Newsgroup sci.math 157955

Directory

Hi,
I am a senior undergraduate student here in Hawaii majoring in
Mathematics.  If I went on to a graduate school my interest would be in
studying sport (football of 2-3 codes in particular) from a statistical
viewpoint to predict team performance, player statistics, rate
performances, and provide other information.  I have seen some papers that
have looked at this in some old journals of the American Statistical
Association. I have some questions that hopefully some
people can provide some insight into or tips or pointers on where to go to
find out.
My questions are :-
1) Is this a feasible area of research?  I have been working on it in a
basic way given my own limited resources and time for the past few years.
2) Following from 1) is that at all useful, employment-wise do you think?
Are professional teams or others interested in this sort of information?
I have had an article or two published in fantasy football magazines,
which is basically all about player performance prediction, so a long-term
study such as is done in the baseball field would be interesting, I think.
3) What are the best programs?
4) What programs might have people interested in the above type of
research?  Operations Research as well, perhaps?  Other areas?
5) Anything else you might like to add to enlighten a newbie would be
great.
Thanks,
Richard
Richard Scott (rscott@hawaii.edu)

Here's one:
Simplify
(x-a)(x-b)(x-c)...(x-z)
as much as possible. Lowest number of ASCII characters wins
(less than ten is possible).
Those of you who have seen it before, or immediately sees
the optimal answer, might wait a day or so before replying,
so we can get some creativity here :-)
olem

In article <32DBBFCC.5532@cfer.ualberta.ca>,
Paul Skoczylas   wrote:
>I have a bunch of small (4-10 points) data sets (x vs y), gathered from
>experimental data.  All can be very accurately approximated by a cubic. 
>However, the curvature of the lines vary--some are very linear.  What I
>need is an accurate measure of the curvature of the lines, so I can
>compare them to each other.  (What I want to do is see if any other
>external variables effect the curvature of the x-y plot.)
Try the quantity that is used to minimize in a fancy definition of cubic 
splines: an approximation of the square root of the integral of the 
square of the second derivative of the function. (Since the data are 
near-cubic, this should be quick - use simple Simpson's Rule on the 
square of the second derivative.)
Cheers, ZVK (Slavek).

mfinney@lynchburg.net writes:
  >But classical logic only allows discussion of non-empty domains.
  Aristotelian logic, perhaps. But there is no problem with discussing
possibly empty domains in ordinary predicate logic, at the cost of
introducing a predicate symbol.

Hi,
I am a computer scientist and working on inductive generalization of
structured objects, that can be represented by directed, coloured
graph or hypergraphs or conjunctions of logical literals.
I am looking for 
1. a good, exact and general maximum clique algorithm.
2. a  good, exact and general algorithm for matching two directed,
   coloured graphs or hypergraphs.
I am aware of the fact that both problems are NP complete. But perhaps
there is a general algorithm that works well for "almost all" graphs
or at least many graphs with a property that is not too restrictive.
My graphs tend to be rather large but are not symmetrical or
regular. They are not planar but are sparsely connected.
Tanks for any hint,
Peter Geibel
-- 
==================================== TU Berlin, FG KI, Sekr. FR 5-8
Peter Geibel =================== Franklinstr. 28/29, D-10587 Berlin
============================================= Tel. +49-30-314-25491 
============================ URL http://www.cs.tu-berlin.de/~geibel

davis_d@spcunb.spc.edu (David K. Davis) wrote:
>Pi, I believe will be discovered by intelligent life where ever and whenever it arises.
No.  Intelligent life will discover 6.283193... or 2pi.
-- Ray Tomes -- rtomes@kcbbs.gen.nz -- Harmonics Theory --
http://www.vive.com/connect/universe/rt-home.htm
http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm

Does this experience sound familiar to you?
(pointless example following)
I'm a chess problem composer, and I sometimes
do it even in my dream. Too bad that when I
awake, my problem is cooked and nothing works.
So: Did you ever dreamt up some nobel-prize
worthy theory, just to realize after awakening
that it violates five conservation laws
and the data too?
-- 
Hauke Reddmann <:-EX8 
fc3a501@math.uni-hamburg.de              PRIVATE EMAIL 
fc3a501@rzaixsrv1.rrz.uni-hamburg.de     BACKUP 
reddmann@chemie.uni-hamburg.de           SCIENCE ONLY

>Mike Housky (mike@webworldinc.com) wrote:
>[...]
>> > Q: "Some of the factors of a locker number are 2, 5, and 9.  If it
>> > has exactly nine additional factors, what is the locker number?"
>> > 
>> > Answer Given: 90
>> > 
>> > My Answer: There does not exist a number with this property.
>
>The divisors of 90 are exactly 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
>They are 12 in total, so nine more than the three ones shown. The answer 
>is unique because the number should be a multiple of 2*5*9 = 90, but 
>any number of the form 90n with n > 1 has more that 12 divisors.
The number of factors can be calculated by multiplying the exponent of
prime factors plus one.
For example, 90 can be written as 2*3^2*5 and the number of
factors is (1+1)(2+1)(1+1)=12.
Therefore the number of factors <-> product of the exponents.
If the product of the exponent is 12, then the number has 12 factors.
In this case, 9 must be a factor, so 3 has to have an exponent of 2 or
higher. The smallest number we can get that way is 90.

