HDTenEightyP/NetNews huggingface dataset:
From: lordSnooty@cup.portal.com (Andrew - Palfreyman)
Newsgroups: sci.math
Subject: Re: Survey on the Future of Electronic Information Distribution
Date: Sat, 25 Jul 92 02:51:22 PDT
Organization: The Portal System (TM)
Distribution: usa

so you don't have a clue?

how unusual.
Newsgroups: sci.math
From: keithw@ccorp.uucp (Keith Weintraub - dpr2)
Subject: Calculus of Variations?
Organization: Citicorp, New York City
Date: Thu, 23 Jul 92 21:24:20 GMT

Netfolk,
	I am working on forward rate curve construction and would like to
solve a problem that I think is of "Calculus of Variations" type. Feel free
to correct me if I am wrong. I would like to find a *continuous* non-negative
function y(t) whose derivative has minimum L_2 norm over [0,T] and integrates
to given constants over disjoint subintervals that cover [0,T]. (I wanted to
write that in English---hope I succeeded---in case people don't like the TeX
notation below). More symbolically I would like to find a *continuous*
function y(t) such that

	\int_0^T (y'(s))^2 ds

is a minimum subject to the constraints

	\int_{t_{i-1}}^{t_i} y(s) ds = a_i > 0 (a_i known) i = 1,...,n

where
	0 = t_0 < t_1 < ... < t_n = T.

Any guidance, references, solutions would be most appreciated.

Respond by e-mail or post and if I get anything interesting I will post a
summary.

Thanks in advance,
KW


-- 
Keith Weintraub (KW) -- Citicorp |    I told you a trillion times:
keithw@Citicorp.COM              |	"Don't exaggerate."
uunet!ccorp!keithw               |
Newsgroups: sci.math,news.answers
From: ycchin@tartarus.uwa.edu.au (Chin Yih Chong)
Subject: A puzzle! (Re)
Summary: A puzzle!
Keywords: A puzzle! (Re)
Organization: University of Western Australia
Date: Thu, 30 Jul 1992 07:23:00 GMT


The series given by P.Nambi can be broken down as follow:

		 	4 = 2^2
		       72 = (2^3)*(3^2)
		    21600 = (2^5)*(3^3)*(5^2)
	        190512000 = (2^7)*(3^5)*(5^3)*(7^2)
	  580909190400000 = (2^11)*(3^7)*(5^5)*(7^3)*(11^2)

I reckoned that the general formula is 

	           
                       n
                      ___
                      | |
                      | | p(i)^p(n+1-i)
                      | |

where p(i) stands for the i-th prime number.


so the next number in the list is 
   
          428616352408083840000000!    phew!

Have a nice time multiplying the next number in the row!


	^ ^
  	O O
	 ~
 	\_/
	
      Y.C.CHIN

Any mistake please email ycchin@tartarus.uwa.edu.au
From: columbus@strident.think.com (Michael Weiss)
Newsgroups: sci.math
Subject: Re: Mathematical reality (was: You know, the integers)
Date: 31 Jul 92 12:01:52
Organization: Thinking Machines Corporation, Cambridge MA, USA
	<COLUMBUS.92Jul23085953@strident.think.com>
	<1992Jul23.171232.6159@galois.mit.edu>
	<1043.Jul3102.24.0992@virtualnews.nyu.edu>
NNTP-Posting-Host: strident.think.com
In-reply-to: brnstnd@nyu.edu's message of 31 Jul 92 02:24:09 GMT

In article <1992Jul23.171232.6159@galois.mit.edu> tycchow@riesz.mit.edu
(Timothy Y. Chow) writes: 
   > I was tempted to use the word "formalism" in the discussion several times
   > but refrained because I didn't think it was necessary.

In article <1043.Jul3102.24.0992@virtualnews.nyu.edu> brnstnd@nyu.edu (Dan
Bernstein) replies:

   ``Formalism'' is a loaded term. People called Ramanujan a ``formalist''
   when he blindly manipulated the zeta function without realizing that it
   had complex zeros. The ``formalism'' of a century ago was ushered out by
   rigor.

   In any case, the purely syntactic viewpoint which I advocate doesn't
   have any difficulties. You may refuse for years to give in and admit
   that you're a symbol-pusher too, but I'll be able to take any paper you
   publish and keep the entire mathematical content while removing every
   appeal to semantics. I win. [chuckle]

"Formalism" has been the standard term for a certain philosophy of
mathematics since Hilbert, at least.

I won't get drawn into an argument about whether formalism is "correct"
(whatever that means).  Why don't we just conclusively solve the easy
problems in philosophy first, like the meaning of quantum mechanics, the
mind-body problem, and the nature of good and evil?

Dan appears to believe that he "wins" because Timothy can't prove that
formalism is wrong.  Philosophical arguments being what they are, such
victories come cheap.

