HDTenEightyP/NetNews huggingface dataset:
From: rose@fsu1.cc.fsu.edu (Kermit Rose)
Newsgroups: sci.math
Subject: Re: Hailstone sequences
Date: 23 Jul 92 04:26:49 GMT
Reply-To: rose@fsu1.cc.fsu.edu
Organization: Florida State University
News-Software: VAX/VMS VNEWS 1.3-4

In article <2020@bigfoot.first.gmd.de>, wolf@prosun.first.gmd.de (Wolfgang Koehler) writes...
>(I hope my memory kept the term right.)
> 
>I would like to know something more about these astonishing sequences.
>Since it is not mentioned in the FAQ-list, let's post it.
> 
>For those of the audience, who haven't heard of them,  the construcion
>rule is as simple as one can imagine:
> 
>1. Start with an arbitrary integer n,
> 
>2. compute the successor n' of n with the rule :
>   if n is even n' = n/2, otherwise n' = 3n+1
> 
>3. repeat this until you reach 1.
> 
>The question is : do all these sequences (for different starting points n)
>converge to 1 ?
> 
>As far as I know it is still unsolved.(?)
> 
>Of course it's of great interest to know connections to other 
>theorems in number theory.
> 
> 
>wolf
> 
>-------------------------------------------------------------------------------
>    ... always look on the bright side of life ... (Monty Python)
>-------------------------------------------------------------------------------
>Wolfgang Koehler                                    wolf@first.gmd.de
> 
> 
Two simple observations:

If n = (2^k+1)m where m is odd, then n' = 3(2^k+1)m + 1 and n'' = 
3(2^[k-1])m + [3m+1]/2 is larger than n.
If m = 3 mod 4, then [3m+1]/2 is odd.

If we could show that for each n, the sequence eventually reaches a value 
less than n, then an inductive proof would be possible.

rose@fsu1.cc.fsu.edu          To be sure I see your response, use e-mail.
-----------------------------------------------------------------------
Be of good cheer, for it is much more fun than being depressed.
From: vbm@mace.cc.purdue.edu (Karen Hunt)
Newsgroups: sci.math
Subject: Re: An interesting limit problem.
Date: 31 Jul 92 19:13:09 GMT
Organization: Purdue University

In article <1992Jul30.150656.14324@husc3.harvard.edu> elkies@ramanujan.harvard.edu (Noam Elkies) writes:
>                                    5 2
>Ouch.  Do they automatically write 2 9  = 2592 too?  ;-)
>
>--Noam D. Elkies (elkies@zariski.harvard.edu)
>  Department of Mathematics, Harvard University
                                         5 2
Well....  A friend and I had discovered 2 9 = 2592, and I even wrote a
program to check the first 100,000,000 numbers (base 10) to see if any
other numbers of the form   b d f h 
                           a c e g  = abcdefgh, and didn't find any.
Does anyone know if is has been shown that no such number other than 2592
exists?  (Yes I know, this is hardly important mathematics :-) ).

Just curious,

Karen Hunt
vbm@mace.cc.purdue.edu
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: Is this game determined?
Date: 31 Jul 92 08:56:45 GMT
Distribution: sci
Organization: M.I.T. Artificial Intelligence Lab.


Inspired by the Axiom of Determinacy, I cooked up the following class of
games.

Let F be a formula in 1 free variable in the language of Zermelo-Frankel set 
theory. Given F, we play the following game: Player I chooses a set x
satisfying F(x). If x is empty, then Player I loses. More generally, anyone
who gets stuck with the empty set loses. If x is not empty, then Player II
chooses an element y of x. If y is empty, Player II loses, otherwise, Player I
chooses an element z of y, and so on.

By the Foundation Axiom, this game always has to terminate in a finite number
of plays. 

Suppose we adopt the axiom: For every F, the game associated to F has a
winning strategy for one of the players.

What conclusions can one draw from this axiom? Is it consistent with ZF?
How does it compare with the Axiom of Determinacy ?

