is open, the inverse
image of it under a continuous mapping must also be open), but I found that
was not insurmountable (after all, the Real line is also closed), but I don't
understand how Gelbaum's Homeomorphism works... He lets

f:[0,1) -> R

be defined by 

f(x) = (1/(1-x)) * Sin[1/(1-x)]

I don't get this at all... f(x) does not appear to be invertible, so I don't
see how it can be a Homeomorphism.

An explanation would be welcome for this non-homework problem's answer either
thru e-mail or (if the author thinks it merits the attention) through this
newsgroup; Alternate Homeomorphisms would also be handy.

Thanks,,,,
Ben Jones
(weishaup@carina.unm.edu
)



-- 
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
- From the desktop of Benjamin Jones (weishaup@carina.unm.edu)                -
+  "Three Quarks for Mr. Mark!!!"  Albuquerque,NM, USA                        +
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: p-adics (was: Re: High Order Undulation Seeds and Binary Undulants)
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Mon, 27 Jul 92 21:23:26 GMT

In article <1992Jul26.040740.27713@galois.mit.edu> tycchow@riesz.mit.edu (Timothy Y. Chow) writes:
>In article <1992Jul25.230156.26155@galois.mit.edu> jbaez@zermelo.mit.edu (John C. Baez) writes:
>
>>By the way, in the very same issue is an article by Allan Adler, in
>>which he uses p-adics to construct a 27x27x27 magic cube!  (I always
>>knew p-adics would eventually have practical uses.)
>
>An interesting way to look at it.  I think my reaction would be:
>
>I always knew magic squares or cubes would someday be used to illustrate
>the power of some important mathematical concept.
>
>:-)

Yes, the notion of "applications" in mathematics is a curious one.  A
result is interesting if it can be used to prove interesting results,
where the latter "interesting" means "interesting to me already".
Newsgroups: sci.math
From: dfrankow@cs.umn.edu (Dan Frankowski)
Subject: Re: Afraid of the future? (WAS DEREGISTERe: An interesting limit problem.
Organization: University of Minnesota, Minneapolis, CSci dept.
Date: Wed, 29 Jul 1992 14:12:10 GMT

In <1992Jul28.165137.5825@iscsvax.uni.edu> kraai4712@iscsvax.uni.edu
   (jim kraai) writes:

>In article <1992Jul28.191037.28756@gdr.bath.ac.uk>, mapsj@gdr.bath.ac.uk
   (Simon Juden) writes:
>> >                            Mathematica should be viewed as a fancy
>> > calculator (which, essentially, is what it is). Very good and very
>> > useful, BUT undergrads HAVE to learn basic concepts and manipulative
>> > skills before they're let near it. Otherwise they will never become
>> > mathematicians, but rather computer operators..

Formerly an undergraduate math major and now a graduate student in
computer science, I think there could be worse things than to be a
computer operator.  :)

>> > .. lots deleted ..
> .. lots deleted ..

>I would guess that using tools like Mathematica to derive tedious results will
>be viewed much the same way in 50 years as we view grabbing a handheld
>calculator to do square roots today.  It won't be given a second thought.

I certainly hope there will be a second thought!  Mathematica must be
treated with great suspicion!  For instance, the absolute value is not
well-respected:

 - Integrate[ 1/x, x ] = Log[x], not Log[Abs[x]]
 - Sqrt[x*x] = x, not Abs[x]

leading to integrals with square roots sometimes being inaccurate by a
large amount (say, 0.1) that is difficult to spot.  Also, due to its
essentially pattern-matching nature, calculations broken up into
several steps and optimized by hand may be 100 times faster than
simply letting it have its way.

The point is, to use Mathematica, one must know a good bit about how
computers work, how math works, and how Mathematica works.  It's not a
black box at all.

> .. more deleted ..

>People like this should dedicate their lives to safeguarding the past instead
>of preventing the next generation from moving on into the future.

>IMHO

Ouch.  Not too humble.

>jim kraai

>young, progressive undergrad math major who has never used Mathematica in his
>life..

Dan Frankowski

-- 
Dan Frankowski                dfrankow@cs.umn.edu
From: mccolm@darwin.math.usf.edu. (Gregory McColm)
Newsgroups: sci.math
Subject: Re: library cutbacks
Date: 17 Jul 92 21:27:40 GMT
Distribution: sci
Organization: Univ. of South Florida, Math Department

