HDTenEightyP/NetNews huggingface dataset:
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Subject: Definiitions and concpts  Was: Re: Integration
Organization: Purdue University Statistics Department
Date: Wed, 23 Dec 1992 15:42:22 GMT

In article <1h9nbuINN4pi@sipi.usc.edu> haddadi@sipi.usc.edu (Navid Haddadi) writes:
>In article <1992Dec18.182743.15553@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>>> Integration is a purely formal exercise in which a formula is
>>> transformed into another formula, using particularly odd rules.

>>Actually, this sounds like a nonmathematician's definition of
>>"mathematics"!  :-)

>Actually, how does a mathematician define math? If we take math to be
>an exercise in logic, then rules of logic that we use to make trivial
>an otherwise nontrivial matter (i.e. give a proof down to AC or ZL) are
>only a set of transformations operating on some language.

This point is raised by Whitehead and Russell in _Principia Mathematica_.
The point out that the definitions may be more important than the 
formal manipulations; they indicate what something is and why it 
is important.

Now they were writing primarily for mathematicians.  For non-mathematicians,
I would say that the concepts are the important item, and the translation
to and from mathematics.  Also, I would prefer using characterizations to
definitions; one can have many characterizations of the same thing, but 
at least in mathematics there can only be one definition.  
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@snap.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!snap.stat!hrubin(UUCP)
Xref: sparky sci.math:17492 comp.edu:2252 misc.education:5582
From: kfl@access.digex.com (Keith F. Lynch)
Newsgroups: sci.math,comp.edu,misc.education
Subject: Re: Education crisis (was RE: how much math...)
Date: 30 Dec 1992 03:36:19 GMT
Organization: Express Access Public Access UNIX, Greenbelt, Maryland USA
NNTP-Posting-Host: access.digex.com

In article <PRENER.92Dec12015805@prener.watson.ibm.com> prener@watson.ibm.com (Dan Prener) writes:
> Little kids learn much faster. ...
> But the fact that little kids' learning capacity is so much greater
> than that of older people ...

Is there any evidence for this?  It goes against my experience.

Keith Lynch, kfl@access.digex.com
Newsgroups: sci.math,sci.philosophy.tech
Subject: Re: Numbers and sets
From: wft@math.canterbury.ac.nz (Bill Taylor)
Date: Wed, 23 Dec 1992 00:49:48 GMT
 <1992Dec15.214124.7444@guinness.idbsu.edu> <1992Dec17.235906.13828@guinness.idbsu.edu> <1992Dec19.140927.18700@husc3.harvard.edu>
Organization: Department of Mathematics, University of Canterbury

In article <1992Dec19.140927.18700@husc3.harvard.edu>, zeleny@husc10.harvard.edu (Michael Zeleny) writes: 

|> The Axioms of Foundation and Choice are analytically
|> true of sets;

What does this sentence mean ? 
Could someone please explain further ?
Why can it be so blithely asserted ?

--------------------------------------------
Bill Taylor.       wft@math.canterbury.ac.nz 
Bill Trylor. que  rwft@maih.casterkury.aa.n! 
Tiel Tryloco quer rwst@maihuc sterkesy.ga.n!
Thelworyd co quer rwsi@mvihus strikesy.gain!
The world conqueror sig-virus strikes again!
--------------------------------------------
Newsgroups: sci.math,rec.games.abstract
From: sillke@math25.mathematik.uni-bielefeld.de (Torsten Sillke)
Subject: Re: Game of pentominos
Date: Tue, 22 Dec 1992 17:31:59 GMT
Organization: Math MadHouse Bielefeld, Germany
Keywords: pentacubes, pentominoes

Games with Pentacubes:                                     22.12.92
======================
These are games described by Ekkehard K"unzell in his Book:
-- Spiele mit Pentakuben - 4th Ed. (available from the author).
  Ekkehard K"unzell,
  PENTAKUBENSPIELE, Schoenrathstr. 79, D-5100 Aachen, Germany
  Tel.: +49-241-58881

1) RESERVAT
   Two players select 12 pentacubes each.
   Then they are placed into a 8*8*2 box.
   The player, who can't fit a tile has lost.
   The winner get as much points, as the loser
   has left. If the winner can place some more
   pentacubes he get one point for each tile
   he can place.
   - tiles must be put parallel to the axis of
     the box. It is allowed to push them into
     holes in the bottom layer.
   - each tile must be placed, that they stand stable.
   (There exists a description of the game in english.
   It is a note, which the author distributed at his
   talk a the computer-game-olympiad 1991 in Mastricht.)