Allan Adler
ara@altdorf.ai.mit.edu
From: v5875bza@ubvmsd.cc.buffalo.edu (Michael M Gorman Jr)
Newsgroups: sci.math
Subject: A question from an ignorant philosopher.
Date: 29 Jul 92 14:55:00 GMT
Organization: University at Buffalo
News-Software: VAX/VMS VNEWS 1.41

Dear mathematicians,

     I'm a philosophy student doing research on something called
"ontological priority".  First I'm trying to get clear on what
"priority" means, and it has to do with order.  My wife pointed out
to me that order is something that mathematicians have defined
rigorously, so I consulted some math dictionaries.  Unfortunately,
I found two different definitions.

     Two of the dictionaries defined order in a way that is modeled
on the inequality relation.  A set S is partially ordered if there
is a relation R for that set such that (if aRb, then not-bRa and a is 
not b), and (if aRb and bRc, then aRc).  In other words, if there
is a relation that is non-symmetrical and transitive.  A totally ordered
set is one that for which it is also true that for any two members a,b
of S, either aRb or bRa or a=b.
     One of the dictionaries modeled it on the "less than or equal to"
relation.  A set S is partially ordered if there is a relation R
such that (aRa), (if aRb and bRa, then a=b), and (if aRb and bRc,
then aRc).  In other words, reflexive, antisymmetric, transitive.
Total ordering is defined by adding the same extra restriction as above.

     Partly I'm curious as to how it came to be that these two things
go by the same name, but mostly what I need to know is which one is
standard usage.

     Any help you can give me would be greatly appreciated!

Thanks!

Michael M. Gorman
Department of Philosophy
State Univ. of NY at Buffalo
Newsgroups: sci.math
From: lairdpg@lub001.lamar.edu
Newsgroups: sci.math
Subject: NEED HELP FINDING ALGEBRA TUTOR PROGRAMS
Date: 21 Jul 92 10:41:00 +1700
Organization: Lamar University - Beaumont

I am looking for anyone who may lead me to some Algebra Tutor programs for
IBM Compatibles.  I would like to know where I can FTP these from and the names
of the programs if at all possible.

I am also looking for any good Geometry Tutor Programs same as above.  Please
E-Mail me at Internet Adddress:  LAIRDPG@LUB001.LAMA.EDU if you can help.

Thanks in advance.
From: dale@imsl.UUCP (Dale Neaderhouse)
Newsgroups: sci.math
Subject: Re: Marquardt Algorithm for Chi-Square Non-Linear Functions
Summary: IMSL 2.0 on PC with Microsoft Fortran 5.1
Keywords: Nonlinear Fitting
Date: 30 Jul 92 14:34:55 GMT
Organization: IMSL, Inc., Houston

In article <Bs5Lw6.3n3@news.cso.uiuc.edu>, magdi@uxh.cso.uiuc.edu (Magdi N Azer) 
writes: 
> I pefer not to use IMSL libraries, simply because I want to do this on a P.C. 

Version 2 of the IMSL Math/Library using Microsoft Fortran 5.1 was available on
the PC in May this year.  Version 1.1 of IMSL Math/Library using Microsoft 4.0
or 5.0 has been available since December, 1989.  Around 500 current licenses are
in use on PCs.  This doesn't include more that are paidup/unsupported.  Many
people are using IMSL on PCs.  

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
From: cliff@watson.ibm.com ("Cliff Pickover")
Newsgroups: sci.math
Subject: High Order Undulation Seeds and Binary Undulants
Date: 24 Jul 92 13:15:38 GMT

"Binary undulants" are numbers of the form 2**N that undulate
(alternate) the digits 1 and 0 in their decimal expansion.

For example, 2**49 is the "highest quality" binary undulant so far
discovered because it has the undulating sequence 101010 in it:

2**949 =
4758454107128905800953799994079681792420032645310062268978469949811010102913
Here N = 949 is called an undulation seed of order 6, since it
gives rise to a 6-digit undulation pattern of adjacent 1's and 0's.

