HDTenEightyP/NetNews huggingface dataset:
From: pruss@unixg.ubc.ca (Alexander Pruss)
Subject: Re: Topos not over SET with natural number system?
Keywords: elementary topos, natural number system, SET
Organization: University of British Columbia, Vancouver, B.C., Canada
Date: Fri, 24 Jul 1992 19:10:21 GMT

In article <1992Jul23.213112.5122@unixg.ubc.ca> I write:
>Can there exist a topos not defined over SET with a natural number
>system?  If so, what would be an example?

[Someone noted I should have said "elementary" topos to distinguish
from a Grothendieck topos.]

Sorry to have bothered people with this.
 
There is indeed a fairly simple topos with this property.
 
Let Z be any set.  We define the category SETZ to be the full subcategory
of SET with objects being sets of cardinality <= P^n Z for some natural
number n.  (P^n Z= P...PZ with n P's, where for any set A, PA is its power
set.)  Then it is very easy to see SETZ is a topos.
 
If Z is infinite, then SETZ clearly contains an infinite object, and so a
natural number system.
 
Now, SETZ is not defined over SET, as we can easily verify there is no
K-indexed coproduct of 1={0} in SETZ if K is a set of cardinality strictly
greater than any P^n Z.  (E.g. K = union(P^n Z), the union being taken
over natural n.)
 
SETZ is a really nice topos.  For Z=0, it is the degenerate topos.  For
Z finite, it is FINSET.  For Z infinite it has a natural number system.
It is never defined over SET, but nonetheless has many of the properties
of SET, and seems to be a generalization of FINSET.  It is Boolean,
bivalent, extensional, any object A not isomorphic to 0 has an arrow
1-->A, and has the axiom of choice (if SET is assumed to have it).
Newsgroups: sci.math
From: alan@highlite.uucp (Alan McConnell)
Subject: Re: Complex Analysis
Keywords: i,e,pi
Organization: Gotham Communications Research
Distribution: na
Date: Tue, 28 Jul 1992 01:22:51 GMT


Isn't Knopp Elements, Functiontheory 1, Functiontheory 2 still in
print in Dover?  Ahlfors is great, but hard work for a first pass
through the material.  The Knopp books are also great, IMHO
Alan McConnell
-- 
Alan McConnell             "What wondrous life is this I lead!
Pixel Analysis              Ripe apples drop about my head . ."
Newsgroups: sci.math
From: chepan@gsusgi1.gsu.edu (Parthasarathy Nambi)
Subject: Re: Hailstone sequences
Organization: Georgia State University
Distribution: usa
Date: Sat, 25 Jul 1992 02:21:31 GMT

 If you are interested in the 3n + 1 problem take a look
 at an interesting paper:

 " Wondrous numbers- conjecture about the 3n + 1 family"

 by Blanton C, Wiggin in the Journal of Recreational Mathematics
 volume 20, pp 52-56 (1988)

 P.Nambi
From: allenk@harry.ugcs.caltech.edu (Allen Knutson)
Newsgroups: sci.math
Subject: Re: Group Theory Question
Keywords: group, coset
Date: 24 Jul 92 09:39:28 GMT
Distribution: usa
Organization: California Institute of Technology, Pasadena

dmassey@sdcc3.ucsd.edu (Daniel Massey) writes:

>I'm reviewing algebra and have gotten stuck on the following
>seemingly simple question:

>G is an abelian group and H a subgroup  of G. Prove their exists
>a subgroup of G which is iso. to G/H.

It's easy once you've classified the finite abelian groups, and false for
many infinite G,H such as the integers and the even integers.	Allen K.
From: carabalo@fine.Princeton.EDU (David G. Caraballo)
Newsgroups: sci.math
Subject: Choice and Measurability:  Con(ZF+M+CC) is true
Date: 24 Jul 92 16:19:21 GMT
Organization: Princeton University Mathematics Department

I have made the claim (based on some course notes, later supported by 
a quote from a textbook) that "M is consistent with ZF+CC" is true, 
where  M  = "all subsets of R^n are Lebesgue measurable"
       CC = Countable Choice  