Scott Phung wrote:
    
> One Final Question for all,
> 
> "Was my answer correct with regards to what the question asked?"
> 
> The original question was, (taken from November 1996 issue of NCTM,
> Question 14 on the calendar problems)
> 
> Q: "Some of the factors of a locker number are 2, 5, and 9.  If it
> has exactly nine additional factors, what is the locker number?"
> 
> Answer Given: 90
> 
> My Answer: There does not exist a number with this property.
I missed most of this thread.  The question, as posed, may have problems
but your answer is clearly wrong.  There does exist at least one common
interpretation of the terms "number" and "factor" such that the property
holds.  Beware of sweeping generalizations.
An important part of the study of mathematics is learning the language 
used by mathematicians.  Maybe that should be "languages"--terminology 
and notation vary.  Here's one bit that's fairly common, though:  The
unqualified use of the term "number" (especially where integers are
implied) generally means "natural number".  A "factor" usually means a
divisor that is not only positive, but also greater than 1.
    All generalizations are false,
    Mike.

Archimedes Plutonium wrote:
>   Thanks but no thanks. In math as in life, it is best to stick to main
> essentials and not be sidetracked with tourist curios knick knacks.
Adeles and ideles are *not* "tourist curios knick knacks". They play an
essential role in number theory, but also in the geometry of algebraic
curves (number fields and function fields have a lot in common). They
are used extensively in the so-called "class field theory". And,
needless
to say, they are a central tool in Andrew Wiles proof of Fermat's
Theorem
(I'm saying this to annoy you, of course).
     David A. Madore
    (david.madore@ens.fr,
     http://www.eleves.ens.fr:8080/home/madore/index.html.en)

Hi
How do I solve this polynomial equation:
y=2X^3+6X+4
What is the method for solving polynoms in an high degree?
Thanks 
Boaz
Tel Aviv

P} forh}nd takk (Thanks in advance) :)
--
* Hans Kr. Ruud						The noble art    *
* Kristine Bonnevies vei 15				of losing face   *
* 0592 ÅRVOLL						may one day save *
* Tlf. 22 65 22 34 (hjemme) 22 77 05 35 (jobb)  	the human race   *

Mike Housky (mike@webworldinc.com) wrote:
[...]
> > Q: "Some of the factors of a locker number are 2, 5, and 9.  If it
> > has exactly nine additional factors, what is the locker number?"
> > 
> > Answer Given: 90
> > 
> > My Answer: There does not exist a number with this property.
The divisors of 90 are exactly 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
They are 12 in total, so nine more than the three ones shown. The answer 
is unique because the number should be a multiple of 2*5*9 = 90, but 
any number of the form 90n with n > 1 has more that 12 divisors.
Miguel A. Lerma

I'm very interested, too. I'm in Seoul, Korea, though. I'm 15 years old,
sophomore and also very good at math and science. I'm not good at HTML or
things like that but am really interested and I think I can pick it up pretty
quickly. Please give me some information on it. Visit my homepage at
http://www.geocities.com/CapeCanaveral/6270/
and download my program. Please remind that my e-mail address is
dankang@nuri.net not dan.kang@nuri.net.
spectrum  wrote
> 
> So email me if you are interested and please include your location of
> residence (City, State, Country will be fine), your interests, your
> computer abilities (i..e programming or HTML or 3D graphics or CGI or
> photoshop or whatever) and ideas with this contest that could help us
> fund an education to CalTech ;)
-- 
><><><><><><><><><><><><><><><><><><><><><><><
Daniel B. Kang - A 10th grader at SIS (Seoul International School)
who's interested in getting into Caltech prior to graduation (after
the junior year). If you have any info on it, please e-mail me at
dankang@nuri.net.
<><><><><><><><><><><><><><><><><><><><><><><>
My return address is intentionally invalid due to an increasing
number of unwanted junk mails. Please take out a period between
dan and kang. Thanks.
><><><><><><><><><><><><><><><><><><><><><><><