Are undulation seeds of higher order easily found using either
mathematical prowess or computation power?

Thanks Cliff   cliff@watson.ibm.com
From: anil@cs.vu.nl (Sukul AR)
Newsgroups: sci.math
Subject: wanted (was: Mathemantical tattoos)
Keywords: wanted, mathematical tattoos
Date: 21 Jul 92 18:50:41 GMT


Hi,

I'm looking for a paper (I think it was in an A4 format) that 
has the following text on it:

=
And so God said:

< 
  a bunch of complex integrals and differential equations, 
  which would cause a normal person to slightly faint and not gain
  conscience for an hour or so.
>

And there was light.
=


Is there anyone out there who has the above meant text in ascii or - 
even better - troff, (la)tex and/or postscript format?

Thanks in advance,
Anil.
From: lkv@mania.hotb.sub.org (Lutz Vieweg)
Newsgroups: sci.math
Subject: Wavelet transform
Date: 24 Jul 92 17:34:43 GMT
Organization: The Funny Farm
X-Newsreader: Arn V1.00 alpha rel3

Hi,

I'd appreciate help in seeking information regarding radial
and two (or more) dimensional wavelet transform.

Please let me know if there's literature or anything else
available on this topic - and pleeeeaaaaaseeee write me
an email - I've got no chance to read this newsgroup.

Thanks in advance,

Lutz Vieweg

EMail: lkv@mania.hotb.sub.org
From: spark@spuddy.uucp (Steve)
Newsgroups: sci.math
Subject: Description of what an FFT is.
Date: 23 Jul 92 22:00:48 GMT
Organization: Spuddy's Public Usenet Domain


Can someone explain briefly what an Fast fourier transformation is,
what it's useful for, and give some kind of brief example?

I have a limited knowledge of complex numbers, which I believe are
involved.

Arey any relation to DCT's, used in jpeg?

Perhaps someone could give me the location of an EASY TO UNDERSTAND
paper on the subject, available for FTP somewhere?

Thanks
Steve

-- 

        ---- Steve Parkinson (spark%spuddy.uucp@uknet.ac.uk) ----
        ----- Call Spuddy for Free UK USENET on 0203 638780 -----
From: wilson@web.ctron.com
Newsgroups: sci.math
Subject: Partition number question
Date: 23 Jul 92 14:09:39 GMT
Reply-To: wilson@web.ctron.com ()
Organization: Cabletron Systems INc.
Originator: wilson@web


    For n >= 0, let p(n) be the unrestricted partition number of n.

    1.  For all k >= 0, is it true that

	a.  5  | p(5k+4)
	b.  7  | p(7k+5)
	c.  11 | p(11k+6)

    2.  Given (1) is true, are there other triples (a > 0, b > 0, c >= 0)
	such that a | p(bk+c) for all k >= 0?

    3.  Why does 11 divide so many small partition numbers?
-- 
David W. Wilson (wilson@ctron.com)

Disclaimer: "Truth is just truth...You can't have opinions about truth."
- Peter Schikele, introduction to P.D.Q. Bach's oratorio "The Seasonings."
From: edwill@ariel.lerc.nasa.gov (Glenn L. Williams)
Newsgroups: sci.math
Subject: "Terminal Summation" functions
Date: 23 Jul 92 18:14:00 GMT
Organization: NASA Lewis Research Center
News-Software: VAX/VMS VNEWS 1.41


In the July 20, 1992, issue of Electronic Engineering Times, page
35, a "new class of functions found" uses the Terminal Summation
technique by Thomas Phipps, Jr.  The method is supposed to be described
in some old government report.  Does anyone know the name/source of
this report and/or any papers on it?
Newsgroups: sci.math
From: carabalo@phoenix.Princeton.EDU (David G. Caraballo)
Subject: Re: Group Theory Question
Originator: news@ernie.Princeton.EDU
Keywords: group, coset
Organization: Princeton University
Distribution: usa
Date: Thu, 30 Jul 1992 05:48:45 GMT

In article <36049@sdcc12.ucsd.edu> dmassey@sdcc3.ucsd.edu (Daniel Massey) 
writes:
>G is an abelian group and H a subgroup of G. Prove their exists
>a subgroup of G which is iso. to G/H.

