HDTenEightyP/NetNews huggingface dataset:
From: greg@phoenix.Princeton.EDU (Gregory Nowak)
Newsgroups: sci.math
Subject: Re: The Value of Science
Keywords: Relativity, Poincare, Whittaker
Date: 30 Jul 92 10:58:27 GMT
Organization: Princeton University
Originator: news@ernie.Princeton.EDU

In article <1992Jul25.014957.18824@panix.com> davidc@panix.com (David C. Chorlian) writes:
}
}	Abraham Pais, in his biography of Einstein, "Subtle is the
}Lord...", has quite a different account of Poincare's contribution
}to the development of the theory of Relativity, and says, 
}"His [Whittaker's] treatment of special theory of relativity ..
}shows how well the author's lack of physical insight matches his
}ignorance of the literature." (168)

I believe Whittaker goes back to Campbell for his account; there are
reasons for providing the history of a Poincare-Lorentz version of
"relativity" which go deeper than mere ignorance.

}	Of Poincare's 1904 address in St. Louis, Pais gives the
}following account on page 128:
}	"All  phenomena seen by one observer [in relative motion to
}another] are retarded relative to the other, but they all are
}retarded equally (Poincare points out) and 'as demanded by the
}relativity principle [the observer] cannot know whether he is at
}rest or in absolute mothion.'  Poincare is getting close.  

Pais' book is nice if you want a good story about Einstein. It falters
in moments like these, when he steps out of the historian's role and
decides he has to deify Einstein and refute claims that other
contemporary actors may have "gotten" relativity. To be fair, some of
these claims are also rather sloppily formulated.

}	Although Poincare had the equations of the Lorentz transformation
}by 1905, HE DID NOT UNDERSTAND WHAT THEY MEANT.  Thus he is rightly
}not credited with the development of special relativity.

I feel I have to step in here in my capacity as a historian of
science. One of the most common mistakes non-historians make about
Einstein is that they assume the moment the 1905 paper hit the
presses, everyone saw it as touching off a revolution in physics and
immediately declared themselves "pro-Einstein" or "anti-Einstein". The
field is a bit more complicated in those first few years, and if one
wants to be a fair-minded historian one has to avoid handing out
"right" and "wrong" awards. Einstein developed special relativity,
true -- but don't imagine from that that Poincare or Lorentwz "didn't
understand" something. I'd suggest that you check out an article by
Andrew Warwick which should be appearing soon in Science in Context
(sorry, I only saw it in preprint) which summarizes the reading of
Einstein in the Cavendish Labs in the years 1905-1911: In short,
Einstein's work was seen as _confirming_ that of Larmor. Warwick's
work serves as a good corrective to the notion that everything was cut
and dried by 1906.

greg
From: rp@llex.ll.mit.edu ( Richard Pavelle)
Newsgroups: sci.math
Subject: Confluent Hypergeometric Functions (Kummer's equation)
Date: 30 Jul 92 13:22:25 GMT
Organization: MIT Lincoln Laboratory
Originator: rp@llex

I am working with Confluent Hypergeometric Functions and am stuck.

                             2
                            d w     dw
                          z --- - z --  - a w = 0
                              2     dz
                            dz

The differential equation above appears in Abramowitz and Stegun 
p. 504, 13.1.1 . However, these Kummer functions M(a,0,z) and
U(a,0,z) are ill-defined when the 2nd argument is 0 (which
is the case of interest). Can someone tell me how to compute
in this case or point me to a more complete reference? One reference
given by A&S, namely Erdelyi V1 Chapter VI does not provide much
insight. In particular I am seeking a first order series expansion 
of the solution about a particular point where z is large.

Any suggestions will be welcomed. Thanks. 