2) Husch-Husch ins K"orbchen
   The same as Reservat without the selection-phase and points.

3) Pentakubino
   Two players select 12 pentacubes each.
   like domino you build a chain of pentacubes. Two pentacubes
   can placed adjacend if they are 'similar'.

4) Pentakubennim
   The game-master, who knows the all numbers of the pentacubes,
   selects one tile. The other players look at the remaining 28.
   Who first says the number of the missing pentacube get a point.
   If you say a wrong number, the first player who finds this
   pentacube gets a point. ...

5) Pentakubenpatience
   Select 25 pentacubes. Then try to arange them into a circle,
   with similar pentacubes adjacent.

6) Fit In
   Place the pentacubes into the 8*8*2 box. You get minus-points if
   you can't touch the last plased pentacube or if you make death space.

7) Pentakuben-Nim
   A real nim-game. Two players get pentacubes. At your move, you can
   get one pentacube and as much similar pentacubes as you like.
   Who selects the last one wins. Or in the misere-game, who
   selects the last one loses.

8) Einr"aumspiel
   Try to fit the 29 pentacubes as fast as possible into a 8*8*3 box.

Torsten Sillke
Newsgroups: sci.math,comp.theory
From: sree@ux1.cso.uiuc.edu (sreenivas rama)
Subject: Cospectral Graphs (need references)
Keywords: graph theory, algebraic graph theory 
Organization: University of Illinois at Urbana-Champaign
Date: Tue, 22 Dec 1992 19:21:46 GMT

Hi:

I would like to get some pointers on a monograph or review article
on Cospectral graphs, that is, graphs whose adjacency matrices have
the same eigenvalues (with same multiplicities).  The only reference
I have is a thesis from Belgrade in the 70's.

Thanks!

-RS
From: robin@ruchem.ru.ac.za
Newsgroups: sci.math
Subject: Silly Q
Date: 3 Jan 93 22:37:18 GMT
Article-I.D.: hippo.1993Jan3.223513.13686
Reply-To: robin@ruchem.ru.ac.za
Organization: Rhodes University, Grahamstown, SA

I WANT A VERY SIMPLY C LANLUAGE JACOBI ROUTINE. Anyone got one?
Robin
Xref: sparky sci.math:17295 sci.physics:21574
From: max@west.darkside.com (Erik Max Francis)
Newsgroups: sci.math,sci.physics
Subject: Re: Help me deal w/ infinity
Date: 22 Dec 92 08:53:23 GMT
Organization: The Dark Side of the Moon +1 408 245 SPAM

mkohlhaa@silver.ucs.indiana.edu (mike) writes:
/
> My skeptical friends point out the "subract N from both sides" lines as
> the problem with the equation.  They think that it's bogus that I am 
> litterally subrtracting an N from one side, but subtracting it's equivalent,
> namely a .9(r) from the other side.

The above isn't a _proof_ that 0.9... = 1, but it is a sufficient 
motivation.  The actual proof would be done with infinite series.

If you define N = 0.9... (or 0.9(r) in your notation), then N = 0.9... 
period.  Talking about N and talking about 0.9... would thus be exactly
the same.  Because of that,

    10 N = 0.9...

you could substitute 0.9... with N (because that's how you _defined_ it), 
and get

    10 N = N

just as you expected.