I have received numerous emphatic objections on sci.math regarding 
my claim, yet I will make it once again, with renewed support.   One 
major criticism is that I omitted mentioning anything about the existence 
of inaccessible cardinals in making the claim.  I asked Ed Nelson about 
the question, and he referred me to Robert Solovay.  The following is 
quoted from some of Bob Solovay's letters during our email discussions
over the past few days.  (It is quoted with his permission.  For whatever 
it's worth, I found him to be extremely nice as well as helpful.)  I am 
quoting a relatively small portion of what he wrote, but I am using his 
words to honor his request that I quote sufficient context that his 
meaning be clear.  Any typos are my own or are the fault of the posting 
software.  

The claim above is not as strong (or useful) as the result concerning
DC (the axiom of dependent choices), but it is nevertheless true,
which is what I have repeatedly claimed.  Earlier, I had claimed that
ZF+M is consistent (as long as ZFC is consistent).  This claim is true
as well, without the need to mention inaccessibles.

David G. Caraballo
Department of Mathematics, Princeton University
Fine Hall Room 1106
----------------------------------------------------------------------------

From Robert Solovay:

"    1) The statement "ZF + M +CC is consistent" is a statement of
     number theory (which is true). Its truth has nothing to do with the
     existence of inaccessibles in the following precise sense. There are
     models of ZFC
	(a) where the statement is true but there are no inaccessibles;

	(b) where the statement is false but there is an inaccessible
	    cardinal.

     2) Next we have the question: in which theories can we prove
     this true statement.

	In ZFC we can prove:

	   "ZFC +'there is an inaccessible cardinal' " is consistent if
	       and only if "ZF + M + CC" is consistent.

	(In fact we can prove this assertion in Peano Arithmetic.)

     To reiterate:

     1) Con(ZF+M+CC) is not provable in ZFC

     2) Con(ZF+M+CC) is provable in ZFC + Con (ZFC+I), hence in ZFC      
       + two inaccessible cardinals exist.

     3) For us dyed-in-the-wool platonists (I'm a card-carrying member of
	the club), 2) is more than enough grounds to conclude:

	Con(ZF +M + CC) is true.

	      As ever,

		      Bob Solovay                                         "
From: cliff@watson.ibm.com ("Cliff Pickover")
Newsgroups: sci.math
Subject: Recreational Math Journals
Date: 24 Jul 92 12:50:53 GMT

I'm interested in what mathematical journals exist that are interested
in "light" math -- math more of a recreational and curiosity nature than
most heavy-duty math journals will publish.

Here are some "light" math journals:
Journal of Recreational Mathematics
Theta
Mathematical Spectrum
Quantum
Mathematics and Computer Education

Are there others?  If so, could you also send me relevant information,
e.g. main editor's address and publisher's address.
Thanks, Cliff              cliff@watson.ibm.com
Newsgroups: sci.math
From: shen@math.psu.edu (Jee Shen)
Subject: Re: Orthogonal Ops (meaning)???
Keywords: direct sum
Reply-To: shen@math.psu.edu
Organization: Dept. of Mathematics, Penn State University
Date: Fri, 24 Jul 1992 01:16:41 GMT

In article chxr7q@rpi.edu, sassoj@vccsouth16.its.rpi.edu (John J. Sasso Jr.) writes:
>Hello,
>
>   When reading about multiresolution analysis (wavelets), I encountered some
>   math I didn't understand.  They refer to operations on sets such as      
>   orthogonal addition (?) and the like.  The symbol for the former was a circle
>   with a + sign in it.  Another symbol I saw was a circle with a - sign in it.
>   What do these operations (and any others similar to these that you can 
>   think of ) mean, that is, their definitions.
>
>   Also, if anyone can give me a good explanation of multiresolution analysis,
>   I would greatly appreciate it.  I have trouble finding one in much of the
>   literature out there.
>
>                       John
>
> 


It means direct sum( of two or more linear vector spaces). Try to read some elementary
linear algebra textbooks to have a better understanding.