Anyone who is seriously interested in such issues should do some background
reading.  I recommend "The Philosophy of Mathematics", a collection edited
by Benacerraf and Putnam.  This dates from c. 1970; most of the essays are
post-Goedel's theorem (the Great Divide for this subject, as Benacerraf and
Putnam point out in their introduction).
Newsgroups: sci.math
Subject: Re: ALGEBRAIC NUMBER ARITHMETIC
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 30 Jul 92 16:21:01 GMT
Keywords: algebraic numbers arithmetic

In <aet.712408532@munagin> aet@mullian.ee.mu.OZ.AU (bert thompson) writes:

>hi!

>i want to perform arithmetic on algebraic numbers.

>if i represent an algebraic number by an polynomial in integers
>and an interval in which is found the root of the polynomial
>corresponding to the represented number.

>so sqrt(2) might look like this:

>  2  
>x   -  2 = 0      ,    [1, 3/2]


>how would i perform the following operations:
>(returning a polynomial-interval pair)

>+
>-
>*
>/
>sqrt
>=	(computable? my guess is yes.)
>and other operations you might think are worth mentioning...

If you want to perform arithmetic on algebraic reals, the result from
mathematical logical the Th(R) is decidable should allow you to compute
using representations as you suggest.
--
Arthur L. Rubin: a_rubin@dsg4.dse.beckman.com (work) Beckman Instruments/Brea
216-5888@mcimail.com 70707.453@compuserve.com arthur@pnet01.cts.com (personal)
My opinions are my own, and do not represent those of my employer.
Our news system is unstable; if you want to be sure I see a post, mail it.
From: steeve@concour.cs.concordia.ca (HARDY j g steeve)
Newsgroups: sci.math
Subject: Re: An interesting limit problem.
Date: 30 Jul 92 14:57:54 GMT
Organization: Concordia University, Montreal, Quebec
	I just finished reading this little thread and I must admit


	For instance, very soon computers will be capable of
correcting not only grammar and spelling but style very efficiently,
already some software do it quite nicely. Would this mean that we
could therefore slack off on learning the basic grammar? 

	Tools in themselves are not to blame, I think it is the
general attitude towards learning which should be addressed. I was
shocked to learned a few months ago that in Quebec (Canada) where the
education is free up to the college level and extremely subsidized at
the university level that we still have a 40% high school drop out
rate (55% apparently with the male population) (don't quote me on
these figures however but they sound quite alarming even if they are
100% off). 

	I guess I would basically agree that these tools in general
should be taught or used but definitely not in the beginning phases.

						Steve.

 _____________    _____              |
(___  |  |__  \  /|__   Steve Hardy  | Youth is not a reason for intolerance
____) |  |_____\/ |__________________| Neither is age an excuse!
   (steeve@concour.cs.concordia.ca)  |
Newsgroups: sci.math,sci.engr.mech
From: jing@resmel.bhp.com.au (Jian Feng)
Subject: HELP! Cross-linked series / recursive formulas
Organization: BHP Research - Melbourne Laboratories, AUSTRALIA
Date: Tue, 28 Jul 1992 02:20:07 GMT

Can someone in the net point me to the solution of the following
problem:

I have two series which are cross-linked:

f(n) = a * f(n-1) + b * g(n-1)
g(n) = c * f(n-1) + d * g(n-1)

where a != b != c != d

I am after an explicit formula for

Sum [f(k)+g(k)] {k=1,n}.

For people with Mechanical Engineering background: This is to solve
the multiple reflection of waves inside a plate. 

Any hints or information welcome.

Thanks in advance.

J.Jing jing@resmel.bhp.com.au
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.math
Subject: Re: Roots Of Integer Poly's
Summary: What is the question?
Date: 23 Jul 92 17:50:12 GMT
Organization: Purdue University Statistics Department

In article <1992Jul23.113837.3173@ucsvc.ucs.unimelb.edu.au> u7023595@ucsvc.ucs.unimelb.edu.au writes:
>>In article <1992Jul21.172356.3167@ucsvc.ucs.unimelb.edu.au>, 
>>u7023595@ucsvc.ucs.unimelb.edu.au writes:
>>>In article <4547@balrog.ctron.com>, wilson@ctron.com (David Wilson) writes:

>>>>I wonder if any one out there knows anything on the following.

>>>>Let F(x) be a monic polynomial with integer coeff's of degree n.
>>>>Let F(x) have roots   \alpha_{1}, ... , \alpha_{n}  is there a
>>>>constant C depending only on n such that

>>>>       | \alpha_{j} - \alpha_{i} | >= C

>>>>For all i,j. Ie the roots cannot be too close together.
>>>>This is trivially true for n=1 or n=2 but what about general n ?

>>> [Stuff deleted]


>> WLOG assume the monic polynomial is irreducible over the rationals as 
>> this is the interesting case.
>I meant the maximum of the absolute values of 
>  |\alpha_j - \alpha_i|  for all i,j.
>Then one has C=\sqrt(3), etc. as in my previous posting. If one is interested
>in the minimum of these absolute values then no such C exists but that is
>another question. 


But that was the original question.  Consider the following example:

	x^3 - A*x^2 + 1 = 0.