 
Newsgroups: sci.math
From: hhassler@iaik.tu-graz.ac.at (Hannes Hassler)
Subject: Integer Sequence Problem
Organization: Institut fuer Angewandte Informationsverarbeitung, TU Graz
Date: Tue, 28 Jul 92 17:34:52 GMT

For S an infinite, increasing sequence of positive integers (1=a_1 < a_2 <
a_3 < ... < a_i < a_{i+1} < ...), we define the VALUE val(S) of S 

        val(S)  :=    sup_{n>1}  \sum_{i=1}^n a_i   / a_{n-1}

(in words: For every n, sum up the first n terms of S and divide this sum
by the (n-1)st term.  Then val(S) is the supremum of all these values).

PROBLEM: Find the minimum (infimum) of val(S) over all possible sequences S.

***************************************************************************
 Hannes Hassler
***************************************************************************
Newsgroups: sci.math
From: cet1@cl.cam.ac.uk (C.E. Thompson)
Newsgroups: sci.math
Subject: Re: Hailstone sequences
Keywords: Hailstone Collatz
Date: 23 Jul 92 23:46:46 GMT
Reply-To: cet1@cl.cam.ac.uk (C.E. Thompson)
Organization: U of Cambridge Computer Lab, UK

In article <1992Jul18.115039.25704@mailer.cc.fsu.edu>,
rose@fsu1.cc.fsu.edu (Kermit Rose) writes:
|>
|> 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.

More generally, if n = -1 mod 2^k, then the 3x+1 and x/2 cases will
strictly alternate k-1 times, and so there are n which get bigger by
arbitrarily large factors. 

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

Quite. One uses this observation in programs to verify the Collatz hypothesis
up to some large N. For example, all but 19 of the residue classes mod 256
produce an iterate smaller than the original number before one loses track
of their parity.

By the way, it is natural to extend the domain of the function being
iterated to include the negative integers (or equivalently, to use
3x-1 instead of 3x+1 in the x odd case). As well as the cycle

   (1, 2, 4)

one then also gets

   (-1, -2)
   (-5, -14, -7, -20, -10)
   (-17, -50, -25, -74, -37, -110, -55, -164, -82, -41, -122, -61,
      -182, -91, -272, -136, -68, -34)

and probably (but as unprovably as before) no more. (I suppose {0}
should be included as a cycle all by itself!)

Chris Thompson
Cambridge University Computing Service
JANET:    cet1@uk.ac.cam.phx
Internet: cet1@phx.cam.ac.uk
Newsgroups: sci.math
From: deghare@daisy.waterloo.edu (Dave Hare)
Subject: Re: Need help!
Organization: University of Waterloo
Date: Thu, 30 Jul 1992 17:05:13 GMT

In article <chepan.712505966@gsusgi1.gsu.edu> chepan@gsusgi1.gsu.edu (Parthasarathy Nambi) writes:
> I need help in solving the equation:
>
>   e^(-x) - x = e^(-y) + y
>
> For what values of x and y this equation is true?

Let W(z) be the inverse of the function z -> z*e^z .  Then solving the
given equation for x in terms of y we get:

    x = W(e^((y*e^y+1) * e^(-y))) - y - e^(-y)

This is the relation you are seeking.

Note that as the function W() has an infinite number of branches, there are
an infinite number of solutions x for each value of y.

(Solution found with the aid of MapleV.)

Dave Hare
Newsgroups: sci.math
From: xu@math.psu.edu (Jinchao Xu)
Subject: 7-th International Conference on Domain Decomposition Methods
Reply-To: xu@math.psu.edu
Organization: Dept. of Mathematics, Penn State University
Date: Wed, 29 Jul 1992 22:11:36 GMT

The Seventh International Conference on Domain Decomposition 
Methods will be held at Penn State during the four-day period 
October 27--30, 1993. If you want to receive further information, 
please contact: Rosemary Manning (secretary), Dept. of Math.,
Penn State Univ., University Park, PA 16802. Tel: 814-865-7527;
Fax: 814-865-3735; Email: ddm7@math.psu.edu.
From: allan@hico2.westmark.com (Allan Kugel)
Newsgroups: sci.math
Subject: turning data points into a continuous function
Keywords: spline? function math
Date: Wed, 22 Jul 1992 21:14:46 GMT
Reply-To: allan@hico2.westmark.com
Followup-To: poster

Well, some parts of math I never learned about.