In article <Jul.14.03.38.05.1992.27933@remus.rutgers.edu> clong@remus.rutgers.edu (Chris Long) writes:
>In article <ARA.92Jul13184912@camelot.ai.mit.edu>, Allan Adler writes:
>
>> I have just learned that the library at the University of Rhode Island
>> has told the math department to come up with $3000 of journal
>> subscriptions that the library should discontinue, and that if this is
>> not done, the library will make its own selection.
>
>This is truely sad.  Don't they realize how little $3000 is compared
>to the budget of any university, how much good that $3000 could
>accomplish?  The amount of waste per year at URI must be *at least*
>a thousand times that.
>-- 
>Chris Long, 265 Old York Rd., Bridgewater, NJ  08807-2618
>

 visited UC Davis and UC Berkeley recently, and I noticed that 
a number of journals (including a few major ones) had disappeared.
My own university (University of South Florida) purchased no books 
during the last academic year, and anticipates a 20-25 % journal 
cut this year.  Part of the problem is the outrageous prices for 
books (eg, $ 100 for a 600-page book of photocopy, published, of 
course, by Elsevier) and journals (in my field, Notre Dame J of 
Formal Logic is $ 45 per year, J Symbolic Logic $ 180, Annals of 
Pure and Applied Logic about $ 1000---the fact that the first two 
journals are non-profit and the third put out by Elsevier is 
obviously relevant).  Another problem is the indifference of 
university administration to the libraries---witness UCDavis's 
recent decision to store most old books (>15 years or so) in 
warehouses of varying accessibility.  A third problem is the 
financial problems of the universities.

I have heard proposals like "we should boycott the publishers", 
or "we should set up cheap non-profit electronic journals", or 
"we should cut salaries of administrators".  A few antisocial 
types have suggested that mathematicians (and academics in general) 
publish too much stuff that no one reads, and ought to cut back 
(lies! never!).  One librarian I know told me that when she went 
to a conference, a session by publishers featured executives 
gloating about their profits.

Comments?

-----Greg McColm

QUOTE FOR THE DAY:  Now, Barabbas was a publisher ... .
Newsgroups: sci.math.research
From: Bruce Reznick <reznick@symcom>
Subject: image of map of affine spaces
Followup-To: poster
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Illinois at Urbana
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 24 Jul 1992 14:52:34 GMT

I am looking for a recent and explicit reference to the following:

THEOREM
	Let p_i(x_1,...,x_n), 1 <=i <= m be complex polynomials.  Then either 
(1) or (2) holds:

(1) There exists a non-zero polynomial T  in m variables so that 
	T(p_1(x_1,...,x_n),...,p_m(x_1,...,x_n)) = 0 for all (x_1,...x_n).
	(ALGEBRAIC DEPENDENCE)

		or

(2)  There exists a non-zero polynomial T  in m variables so that, if
(v_1,...,v_m) is a complex m-tuple and T(v_1,...,v_m) != 0, then there exist
(u_1,...,u_n) so that p_i(u_1,...,u_n) = v_1
	(ALGEBRAIC INDEPENDENCE)

 By the way, I know that this is a theorem, as several kind algebraic geometers
have proved for me, and I know that this is a special case of some more
sophisticated mathematics.  I am interested in a source which states the above
as explicitly as possible.  Surely this was done by one of our 19th century
friends.
 I will e-mail a summary of responses on request.

Many thanks,
Bruce Reznick
From: allenk@harry.ugcs.caltech.edu (Allen Knutson)
Newsgroups: sci.math.research
Subject: A noncompact group rep
Keywords: noncompact group, L^2
Date: 20 Jul 92 03:36:16 GMT
Organization: California Institute of Technology, Pasadena
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu

Let G be locally compact, dg a nonzero Haar measure on G.

If G is compact (equivalently, \int_G dg is finite), then L^2(G) with G
acting by translation contains all the reps of G. If G is noncompact, it 
doesn't.

What about the space of functions that are L^2 on compact subsets of G?
That seems another natural generalization of the compact G case, and looks much
"bigger": what does it have?					Allen K.
From: tarokh@server.uwindsor.ca (TAROKH VAHID             )
Newsgroups: sci.math.research
Subject: A Question About Fourier Series
Keywords: L^p convergence of the Fourier Series
Date: 27 Jul 92 19:02:21 GMT
Followup-To: poster
Organization: University of Illinois at Urbana
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu


Dear Readers,

Let f denote a continuous function. By Parseval equality, we know that the
Fourier series of ' f ' converges in L^2 to f. It was told to me that a theorem
of Fefferman gives a similar result for L^p , where p>1.  Is this true?  Second
what can be said if p < 1?  Third is there a function f periodic and continuous
whose Fourier series nowhere converges?  Fourth what could be said about
functions of locally compact groups to the real line?  Is there any theory
similar to Fourier series for them?

              Thank You 
              Vahid Tarokh
Newsgroups: sci.math.research
From: jtrsmith@garnet.Berkeley.EDU ()
Subject: Off-center ensemble average
Originator: jtrsmith@garnet.berkeley.edu
Followup-To: poster
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of California, Berkeley
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 24 Jul 1992 07:57:31 GMT

Hi,
Does anyone know "off-center ensemble average"?
If yes, could you explain it to me and give me some reference?
Thanks.
(please reply to this account if possible.)

