HDTenEightyP/NetNews huggingface dataset:
From: heine@barsoom.nhh.no (Heine Rasmussen)
Newsgroups: sci.math
Subject: CW-complexes and such
Keywords: CW-complexes, function spaces
Date: 13 Apr 92 14:34:10 GMT
Organization: Norwegian School of Economics

I've been self-studying my way trough a couple of texts on algebraic
topology, and have some questions regarding CW-complexes.  Most books
(even Spanier) give the definition, then some examples of CW-complexes
in Euclidean space, and then go on to prove various interesting things
about CW-complexes in general.  This is all fine, but for the work I
am doing, I am mainly interested in function spaces.  And I have REAL
trouble visualizing CW-complexes in such spaces.

So here comes the (possibly stupid) question: Is there any "canonical"
way of showing that a non-Euclidean space is a CW-complex?  By
embedding it in Frechet space/Hilbert cube, or something like that?
Can anyone give me enlightening examples of non-trivial, non-Euclidean
spaces that are/are not CW-complexes?  Is for instance the space of
measurable real functions (bounded between 0 and some value a) on the
unit interval with one of the L^p topologies a CW-complex?  What about
the subset of continuous functions?

Thanks,

-heine
--
Heine Rasmussen  ---  <sam_hr@debet.nhh.no> or <heine@sterling.nhh.no>
___________________________________________________________________________
Center for Research in Economics and Business Administration
The Norwegian School of Economics, N-5035 Bergen, NORWAY
From: rose@fsu1.cc.fsu.edu (Kermit Rose)
Newsgroups: sci.math
Subject: plastic soda bottle water glass
Date: 3 Apr 92 17:56:52 GMT
Article-I.D.: mailer.1992Apr3.125652.27004
Reply-To: rose@fsu1.cc.fsu.edu
Organization: Florida State University
News-Software: VAX/VMS VNEWS 1.3-4

Hey, I would like to construct a hourglass made like you described with 
plastic soda bottles.  I do not have your address so I can not e-mail you.  
I have not yet found a way to look at the beginning of the post so I could 
not read your from line.

Kermit@FSU or rose@fsu1.cc.fsu.edu.bitnet
If you want to be sure I see your response, please e-mail me.
-----------------------------------------------------------------------
This is the signature file of Kermit Rose.

Believing in dichotomies leads to hardening of your logic.

What determines the existence of Free Will?
I strive to believe only what is true. I have faith that whatever is 
true will also be logically consistent and knowing truth will increase my 
capacity to be kind.
Peace is the way to peace.  Hostility is the way to hostility.
Newsgroups: sci.math
From: giulio@alessia.dei.unipd.it (Giulio Rigo 345123/IL)
Subject: ARE equations
Originator: giulio@alessia
Organization: D.E.I. Universita' di Padova (Italy)
Date: Sat, 11 Apr 1992 11:19:00 GMT



I'm looking for something about the theory of the convergence of the Algebric
Riccati Equation (ARE) with matrices. May anyone tell me where to find 
somethin interesting? Thanx in advance.

                                             Giulio Rigo

                                     giulio@alessia.dei.unipd.it 
                            
 
Newsgroups: sci.math
From: fbagohkh@nuscc.nus.sg (Mark Goh (Dr))
Subject: closed form solution to d.e.
Organization: National University of Singapore
Date: Thu, 9 Apr 1992 04:26:57 GMT

Is there a closed form solution for this d.e.

y' + a(y)^b=1, 0<a,b<1 ?
Newsgroups: sci.math
From: cyeomans@ms.uky.edu (Charles Yeomans)
Subject: Re: need good intro simplical homology
Distribution: usa
Date: Tue, 14 Apr 1992 14:23:43 GMT
Organization: University Of Kentucky, Dept. of Math Sciences
X-Bytes: 

In article <5NQHBYJR@cc.swarthmore.edu> nave@cs.swarthmore.edu (Lee Nave) writes:
>
>     I'm taking an undergraduate seminar in topology.  For the first half of
>the seminar we used Munkres' Topology.  I found it an excellent textbook.
>Now we're working on simplical homology and reading from Armstrong's Basic
>Topology.
>
>     Can anyone recommend a better introductory undergraduate-level text, if
>such a thing exists?  Any advice would be appreciated.
>
>Thanks,
>
>Lee Nave
>nave@cs.swarthmore.edu

If you can find it, I would recommend "Basic Concepts of Algebraic 
Topology" by Fred Croom, now out of print but published in the Springer
UTM series.  You might also try VIck's book on homology.  Or 
go ask Tom Hunter.

