HDTenEightyP/NetNews huggingface dataset:
Newsgroups: sci.math
Subject: Re: "Sneakers" & cryptography
From: chisnall@cosc.canterbury.ac.nz (The Technicolour Throw-up)
Date: Mon, 28 Sep 1992 09:04:29 GMT
Organization: Computer Science,University of Canterbury,New Zealand

From article <1992Sep21.183013.9061@galois.mit.edu>, by jbaez@riesz.mit.edu (John C. Baez):
> I just realized what the mathematician in "Sneakers" might have done.
> (Don't worry, this will NOT give away any of the plot; I am
> "supplementing" the plot to make it more interesting.  Frankly I thought
> it was a silly movie.)  He proved that P = NP!  This would eliminate
> ALL one-way functions.  That's why they... ok, I won't give it away.
> 
> This relates to a paranoid theory I have about why the P = NP? question
> has taken so long to resolve.  Whenever anyone comes too close to
> solving it they are paid large sums of money by the NSA to hush up, or
> else are hired to work for the NSA.  

In Rudy Rucker's novel "Wetware" it transpires that computer security, on
some systems anyway, is dependent not on any of the usual techniques but,
quite literally, on mathematical proofs.  Apparently the government bought a
bunch of hard mathematical proofs, prevented them from being published, and
used them to encrypt things.  One of the proofs, for example, is FLT.

This is not all that unreasonable.  FLT has taken us more than 300 years so
far and we still haven't solved it.  With the kind of hardware they have in
this story you could probably factorise some fairly large numbers in 300
years.

--
Just my two rubber ningis worth.
Name: Michael Chisnall  (chisnall@cosc.canterbury.ac.nz)
I'm not a .signature virus and nor do I play one on tv.
From: columbus@strident.think.com (Michael Weiss)
Newsgroups: sci.math
Subject: Re: Infinity
Date: 2 Oct 92 17:25:59
Organization: Thinking Machines Corporation, Cambridge MA, USA
	<1992Sep30.214743.18350@cs.rose-hulman.edu>
	<1992Oct1.204515.11508@galois.mit.edu>
NNTP-Posting-Host: strident.think.com
In-reply-to: jbaez@riesz.mit.edu's message of Thu, 1 Oct 92 20:45:15 GMT

In article <1992Oct1.204515.11508@galois.mit.edu> jbaez@riesz.mit.edu (John
C. Baez) writes: 

   .... The notion of "sqrt(2)" is an abstraction - hence the term
   "irrational"....

I believe the term "irrational" actually derives from "not a ratio", i.e.,
of two integers.
Newsgroups: sci.math
Subject: Re: Compactness in infinite chess ?
From: elkies@ramanujan.harvard.edu (Noam Elkies)
Date: 30 Sep 92 10:55:45 EDT
Organization: Harvard Math Department

In article <BvDFs5.7K8@cantua.canterbury.ac.nz>
wft@math.canterbury.ac.nz (Bill Taylor) writes:
>==============
>If mate can be forced (with certain piece combinations) on an arbitrarily
>large finite board, then it can be forced (with the same pieces) on an
>infinite board.
>==============


This is not true, basically because many mates on a finite board
depend crucially on an edge or corner to hem in the enemy King, and
an infinite board has no such thing.  For instance, K+Q or K+R can
mate a lone King on any finite board, but not on an infinite board.

Perhaps instead of "arbitrary large finite [rectangular] board"
try "arbitrary large finite toroidal board"?

--Noam [not "Noan"] D. Elkies (elkies@zariski.harvard.edu)
  Department of Mathematics, Harvard University
From: rjchapma@cen.ex.ac.uk (R.J.Chapman)
Newsgroups: sci.math
Subject: Re: finding the units digit of a big number
Date: 30 Sep 92 09:26:13 GMT
Organization: Computer Unit. - University of Exeter. UK

In article <1992Sep29.004246.14564@news2.cis.umn.edu> hoffman@n1.math.umn.edu (John R. Hoffman) writes:

   Recently someone posted about finding the first nonzero digit of 
   (10^6)!

   I was going through an old math contest that I took in high school and came 
   across a similiar question (which I couldn't solve)

   What is the units digit in the decimal expansion of 

   (15 + \sqrt{220})^19 + (15 + \sqrt{220})^82.