I'd like to generate a function f(x)
given evenly-sized intervals x1 ... xn
and values y1 ... yn.

s.t.

Integral from x sub i-1 to x sub i of f(x) = (y sub i)
(I'd like the volume under the curve between i-1 and i
 to be equal to a cooresponding volume ( 1 * y sub i)
 that I am given.)

f(x) over the interval 0 to n is continuous
f'(x) over the interval 0 to n is continuous
and maybe f''(x) over the interval 0 to n is continous.

the LENGTH of the function line over this interval is minimized

(and, just to make things tricker, I'm going to want to integrate
 this function later)

Does anybody out there know how to solve this kind of problem?
I don't even know what branch of math to look at.

( Reply-by-email-as-we-don't-normally-get-this-group-here,)

Thanx in advance,
Allan Kugel
allan@hico2.westmark.com
Newsgroups: sci.math
Subject: Sieve  (Was Re; Re; prime quadruplets ... partial apology)
From: kubo@zariski.harvard.edu (Tal Kubo)
Date: 30 Jul 92 17:16:02 EDT
Organization: Dept. of Math, Harvard Univ.

In article <1992Jul29.222749.18849@spool.cs.wisc.edu>
bach@jalapeno.cs.wisc.edu (Eric Bach) writes: 
>
>	Questions like this have received a fair amount of study.  The
>	conjectured density of quadruplets <= N is ~ C * N / (log N)^4,
>	where C is expressible as an infinite product over the primes.

i.e. the conjectured density is the product of local densities 
[essentially  (1-4/p)]  taken over few enough primes less than N
to maintain the 'independence' of congruences modulo different
primes.  Some questions for the experts:

>	This is based on probabilistic arguments, 
                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^        
   1)  Are there problems where the heuristic arguments fail?

   2)  Can one guess the prime number theorem from heuristics?

>                                                 and agrees with
>	numerical data, as far as we know.  Using sieve methods, it can 
>	be shown that the number is O( N / (log N)^4 ).


   3)  How convincing is the numerical data?  Is there reason
       to believe that breakdown of heuristic hypotheses such as
       independence could be tested in the range of computations
       feasible today? 


tal  kubo@zariski.harvard.edu

Newsgroups: sci.math
From: bm477@cleveland.Freenet.Edu (Andy F. Johnston)
Subject: Re: Advice Needed : How to contain a net defamation campaign ?
Reply-To: bm477@cleveland.Freenet.Edu (Andy F. Johnston)
Organization: Case Western Reserve University, Cleveland, OH (USA)
Date: Wed, 22 Jul 92 21:35:23 GMT


In a previous article, U53644@uicvm.uic.edu () says:

>The question is : How do I put a stop to this sort of thing ?
>
>            Having interests in research, and working in preperation for
>            private sector work as I am (Math/EE), and partially supporting
>            myself with consulting work as I do, I really don't need to have
>            this kind of rumor spread.
>
>Well, where do I go from here to maintain and repair my reputation (minor as
>it is) ? (Best part - this happened as a result of posting job advice for
>younger graduate students. No good deed goes unpunished, I guess).
>
>                                           Worriedly yours,
>
>                                               Joseph B. Dunphy

I think that you have already done the right thing by posting this
notice, in so far as you needed to do anything at all.  You may find
that these newsgroups are not read as widely in the private sector as
in the academic world.  You may also find that this sort of thing
doesn't carry a great deal of weight in a job interview.  They are
usually worried about other things.
From: whorf@vnet.ibm.com
Newsgroups: sci.math
Subject: sci.math archives
Date: 22 Jul 1992 04:57:38 -0500
Organization: UTexas Mail-to-News Gateway
NNTP-Posting-Host: cs.utexas.edu

I am interested to get information where the sci.math and
sci.math.num.analysis fora are archived for the last months or years?
Newsgroups: sci.math
From: djvelleman@amherst.edu
Subject: Re: You know, the integers (was: Re: Stupid question about FLT)
Organization: Amherst College, Amherst Mass.
Date: Wed, 22 Jul 1992 13:54:55 GMT