Jee Shen




Newsgroups: sci.math
From: victor@watson.ibm.com (Victor Miller)
Subject: Re: An interesting limit problem.
Date: Wed, 29 Jul 1992 19:32:36 GMT
Reply-To: victor@watson.ibm.com
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
	<1992Jul25.201805.14172@husc3.harvard.edu>
Organization: IBM, T.J. Watson Research Center

>>>>> On 25 Jul 92 20:18:04 EDT, elkies@ramanujan.harvard.edu (Noam Elkies) said:

Noam> In article <1992Jul25.212844.1@lure.latrobe.edu.au>
Noam> mattm@lure.latrobe.edu.au writes:

>A challenge to all mathematicians. A 100 years ago, this would probably have 
>been solved fairly simply in a natural way, but can you? I think that this
>problem was first posed by the Russian mathematician Arnold. Hope you find this
>problem as interesting as I did when I first solved it.
>
>                sin(tan x)    -    tan(sin x)
>	lim  ----------------------------------  = ???
>	x->0 arcsin(arctan x) - arctan(arcsin x)

Noam> I don't know how they sould have done this 100 years ago.  One direct
Noam> approach is to expand both numerator and denominator in Taylor series
Noam> about x=0 and compare leading terms.  Since we're doing this today instead
Noam> of 100 years ago, we can obtain the Taylor expansions instantaneously using
Noam> a symbolic manipulation package.  We find that both numerator and denominator
Noam> are -x^7/30+O(x^9), so the limit equals 1.  This also suggests that you
Noam> *don't* want to find this limit using the L'Hospital rule, especially if
Noam> you have to do all the derivatives by hand!

This problem is rather interesting, in that it is true in the
following general sense: let f and g be distinct elements of k[[x]]
(the power series ring, k is an arbitray field), which have 0 constant
term, and linear term x.  Then the Laurent series

	     f(g(x)) - g(f(x))
	-------------------------------------
	f^{-1}(g^{-1}(x)) - g^{-1}(f^{-1}(x))

starts 1 + ...
Noam> --Noam D. Elkies (elkies@zariski.harvard.edu)
Noam>   Dept. of Mathematics, Harvard University
--
			Victor S. Miller
			Vnet and Bitnet:  VICTOR at WATSON
			Internet: victor@watson.ibm.com
			IBM, TJ Watson Research Center
From: v5875bza@ubvmsd.cc.buffalo.edu (Michael M Gorman Jr)
Newsgroups: sci.math
Subject: Thanks from a less ignorant philosopher.
Date: 30 Jul 92 03:40:00 GMT
Organization: University at Buffalo
News-Software: VAX/VMS VNEWS 1.41


Many thanks to the more than one dozen people who wrote or posted
to help me out.  With your help, I am moving from ignorance to
knowledge.

Thanks again!

MG
Newsgroups: sci.math
From: luzeaux@bellini.berkeley.edu (Dominique Luzeaux)
Subject: Re: Non-linear stabilty
Reply-To: luzeaux@bellini.berkeley.edu (Dominique Luzeaux)
Organization: University of California, Berkeley
Date: Wed, 29 Jul 1992 20:06:40 GMT

Phase plane analysis, or direct stability proofs
Send the equation, it will be easier.

	Dominique
From: sichase@csa2.lbl.gov (SCOTT I CHASE)
Newsgroups: sci.math
Subject: Re: An interesting limit problem.
Date: 26 Jul 92 20:40:29 GMT
Reply-To: sichase@csa2.lbl.gov
Distribution: na
Organization: Lawrence Berkeley Laboratory - Berkeley, CA, USA
NNTP-Posting-Host: 128.3.254.197
News-Software: VAX/VMS VNEWS 1.3-4

In article <1992Jul26.150627.14192@husc3.harvard.edu>, kubo@zariski.harvard.edu (Tal Kubo) writes...
> 
> 
>See "Huygens, Barrow, Hooke and Newton" by V.I. Arnol'd.
>He gives the above limit as an example of a problem
>that mathematicians today simply can't solve quickly (in
>contrast to their predecessors). He remarks that the only
>exception known to him, G. Faltings, proves the rule.

Then I am disappointed in Arnol'd who should know better about what the
phrase "the exception proves the rule" means.  The word "prove" does not
mean "demonstrates" in this usage, but rather "tests" as in the 
"Proving Grounds" where they test nuclear weapons.  The phrase "The 
exception proves the rule" means that if an exception can be found then
then rule is shown to be false.