   Any simple solution would be appreciated.  ( I think calculators were not  
   allowed during the exam)

   Thanks

   JRH

The last digit is 9.
Let

    A = 15 + \sqrt{220}

and

    B = 15 - \sqrt{220}

be the roots of

    x^2 - 30x + 5 = 0.

Now as A is approximately 30 and AB = 5, then B is approximately 1/6
and so for large n B^n is a very small positive number.
Let

    C_n = A^n + B^n

and we see that C_0 = 2, C_1 = 30 and

    C_{n+2} = 30 C_{n+1} - 5C_n.

It is apparent that if n>0 then C_n is an integer multiple of 10.
Hence as A^19 + A^82 is just less than C_19 + C_82, then the last digit
of its integer part is 9.

    
--
Robin J. Chapman                 *
Department of Mathematics        *
University of Exeter, UK         *
R.J.Chapman@cen.exeter.ac.uk     *
-- 
Robin J. Chapman                 *
Department of Mathematics        *
University of Exeter, UK         *
R.J.Chapman@cen.exeter.ac.uk     *
From: atteson@grip.cis.upenn.edu (Kevin Atteson)
Newsgroups: sci.math
Subject: consequences of the Axiom of Choice
Date: 30 Sep 92 14:58:32 GMT
Distribution: usa
Organization: GRASP Lab, University of Pennsylvania


Does anyone know of any elementary results which are
dependent upon the axiom of choice?  By elementary
results, I mean something from elementary calculus, etc.

Please reply directly to me,

Kevin Atteson
Newsgroups: sci.math,sci.math.num-analysis
From: ts@uwasa.fi (Timo Salmi)
Subject: Re: Info wanted on "mps" format
Organization: University of Vaasa, Finland
Date: Sat, 3 Oct 1992 20:22:00 GMT

In article <dfs.718041602@pulaski> <dfs@doe.carleton.ca> writes:
>I need to embed an LP or mixed integer-linear programming solver into
>an application.  The solver requires input in the "MPS" format, apparently
>a standard format.
>If anyone could point me in the direction of documentation about MPS, I'd
>appreciate it.

If you look at my recently updated linear programming package
 76337 Sep 20 19:51 garbo.uwasa.fi:/pc/ts/tslin33b.zip
you probably can deduce something from its programs and
documentation.  The main feature of the MPS (often called the
instrustry standard) format is that you give each constant of the
problem matrix separately, column by column. 

"If you do not know how to go about getting this material, users are
welcome to email me for the prerecorded garbo.uwasa.fi instructions
(long, circa 29Kb).  North American users are referred to the Garbo
mirror on wuarchive.wustl.edu.  Australian users are referred to the
archie.au mirror.  For the Asian users there is the NCTUCCCA.edu.tw
mirror.  The mirrors may lag occasionally, or might not have all the
files.  If you do not receive my reply within five days, please ask
your own site's system manager to construct a returnable mail path
for you". 

P.S.  If you put followup to sender in the posting's header, there
is no guarantee that it will work as one would expect.  Use
"poster".  (Even that does not always work). 

..................................................................
Prof. Timo Salmi
Moderating at garbo.uwasa.fi anonymous FTP archives 128.214.87.1
Faculty of Accounting & Industrial Management; University of Vaasa
Internet: ts@uwasa.fi Bitnet: salmi@finfun   ; SF-65101, Finland
From: cet1@cus.cam.ac.uk (C.E. Thompson)
Newsgroups: sci.math
Subject: Re: Could have Archimedies invented Calclus?
Date: 30 Sep 92 19:57:23 GMT
Organization: U of Cambridge, England

In article <israel.717233288@unixg.ubc.ca>, israel@unixg.ubc.ca (Robert B. Israel)
writes:
|> 
|> (2) The contribution of physics to calculus shouldn't be underestimated.
|> Greek physics was generally qualitative and not quantitative (especially
|> with Aristotle).  The mathematical investigations of accelerated motion
|> (in particular, falling bodies) by Galileo and others introduced the
|> important concept of a rate of change.

The classical Greeks didn't have a useful mathematical theory of dynamics,
but this is far from true for statics, to which indeed Archimedes made 
several contributions. Moreover, one of the most famous of Archimedes'
works, `Ephodos' (= (the) method), is *precisely* about the use of ideas
from statics in the investigation of `pure' mathematical problems. This
is not to contradict what you say above, of course, but it shouldn't be
thought that the influence of physics on mathematics was absent in 
classical times.