Charles Yeomans
cyeomans@ms.uky.edu
yeomans@austin.onu.edu

Newsgroups: sci.math
From: bs@fatima.mitre.org (Robert D. Silverman)
Subject: Re: Prime numbers (Was Re: Lackey again)
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Thu, 2 Apr 1992 18:10:58 GMT

In article <1992Apr1.200612.9103@descartes.waterloo.edu> gjschmid@descartes.waterloo.edu (Greg Schmidt) writes:
:In article <3184@daily-planet.concordia.ca> gsmith@concour.cs.concordia.ca (Gene Ward Smith) writes:
:>In article <!ngjqfj.dani@netcom.com> dani@netcom.com (Dani Zweig) writes:
:>
:>>   It was mentioned on CNN that the new prime number discovered
:>>   recently is four times bigger then the previous record.
:>>				-- John Blasik
:>
:>When we did the previous record, Dan Shanks said it was "just a 
:>fart bigger" than the old record. This is more than a fart, and might
:>be the record for a little longer.
:
:If the new prime number was four times bigger than the previous record,
:then the new prime number is 4 * previous_record, which is not prime. :-)
 
This is a popular misconception. The SIZE of a number is its number of
digits [or number of bits in binary].

Saying one number is 4 times the size of another is saying that it has
4 times as many bits.

:Actually, the _order of magnitude_ (ie exponent of ten when the number is
:in scientific notation) is approximately four times that of the old record
:(somewhere near 10^227 or 10^272, I'm not sure which).

Want to try again??  The new prime is near 10^227831. You are off by a factor
of 1000 in your EXPONENT.
--
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: abc@smoke.brl.mil (Brinton Cooper)
Newsgroups: sci.math
Subject: Re:  Information Theory
Keywords: information theory, texts, gallager,
Date: 16 Apr 92 16:26:51 GMT
Organization: The Ballistic Research Laboratory

I tried e-mail but phnom-penh.berkeley.edu refused connection to an Army
computer.  No surprise, I guess!

 ^]^
 \_/

Anyhow...

   ----- Transcript of session follows -----
421 phnom-penh.berkeley.edu: Connection refused by phnom-penh.berkeley.edu

   ----- Unsent message follows -----
Received: from SMOKE.BRL.MIL by math.berkeley.edu (4.1/1.33(math))
	id AA05409; Wed, 8 Apr 92 11:50:33 PDT
To: william@phnom-penh.berkeley.edu
Subject: Re: Information Theory
Newsgroups: sci.math
Organization: The Ballistic Research Laboratory
Date: Wed, 8 Apr 92 14:40:31 EDT
From: Brinton Cooper <abc@BRL.MIL>
Message-Id:  <9204081440.aa12095@SMOKE.BRL.MIL>


The most readable and thorough introduction to the subject remains
"Information Theory and Reliable Communication" by Robert Gallager,
Wiley, 1968.

_Brint

----- End of forwarded messages
Xref: sparky sci.math:5670 sci.physics:6579 sci.comp-aided:37
From: jac@ds8.scri.fsu.edu (Jim Carr)
Newsgroups: sci.math,sci.physics,sci.comp-aided
Subject: Re: Complex Hermitian eigenvalues
Date: 6 Apr 92 18:33:26 GMT
Reply-To: jac@ds8.scri.fsu.edu (Jim Carr)
Followup-To: sci.math
Organization: SCRI, Florida State University

In article <1992Apr6.165255.17487@gmuvax2.gmu.edu> semmett@gmuvax2.gmu.edu (Steve Emmett) writes:
>
>My preference is to understand why CH doesnot give the results I expect.

I think it is because you made some sort of error...

>The trivial examples is as follows:  let the matrix be
>
>            |  0   i  |
>            | -i   0  |
>
>CH correctly gives the eigenvalues as +/- 1.  Now, put 1, say, in the
>trace.  You would expect the eigenvalues to be 2 and 0.  However, CH
>gives you -.618 and 1.618 (the golden mean).  There is something going
>on that I don't understand.  

I get that 
                   | 1-E  i | 
               det |        | = (1-E)(-E) - (i)(-i) = E^2 - E - 1
                   | -i  -E |

for the characteristic equation.  Now b^2-4ac = 1+4 = 5; E= (1 +/- sqrt(5))/2, 
which is the result CH and the computer gave you.  Granted it is monday and 
I havent done this by hand in a decade, but I do not see where you got 2 and 0.