In article <BrquHt.E5p@immd4.informatik.uni-erlangen.de>, jnjohann@immd4.informatik.uni-erlangen.de (Jan Johannsen) writes:
> 
> Following this thread I always wondered why noone ever mentioned the following
> possible answer:
> 
> Take the axioms for the upper half of a discretely ordered ring (about 15 axioms)
> and add the (infinite) \omega-rule of induction:
> 
>   A(0)   A(s0)  A(ss0)  A(sss0) ....
> --------------------------------------
>              \forall x A(x)
> 
> Then every true (first order) sentence about the integers is provable 
> with this machinery, and vice versa.
> Thus we have characterized the integers up to elementary equivalence.

  And what exactly does the "..." in the rule above refer to?  Your
"characterization" of the integers has the integers hidden in it.

  Dan Velleman
  Dept. of Mathematics & Computer Science
  Amherst College

Newsgroups: sci.math
From: chepan@gsusgi1.gsu.edu (Parthasarathy Nambi)
Subject: Re: Hailstone sequences
Organization: Georgia State University
Distribution: usa
Date: Fri, 24 Jul 1992 17:21:24 GMT

 I remember seeing a nice generalization of the Collatz problem by one
 Wiggins in the Journal of Recreational Mathematics in 1988 or 1989?

 Any one recall the correct full reference?

 P.Nambi
From: fc03@ns1.cc.lehigh.edu (Frederick W. Chapman)
Newsgroups: sci.math
Subject: Re: Iteration problem
Date: 24 Jul 92 20:47:04 GMT
Organization: Lehigh University

In article <4578@balrog.ctron.com>, wilson@ctron.com (David Wilson) writes:

>	(2)  h (x) = 2 cosh(p arccosh(x/2)).
>              p
>
>It turns out that for integer p, hp is a polynomial.  

[description of properties of h_p deleted]

The h_p's sure are polynomials for integer p... the Tchebyshev polynomials
(more or less)!  More precisely,

                          h_p (x)  =  2 T_p (x/2)

where T_p is the Tchebyshev polynomial of degree p.  The properties you
discovered for the h_p's can also be derived from similar properties of the
T_p's.  In fact, there is an entire book on the wonderful properties of
Tchebyshev polynomials, published recently by Wiley Interscience, if memory
serves me.

-- 

o ------------------------------------------------------------------------- o
|  Frederick W. Chapman, User Services, Computing Center, Lehigh University |
|    Campus Phone:  8-3218     Preferred E-mail Address:  fc03@Lehigh.Edu   | 
|  "I do comedy and magic; what you don't find funny -- that's the magic."  |
o ------------------------------------------------------------------------- o
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: Cardinarity of a Borel field--antichoice version
Date: 21 Jul 92 14:40:49 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: carabalo@phoenix.Princeton.EDU (David G. Caraballo)

In article <1992Jul20.171849.17294@Princeton.EDU>, carabalo@phoenix (David G. Caraballo) writes:
>I still believe the above to be accurate.  I will state a slightly more 
>powerful result (I do not have a reference, but I'm fairly sure it
>is a result of Solovay's, probably in the mid 1960's.).

It's in the ANNALS OF MATHEMATICS, late 60s, if you want the original.
Jech SET THEORY contains the proof also.

>							  Let M be the axiom 
>"All subsets of R^n are measurable".  Then the following is true:

>   M is consistent with ZF and Countable Choice, but not with ZF and AC.

The first clause remains inaccurate and not interesting.  I won't repeat
myself--an accurate subset of Solovay's theorem is in the posting of mine
you replied to.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
From: clarke@acme.ucf.edu (Thomas Clarke)
Newsgroups: sci.math
Subject: Re: Cardinality of sigma-rings
Date: 21 Jul 92 19:41:54 GMT
Organization: University of Central Florida

In article <1992Jul21.175055.13821@schaefer.math.wisc.edu>  
horn@schaefer.math.wisc.edu (Jeffrey Horn) writes:
> Is there a way to prove that no sigma ring can have the cardinality of the
> natural numbers without referring to the Hausdorf maximality theorem?