Chris Thompson
JANET:    cet1@uk.ac.cam.phx
Internet: cet1@phx.cam.ac.uk
Newsgroups: sci.math
Subject: Polya Question
From: corleyj@helium.gas.uug.arizona.edu (Jason D Corley )
Date: 4 Oct 92 19:19:42 GMT
Distribution: sci.math
Organization: University of Arizona, Tucson, AZ
Summary: A dumb math major shows his ignorance

Hello:

	I just have a short question.  I was reading
through _The Mathematical Experience_ again today when
I found a picture of Polya marked (1888-).  My edition
was published in 1981, which makes him (ponder cogitate
count on fingers) 93 years old when the book was published.
I assume he is dead.  When exactly _did_ he die?

You can just e-mail me if you want.  I'm really enjoying
this newsgroup- even the dumb math jokes!

	Yours,
	Jason
	"They'
re not dead, they're metaphysically challenged." -Tom Servo
C
r
From: mantell@phage.cshl.org (Lin Mantell at Cold Spring Harbor Lab)
Newsgroups: sci.math
Subject: Ramsey Number book fro sale...
Date: 5 Oct 92 01:30:06 GMT
Organization: Applied Mathematics, SUNY @ Stony Brook, New York

Hello Number Enthusiasts,

I have the following book for sale:

Asymptotic Bounds for Classical Ramsey Numbers, by John A. Winn,

Polygonal Publishing House, 1988.    (paperback...102 pages)

I believe this book costs about $15 new....

I ask $10....

Please respond to:  mantell@ams.sunysb.edu 


Abe
Newsgroups: sci.math,sci.math.num-analysis,sci.physics,sci.chem
From: jimbo@leland.Stanford.EDU (Godfather of Soul)
Subject: Fitting nonlinear multivariate functions
Organization: NewsRUs
Date: Wed, 30 Sep 92 23:04:56 GMT


I am interested in finding software that will, given an equation of
the general form

z = f(x,y,c1,c2...cn)

and datapoints (x,y,z), will fit the data and extract the parmeters
c1 through cn.  Any ideas?  Thanks for responding by email.

James
-- 
James W. Brown		-  I dream of the day when conservatives learn   -
			-  the difference between a sin and a crime and  -
			-  liberals learn the difference between a       -
			-  virtue and a requirement.                     -
Xref: sparky sci.math:12583 sci.math.stat:2036
From: bradtke@lust.cs.umass.edu
Newsgroups: sci.math,sci.math.stat
Subject: stable implementation of recursive IV method?
Date: 1 Oct 92 17:34:49 GMT
Reply-To: bradtke@lust.cs.umass.edu ()
Followup-To: sci.math
Distribution: usa
Organization: University of Massachusetts, Amherst

Hi.

	I've implemented a recursive instrumental variable (IV) algorithm
for estimating the parameters of a linear system, as described in 
"Theory and Practice of Recursive Identification" by Ljung and 
Soderstrom (with umlauts appropriately placed).  My current implementation
is naive, and seems to suffer from numerical instability.  I am aware of
Bierman's U-D factorization algorithm (p. 332 of Ljung and Soderstrom) that
could be used to increase the numerical stability for a SYMMETRIC
IV algorithm.  Unfortunately, I cannot use this because I have an
asymmetric IV algorithm.  

	I would appreciate it if those in the know could refer me to a
similar numerically stable algorithm for asymmetric IV methods.

Thank you,

Steve

bradtke@cs.umass.edu
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: Function Problem
Date: 6 Oct 92 02:33:22 GMT
Organization: U of Cambridge, England

The problem was: Define f recursively by f(1)=1 and f(n) = sum over 2,3,..,n
of f(floor(n/k)); then let g be such that f(n) = sum from 1 to n of g(k);
show that g(n) depends only on the parity and multiset of prime exponents
of n.