--
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: andreas@etl.go.jp (Andreas Knobel)
Newsgroups: sci.math
Subject: Re: On knowing who's who (was: Fermat's Last Theorem)
Date: 13 Apr 92 08:06:12 GMT
Organization: Electrotechnical Lab.

| Erdos is probably the best known active mathematician, possibly the
| best known living mathematician.

In fact Erdos is so famous that I am sure you are aware of the existence
of the _Erdos distance_, defined on the set of mathematicians:

you have Erdos distance 0 if you are Erdos himself;
you have Erdos distance 1 if you have co-authored a paper with Erdos but
    are not Erdos himself;
you have Erdos distance 2 if you have co-authored a paper with a person
    of Erdos distance 1 but...

I heard this function was first defined by Erdos.

Andreas (Erdos distance 7)






-- 

Andreas Knobel                      e-mail andreas@etlcom.etl.go.jp
ETL, Tsukuba, Japan.
Newsgroups: sci.math
From: steele@isis.cgd.ucar.edu (Alfred Steele)
Subject: Re: Fermat's Last Theorem
Organization: Climate and Global Dynamics Division/NCAR, Boulder, CO
Date: Tue, 7 Apr 1992 06:21:27 GMT

In article <1992Mar31.171529.4532@linus.mitre.org> bs@gauss.mitre.org (Robert D. Silverman) writes:
-In article <1992Mar31.074735.28595@augean.eleceng.adelaide.edu.AU> dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott) writes:
->>No, Erdos only offers money for his own problems.
->
->Pardon my ignorance. Who is this Erdos dude?
- 
-You're joking right???  April 1 is tomorrow, not today, right???
-
-This must be a joke. How can anyone who reads or posts to this newsgroup
-not know who Paul Erdos is???
-
-I can understand Joe Blow off the street not knowing, but how can anyone
-with an interest in math [evidenced by the fact that he reads this group]
-not know??
-
-
-
---
-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"

Relax Bob relax!!


Newsgroups: sci.math
From: chappell@symcom.math.uiuc.edu (Glenn Chappell)
Subject: Probabilistic Arguments
Summary: Are they really worthwhile?
Organization: Math Dept., University of Illinois at Urbana/Champaign
Date: Thu, 16 Apr 1992 15:28:31 GMT

Lately There have been many references on sci.math to probabilistic or
heuristic arguments concerning statements whose truth/falsehood is
unknown. I'm wondering if these are really worthwhile. After all, one of
the basic ideas behind probability is the idea that the probability
distribution is what you get as the number of trials approaches infinity.

But in any particular formal system, any particular statement either has
a proof or it doesn't - period. You get one "trial" and then you're done.
It is quite conceivable for a probabilistic argument to suggest very
strongly that a statement is true, while the statement is in fact false.

On the other hand, such arguments certainly seem to be worthwhile, from
an intuitive viewpoint.

Therefore, I propose the following test of the worthiness of
probabilistic arguments:

Let's take a look at history and find those mathematical statements for
which probabilistic/heuristic arguments were advanced, after which the
statement was either proven or disproven. In what portion of these cases
did the probabilistic argument turn out to be correct?

I can see two ways the results of this test could be skewed. Both have
to do with the fact that there are people involved:

(1) If a probabilistic argument suggests that a statement is false, then
few will look for a proof - even if the statement is in fact true. This
might tend to make such arguments look more successful than they really
are, since, when they succeed, we often find out about it, but when they
fail, we often don't.

(2) Someone with an axe to grind about probabilistic arguments can dig
up all the successful ones he can find, ignoring all the unsuccessful
ones. Or the reverse could happen with someone who doesn't like such
arguments.

So, does anyone know of any probablistic arguments that have definitely
succeeded or definitely failed? I get the feeling that I might not get
too much of a response from this, but, if you like, e-mail me and I'll
summarize here.

				Glenn Chappell  <><
				chappell@math.uiuc.edu

Xref: sparky sci.math:5942 comp.os.msdos.apps:2813 comp.sys.ibm.pc.misc:7434
From: seanp@undr.org (Sean Petty)
Newsgroups: sci.math,comp.os.msdos.apps,comp.sys.ibm.pc.misc
Subject: Looking for a function plotter?
Date: 10 Apr 92 16:32:34 GMT
Reply-To: Sean Petty <undr!seanp@gvls1.GVL.Unisys.COM>
Organization: The Underground - Pennsylvania



        I am in need of a very simple function plotter that will allow
        me to print what I plot to the screen.  What I am looking for in
        the program includes the following:

        It should be able to plot very simple functions like 'sin X +2',
        etc.