In article <32dbcf78.1098335@tar-news.tpgi.com.au>,
stan  francuz  wrote:
>would  appreciate  help  with  this  MI  question .
>
>Consider  the  Fibonnaci  sequence  1,1,2,3,5,8,....
>
>which  may  be  defined  as  t(1) = t(2) = 1 , 
>
> and    t(n+2) = t(n+1) + t(n)
>
>Prove   by  MI 
>
>t(2n)  =  t(n){t(n+1)  +t(n-1)} 
>
>  stan
From many possible proofs, I choose the one that needs extra work to 
remove symptoms of outside help:
Use 2x2 matrices T(n) = [t(n-1)  t(n)  ]
                        [t(n)    t(n+1)]
and to start, define T(0)=I, t(0)=0. (Notice that t(0)=1 fits into the 
definition of t(n), extended to n=0 by the same formula.)
Then induction shows that  T(n+1)=T(1)*T(n),  so that  T(n)=(T(1))^n.
By properties of powers, we find that  T(2*n) = T(n) * T(n), and then 
write the last equation in coordinates.
As a bonus, you also obtain a shortcut formula for  t(n)^2 + t(n+1)^2.
Good luck, ZVK (Slavek).

In article <5b3f3c$5qs@news.fsu.edu>, Jim Carr  wrote:
> Pascal was invented as a teaching tool.  BASIC was invented so you 
> could write very crude programs on exceedingly primitive computers, 
> AFAIK.  If it was invented as a teaching tool, who is guilty? 
I have read that the original purpose of BASIC was to teach beginning
programming students about concepts of assembly language, hence the
line numbers, the global namespace, and the lack of structured
programming concepts.
-- 
Dave Seaman			dseaman@purdue.edu
      ++++ stop the execution of Mumia Abu-Jamal ++++
    ++++ if you agree copy these lines to your sig ++++
++++ see http://www.xs4all.nl/~tank/spg-l/sigaction.htm ++++

In article <5bc75q$1kj@news.usit.net>, Heath David hart 
heath@homemail.com says...
>macchi@marina.scn.de (Gian Carlo Macchi) wrote:
>>I've not followed this thread until now. Anyway, in your example, Roman
>>I always counts 1, independently of its position, and X always counts
>>10. 
>>That is why this numbering system is not positional.
>I think it could reasonably be argued that in 'VI' the symbol 'I' has 
>a value of 1, but in 'IV' the symbol 'I' has a value of -1.  
Negative numbers do not apply to Roman numbering system. So the I in IV 
can be seen as the number 1 that has to be subtracted to V; so we can say 
that IV corresponds to 4, i.e. 5 - 1, where the minus is an operator 
applied to the couple of numbers 5 and 1, not the sign of the number -1.
Ciao.
Gian Carlo  macchi@scn.de

Richard Scott   wrote:
> I am a senior undergraduate student here in Hawaii majoring
> in Mathematics.  If I went on to a graduate school my interest
> would be in studying sport (football of 2-3 codes in particular)
> from a statistical viewpoint to predict team performance, player
> statistics, rate performances, and provide other information. 
> I have seen some papers that have looked at this in some old
> journals of the American Statistical Association.  I have some
> questions that hopefully some people can provide some insight
> into or tips or pointers on where to go to find out. 
> My questions are :-
>
> 1) Is this a feasible area of research?  I have been working on
>    it in a basic way given my own limited resources and time for
>    the past few years.
Yes
> 2) Following from 1) is that at all useful, employment-wise do 
>    you think?  Are professional teams or others interested in
>    this sort of information?  I have had an article or two
>    published in fantasy football magazines, which is basically
>    all about player performance prediction, so a long-term study
>    such as is done in the baseball field would be interesting, I 
>    think.
Congratulations on publication!!  The interest of professional 
teams is fairly limited.  You might try surveying some teams to
see what they are doing and what their interests are.
> 3) What are the best programs?
I have no idea.  But you might see who is publishing these type
of papers in Stat journals and Sport journals and ask them.
> 4) What programs might have people interested in the above type
>    of research?  Operations Research as well, perhaps?  Other 
>    areas?
Good question to ask of people in the Sport Behavior research
business.
> 5) Anything else you might like to add to enlighten a newbie
>    would be great.
Keep publishing!!  It's good karma!!
Dick

rtomes@kcbbs.gen.nz (Ray Tomes) wrote:
>davis_d@spcunb.spc.edu (David K. Davis) wrote:
>>Pi, I believe will be discovered by intelligent life where ever and whenever it arises.
>No.  Intelligent life will discover 6.283193... or 2pi.
Looks like Ray considers the discovery of pi and 2*pi to be mutually
exclusive...maybe he just doesn't qualify as intelligent life.  ;-)
JeffMo
"A valid argument is not formed solely by ignorance." -JeffMo
"A valid argument is not formed solely by assertion." -JeffMo
Religion : Science :: Methamphetamine : Exercise
For email replies, remove the "dipstick." from my eddress.
It should be self-evident that I am not a dipstick.  ;-)