SPOILER AHEAD. Some blank lines follow.








































We have  g(n) = f(n)-f(n-1)  and (by convention) f(0)=g(0)=0.
Substituting the recursive definition for f(n) and f(n-1), we get
(provided n>2):
  g(n) = sum{k=2,3,..,n-1} of f(floor(n/k))-f(floor((n-1)/k)), plus 1.
But floor(n/k)=floor((n-1)/k) unless k divides n, in which case they
differ by 1. So we have
  g(n) = sum{1<k<n, k|n} of g(n/k), plus 1.
We might as well write this as
  g(n) = sum{k|n, k<n} of g(k)  since g(1)=1.

At this point we are done, modulo a small amount of care with the case
when n is 1 or 2, and its repercussions. The main thing to notice here
is that g(2^s) = g(p^(s-1)) for odd p. (g(2)=0.)

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
Newsgroups: sci.math
From: nissim@mary.fordham.edu (Leonard J. Nissim)
Subject: Re: Mattel says "Math is tough."
Organization: Fordham University
News-Software: VAX/VMS VNEWS 1.41    
Distribution: usa
Date: Mon, 5 Oct 1992 22:04:00 GMT
X-Posted-From: mary.fordham.edu
NNTP-Posting-Host: sol.ctr.columbia.edu

In article <1992Oct5.084002.25808@nuscc.nus.sg>, matmcinn@nuscc.nus.sg 
(Mcinnes B T (Dr)) writes...
>iltiss@owlnet.rice.edu (Steven Patrick Iltis) writes:
>: 
>:         Mattel has just released a new product. A Barbie doll that says
>: "Math is tough".
> 
>What would you have her say?: 

I'd have her say "I can learn math!" or "Math is beautiful!"  Note that neither
of these contradict "math is tough".
-------------------------------------------------------------------------------
Leonard J. Nissim  (nissim@mary.fordham.edu)   
Disclaimer:  "I speak only for myself."
-------------------------------------------------------------------------------
Newsgroups: sci.math
From: martin@lyra.cis.umassd.edu (Gary Martin)
Subject: Re: Mattel says "Math is tough."
Organization: University of Massachusetts Dartmouth
Date: Tue, 6 Oct 1992 12:58:16 GMT

In article <1992Oct5.212115.3356@bnlux1.bnl.gov> kyee@bnlux1.bnl.gov (kenton yee) writes:

     Why do you assume women will be turned off by math simply
    because it is tough?   I know lots of people who like math
     BECAUSE it is tough.  

But how many of these people are women?  I keep hearing the theory that
women aren't as likely to be attracted by the difficulty of a problem
because (for whatever reason) they are usually less competitive than
men.  Unfortunately, it seems that today's generation of students of
both genders are not as turned on by the challenge of a difficult problem
as they should be.



--
Gary A. Martin, Assistant Professor of Mathematics, UMass Dartmouth
Martin@cis.umassd.edu
Xref: sparky sci.math:12275 rec.puzzles:6472 comp.theory:2055
From: lbaum@bcsaic.boeing.com (Larry Baum)
Newsgroups: sci.math,rec.puzzles,comp.theory
Subject: Re: more on .999... = 10.0
Date: 26 Sep 92 16:48:30 GMT
Organization: Boeing Computer Services AI Center, Seattle

In article <1992Sep24.221750.4254@massey.ac.nz> news@massey.ac.nz (USENET News System) writes:
: 
: PS Some people seem to see 0.999... as different in principle to
: 0.333... - is it because the latter has only one decimal representation,
: whereas 1.0... has two (assuming we don't distinguish between different
: numbers of trailing zeros [inserted for humour impaired pedants])?
: A little later, we had a new appointee. He was shown the proof and,
: said, "Of course it is." even more curtly than I did.

The reason that .3333... = 1/3 is easier to accept is that
this is precisely what you get when you do the long division.
You do not have to resort to arguments about limits or
subtracting or multiplying infite representations, etc.  The
long division approach fails for .99999 unless you do
something like:

    .9999999...
  -------------
 2|2.0000000...
   18
   --
    20
    18
    --
     20
     18
     --
...