        I would like the X axis to show radian measures (and be
        configurable), such as .2 pi, .4 pi, .6 pi, etc.

        It should be able to have multiple graphs on one screen, and
        have 3 different line types (solid, dotted, dashed).

        If anyone knows where I can get such a program via ftp, dialin,
        etc, PLEASE let me know.  I saw just such a program called
        'Algebra Plotter' by Houghton-Mifflin, but I can't find a source
        to purchase it from.  I have tried simtel, but the two programs
        I got weren't even close to what I need.

        Any help at all would be tremendously appreciated.

        Sean

---
Sean Petty                           undr!seanp@tredysvr.Tredydev.Unisys.COM
ICBMnet: 39'58'12"N 75'84'26"W       seanp@undr.org
From: ts@cup.portal.com (Tim W Smith)
Newsgroups: sci.math
Subject: Re: factoid about new prime
Date: 8 Apr 92 01:45:53 GMT
  <1992Apr1.201324.25572@linus.mitre.org>
  <SMITH.92Apr7102215@gramian.harvard.edu>
Organization: The Portal System (TM)

> > This is a (slight) exaggeration. 756839/216091 = 3.5024 times as big.
> 
> Pardon me, but
> 
>                756839
>               2       - 1                                          162781
>               -----------  ~=  2.33397019895780128135136676956 x 10
>                216091
>               2       - 1
>
>which is larger than four.  It appears that CNN was conservative in
>their report.

No, the *value* of the new prime is 2.3E162781 times the *value* of the old
one.  The size is 3.5 times.  It would take 3.5 times as much space to
write it.

If I ever have a bit of spare cash, I'm going to construct a new largest
prime.  Its value will be 2, but its size will be as big as the skywriter
can make it...

							Tim Smith
From: cet1@cl.cam.ac.uk (C.E. Thompson)
Newsgroups: sci.math
Subject: Re: Large primes; largest pi(n) known.
Date: 8 Apr 92 16:37:34 GMT
Reply-To: cet1@cl.cam.ac.uk (C.E. Thompson)
Organization: U of Cambridge Computer Lab, UK

In article <1992Apr7.103427.4558@csc.canterbury.ac.nz>,
 wft@math.canterbury.ac.nz (Bill Taylor) writes:
|> It doesn't seem to be on the FAQ, so can someone tell us...
|> 
|> what is the largest known prime for which all smaller primes are known;
|> 
|> i.e.
|> 
|> how far does the list of known primes extend, without gaps;
|> 
|> i.e. (I presume equivalently)
|> 
|> what is the largest n for which pi(n) is known ?

A natural assumption, but false. There are methods of calculating \pi(x)
which do not involve determining all primes less than x. See

  "Computing $\pi(x)$: The Meissel-Lehmer method"
   J.C.Lagarias, V.S.Miller, & A.M.Odlyzko
   Math. Comp. 44 (1985) pp. 537-560

The largest x for which \pi(x) is presented in this paper is 4 * 10^16; 
I expect it has pushed quite a bit higher by now.

The method used is based on Meissel's work in the 1870s, and can 
calculate \pi(x) in time proportional to x^{2/3}, give or take a few
(log x)'s. The above paper mentions a different (unublished) method due
to Lagarias and Odlyzko which can achieve x^{3/5}. Does anyone know where
and when (and if) this was eventually published?

Chris Thompson
JANET:    cet1@uk.ac.cam.phx
Internet: cet1@phx.cam.ac.uk
From: khanhng@guava.ucsb.edu (Nguyen)
Newsgroups: sci.math
Subject: LINEAR PROGRAMMING - A new and very simple algorithm.
Date: 16 Apr 92 19:39:38 GMT
Distribution: usa
Organization: University of California, Santa Barbara


		* * * * * * * * * * * * * * * * *     

	I have just found an extremely simple algorithm to solve linear 
programming (and even nonlinear) problems. The whole algorithm can be stated
in two line and a couple of short algebraic equations.  I am so excited that I
can not wait to have my work published in traditional journals. So I want to 
announce it through this computer network. But I wonder if I can have credit 
for my finding if I do so. I need some advice regarding publishing my work.


	I believe that the new algorithm is a revolution in the field of 
optimization. If you have any advice, please send me a mail to:

          khanhng@cs.ucsb.edu
or call   Khanh at (805)562-5840

        Your help will be appreciated.
From: ronse@geocub.UUCP (Christian RONSE)
Newsgroups: sci.math
Subject: Lipschitz functions references?
Keywords: Lipschitz condition, metric space
Date: 8 Apr 92 12:41:14 GMT
Followup-To: poster

Which books would you recommend for detailed properties of Lipschitz
functions? A function E -> R, where E is a metric space, is Lipschitz
if for all p,q in E we have

	|f(p)-f(q)| <= d(p,q).