Newsgroups: sci.math.research
From: werner@pell.anu.edu.au (Werner Nickel)
Subject: Re: presentation of 2.HJ
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Australian National University
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Thu, 23 Jul 1992 16:24:07 GMT


The argument in my previous posting is not complete because one has to
show that the generator  e  is not trivial. This can be done easily by
doing a coset enumeration of the given presentation over the subgroup
of order 15 generated by c. The index of <c> is 80640 = 2*604800/15.

Werner Nickel

Newsgroups: sci.math.research
From: poonen@digel.Berkeley.EDU (Bjorn Poonen)
Subject: paths and multisets
X-Submissions-To: sci-math-research@uiuc.edu
Organization: U.C. Berkeley Math. Department.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Follwup-To: poster
Date: Thu, 30 Jul 1992 14:45:26 GMT

QUESTION: Suppose you have an n-element multiset S deforming into another
n-element multiset T.  Can you find a path from a given element of S to some
element of T?

More precisely, let M be a topological space and give M^n the product topology.
Let the symmetric group S_n act on M^n by permuting the coordinates, and give
M^n/S_n the quotient topology.  (M^n/S_n is the space of n-element multisets.)
Suppose w : [0,1] -> M^n/S_n is a continous path, and P is an element of the
multiset w(0).  Can one find a path w_1 : [0,1] -> M such that w_1(0)=P and
w_1(t) is an element of w(t) for all t in [0,1]?

Assume that M has nice properties, if it helps.  I need the case M=R^2 (i.e.,
the plane).  (The application is the following: take all polynomials
	1 + e_1 z + e_2 z^2 + ... + e_n z^n
where each e_i is 0 or 1, and n is arbitrary.  Let W be the set of all complex
zeros of such polynomials.  I have proved that the closure of W is connected.
If the question above has a positive answer, I can prove that it is path
connected as well.)

More generally one can ask whether the path w : [0,1] -> M^n/S_n can always be
decomposed into n paths w_1,w_2,...,w_n in M.  This is equivalent to asking
whether the path can be lifted to a path in M^n.  (This would certainly imply a
positive answer to the first question.)

Here is what I know so far.  If M=R this general result is true.  (Let w_k(t)
be the k^th largest element of w(t).)  If M=R^2 and n=2, the result is true.
(The map M^n -> M^n/S_n is a covering projection if one deletes the places
where two elements of the multiset coincide, so one can lift the path on each
(open) connected component of the set of t for which w(t) has distinct
elements.  For n=2, this suffices, since for the remaining values of t, there
is only one possible lift of w(t).)

Please e-mail solutions, useful references, or comments to me at

	poonen@research.att.com		before August 24
	poonen@math.berkeley.edu	after August 24

Bjorn Poonen
From: werner@pell.anu.edu.au (Werner Nickel)
Newsgroups: sci.math.research
Subject: Re: presentation of 2.HJ
Date: 23 Jul 92 06:29:00 GMT
Organization: Australian National University
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu


The following is a presentation for the double cover 2.HJ of HJ:

           < a, b, c, d, e | c = ab, d = ab^(-1)e, a^2 = e,
	                     b^3 = e, c^15,
		             (c^4d^2c^3d^3)^2 = e,
	                     (c^3d(c^2d^2)^2)^2 = e,
	                     [a,e], [b,e], [c,e], [d,e], e^2 >

Comparing this presentation with the ATLAS presentation for HJ shows
that HJ.2/<e> = HJ. By computing the largest abelian quotient one
shows that the group above is perfect. Therefore the group given by
the presentation above is the double cover of HJ.2.

Werner Nickel
Mathematics Research Section
Australian National University
Canberra
Newsgroups: sci.math.research
From: Bruce Reznick <reznick@math.uiuc.edu>
Subject: Re:  image of map of affine spaces
Followup-To: poster
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Illinois at Urbana
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 24 Jul 1992 20:06:08 GMT

PS: My full email address is reznick@math.uiuc.edu
From: lee@math.washington.edu (John M. Lee)
Newsgroups: sci.math.research
Subject: Re: Negatively curved conformally flat manifolds
Date: 24 Jul 92 00:07:05 GMT
Organization: Mathematics Dept., U. of Washington
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu

In article <BruE8L.AnD@watserv1.waterloo.edu> yang@fields.waterloo.edu (Deane Yang) writes:

   Here's an easy sounding question for differential geometers
   that I can't answer off the top of my head:

   Is a negatively curved conformally flat manifold necessarily
   isometric or diffeomorphic to a hyperbolic manifold?

Hi Deane--

Here are a couple of simple observations that might be useful.  