Gian Carlo Macchi wrote:
> 
> In article <5bc75q$1kj@news.usit.net>, Heath David hart
> heath@homemail.com says...
> 
> >macchi@marina.scn.de (Gian Carlo Macchi) wrote:
> 
> >>I've not followed this thread until now. Anyway, in your example, Roman
> >>I always counts 1, independently of its position, and X always counts
> >>10.
> >>That is why this numbering system is not positional.
> 
> >I think it could reasonably be argued that in 'VI' the symbol 'I' has
> >a value of 1, but in 'IV' the symbol 'I' has a value of -1.
> 
> Negative numbers do not apply to Roman numbering system. So the I in IV
> can be seen as the number 1 that has to be subtracted to V; so we can say
> that IV corresponds to 4, i.e. 5 - 1, where the minus is an operator
> applied to the couple of numbers 5 and 1, not the sign of the number -1.
According to Conway and Guy, the Romans didn't really use the 
positional subtraction - widespread use started in medieval times.
-- 
D.
mentock@mindspring.com
http://www.mindspring.com/~mentock/index.htm

Etherman wrote:
> 
> Recently I have been thinking a lot about how to find a curve that best
> matches a given set of points.  Today I got an idea.  Why not try
> to find the differential equation that best describes a set of points?
> It's fairly trivial to find the best simple harmonic oscillator diff. 
This can be done and is a very useful technique for physical modelling. 
For systems in which the solution to the DEQ doesn't have an analytic
form, one can still compute a numerical table of the solution, compute
chi^2 from this, and apply a minimizing algorithm to solve it.
Marcus Mendenhall
Vanderbilt University

On Tue, 14 Jan 1997 20:47:05 -0800, Rodney Hunsicker 
wrote:
>...  God is known through faith, and faith is grown in love.
>Love is the only "light" that can reveal the existance of God.
  But only if the "love" in question is on the "approved list", right?
  Gay and lesbian love is not on that list, is it, Rodney?
  Can you spell "HYPOCRISY", Rodney?

Richard Mathar (mathar@qtp.ufl.edu) wrote:
: dasher@netcom.com (Anton Sherwood) wrote on Mon, 30 Dec 1996:
: > Wanted: number of spheres that can pack around a sphere
: > in n dimensions; I have for n up to 10 (2 6 12 24 40 72 
: > 126 240 272 306), want up to 16.
See "New Sphere Packings inDimensions 9-15" by J. Leech & N. Sloane,
A.M.S. Bulletin, September 1970, pages 1006-1010.They show maximums:
Dimension	Spheres touched
9		306
10		500
11		576
12		840
13		1130
14    		1582
15		2564
Of course higher values may have been discovered since.
Brian Calvert

In article <5bhcu9$go3@sun001.spd.dsccc.com>,
Mike McCarty  wrote:
>
>You are confusing proper time and time as measured by an observer. The
>collapse proceeds very speedily in proper time (i.e. time as actually
>seen by the one falling into the black hole). You might investigate the
>Kruskall coordinates for a black hole.
This sounds like an improved modern version of the Zeno paradox about
Achilles and the tortoise: In the original paradox Achilles cannot pass
the tortoise because he first has to pass an infinite number of points,
and this may be solved by noting that the length of time is still finite.
In the new version, the black hole cannot form because it takes an
infinite length of time, and this is solved by noting that this time is
finite from another point of view.
Greetings,
Ørjan.

This should make it clear once and for all.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Define a perfect continuous function as being a function
f:[0,1]->R(the set of real numbers)
    ^ the compact[0,1]
and for all x in [0,1] there is a sequence {x_n} which converges to x
(but it is not constant (=x) starting from any n) such that f(x_n)=f(x)
Prove:
The sum of two perfect continuous functions is a perfect continuous
function.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Bob

Dave Seaman wrote:
> 
> 
> I have read that the original purpose of BASIC was to teach beginning
> programming students about concepts of assembly language, hence the
> line numbers, the global namespace, and the lack of structured
> programming concepts.
> 
Are you sure?  I don't see how the concepts of assembly language can
ever be taught by teaching BASIC.  Rather, I think BASIC was developed
so that people did not have to learn the concepts of assembly language
and still be able to program a computer by using an English-like
language.
Regards,
Shyang Hwang