  ____  Erik Max Francis -- ..!apple!uuwest!max -- max@west.darkside.com   __
  \  /  1070 Oakmont Dr. #1  San Jose, CA  95117  37 20 N 121 53 W  ACGT  /  \
   \/   Like strategic interstellar conquest games?  Ask about UNIVERSE!  \__/
        Omnia quia sunt, lumina sunt.   All things that are, are lights.
From: allenk@ugcs.caltech.edu (Allen Knutson)
Newsgroups: sci.math
Subject: Re: Measures, and Measurability
Date: 21 Dec 1992 17:01:03 GMT
Organization: California Institute of Technology, Pasadena
NNTP-Posting-Host: torment.ugcs.caltech.edu

hrubin@pop.stat.purdue.edu (Herman Rubin) writes:

>>remember it as being very clear and intuitive.  Starts out with nice
>>proof of metric density theorem, which says that if a set of an
>>Euclidean space is measurable, then it contains rectangles whose
>>measures are arbitrarily close to 1.

>This certainly is not the case unless a very unusual definition of 
>rectangle is given. 

Or a very usual measure, counting measure! 			: -8 )
From: kedlaya@husc8.harvard.edu (Kiran Kedlaya)
Newsgroups: sci.math
Subject: Re: Composition-commuting polynomials
Keywords: Polynomials commuting composition
Date: 28 Dec 92 22:14:07 GMT
Article-I.D.: husc.kedlaya.725580847

Yes, in fact, if f(x^2 + 1) = f(x)^2 + 1, then for some n
         f(x) = g[n](x),
where g1(x) = x^2 + 1 and g[n] denotes the n-th composition.
(Under this notation, g[0](x) = x.)

First notice that f(x)^2 = f(x^2 + 1) - 1
                         = f((-x)^2 + 1) - 1
                         = f(-x)^2.
Hence either f(x) = f(-x) or f(x) = -f(-x) is a polynomial identity.
In other words, f is either even or odd, and clearly f is even
iff deg(f) is.

If f is even, let x = y^2 + 1. Now
   f(x) = f(y^2 + 1) = f(y)^2 + 1
and furthermore, f(y), being even, can be expressed as a polynomial
in y^2, and hence as a polynomial in x, which we call h(x).
In other words, f(x) = g(h(x)). Furthermore,
   h(y^2 + 1) = h(x) = f(y) = g(h(y))
so h commutes with g as well. Observe that the degree of h is
half that of f.

We can repeat this process k times, where k is the highest power
of 2 dividing deg(f), and deduce that f(x) = g[k](h(x)), where
h is odd and commutes with g. Note that since h is odd, h(0) = 0.
Define the sequence x_n recursively as follows: x_0 = 0, and
x_{n+1} = x_n^2 + 1. By induction h(x_n) = x_n for all n, so
that h(x) = x identically, and f(x) = g[k](x), as desired.

This generalizes (it would appear) to g(x) = x^2 + c for any
nonzero c.

And I do believe this was a Putnam problem (though I don't remember
offhand when. Anyone?)

Kiran Kedlaya
Harvard University
"Lo \'unico peor que la mala salud es la mala fama."
      -Gabriel Garc\'ia M\'arquez,
         from "El amor en los tiempos de c\'olera"
From: gore@pepper.rutgers.edu (Bittu)
Newsgroups: sci.math
Subject: Combinatorial? problem
Keywords: binomial coefficients
Date: 23 Dec 92 23:15:50 GMT
Organization: Recreation Center, Busch Campus


Someone please help me with the following problem. I have pretty much
given up on it after a lot of thinking. We want to show the following:

given m,n nonnegative integers, the quantity

     (2m)! (2n)!
    -------------      is an integer.
     m! n! (m+n)!


Note that this is very easy to show by the standard argument where for
every prime p, you find the highest power of p (say p^k) that divides
the denominator and then show that p^k divides the numerator as well.

I want a combinatorial proof of this. I have tried rewriting the above
as C(2m,m)*C(2n,n)/C(m+n,m) where C(a,b) is "a choose b" and also in
other ways, but I still haven't come up with a combinatorial proof.