Granted, most people don't understand this for some reason.

-Scott

--------------------
Scott I. Chase			"The question seems to be of such a character
SICHASE@CSA2.LBL.GOV		that if I should come to life after my death
				and some mathematician were to tell me that it
				had been definitely settled, I think I would
				immediately drop dead again."      - Vandiver
Organization: University of Illinois at Chicago
Date: Thursday, 30 Jul 1992 19:27:46 CDT
From: <U53644@uicvm.uic.edu>
Newsgroups: sci.math
Subject: Re: ? Quick algorithm for random covering sets ?
 <92210.014509U53644@uicvm.uic.edu>


A clarification.............

        In a previous post, I mentioned the power set of the set 1,...,N.
Unfortunately, there seems to be some compatability problem between CMS
(the operating system used by the particular computer this account is on), and
some of the other operating systems, and this came out as " The power set of
the set $1,...,N"  ". Terribly sorry about that, if you saw that, the $ here
appeared here as a left set theoretic bracket, and the " as a right one.

                                                       Joseph B. Dunphy
Newsgroups: sci.math
From: pyacm@trentu.ca (A Colin Morton)
Subject: Re: American mathematical hegemony
Organization: Trent University, Ontario
Date: Tue, 21 Jul 1992 18:12:04 GMT

In article <1992Jul21.172125@sees.bangor.ac.uk> graham@sees.bangor.ac.uk (The Land of Confusion) writes:
>
>In article <1992Jul21.135206.25360@dcs.qmw.ac.uk>, mmh@cs.qmw.ac.uk (Matthew Huntbach) writes:
>> From: sooz@iastate.edu (Susan F Bradley)
>> > I lived in Leicestershire for 1 1/2 years, with the same people day in,
>> > day out. After all that time, I still couldn't say the words "water" or
>> > "tomato" without sending them all into paroxysms of laughter. One day, an
>> > elderly guest at the place I worked pitched a fit at me when she heard me
>> > say that I had "gotten" something. She did this in front of maybe 20-25
>> > people and serves as a good argument against another point of discussion --
>> > this idiotic notion that the British are more polite than Americans.
>> > This woman was decidedly middle class, supposedly well-bred. Where I come
>> > from, what she did was not only rude, but mean-spirited and completely
>> > uncalled for.
>> 
>> I doubt the intention was to be deliberately rude. Probably
>> they just found your accent quaint and amusing. Remember that
>> in the UK we are familiar with American accents mainly through
>> cartoons and TV shows, particularly in areas like Leicestershire,
>> outside the tourist circuit. Hearing your accent would be rather like
>> having a character come alive and step out of the TV. I think
>> you are also running into the common phenomenon that it is
>> considered acceptable to poke fun at groups of people who are
>> in an economically and politically superior position to
>> yourself, but not vice versa. Anti-Americanism is acceptable
>> because Americans tend to be wealthy, and the USA bosses the
>> world around. It is not so acceptable to laugh at disadvantaged
>> groups.
>> 
>> Matthew Huntbach
>
>Sounds like the old crone was just plain being rude, intentionally
>or not, so what's the point in trying to make excuses for her
>typical English middle-class parochialism? 
>
>--
>graham a stephen                        ``The only key to your riddle is
>(e-mail: graham@sees.bangor.ac.uk)        to accept the absence of a key.''
>                                              --  Laibach, 1992     
>Aposiopesis is not really all that it

Excuse me people, but one example does not make a "good argument"
against anything, nor is it necessarily "typical".  Yes, the elderly
lady involved was rude, but this does not mean that everyone in the
United Kingdom is.  To bring this discussion back to math, consider
sample size when trying to draw inferences (OK, so it's more statistics
than math -- sue me).

Colin.