"John P. Boatwright"  wrote:
Bloatwad is in prime shape for his table dance routine.
He will be leading a contingent of Whores For Christ at Easter.
At a certain point in the Easter parade, Bloatwad and his mom will
drop their robes and do their table dance routine to adoring fans
(each other).
I hope they arrest him again.
Geo
If atheism ever becomes a capital offense,
then I want to be regarded as the Charles Manson
of atheism. - Geo

In article <5bifum$lc8@rzsun02.rrz.uni-hamburg.de>,
Hauke Reddmann  wrote:
>Does this experience sound familiar to you?
>
>So: Did you ever dreamt up some nobel-prize
>worthy theory, just to realize after awakening
>that it violates five conservation laws
>and the data too?
	I have read and composed verse in dreams that 
simply didn't rhyme at all in real life.  The meter always
seems to work but the rhymes tend to be not even close.
Nothing Nobel-worthy, however.  
	While we're on the subject, I once collected a list
of "You know you've been mathing too long when..." stories,
many of which involved zany things that occurred to people
in dreams (one fella was awakened by roomies when he was
found on the floor, trying to find x).  In any case, if you
have any such stories (or even jokes, but make it clear
if you're presenting a joke), email yours truly at 
caj@niu.edu.  Thanks a googol.
>Hauke Reddmann <:-EX8 
 ,oooooooo8    o     ooooo@math.niu.edu  -==-  http://www.math.niu.edu/~caj/
o888'   `88  ,888.    888   
888         ,8'`88.   888 "Hey, you got your chocolate in my cod liver oil!"
888o.   ,oo,8oooo88.  888 "Hey, you got your cod liver oil in my chocolate!"
`888oooo88o88o  o888o 888                       -Common occurrence in the
___________________8o888'________________________days before peanut butter__

cyberman@zerocity.it (Cyberman) wrote:
>Hello. I've a little problem:
>I must invert this function: y = (x^2) + x     for x >= 0
>Is there anybody that could help me?
x^2 + x = x^2 + x + 1/4 - 1/4 = (x+ 1/2)^2 - 1/4  Complete the square.
(x + 1/2)^2 - 1/4 = y
(x + 1/2)^2 = (y + 1/4)
x + 1/2 = +-SQRT(y + 1/4)
You take it from there.

In article <32D9DC04.C68@weirdness.com>, Keith Pitcher  writes:
>Hello,
>	recently my sister's math teacher asked a question, and did not accept
>her
>logical answer (He gave an "F" to the poor girl). I will be meeting with
>the teacher this week to discuss this matter, and am seeking support to
>show the teacher the error in his ways.
>
>His question for his standard 7th grade math class, in verbatim,  was as
>follows:
>
>Q) Take a square piece of paper. Fold it in half. Do it again. Repeat 25
>times. How many sheets thick is the final folded piece of paper.
>
>
>My sister realized that this was a trick question, as she knew a piece
>of paper can
>not be folded that many times in half, and so far every question had
>been based in reality. She came up with this description of her answer :
>
>A) Take a piece of paper and fold it in half. Now, to "Do it again" you
>have to unfold the piece of paper and refold it again. (This would be
>like closing your hand into a fist and being told to "Do it again." You
>first have to open your hand) Repeat this 25 times. The final paper
>would have just one fold, being two sheets thick.
>
>
>The teacher gave this answer an "F", stating that the answer was wrong.
>I disagree.
>He asked a trick question, and he recieved a very logical answer. In
>fact, the only answer that I can concieve that can actually work. She
>has been able to answer the questions using first hand examples to
>determine other problems. (Such as blocks of wood for area problems).
>Further, if he wanted to reach an answer of 2^25 he should have phrased
>the question much better, such as "Assuming you can fold a piece of
>paper...."
>
>I am seeking opinions on his grade. 
Since you are asking for opinions, I will give you mine ....
The question is ambiguously worded, as it is not clear what you are
repeating 25 times (it asks for one fold, then a second, then to
repeat - both folds, repeat one fold, repeat to a total of 25 times,
etc.).  However, I think that your sister's answer was probably not 
right.
How many times was your sister's test paper folded?  If you are going
to interpret the question literally, then I would say that, unless the
paper was folded at least twice, your sister got the question wrong.
After all, the question does clearly say to "Take a square piece of 
paper.  Fold it in half [etc. etc.]".  I am guessing that the paper 
wasn't folded, in which case I would conclude that your sister realized 
that this was a hypothetical example and so should have answered it 
with a number like 2^25 (or 2^26, or even 2^50, depending on how one 
interprets the word "this" in the phrase "repeat this 25 times").
For further examples of the consequences of taking things literally, I
refer you to the episode of "The Brady Bunch" where Greg gets hung-up
on his parents "exact words" when issuing instructions, rather than
the intent of the words (e.g., Greg drives a friend's car after being
forbidden from driving because his dad told Greg he couldn't drive
the family station wagon for a week).
I am also a littled baffled as to why she got an "F" when she answered
many other problems correctly.  Did she get several other questions
wrong?  Is there more to the story than what you wrote?
Regards,
Mike Diebold
**********************************************************************
            Opinions are of the author, not DuPont
**********************************************************************

The event horizon is not static: it expands to engulf the 
incoming matter.  This happens in finite time even from the
point of view of an external observer. See "Black Holes: The
Membrane Paradigm" by Kip Thorne.