--Bittu
Newsgroups: sci.aeronautics
From: clarke@acme.ucf.edu (Thomas Clarke)
Subject: Re: Tire burn-out on landings
Organization: University of Central Florida
Date: Mon, 21 Dec 1992 14:17:54 GMT

In article <BzHBrM.9uF@specialix.com> jim@specialix.com (Jim Maurer) writes:
> todamhyp@unlv.edu (Brian M. Huey) writes:
> 
> >I realize this a relatively basic question (I think) nevertheless:
> 
> >	I am neither a pilot nor an airliner engineer. However,
> >everytime I watch a airliner land, a cloud of smoke is produced when
> >the wheels come in contact from the ground due to friction. Couldn't
> >this cloud and the effect of friction be lessened by inducing a
> >angular velocity upon the wheels to match the airliners speed with
> >respect to the runway?
> 
> This has been tried.  It did reduce tire wear, but it did cause
> some problems.  How would you like to try landing a 747 with a
> bunch of gyroscopes attached?  It adversely affects handling qualities
> of the aircraft.  :-)

Doesn't a 747 already have four rather large gyroscopes slung
under the wings?:-)  Or do the engines rotate in different direction?

--
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
From: rbw3q@rayleigh.mech.Virginia.EDU (Brad Whitehurst)
Newsgroups: sci.aeronautics
Subject: Re: Speed of sound (was MACH 1)
Keywords: formula
Date: 21 Dec 92 14:53:41 GMT
Organization: University of Virginia

In article <1992Dec20.023400.6822@cbnewsd.cb.att.com> jfb200@cbnewsd.cb.att.com (joseph.f.baugher) writes:
>Most of the formulae I have seen posted here for the speed of sound in 
>air are wrong.  In fact, some of them are not even dimensionally 
>correct.  
>
>Here's what Resnick and Halliday (a well-known freshman physics text) 
>have to say.  
>
>The formula for the speed of sound in an elastic medium (either liquid 
>or gas) is 
>
>		c = sqrt (B/rho) 
>
[some deletions...]
>Let us now look at the well-known ideal gas formula: 
>
>		PV = nRT 
>
...
>The factor n/(V*rho) is simply the inverse of the molecular weight of 
>the gas (MW), so the formula for the speed of sound in a gas is 
>
>		c = sqrt( gamma*R*T/(MW) ) 
>
>The ratio of specific heats is for all practical purposes a constant.  
>R is a universal constant of nature, so the speed of sound depends 
>only on the absolute temperature and on the molecular weight of the 
>gas.  

	Yup, but the previous posters were using the convention
(though they may not have said it) of using a gas-specific gas
constant rather than the universal gas constant, like so:  R=Ru/MW.
That is the the source of your confusion, not a real error in their
formula.  Most gas dynamics books have got the specific R's tabulated,
so we just use them, rather than Ru/MW, since you have to look up MW
anyway.

>Since the temperature of the air decreases with altitude in the 
>troposphere, the speed of sound decreases with altitude.  
>
>Hope this helps.  
>
>Joe Baugher			**************************************
>AT&T Bell Laboratories		*  "You see, something's going to    *



-- 

Brad Whitehurst    |   Aerospace Research Lab
rbw3q@Virginia.EDU |   We like it hot...and fast.
From: j.r.branstetter@larc.nasa.gov (james r. branstetter)
Newsgroups: sci.aeronautics
Subject: Re: GPS (DGPS) RTCA std.?
Date: 30 Dec 1992 16:01:28 GMT
Organization: NASA Langley Research Center, Hampton, VA  USA
Distribution: world
Reply-To: j.r.branstetter@larc.nasa.gov (james r. branstetter)
NNTP-Posting-Host: b1244amac5.larc.nasa.gov

Several RTCA activities are underway.  First, they have published the "RTCA Taskforce 
Report on Global Navigation Satellite System Transition and Implementation 
Strategy", now available for sale.  Second, Special committee-169, Aeronautical 
DataLink Applications, is looking at various applications and operational modes as you 
describe, which may be influenced by the early need for a DGPS data channel.  

Also the FAA is in the process of defining the Aeronautical Telecommunications 
Network (ATN) which is being worked by MITRE.  ATN concept proposes using the 
ISO/OSI protocols.

Obligatory disclaimer: All this is from a limited perspective, check with the 
aforementioned groups for detailed information.