Of course, explaining why you are saying that 2 goes into 20 9
times is another obstacle!
-- 
Larry Baum
Computer Science Organization
Boeing Computer Services     uucp:       uw-beaver!bcsaic!lbaum
(206) 865-3365               internet:   lbaum@atc.boeing.com
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart Goddard)
Newsgroups: sci.math
Subject: Re: Infinity
Date: 30 Sep 92 21:47:43 GMT
Article-I.D.: cs.1992Sep30.214743.18350
Organization: Rose-Hulman Institute of Technology


In article <1367.2ac9ae4e@atlas.nafb.trw.com> dsimon@atlas.nafb.trw.com  
writes:
> Does infinity actually exist, or is it simply a mathematical tool?  
> Does an infinity of something actually exist?  Is it *possible*
> for there to be an infinity of something?
> ----------
> Dan Simon

Answer 1:
There are an infinite number of places to stop and rest while walking
from Lincoln Nebraska to Terre Haute Indiana, and an infinite number of  
possible times each rest can last.

Answer 2:
Does "one" actually exist, or is it simply a mathematical tool, 
(an abstraction) with which we are so familiar that it seems 
concrete?

bart  
Newsgroups: sci.math
From: mkrogers@unix.amherst.edu (MICHAEL K ROGERS)
Subject: Re: Opinions Sought (Why major in math?)
Organization: Amherst College
X-Newsreader: TIN [version 1.1 PL6]
Date: Thu, 1 Oct 1992 20:16:06 GMT

Kaushik Banerjee (kbanerje@grad09.math.ncsu.edu) wrote:
: Another possibility for a math major is to be an actuary.
: I would reccomend to someone considering the actuary field
: to major in statistics or computer science; if the actuary
: field doesn't work out, there are more doors open for
: a statistics or computer science major.

One interesting facet of the actuarial field is that you
do not have to have a college degree to be an actuary.  You
do have to know a lot of special mathematics.  Anyone
who can pass the tests can be an actuary.  But what tests
I am told!

I am also told that universities want the Society of Actuaries
(or whatever the governing body is called) to set curriculum
standards so that a B.S. in actuarial science would be
equivalent to passing the first few tests, but the actuarial
society refuses.  I hope they continue to do so.
Newsgroups: sci.math
From: bpb9204@tamsun.tamu.edu (Brent)
Subject: Re: Help: inscribed circle of three circles
Organization: Texas A&M Univ., Inc.
Date: Sun, 27 Sep 1992 22:00:14 GMT

czako@yoko.rutgers.edu (Gabor M. Czako) writes:
|In a computer program I am writing I need to find the inscribed
|circle(s) of three circles.  In detail, I have three circles with
|centers (x_1, y_1), (x_2, y_2), and (x_3, y_3) and radii r_1, r_2,
|r_3.  I need to find the inscribed circle(s) with center (x, y) and
|radius r which satisfies the following equations:

|I have not been able to analytically solve for the 0, 1, or 2
|solutions of x, y, and r.  

Roger T. Stevens works through this math for a special case: when the
three circles are tangential to each other and you want to draw a 
circle in the curved triangular region inbetween the three.  This is
detailed in his book, _Fractal_programming_in_C_, page 242.

You didn't say if your circles are co-tangential or not, but you
may want to look up Stevens' method.

-Brent
-- 
------------------------------------------------------------------------------
Brent P. Burton, N5VMG                          Department of Computer Science
bpb9204@tamsun.tamu.edu                                   Texas A&M University
      What are typical family values?      Good buys at WalMart.
Newsgroups: sci.math,sci.logic
From: proberts@informix.com (Paul Roberts)
Newsgroups: sci.math
Subject: Re: Mattel says "Math is tough."
Date: 5 Oct 92 23:51:37 GMT
Organization: Informix Software, Inc.

In article <1992Oct5.165510.3841@cylink.COM> tedh@cylink.COM (Ted Hadley) writes:
>In article <1992Oct5.084002.25808@nuscc.nus.sg> matmcinn@nuscc.nus.sg (Mcinnes B T (Dr)) writes:
>>iltiss@owlnet.rice.edu (Steven Patrick Iltis) writes:
>>: I don't normally read this news group, so I apologize if this is not
>>: the appropriate place to post this. But I believe this is relevant.
>>: 
>>:         Mattel has just released a new product. A Barbie doll that says
>>: "Math is tough".
>>
>>What would you have her say?: 
>
>How about "Math is Important" or "Learn math well and get a good job as a
>[computer scientist | engineer | physicist | ...]"
>