In article <32DC6149.6C9C@fast.net>, Rodney Hunsicker   wrote:
	[snip snip snip, snippy snippy snip]
>God made light.  By it we see.  Without it we cannot focus are attention
>on externals.  God made the world.  We see it in light.  
>An infinite multitude of world exists in darkness and we see only what
>the flashlight of our preception can capture momentarily.  Math is a
>vain attempt to place order on that which is already ordered.  God is
>said to be within.  God cannot be seen in the light because he is not in
>the darkness.  God is known through faith, and faith is grown in love.
>Love is the only "light" that can reveal the existance of God.
	God made vi.  By it we edit.  Without it we quote an entire 
article without removing irrelevant text.  God made morons.  We see
them on USENET.
	An infinite multitude of people who can barely write articles
about subjects they simply don't understand exists on USENET and we
see only what the flashlight of our newsreaders can capture 
momentarily.  These articles are a vain attempt to put down that which
the authors know nothing about.  God cannot be seen in the light of
the newsreader because s/he is not on usenet, because s/he is not a 
one-taco-short-of-a-combination-plate moron.  Furthermore, s/he clips
quotes that aren't relevant to the discussion, and knows how to 
indent a damn paragraph.  
	Oh, and s/he can spell big long hard words like "existence."
  .,-:::::   :::.         ....:::::: @niu.edu -- http://www.math.niu.edu/~caj/
,;;;'````'   ;;`;;     ;;;;;;;;;````
[[[         ,[[ '[[,   ''`  `[[.     "I'd like a large order of FiboNachos."
$$$        c$$$cc$$$c ,,,    `$$      "Okay sir, that'll cost as much as a
`88bo,__,o, 888   888,888boood88    small order and a medium order combined."
  "YUMMMMMP"YMM   ""` "MMMMMMMM"  _____________________________________________

In article <5bhhau$edv@news.iastate.edu>,
Alexander Abian  wrote:
>
>Abian answers:
>
>Dear Mr.Kastanas,
>
> First of all thank you for your informative e-mail.
	You are welcome.
> However, I still tend to believe that with very clever choices  for
> postes and  extremely clever usage of dense subsets - the language
> of Forcing can be avoided.
>
> I would like to see if you can consider proving the following two
> statements in a straight forward way using suitable posets and
> their dense subsets.
>
> Let  M  be Cohen's minimal model. Let us assume that we DO NOT
>                                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> KNOW THAT   CH  and  Zorn's Lemma are  valid in  M.
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>
> (1)  Can you prove that some generic  extension of  M  would 
>      be a model for ZF+ CH ?
>
>(2)   Can you prove that some generic extension of  M  would
>      be a model for  ZF + Zorn's Lemma  (preferably Zorn's
>      Lemma and not its equivalent  AC)?
	I'm in favor of a "dense sets" view of forcing; e.g. forcing in
   arithmetic or analysis.   Incomparable degrees (Kleene-Post) were really
   an early forcing result, and by using only certain dense sets one got
   recursiveness in 0-jump.  In set theory, on the other hand, one typically
   has G meeting _all_ dense sets in M; one then argues that this dense set
   or that one is in fact in M.  The language of forcing ("L.F.") provides
   a systematic, if not clever, way of doing so over a wide range.
	One cannot exactly "forget" the properties of the minimal model,
   since what happens in M[G] is very much affected by what is the case in
   the ground model.  I would interpret this request as one to start with
   some M, countable transitive model of ZF, and if AC or (G)CH do not hold,
   produce a model where they do.   (I don't quite get the point about Zorn.
   The proof of  AC <=> Zorn (<=> Wellordering <=> ...) is straightforward,
   good for any model, and at worst one can just repeat it).
	Also, the 'test cases' do not _need_ a forcing extension; obviously
   it is enough to construct L (in M... getting  (L)^M, = some L_a).  But let
   us consider M[G] anyway.
	Well, the fact is: L.F., the language of forcing, is for one thing
   the way one _defines_ M[G].  Note that if M = an L_b, the minimal one or
   otherwise, then Cohen's  L[b, G]  definition is an equivalent road to
   M[G]; but not in general.  The iterative buildup of M[G] is by L.F., not
   by constructibility!   It's a Catch-22; in the cases for which we know
   how to avoid the L.F. definition, AC and CH hold to begin with!
	Finally, suppose the above is overcome.  Say we have 2^w = k > w_1
   in M.  We can go about adding a function that collapses k "without L.F.";
   but can we actually control global stuff like how many reals are added
   overall?  I suspect the nitty-gritty of doing so is tantamount to using
   L.F. ... even if we don't call it by that name.
							Ilias