Newsgroups: sci.aeronautics
From: bowers@rigel.dfrf.nasa.gov (Al Bowers)
Subject: Re: MACH 8
Organization: NASA Dryden, Edwards, Cal.
	<1992Dec23.173753.14938@mksol.dseg.ti.com>
Date: Thu, 24 Dec 1992 16:30:05 GMT

In article <1992Dec23.173753.14938@mksol.dseg.ti.com> martinn@mksol.dseg.ti.com (niels r martin) writes:

>In article <alien.020z@acheron.amigans.gen.nz> alien@acheron.amigans.gen.nz (Ross Smith) writes:
>>In article <10302@ncrwat.Waterloo.NCR.COM> tjgerman@53iss6.Waterloo.NCR.COM (Trevor German) writes:

>>>       I have been following the thread about the Mach 8 spy plane
>>>       and have a general question. What exactly is MACH 1. I understood
>>>       it to be the speed of sound at sea level (or more accurately at
>>>       an air pressure defined to be sea level).

>>Mach 1 is defined to be the *local* speed of sound, so it varies with
>>altitude, but not in the way you describe. To a rough approximation (from

>If the point of the question is: "can you go faster at Mach 1 at sea
>level or at high altitude?"  The answer is probably not yes or no, but
>rather gets into the max dynamic air pressure that the structure can
>handle--for example, the SR-71 could apparently not go much faster
>than 200 mph at sea level because of the dense air causing structural
>damage if it exceeded that speed--therefore most high-Mach flight will
>be done at relatively high altitude and I suppose that when that is
>translated into mph (or knots for you aviation buffs) it's not as
>impressive as one might imagine.

Actually, the envelop of the SR-71 at sea level is 145 KEAS to 450
KEAS (that's knots equivalent airspeed; at sea level that's pretty
close to _true_ airspeed).

And you are confusing several issues.  Specifically, air speed.

true airspeed: the speed you are actually flying through the air,
regardless of density or Mach number.

calibrated airspeed: the sea level impact pressure airspeed corrected
for compressibility (this one is not used often).

equivalent airspeed: the sea level impact pressure _NOT_ corrected for
compressibility (this one is used in most pilot manuals).

indicated airspeed: the airspeed you read off of the cockpit guage
(sea level impact pressure with errors due to position and
instrumentation errors).

Note that at max Mach and altitude (std day) the SR-71 is at Mach 3.2
and 85,000 feet msl.  The _true_ airspeed is 1835 KTAS (2112 mph), and
the _equivalent_ airspeed is 310 KEAS.  And the airplane is really
covering ground at 2112 mph.

--
Al Bowers                       bowers@rigel.dfrf.nasa.gov
NASA F-18 High Alpha Research Vehicle, Lead Aero
NASA, Dryden Flight Research Facility, Edwards, California
From: doug@alliant.com (Doug Bloomberg)
Newsgroups: sci.aeronautics
Subject: Re: Unflattering descriptions
Summary: Aircraft nicknames
Date: 2 Jan 93 23:26:20 GMT
Article-I.D.: alliant.1993Jan2.232620.10377
Organization: Alliant Computer Systems Corp.

In article <alien.026m@acheron.amigans.gen.nz> alien@acheron.amigans.gen.nz (Ross Smith) writes:
>I'm trying to compile a list of the more, shall we say, unflattering
>descriptions that have been applied to various aircraft over the years.
>Does anyone know any good ones? The short list I've been able to recall
>myself goes something like this ... sources omitted to protect the
>guilty :-)
>
>Buccaneer : "The Banana Bomber." (The prototype was given the codename ARNA
>(A Royal Navy Aircraft), and "Blackburn ARNA" soon became "Black Banana".)
>
>E-3 Sentry : "A Boeing 707 being raped by a flying saucer."
>
>  etc.

	Beech Bonanza   "Forktailed Doctor Killer"

	Doug Bloomberg
	V-35B  N8171R
Newsgroups: sci.aeronautics
From: hinz@picard.med.ge.com (David Hinz Mfg 4-6987 ~BHOSVWZ#097)
Subject: Re: Aviation Fuel for Piston Engines Question
Organization: GE Medical Systems, Magnetic Resonance
X-Newsreader: TIN [version 1.1 PL6]
Distribution: usa
Date: Tue, 29 Dec 92 07:35:29 GMT

Mark Robert Thorson (mmm@cup.portal.com) wrote:
: Do any fuels presently available for piston-engine general-aviation
: aircraft contain tetraethyl lead as an additive (it's an octane booster)?
: If so, are there any deadlines with regard to the phase-out of these fuels?