Obvious counterexamples have been given, but consider the following related
problem:

Let G be a group such that each of its subgroups is normal in G (e.g., G 
could be abelian).  Suppose G is additionally characterized by the property:
  
   For each subgroup H of G, there exists a subgroup of G isomorphic to G/H.

Find all such groups G, or at least good necessary and sufficient conditions 
for G to be such a group.  

In particular,

1) Must G be abelian?  (If not, find a non-abelian group with these properties)
2) Must G be finite?   (If not, find an infinite group with these properties)

Have fun.
Newsgroups: sci.math
Subject: Re: An interesting limit problem.
From: news@massey.ac.nz (USENET News System)
Date: Wed, 29 Jul 92 00:02:23 GMT
Organization: Massey University

In article <1992Jul28.191037.28756@gdr.bath.ac.uk>, mapsj@gdr.bath.ac.uk (Simon Juden) writes:
> 
> >mattm@lure.latrobe.edu.au writes:
> 
> [stuff deleted]
> 
> >Will someone please back me up, and say that no one learning
> >Calculus should ever be allowed anywhere _NEAR_ Mathematica?
> >(When I say 'learning Calculus' I mean the first two or three
> >semesters)
> 
> I could hardly agree more. 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. Also they'll never FULLY understand subtle concepts or follow harder
> arguments used in difficult proofs if they haven't had to do things with their
> bare hands first. Like any good similar system Mathematica can be very helpful
> to the professional mathematician. But I believe such gadgets can also do
> irreparable harm unless used appropriately. I also believe children should not
> be given calculators until they can do sums without them. But doubtless these
> views will get me flamed...
> 
Since flames were explicitly invited :-), I'll start the ball rolling.

I believe that it is far more important to understand the meaning of
the operations of arithmetic than to be able to work through the
algorithms like trained monkeys without having a clue why they work.
(I know some bright spark will ask how many monkeys I've trained to
do long division - well, no actual monkeys, but a lot of great apes :-)).

I would probably agree on something like Mathematica - but perhaps
I'm being illogical in making a distinction.
Newsgroups: sci.math
From: charlie@ernie.stat.washington.edu (Charlie Geyer)
Subject: Re: Journal prices (was: Gordon & Breach suit against AMS
Organization: Univ of Wash , Stat Dept.
Date: Thu, 30 Jul 1992 03:50:03 GMT

In article <92211.214342U53644@uicvm.uic.edu> <U53644@uicvm.uic.edu> writes:

>You know, there is the small matter here of there being more Statisticians
>than applied analysts (yes, I know that Stats can be viewed as a branch of
>applied measure theory, but that doesn't change the fact that more people will
>be interested in the material covered in J. American Statistical Association
>than in Applicable Analysis). I don't think that comparisons between the two
>Journals can tell one much.

We have the same problem in statistics.  The best journals are affiliated
with professional societies and are relatively cheap.  Some of the worst
journals come from commercial publishers and are outrageously expensive.

-- 
Charles Geyer
School of Statistics
University of Minnesota
charlie@umnstat.stat.umn.edu
Newsgroups: sci.math
From: palais@binah.cc.brandeis.edu
Subject: Re: Request: Phone + FAX numbers for Publish or Perish, Inc.
Reply-To: palais@binah.cc.brandeis.edu
Organization: Brandeis University
Date: Wed, 22 Jul 1992 20:08:11 GMT


>>    I am looking for the phone and/or the FAX number(s) of 
>>   Publish or Perish, Inc. 
>>   (they are located somewhere in Houston, Texas).