Newsgroups: sci.math
From: nextc.Princeton.EDU!mdd (Mark D. Doyle)
Subject: Re: Another puzzle
Originator: news@ernie.Princeton.EDU
Reply-To: mdd@nextc.princeton.edu
Organization: Princeton University
Date: Thu, 30 Jul 1992 22:46:33 GMT

In article <1992Jul30.073426.14230@uniwa.uwa.edu.au>  
ycchin@tartarus.uwa.edu.au (Chin Yih Chong) writes:
> Here is another fun puzzle......
> 
> Try to crack this
> 
> 
> 				10
> 				11
> 				12	
> 				13
> 				14
> 				15
> 				16
> 				17
> 				20
> 				22
> 				24
> 				31
> 			       100
> 			       121
> 					      10000
> 		  1111111111111111 (16 ones)
> 
> Can you observe any relationship between each numbers?
> Can you find a general formula for it?
> 
16 written in base 16, 15, .... 3,2, and 1.

Mark
mdd@nextc.princeton.edu
From: st_waldman@zodiac.dsto.oz.au
Newsgroups: sci.math.num-analysis
Subject: Re: Constrained minimization source
Date: 31 Jul 92 01:17:50 GMT
Organization: D.S.T.O. Aeronautical Research Laboratory

I would also like to obtain source code for a constrained
minimization solver that makes use of user-supplied
derivatives.

Thanks in advance if anyone can help...

Witold Waldman

ST_WALDMAN@ZODIAC.DSTO.GOV.AU
WITOLD@HOTBLK.DSTO.GOV.AU
Xref: sparky sci.math.num-analysis:2297 comp.lang.c++:11580
From: mbk@lyapunov.ucsd.edu (Matt Kennel)
Newsgroups: sci.math.num-analysis,comp.lang.c++
Subject: Re: SUMMARY: Automatic differentiation
Date: 26 Jul 1992 23:39:05 GMT
Organization: Institute For Nonlinear Science, UCSD
NNTP-Posting-Host: lyapunov.ucsd.edu
X-Newsreader: Tin 1.1 PL3

ajayshah@almaak.usc.edu (Ajay Shah) writes:
: 
: I think this strategy is going to revolutionise the way we actually do
: nonlinear maximisations.  I think it's going to obsolete algorithms
: like the BFGS and conjugate gradients etc. because with this in hand
: we get exact hessians and higher.

In most of my problems, the number of variables I'm minimizing over is
quite large, similarly for neural networks.  Don't "BFGS" and Hessian
methods require O(N^2) storage space, at least, in contrast to 
O(N) conjugate gradient.  I don't know what the speed is, but when
N=200 say, the internal matrix multipies that are normally considered trivial
next to function evaluations might not be so trivial.

:  We get large gains in efficiency by
: using higher derivatives (see the Kalaba-Tisher paper for example).

If you have something other than a simple quadratic minimum does this
really do that much good?

: We will endup replacing the status quo of libraries like NPSOL by
: something totally different, and the bonus is that the replacement is
: not in fortrash!  I like it!

Will C++ be able to do:
	A = B*C + D

with A,C,D vectors, and B a matrix  without any copying and creation
of intermediate variables?  (i.e. see Matrix * Vector--- create a new
result vector.  Do + operation on 2 vectors, make another new vector.
Now do the "=" operation and copy it into A)

Perhaps the problem is that C++ let's you define overloaded operators to
do anything, without regard to the normal "rules of algebra", so that it
must assume less.
That's one of the reason's I'm not using it now.

: 
:         -ans.
: -- 
: Ajay Shah, (213)749-8133, ajayshah@usc.edu

--
-Matt Kennel  		mbk@inls1.ucsd.edu
-Institute for Nonlinear Science, University of California, San Diego
Newsgroups: sci.math.num-analysis
From: efang@pomona.claremont.edu
Subject: looking for EISPACK in C
Organization: Pomona College
Date: 27 Jul 92 15:44:01 PDT


Hello,
I am looking for a copy of the EISPACK routines in C. Does anyone know if they
exist and if so where I can obtain them? E-mail if you can, or post please.