geibel@cs.tu-berlin.de (Peter Geibel) writes:
< I am looking for ... a good, exact and general maximum clique
< algorithm. ... perhaps there is a general algorithm that works well
< for "almost all" graphs or at least many graphs with a property that
< is not too restrictive.  My graphs tend to be rather large but are not
< symmetrical or regular. They are not planar but are sparsely connected.
If this sparseness holds not just for the whole graph but also for any
subgraph, i.e. if there is a constant c such that any k-vertex subgraph has
at most ck edges, then you can find the max clique in time something
like O(2^{2c} n).  Here's one easy algorithm (from my paper ChrEpp-TCS-91, for
an earlier linear time algorithm see ChiNis-SJC-85, full references below):
repeat until graph empty:
	find a minimum-degree vertex v
	check whether each large subset of neighbors is a clique
	delete v from the graph
To make this linear time you need some simple data structures to find
the min degree vertex and to test whether an edge exists in the graph
Both can be done in constant time per operation (the main point of
ChrEpp-TCS-91 is to address the edge existence test using a method based
on similar ideas of ordering the vertices by degree).
Probably the 2^{2c} (which is the number of subsets of neighbors) can be
improved to a smaller exponential term by using a faster dense-graph
clique algorithm (e.g. that of Rob-Algs-86) in the graph induced by the
neighbors of v.
Sorry, I have less info on your matching problem, although I do have
some references on matching pairs of graphs in one of my
bibliography files, http://www.ics.uci.edu/~eppstein/bibs/subiso.bib
References:
@article{ChiNis-SJC-85,
  title = {{Arboricity and subgraph listing algorithms}},
  author = {N. Chiba and T. Nishizeki},
  journal = {SIAM J. Computing},
  volume = {14},
  pages = {210--223},
  year = {1985}}
@article{ChrEpp-TCS-91,
  title = {{Planar orientations with low out-degree and compaction of adjacency matrices}},
  author = {Marek Chrobak and David Eppstein},
  journal = {Theoretical Computer Science},
  volume = {86},
  pages = {243--266},
  year = {1991}}
@article{Rob-Algs-86,
  title = {{Algorithms for maximum independent sets}},
  author = {J. M. Robson},
  journal = {J. Algorithms},
  volume = {7},
  pages = {425--440},
  year = {1986}}
--
David Eppstein		UC Irvine Dept. of Information & Computer Science
eppstein@ics.uci.edu	http://www.ics.uci.edu/~eppstein/

luke wrote:
> how big would a black hole be?  i don't know much about astrophysics, so
> i
> don't even know in what units the answer would be.  how big would it be
> compared to the earth or to the sun?  when i say big i mean diameter or
> circumference.
The Schwarzschild radius R for a black hole of mass m is 
    R = 2 G m/c^2, 
where G is the universal constant of gravitation and c is the speed of
light in vacuum.  The Schwarzschild radius for the Sun is about 3 km,
whereas it is about 1 cm for the Earth.
-- 
                             Erik Max Francis | max@alcyone.com
                              Alcyone Systems | http://www.alcyone.com/max/
                         San Jose, California | 37 20 07 N 121 53 38 W
                                 &tSftDotIotE; | R^4: the 4th R is respect
     "You must surely know if man made heaven | Then man made hell"

I've looked through the Griess and Schneider materials, and they look
interesting.  However, one thing that seemed to be lacking was discussion
of how to read and write proofs in conventional mathematical English.  
Given that students will ultimately have to read and write proofs in
this style, how do you motivate the transition from proofs in this 
very formalized style to proofs written in English?  
-- 
Brian Borchers                              borchers@nmt.edu
Department of Mathematics                   http://www.nmt.edu/~borchers/
New Mexico Tech                             Phone: 505-835-5813
Socorro, NM 87801                           FAX: 505-835-5366