>>   Anyone out there can help me with this matter ?

>>   (BTW, I am interested in Spivak's books, which they publish.)

Publish or Perish is Mike Spivak's own company. 

Publish or Perish Inc.
3701 West Alabama 450-130
Houston, TX,   77027
713  524  5515 
IN%"spivak@rice.edu"    
FAX:  713 523 6743
From: u7023595@ucsvc.ucs.unimelb.edu.au
Newsgroups: sci.math
Subject: Re: Roots Of Integer Poly's
Date: 21 Jul 92 07:23:56 GMT
Organization: The University of Melbourne

>In article <4547@balrog.ctron.com>, wilson@ctron.com (David Wilson) writes:
> 
>>I wonder if any one out there knows anything on the following.
>>
>>Let F(x) be a monic polynomial with integer coeff's of degree n.
>>Let F(x) have roots   \alpha_{1}, ... , \alpha_{n}  is there a
>>constant C depending only on n such that
>>
>>       | \alpha_{j} - \alpha_{i} | >= C
>>
>>For all i,j. Ie the roots cannot be too close together.
>>This is trivially true for n=1 or n=2 but what about general n ?
> 
> [Stuff deleted]
> 
> For n > 2, let p(x) = x^n+bx^(n-1)-x^(n-2).  For b >= 3, p has the
> distinct real roots 0 and (sqrt(b^2+4)-b)/2, which differ by less than
> 1/b.  Hence these roots may be brought arbitrarily close together by
> choosing b sufficiently large, and there is no positive lower bound on
> the distance between distinct roots of p.  
> 
WLOG assume the monic polynomial is irreducible over the rationals as 
this is the interesting case.
For n=2 it is easily verified that \sqrt(3) is the lower bound, attained
for x^2 + x + 1 (cube roots of unity).
Consider n > 2. 
In Wilson's example (not irreducible) the roots are 0, (-b + \sqrt(b^2+4)/2
and (-b - \sqrt(b^2+4)/2.  The difference between the latter two roots is
\sqrt(b^2+4) > 2 , not less than 1/b as claimed. 
Actually the answer to the question posed above is YES.
In 1930 J. Favard showed that one can take C = \sqrt(3/2).
Blanksby, Lloyd-Smith and McAuley gave C = \sqrt(3) + \epsilon for n 
sufficiently large and suitable \epsilon > 0. 
The problem is completely solved through the efforts of Langevin, Reyssat
and Rhin. They show that C = \sqrt(3) always works. Also they found that
one can take C = 2 - \epsilon for given \epsilon > 0 for n sufficiently
large. 
The second edition of Narkiewicz's book on algebraic number theory gives
some references (first chapter? and also a postscript at the back of the
book). Also see M. Langevin, E. Reyssat and G. Rhin "Diametres Transfinis
et Probleme De Favard", Annales Institut Fourier de l'Universite de Grenoble, 
1988 and M. Langevin "Solution des problemes de Favard" in same publication
(both Vol. 38).

Bill Lloyd-Smith
Newsgroups: sci.math
From: tycchow@riesz.mit.edu (Timothy Y. Chow)
Subject: Re: Buckets of water (references sought)
Organization: None.  This saves me from writing a disclaimer.
Distribution: sci
Date: Mon, 27 Jul 92 18:13:32 GMT

In article <KAI.92Jul26211336@cyklop.nada.kth.se> kai@cyklop.nada.kth.se (Kai-Mikael J-Aro) writes:
>I have been thinking about those old puzzles where you are given two
>buckets of specific volumes and have to measure up a certain,
>different, volume of water in one of them.
>
>Has anything been written on this subject?