How about "I want to date mathematicians", "CS guys are *real* men", etc?
From: sklar@picasso.ocis.temple.edu (Dave Sklar)
Newsgroups: sci.math
Subject: Re: Closed form solution for Sum[ 1/x , {x,1,n} ] ?
Date: 2 Oct 92 03:19:01 GMT
Organization: Temple University
X-Newsreader: Tin 1.1 PL5


	This is kind of cheesy, but Sum(1/x,{x,1,n}) does equal ln n -
Euler's Gamma Constant, which is approx. 0.577+
Newsgroups: sci.math
From: mantell@phage.cshl.org (Lin Mantell at Cold Spring Harbor Lab)
Subject: Graph Theory Book For Sale...
Organization: Applied Mathematics, SUNY @ Stony Brook, New York
Date: Mon, 28 Sep 1992 17:21:54 GMT

Hello,

I have the following book for sale:

Advances in Graph Theory, ed. by B. Bollobas, North-Holland Publishing, 1978.

It is Vol. 3 in the Annals of Discrete Mathematics.

It lists for $70.25, if you can get it...I believe it is out of print!!!

I will sell for $50  OR  Best Offer (make me an offer)!!!

Reply to:  mantell@ams.sunysb.edu

Abe


Newsgroups: sci.aeronautics
From: shafer@rigel.dfrf.nasa.gov (Mary Shafer)
Subject: Re: PAUL GARBER
Organization: NASA Dryden, Edwards, Cal.
	<1992Sep26.123729.21024@eng.umd.edu> <155@newave.newave.mn.org>
	<1992Sep28.115025.20843@eng.umd.edu>
Date: Sun, 4 Oct 1992 01:13:34 GMT

I was just at the NASM on Friday (2 Oct).  They had a little video
tape display about the restoration of the Enola Gay (up on the second
floor, near the Naval Aviation gallery).

While it won't be in the Museum on the Mall, it will be on display
when they finally get their big airplane addition.  That currently
planned for Dulles, where they have some real estate already.  The
Space Shuttle Enterprise is already there, in storage.

--
Mary Shafer  DoD #0362 KotFR NASA Dryden Flight Research Facility, Edwards, CA
shafer@rigel.dfrf.nasa.gov                    Of course I don't speak for NASA
 "There's no kill like a guns kill." LCDR "Hoser" Satrapa, gunnery instructor
                       "A kill is a kill."  Anonymous

Newsgroups: sci.aeronautics
From: henry@zoo.toronto.edu (Henry Spencer)
Subject: Re: Ram Jet
Date: Tue, 6 Oct 1992 20:18:04 GMT
Organization: U of Toronto Zoology

In article <1992Oct6.123853.3119@comp.lancs.ac.uk> egb008@comp.lancs.ac.uk (Mr R D Felton) writes:
>While I'm here, has anyone out there got any info on how to make small
>model rockets capable of going 50-100 meters or so?

See the Frequently Asked Questions posting (posted just a day or two ago)
in rec.models.rockets for detailed references.  Model rockets easily
make it up several hundred meters; their big brothers, dubbed "high-
power rockets" for historical reasons, have reached several kilometers.

This assumes that you want to use factory-built solid-fuel engines.
If you want something simple and safe, that is what you want to do.
Building your own engines, while possible, is dangerous.
-- 
There is nothing wrong with making      | Henry Spencer @ U of Toronto Zoology
mistakes, but... make *new* ones. -D.Sim|  henry@zoo.toronto.edu  utzoo!henry
From: shafer@rigel.dfrf.nasa.gov (Mary Shafer)
Newsgroups: sci.aeronautics
Subject: Re: Inflatable aircraft
Date: 7 Oct 92 03:50:01 GMT
Organization: NASA Dryden, Edwards, Cal.

It was called inflate-a-plane or the rubber airplane and the US Navy
tested it.  A friend of mine, Chuck Berthe, was the project manager
and test pilot.  He's got a paper about it floating around somewhere
and a literature search on his name should turn it up.  I think it was
an SETP Saturday morning paper in the last 15 years or so.

--
Mary Shafer  DoD #0362 KotFR NASA Dryden Flight Research Facility, Edwards, CA
shafer@rigel.dfrf.nasa.gov                    Of course I don't speak for NASA
 "There's no kill like a guns kill." LCDR "Hoser" Satrapa, gunnery instructor
                       "A kill is a kill."  Anonymous