I know you were able to buy "LL-100", meaning low-lead 100 octane, up to a few
years ago.  Does wonders in a car with a knock sensor so it can take advantage
of the extra octane points, but it isn't a good idea if you have a cat.

Don't know about phase-out, if it's happened already, or what.  The AvGas
was pretty expensive, though.

--

Dave Hinz  -  Opinions expressed are mine, not my employer's.  Obviously.
Don't blame me; I voted for Perot!                hinzd@picard.med.ge.com 
SAAB - Because you get what you pay for.             Pherrets are Phun!!!
Newsgroups: sci.aeronautics
From: cnaf244@chpc.utexas.edu
Subject: Looking for information for buying second hand aircraft
Organization: The University of Texas System - CHPC
Distribution: na
Date: Thu, 24 Dec 92 21:08:00 GMT

I am new to this group and was wondering if anyone could provide me with
any hints or suggestions, regarding buying second hand planes (of the type
Cessna etc.). The information that I am looking for, is, who sells these
and in what price range.

If a FAQ exists, please let me know the source.

Regards.

	Pushkar Tamhane
From: fiddler@concertina.Eng.Sun.COM (steve hix)
Newsgroups: sci.aeronautics
Subject: Re: MACH 8
Date: 23 Dec 1992 19:53:08 GMT
Organization: Sun
NNTP-Posting-Host: concertina

In article <1992Dec23.173753.14938@mksol.dseg.ti.com> martinn@mksol.dseg.ti.com (niels r martin) writes:
>
>If the point of the question is:  "can you go faster at Mach 1 at sea level
>or at high altitude?"  The answer is probably not yes or no, but rather
>gets into the max dynamic air pressure that the structure can handle

and various airframe and engine heat limits

>--for example, the SR-71 could apparently not go much faster than 200 mph at sea
>level because of the dense air causing structural damage if it exceeded that
>speed--

In 1968 on Armed Forces Day, I was a guest of the father of a high-school friend
at the air show at Pt. Mugu NAS.

*The* highlight of the day was a flyby (suprise!) by an SR-71.  Two, actually:
The first with everything hanging out at a bit over 200 mph.

The second was better: cleaned up, just barely sub-Mach 1 until it passed over
the beach, went into afterburner and climbed away and out of sight in a few
seconds.  Took hours for the grins to dissipate. (Huge noise as the throttles
went forward, too.)

--
-------------------------------------------------------
| Some things are too important not to give away      |
| to everybody else and have none left for yourself.  |
|------------------------ Dieter the car salesman-----|
From: esdave@sgies4.sdrc.com (Dave Pinella)
Newsgroups: sci.aeronautics
Subject: Re: Speed of sound (Re: MACH 8)
Date: 30 Dec 92 16:34:49 GMT
Organization: SDRC

This is a test. Sorry to bother anybody.
From: rdd@cactus.org (Robert Dorsett)
Newsgroups: sci.aeronautics
Subject: Re: archives/faq?
Date: 31 Dec 92 09:18:28 GMT
Organization: Capital Area Central Texas UNIX Society, Austin, Tx

In article <1992Dec31.050721.22786@magnus.acs.ohio-state.edu> gburton@magnus.acs.ohio-state.edu (Garland O Burton) writes:
>could someone e-mail me the address where i could find archives
>and faq for this group?

About 10% of current posts are included in the Aeronautics Digest, archived
on rascal.ics.utexas.edu, in misc/av/aeronautics-digest-folder.  Earlier
editions echo up to 80% of sci.aeronautics' traffic.  The Digest was intended
as a "clipping service" from  this group.

There is no faq list for the group.  






---
Robert Dorsett
rdd@cactus.org
...cs.utexas.edu!cactus.org!rdd
Newsgroups: sci.aeronautics,misc.books.technical,alt.books.technical,misc.forsale