Check out Thomas H. O'Beirne's _Puzzles_and_Paradoxes_.  There's a lot of
other interesting material in this book, though my opinion is that O'Beirne
is not a terribly good explainer.  I have never been able to understand the
chapter on how to calculate the date of Easter.
-- 
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
From: U53644@uicvm.uic.edu
Newsgroups: sci.math
Subject: Re: ? Quick algorithm for random covering sets ?
Date: 28 Jul 92 06:45:09 GMT
Organization: University of Illinois at Chicago

I'm not quite sure of what the original poster is looking for in terms of a
probability distribution on the power set of $1,...,N, but one approach that
comes to mind is the following.......

        1. Choose some probability p in the interval (0,1)
        2. Randomly select some number between 1 and N (the tentative number
               of sets chosen). Call it K.
        3. For each number from 1 to K, set up an array (1 x N), and randomly
               fill it with 0's and 1's (latter with probability p).
                  (1 signifies inclusion, 0 exclusion)
        4. To find the intersection of our sets : multiply the arrays
               componentwise. (We now have the array for the intersection).
        5. Take this new array, and subtract each of its' components from 1
               to get the array for the complement of the intersection.
        6. Now, multiply this array (the one for the complement of the
               intersection) by the one for the K-th set to exclude the
               intersection from the K-th set.
        7. Now, take the 'complements' of the arrays for sets 1 through K :
               again, subtract each component of an array from 1 to get the
               corresponding element of the 'complementary array'.
        8. Once again, multiply the 'complementary arrays' together
               componentwise to form the array for the intersection of the
               complements of the sets. We now have an array corresponding to
               the set of all elements of $1,...,N not in any of the K sets.
        9. Add this array componentwise to the one for the K-th set.

Then, just use the usual algorithms to pick out which places in our arrays are
filled with 1's (if the n-th element of the m-th array is 1, print n. If not,
let n be replaced by n+1 and repeat. If n>N, replace m by m+1 and n by 1. If
m>K, stop, if not go to first direction in parantheses).

No promises are offered as to the uniformity of the resulting sampling
procedure. One might even things out a bit by setting the weights (when one
selects K) for the various values of K proportional to the number of possible
distinct collections of K sets satisfying the conditions. Having done so, one
might also preselect the numbers of elements for sets 1 through K-1, setting
weights in an analagous fashion (randomly setting entries to 1 or 0 until one
either uses up one's allotment of 1's or 0's for a given array, then filling
in the rest of the array with whatever is left (1's if 1 needs more 1's : i.e.
one has already excluded as many elements from the set as one can and still
have the desired number of elements. 0's if one has already included as many
elements as desired). One then fills in set K as before.

So I guess that it depends on what one wants, and how much effort is
acceptable.

                                             Joseph B. Dunphy
Xref: sparky sci.math:9448 soc.culture.british:10560
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math,soc.culture.british
Subject: Re: American mathematical hegemony
Date: 22 Jul 92 16:24:06 GMT
Followup-To: sci.math
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <1992Jul21.151348.29570@pixel.kodak.com> dj@ssd.kodak.com (Dave Jones) writes:
>In article <2176@sjfc.UUCP> dlm@sjfc.UUCP (Don Muench) writes:
>>Look me up in London and I'll give ya all an authentic upstate NY
>>(in particular, RAH-chisster) accent, in exchange for your inviting me and
>>my wife to your home for dinner.  

>Be warned that "dinner" should include the wings of about a dozen
>chickens, properly detached from the breast portions, plucked and deep
>fried (no batter please), served with a sauce whose pungency would bring
>a smile to the face of Red Dwarf's lone human occupant.  The meal should
>be accompanied by short sticks of celery and Blue Cheese salad dressing.
>I've never been able to fathom the origins or purpose of those last
>items.

- This doesn't sound right - I though he claims to live in Rochester, not
Buffalo. I also suspect him of not being autocthonous. People from both
Rochester and Buffalo know they live in _Western_ New York, not _upstate_.

I suspect that the guy is originally from downstate - NYC or Long Island and
that this means the wings may not be hot enough...

Later,
Andrew 'Born in Buffalo' Mullhaupt
Newsgroups: sci.math