Had this as a homework once.  I did a diagonal argument:  
list the elements of the sigma ring, then use the countable
union/intersection property to get an element (i.e. set) not
in the list.  Details are a little vague now, but I recall
it was pretty straightforward.
--
Thomas Clarke
Institute for Simulation and Training, University of Central FL
12424 Research Parkway, Suite 300, Orlando, FL 32826
(407)658-5030, FAX: (407)658-5059, clarke@acme.ucf.edu
Newsgroups: sci.math
From: jamess@athena.mit.edu (John A Mess)
Subject: Geometric Proofs (re: Median Controversy)
Organization: Massachusetts Institute of Technology
     First, to every issue there are three sides; in this case, the student's,
     For most high school geometry, the goal is to teach proof via deduction.
     While the student was not *wrong*, he invoked a method of proof which was
     If the problem is so trivial, then the detractors may set down a proof
     Coxeter would make a wonderful text.  Introducing non-Euclidean geomet-
Date: Mon, 27 Jul 1992 15:41:24 GMT
From: wilson@ctron.com (David Wilson)
Newsgroups: sci.math
Subject: Re: Iteration problem
Date: 24 Jul 92 13:30:17 GMT
To: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)




Thanks for the reply on the iteration problem.  Not being well versed in
the hyperbolic functions, I came up with the solution

	(1)  h (x) = ((x+sqrt(x^2-4)/2)^p + (x-sqrt(x^2-4)/2)^p).
	      p

which, I believe, is equivalent to your more concise

	(2)  h (x) = 2 cosh(p arccosh(x/2)).
              p

It turns out that for integer p, hp is a polynomial.  A few interesting
properties of hp can be deduced from (1) and (2).  For instance, the hp
are compositionally commutative on the range x >= 2, since

	h (h (x)) = 2 cosh(p arccosh((2 cosh (q arccosh(x/2)))/2))
         p  q
		  = 2 cosh(pq arccosh(x/2))

		  = h  (x)
                     pq

Also, (1) is reminiscent of the closed form expression of the Fibonnaci
numbers, suggesting a similar recurrence, and indeed we find

	h (x) = x*h (x-1) - h (x-2)
         p         p         p

Anyway, I thought it was a cute problem, but I probably wouldn't have
posted it had I known it had such a straightforward solution.

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."
Newsgroups: sci.math
From: hpassaue@silver.ucs.indiana.edu (Billy Passauer)
Subject: Square roots
Organization: Indiana University
Date: Tue, 28 Jul 1992 23:31:50 GMT

I ran across this algorithm for finding the square root of a number a
long time ago.  I was wondering if someone could tell me where I could
find more information about it.

To find the INTEGER portion of a square root:
  Take the number you want the square root of, and successively
subtract the odd numbers (starting with 1.)  Each time the result is
positive, add 1 to a counter.  Repeat with the new number.  When the
subtraction yields an odd number, the counter contains the answer.
(integer only)  For instance the square root of 24:

	              Counter
	24 - 1 = 23  :   1
	23 - 3 = 20  :   2
	20 - 5 = 15  :   3
	15 - 7 =  8  :   4
	 8 - 9 = <0 

Any information about this would be greatly appreciated.
-- 
  _
 /_)  *  /    /    /  /     hpassaue@silver.ucs.indiana.edu
/__) /  (__  (__  (__/      hpassaue@ucs.indiana.edu
     Passauer    ___/
From: dik@cwi.nl (Dik T. Winter)
Newsgroups: sci.math
Subject: Re: American mathematical hegemony
Date: 22 Jul 92 01:31:38 GMT
Organization: CWI, Amsterdam