give a nigga yo adress

In <5bi86p$2kp@nntp1.u.washington.edu> hillman@math.washington.edu
(Christopher Hillman) writes: 
>
>In article <5bhpbg$hfq@dfw-ixnews9.ix.netcom.com>,
>odessey2@ix.netcom.com (Allen Meisner) writes:
>
>|>     Mr. Hillman, you explained in another post that mass and
kinetic
>|> energy both contribute to the mass-energy of a particle.
>
>Yes, the total energy (expanded in a power series in v) is
>
>  m/Sqrt{1-v^2} ~ m + (1/2) m v^2 + (3/8) m v^4 + ...
>
>where the first term is the mass, the second term is the Newtonian
>value for the kinetic energy, and the remaining terms may be
considered
>relativistic corrections to the kinetic energy (which are important
only
>for values of v close to 1).
>
>|> You stated in another post that the
>|> velocity space of a body is a Lobachevsky geometry.
>
>Yes,  The velocity space is space of forward pointing unit vectors,
which
>can act as tangent vectors to world lines; the spacelike components of
such
>vectors are interpreted as the components of the velocity and the
timelike
>component gives the time dilation rate at that event (for a clock
carried
>with the particle, relative to the rest frame).
>
>|> Mr. Archimedes
>|> Plutonium has stated that the Lobachevsky geometry does not have a
zero
>|> reference point.
>
>In the same sense that ordinary euclidean space does not have any
distinguished
>points, he is correct.   The euclidean plane, the ordinary sphere, the
Lobachevsky
>"hyperbolic" space (topologically a plane and thus often called "the
hyperbolic
>plane") and the velocity space of tachyons (topologically a cylinder)
are all
>surfaces of constant curvature and thus have no geometrically
distinguished points.
>Thus, the choice of an origin for any coordinate system is arbitrary. 
The
>euclidean plane has constant curvature zero, and can be given the
familiar
>Cartesian coordinates.  The remaining surfaces have constant nonzero
curvature
>and cannot be given a Cartesian coordinate system; in fact, the sphere
cannot
>be given ANY global coordinate system (i.e. one which avoids
coordinate
>singularities at all points) whereas the others can be given global,
nicely
>behaved conformal coordinate systems.  One popular conformal system
for
>the Lobachevsky space was introduced by Poincare and maps this space
onto
>a disk of unit radius (with the geodesics represented as circular arcs
>whose ends are orthogonal to the bounding circle).  A good conformal
>system for the tachyon velocity space is the exact analog of the
Mercator
>projection for the sphere (it represents lightlike geodesics as
straight
>line segments).
>
>|> Since a body with constant velocity has a non-zero slope in the
Loba geometry,
>
>Unfortunately present technology does not support the drawing of a
freehand
>picture or two which would have greatly clarified my posting
discussing
>velocity spaces.  In fact, a body with constant velocity (i.e. whose
world
>line has a constant unit tangent vector all along the world line) is
>represented in the velocity space by a POINT.  On the other hand, a
body
>with a curved world line experiences accelerations and such a world
line
>corresponds in the velocity space to a curve; in the case of constant
>acceleration this curve is a geodesic (topologically a line) on the
>Lobachevsky space.  "Velocity space" is called that because its POINTS
>correspond to possible values for the velocity associated with a
>particular event on a given body's world line.
>
>What you wrote after the quoted remark seemed pretty far off the mark
to
>me--- possibly because of the misunderstanding just noted.
>
>Chris Hillman
>
>
>
    Ok Mr. Hillman, what I would like to ask now is whether the
topology of the velocity space is responsible for the inertial motion
of a body in the same way that the topology of the gravitational field
is responsible for the acceleration of a body. My ideas that you say
are far off the mark arose because I was confused about how a static
curvature in spacetime could cause the motions of bodies. Why does a
curvature in space time constrain an object to move? Obviously you can
not use gravity to explain gravity. This problem was worrying me and I
am wondering if you can ease my mind. Also, if the topology of the
velocity space is the cause of inertial motion, is time dilation the
only explanation for the Lobachevsky curvature? I must admit that I can
not see how this is so. Wouldn't time dilation give you the flat
spacetime of SR and the Lorentz metric? It seems to me that only
absolute time and length dilation can give the Lobachevsky metric.
Regards,
Edward Meisner

Jeffrey Rubin wrote:
> 
> David Ullrich (ullrich@math.okstate.edu) wrote:
> <>
> 
> Thank you David.  As in the past, you have come through for me with a
> clear direct answer to my question.  I really appreciate you volunteering
> so much of your time to help people out on the net (sci.math in particular)
> and I hope you will continue to do so.
	What a curious attitude...
-- 
David Ullrich
?his ?s ?avid ?llrich's ?ig ?ile
(Someone undeleted it for me...)

Howard wrote:
[...]
> What does "physically impossible" mean in math?
It means "a not true statement in a (fictitious) system called
'Physical Reality.'"  Of course, fictitious is a bit strong;
there's a readily available model. :)
-- 
		-- Eric Gindrup ! gindrup@okway.okstate.edu