All I have is a paper by Matheron in a book on mathematical
morphology, showing in particular that Lipschitz functions on R^n are
differentiable a.e. However I do not restrict myself to the Euclidean
space.

PLEASE ANSWER BY E-MAIL. I usually DON'T read sci.math.

Christian Ronse				ronse@geocub.greco-prog.fr
LaBRI
Universite Bordeaux-I
351 cours de la Liberation
33405 TALENCE				Tel. (33) 56.84.69.33
FRANCE					Fax. (33) 56.84.66.69
Newsgroups: sci.math
From: sinclair@aero.org (William S. Sinclair)
Subject: Does Goedel's work apply to number theory?
Organization: The Aerospace Corporation, El Segundo, CA
Distribution: usa
Date: Thu, 9 Apr 1992 21:36:53 GMT

A colleague where I work insists that Goedel's work shows that there
can be unprovable statements in the field of number theory. Even if they
exist, are the any KNOWN unprovable statements in this field? Has there 
been much conjecuture about the prvability of conjectures such as Fermat's
theorem, or Goldbach's conjecture?
From: neil@dehn.mth.pdx.edu (John Neil)
Newsgroups: sci.math
Subject: Re: A Proof about Groups
Date: 14 Apr 92 19:28:50 GMT
Article-I.D.: dehn.neil.703279730

teacher@netlink.cts.com (Daniel Pick) writes:

>In Joseph Landin's book, 'An Introduction to Algebraic Structures,'
>the author makes the following definitions:
>A group G which contains only a finite number of elements is a 
>finite group.
>An element x of a group G has finite order if and only if
>there is a positive integer n such that x^n = e, where e
>is the neutral element.
>Then he asks the reader to prove that if G is a finite group,
>then every element in G has finite order.
>This proof stumps me.  If you induct on the number of elements in
>the group, how do you show that each successive element has finite
>order?

>--                    
>INTERNET:  teacher@netlink.cts.com (Daniel Pick)
>UUCP:   ...!nosc!ryptyde!netlink!teacher
>NetLink Online Communications * Public Access in San Diego, CA (619) 435-6181

Your mistake here is trying to prove this by induction.  Instead of that, you
should note that the cyclic subgroup generated by each element of a group must
be a subgroup of that group since groups are closed under multiplication.
Thus, to have an element which was not of finite order in a finite group would
mean that a finite group had an infinite subgroup.  OOPS.  It is usually a
mistake to do proofs in algebra by induction.  There are some problems for
which it is required, but most of the problems in algebra are best proved by
contradiction or directly.

--John Neil


John Neil, Graduate Teaching Assistant           e-mail:  neil@math.mth.pdx.edu
Mathematics Department                         NeXTMail:  neil@dehn.mth.pdx.edu
Portland State University
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
--
John Neil, Graduate Teaching Assistant           e-mail:  neil@math.mth.pdx.edu
Mathematics Department                         NeXTMail:  neil@dehn.mth.pdx.edu
Portland State University
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
From: jjhi@lesti.hut.fi (Jari Juhani Hiltunen)
Newsgroups: sci.math
Subject: Palindrome problem
Date: 8 Apr 92 15:09:27 GMT
Reply-To: jjhi@lesti.hut.fi (Jari Juhani Hiltunen)
Organization: Helsinki University of Technology


I friend of mine presented me the following problem:

1)  Take number i and make j out of if by reversing the order of
    digits.
2)  Let k=i+j.  If k is palindrome then stop.  Otherwise, let
    i=k and go back to step 1).

    i=25           25 +  52 =  77  palindrome

    i=150         150 + 051 = 201  continue
                  201 + 102 = 303  palindrome

Question:  Will every number eventually yield to a number which
is palindrome?

I have tried numbers 1..200 and 196 seems to be a tough one.  A
program of mine has already done over 100 000 iterations and the
length of the number is currently more than 42 000 digits.

I don't know how to prove this one way or other.  I also don't
know where to look for a solution.  Is this a widely known
problem?  Can somebody refer me to a book that explains this?

Thanks,

-- 
$----------------------------------------------------------$
$   Jari Hiltunen               $  jjhi@niksula.cs.hut.fi  $
$   If in doubt, DON'T          $  jjhi@vipunen.hut.fi     $
$----------------------------------------------------------$