Thanks you,
Eric Fang
EFANG@POMONA.CLAREMONT.EDU

Newsgroups: sci.math.num-analysis
From: Dick Rinewalt <rinewalt@gamma.is.tcu.edu>
Subject: Re: WANTED: Algorithm to fit data points to ellipse
Organization: Texas Christian Univ Comp Sci Dept
X-Useragent: Nuntius v1.1b3
Date: Fri, 31 Jul 1992 16:13:07 GMT

In article <1992Jul30.235659.23179@terminator.cc.umich.edu> Dave Reimann,
reimann@terminator.cc.umich.edu writes:
>I need an algorithm to fit a general ellipse to a set of data points.
>By generalized ellipse, I mean one that accounts for any tilt in the
>major axis wrt the x-axis.  The data is expected to have some estimation 
>error, so I need to handle that.

There is an ellipse fitting routine in NIH Image available by anonymous
ftp from alw.nih.gov in the /pub/image directory. Comments in the Pascal
code say that the routine is due to
  Bob Rodieck
  Department of Ophthalmology, RJ-10
  University of Washington
  Seattle, WA, 98195
  (206) 543-2449
The comments also reference
  Cramer, Mathematical Methods of Statistics, Princeton Univ. Press, 945,
page 283
From: dale@imsl.UUCP (Dale Neaderhouse)
Newsgroups: sci.math.num-analysis
Subject: Re: Can you call IMSL from C program?
Summary: IMSL from C
Keywords: IMSL
Date: 31 Jul 92 15:50:59 GMT
Organization: IMSL, Inc., Houston

In article <9246@emory.mathcs.emory.edu>, riddle@mathcs.emory.edu (Larry Riddle)
writes:
> She would like to call some of the IMSL routines from a C program. 

I'll fax two articles (3 pages each) from IMSL's quarterly magazine "Directions"
which explain how to call Fortran from C.

IMSL has math and stat libraries available in C, as well as Exponent Graphics
for C in Sep 92.  They are available on Sun4, RS6000, HP9700, Silicon Graphics,
and DECstations.

Dale

Have a good day!
 
Dale L. Neaderhouser          dale@imsl3.imsl.com   FAX: 713-242-9799
Senior Software Engineer      uunet!imsl!dale      IMSL: 713-242-6776
Post Sales Technical Support: 800-324-4675        Sales: 800-222-4675
Newsgroups: sci.math.num-analysis
From: lampard@titan.trl.OZ.AU (Greg Lampard)
Subject: Help: Routines for signal processing
Keywords: signal processing mathematica
Organization: Telecom Research Labs, Melbourne, Australia
Date: Fri, 24 Jul 1992 05:30:44 GMT

I am doing some basic signal processing (looking at signals in the time
and frequency domains, filtering, modulation etc.) and I'd like some
decent tools.  At the moment I'm using Mathematica, which is OK but
certainly not ideal for the task.  
Does anyone know of any cheap/free software for doing this kind of thing?
I dimly recollect seeing a reference (on this group?) to a Mathematica
package.  That, or any other software for a Mac or a Unix workstation
under X11 would be a great help.

Thanks for any and all help.  As usual, please e-mail, and I'll
summarize the responses.

Greg
---
Greg Lampard                    | Showing you how you can turn your old
Telecom Research Laboratories   | nuclear physicist into a brand new
g.lampard@trl.oz.au             | communications engineer.
From: st_waldman@zodiac.dsto.oz.au
Newsgroups: sci.math.num-analysis
Subject: Re: Finding C Code for LINPACK/EISPACK Routines
Date: 31 Jul 92 01:09:46 GMT
Organization: D.S.T.O. Aeronautical Research Laboratory

I would also like to know the location of C (and Fortran)
versions of the LINPACK and EISPACK source codes.
You can post replies directly to me, or to this
news group.

Thank you.

Witold Waldman
ST_WALDMAN@ZODIAC.DSTO.GOV.AU
From: aglgrad@sdphu1.ucsd.edu (A Garret Lisi)
Newsgroups: sci.math.num-analysis
Subject: Symplectic Integrators
Date: 27 Jul 92 23:22:05 GMT
Distribution: world
Organization: Physics Department, UCSD
NNTP-Posting-Host: sdphu1.ucsd.edu


Howdy,
Has anyone out there had experience with symplectic integrators
for hamiltonian systems?  If so, I would greatly appreciate your
comments and/or source code.

advaTHANKSnce,
-G