In article <1992Jul21.212224.18859@cl.cam.ac.uk> cet1@cl.cam.ac.uk (C.E. Thompson) writes:
 > In a desperate attempt to save this thread from degenerating into a
 > discussion of the rudeness of the British, or even a Welsh vs. English
 > slanging match, might we violate Usenet custom and return to the
 > original subject?
Oh yes, Usenet is there to violate the rules.
 > 
 > Well, the sources seem to be in some doubt here. I seem to recall that when
 > I was taught such things (c.1960), the two systems were distinguished as 
 > "American" and "Continental" (which I took to mean "French"). However, the
 > OED seems to be sure that French custom matches the American in making
 > "billion" = 10^9, "trillion" = 10^12. On the other hand, they also believe
 > that French "milliard" = 10^9. Is this really a case of two words for the
 > same number?
Darn.  I have now two French dictionaries, one dated 1953 and one dated 1988.
They disagree!  The 1953 one translates "billion" to "miljard" while the
1988 one translates "billion" to "biljoen".  But there is a rescue.  The
1988 dictionay tells us for "trillion": "biljoen", "triljoen" (after 1948).
So apparently there was a change in 1948 (amazing that the 1953 dictionary
did not pick it up).

So, apparently, while the UK is succumbing to US customs, the French moved
the other way!  But perhaps some French reader can comment on it.
 > 
 > By the way, it is by allowing the perfectly good imported word "milliard"
 > to fall into disuse in English that we have allowed the Americans to win
 > this particular battle by default. Discussion of (inter)national economics
 > especially encourages one to find a single word for 10^9.
In Dutch "miljard" is still very common.  "Biljard" is less common, but also
used.
 > 
 > |> >Now I wonder how much longer it will take before the "centre" of a sphere
 > |> >becomes a "center".
 > 
 > No, no. Never. We shall fight them on the beaches...
Go just between the "centre" and the "center" and make it "centrum" (though
I would prefer "middelpunt").
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland
home: bovenover 215, 1025 jn  amsterdam, nederland
dik@cwi.nl
Newsgroups: sci.math
From: chalcraft@uk.tele.nokia.fi (Adam Chalcraft)
Subject: Re: Olympic question
Organization: cpd
Date: Fri, 31 Jul 1992 15:03:55 GMT

In article <1992Jul30.235117.6123@access.usask.ca> bula@snoopy (W. Bula) writes:

>   I wonder if this question comes up every four years, but anyway...
>   Has anyone on the net ever considered topology of the complement of
>   olympic rings in the 3D space? It would be nice to see e.g. the first
>   homotopy group of this space.

 pi_1(complement) is <a,b,c,d,e | ab=ba, bc=cb, cd=dc, de=ed>

--
| Adam      | #include <stddisclaimer.h>                                   |
| Chalcraft | You can tell how tall a story is by how many flaws it's got. |
From: ddailey@williams.edu
Newsgroups: sci.math
Subject: Re: Hailstone sequences
Date: 24 Jul 92 15:22:38 GMT
Reply-To: ddailey@williams.edu
Distribution: usa
Organization: williams college

In article <CHALCRAFT.92Jul24095243@zebedee.uk.tele.nokia.fi>
chalcraft@uk.tele.nokia.fi (Adam Chalcraft) writes:
>In article <1992Jul23.234646.7306@cl.cam.ac.uk> cet1@cl.cam.ac.uk (C.E.
Thompson) writes:
>
>>   By the way, it is natural to extend the domain of the function being
>>   iterated to include the negative integers (or equivalently, to use
>>   3x-1 instead of 3x+1 in the x odd case). As well as the cycle
>>
>>      (1, 2, 4)
>>
<deletion>
>
>The result that on the positive integers, the function
>  f(x)=3x+1 or x/2
>seems to eventually send every positive integer to 1, whereas the function
>  f(x)=3x-1 or x/2
>does not is rather strange. Clearly the first function is "larger" than the
second.
>All that this shows, of course, is that the word "larger" has no useful
meaning here,
>and so any proof that the first function always goes to 1 must use something a
bit
>more subtle.

I first heard of these sequences from Stan Ulam and assumed they originated
with him. Did they?

David Dailey