First, it certainly need not be isometric to a hyperbolic manifold: just
multiply a hyperbolic metric by a function very close to 1 in the C2 norm,
and the resulting metric is conformally flat and still negatively curved.

Second, it may not even be conformally diffeomorphic to a hyperbolic
manifold.  An example is the catenoid, which is conformally covered by the
plane but not by the disk.   

I don't know the answer in the diffeomorphism category, but I suspect it
might not be easy.

Cheers!

Jack Lee
Newsgroups: sci.math.research
From: yang@fields.waterloo.edu (Deane Yang)
Newsgroups: sci.math.research
Subject: Negatively curved conformally flat manifolds
Date: 23 Jul 92 12:48:20 GMT
Organization: Fields Institute
X-Useragent: Nuntius v1.1
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu


Here's an easy sounding question for differential geometers
that I can't answer off the top of my head:

Is a negatively curved conformally flat manifold necessarily
isometric or diffeomorphic to a hyperbolic manifold?

Deane Yang
Polytechnic University
(visiting the Fields Institute until 8/31/92)
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math.research
Subject: zeta functions
Date: 21 Jul 92 05:54:02 GMT
Followup-To: poster
Organization: M.I.T. Artificial Intelligence Lab.
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu



Does anyone have software for computing the zeta functions of algebraic
varieties? I'm particularly interested in the case of modular curves X(N)
and the local factors over certain finite fields.

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math.research
From: amstanko@athena.mit.edu (Aleksandar M Stankovic)
Subject: probability distributions with bounded unit support
Followup-To: poster
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Massachusetts Institute of Technology
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Wed, 29 Jul 1992 05:57:33 GMT

Hello,

As a part of an optimization problem in random modulation, I need
an efficient description (paramatrization) of the set of all
probability distributions (cumulative distributions) with a
BOUNDED (unit) support.

Specifically, I am looking at a set of characteristic functions (in
probabilistic language, Fourier transforms of prob. distributions) and need a
way to optimize a convex functional over it. If need be, I am ready to shrink
the domain by considering only distributions which are absolutely continuous,
or only the discrete distributions.

Any pointers to literature will be graetly appreciated. I am familiar with 
books by Lukacs, Feller and Kawata. If there is interest, I'll be glad to
post a summary.

Regards,

                               Alex Stankovic
                     
                              amstanko@athena.mit.edu    


Newsgroups: sci.math.research
From: rossini@biosun4.harvard.edu (Anthony Rossini)
Subject: Cramer'-Wold device
Followup-To: sci.math.stat 
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Biostat Dept, HSPH, Boston MA, USA.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 24 Jul 1992 16:25:13 GMT



The Cramer'-Wold device is useful for showing the asymptotic normality of
estimators, for a fixed dimension K, by saying that if all linear
combinations of components of a vector are asymptotically normal, then the
vector is asymptotically normal as well.  I've been trying to prove (no luck
yet, either way) that it holds for K -> \infty  (i.e. the number of
parameters estimated goes to infinity).  Does anyone have a reference,
ideas, or a counter-example for this?

(I'm not sure where this problem really belongs, but it seems more like
probability than statistics at this point!)

thanks,
-tony
--
Anthony Rossini       -       rossini@biostat.harvard.edu
Department of Biostatistics, Harvard School of Public Health
677 Huntington Ave, Boston MA 02115  617-432-1056

Newsgroups: sci.math
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Re: Prime quadruplet records?
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Tue, 28 Jul 1992 15:13:05 GMT

In article <AeRJFQW00WBNI1kVwn@andrew.cmu.edu> ow0a+@andrew.cmu.edu (Oswald Wyler) writes:
:A quadruplet of primes occurs when four out of five consecutive odd numbers
:are prime.  Except for the first two quadruplets, 3,5,7,11 and 5,7,11,13,
:all quadruplets of primes are of the form 30n + 11, 30n + 13, 30n + 17,
:30n + 19.  It is well known that there are only finitely many prime
:quadruplets.
 
Where did you get your information?

It is NOT well known that there are only finitely many because almost
certainly there are infinitely many. This is based upon the prime k-tuples
conjecture (which in turn is a special case of Schinzel's conj. which in turn
is a special case of the Bateman-Horn conj.)

Heuristically, up to N, one should expect about 1/phi(30) N/(log N)^4 such
quadruplets.

Since your assertion that there are only finitely many is false your other
questions are a non-sequitur.

:Question 1.  Is the largest prime quadruplet known?
 
Name one. I'll find another larger one very quickly.

:Question 2.  If not, what is the largest known prime quadruplet?

Who knows? The question (IMO) is not very interesting.

:Question 3.  Up to which n (see above) are all prime quadruplets known?

Since all primes up to 10^12 have been tabulated I believe this is the n
you seek.
--
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"
Newsgroups: sci.math