Since every rational root is 1 or -1, this is irreducible if A is not 0 or 2.
Let 1/A = v^2.  Then for v small, the equation, written in the form

	x^2 = v^2 + v^2 * x^3,

has a solution which is given by a convergent power series in v.  This
series is

	x = v + v^4/2 + (5/8)*v^7 + ... .

Thus, the sums for the positive square root v and the negative square root
are both roots of the equation, and they differ by  2*v + (5/4)*v^7 + ...
Clearly, this can be made arbitrarily small.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)
From: carabalo@phoenix.Princeton.EDU (David G. Caraballo)
Newsgroups: sci.math
Subject: Cardinality of Borel field
Date: 29 Jul 92 17:34:56 GMT
Organization: Princeton University
Originator: news@ernie.Princeton.EDU

Recently, someone (Gerald Edgar?) suggested we consider whether AC is 
required to prove card(Borel subsets of X) = card(R), if X is a separable
metric space.  I recall seeing some results, but for some reason I can not
find the appropriate files.  Here's what I remember:

I posted something to the effect that I believed it was necessary (but I did
not have a proof).  Someone suggested that ZF+DC suffices, and then someone 
else showed that ZF+DC does not suffice after all.  Does the provability of 
card(Borel sets) = card(R) imply AC?  (and, am I remembering the results 
correctly?)

David Caraballo
Newsgroups: sci.math,sci.engr.mech
From: jing@resmel.bhp.com.au (Jian Feng)
Subject: Thanks for suggestions (cross-linked recurrences)
Organization: BHP Research - Melbourne Laboratories, AUSTRALIA
Date: Wed, 29 Jul 1992 05:06:13 GMT

Thanks for all those who reply to my request.
Three different ways were suggested:

a) matrix formulation
b) solve difference equation
c) using generating series

They all worked, although a,b were straightforward, c) complicated but
mathimatically brilliant.

I wonder how I forgot all my math tricks (haven't touched it for > 8 years!)

Many thanks again.
J.Jing


Newsgroups: sci.math
From: ycchin@tartarus.uwa.edu.au (Chin Yih Chong)
Subject: Re:A puzzle!
Summary: Re: A puzzle!
Keywords: Re: A puzzle!
Organization: University of Western Australia
Date: Mon, 27 Jul 1992 02:43:44 GMT


Reply to the puzzle:


 4  72  21600 ...


Observation                  4 = 2^2
                            72 = (2^3)*(3^2)
                         21600 = (2^5)*(3^3)*(5^2)
                    1905120000 = (2^7)*(3^5)*(5^3)*(7^2)
               580909190400000 = (2^11)*(3^7)*(5^5)*(7^3)*(11^2)

I reckon that the general formalu is

       _n_
       | |  
       | | P(i)^P(n-i+1)
       i=1

where P(n) stands for the nth prime number.

So, I supposed the next number to the list is

    428616352408083840000000  phew!

Hope this answer the question....


	^ ^
	O O
	 ~
	\_/

	Y.C.CHIN

Please email me if I have made any mistake!
Address: ycchin@tartarus.uwa.edu.au
From: rose@fsu1.cc.fsu.edu (Kermit Rose)
Newsgroups: sci.math
Subject: Re: Quadratic Residue Question
Date: 23 Jul 92 04:29:18 GMT
Reply-To: rose@fsu1.cc.fsu.edu
Organization: Florida State University
News-Software: VAX/VMS VNEWS 1.3-4

In article <1992Jul17.210332.2105@cs.umn.edu>, pires@cs.umn.edu (Luiz S. Pires) writes...
> 
>  ....
> 
>  Given an arbitrary number a and an odd prime p, I am trying to write a 
> subroutine that decides whether a is a quadratic residue mod p.
> 
> ....

>  For example, if we have, say, a=31123 and p=45667, then I am not clear on
> how to proceed. I thought of using Euler's lemma (or whatever it is called)
> and calculate a^((p-1)/2) (mod p). That, however, would seem to have very poor
> worst case performance. 
> 
>   Does anyone have an efficient algorithm for determining this? Am I missing
> something obvious here? Any help would be most welcome!
> 
>  Thanks in advance.
> 
>    Luiz.
>    (pires@cs.umn.edu)

Actually, you can calculate a(([p-1]/2) (mod p) very efficiently.  Example, 

a^3 = a^2 a^1
a^4= (a^2)^2
a^5 = (a^2)^2  a^1
a^6 = (  (a^2 a^1)  )^2
a^7 = ( (a^2 a^1) )^2   a^1

etc.   
simply think of k = [p-1]/2 in base 2.

k = a_m 2^m + a_(m-1) 2 ^(m-1) + ... + a_1 2 + a_0

k = ((((( ....  a_m 2+a_[m-1] )2 +...   )2 + a_1   2)+ a_0

b_0 = b^k
b_m = b^a_m
b_[m-1] = b_m^2  b^a_m-1
..
b_1 = b_2 ^2  b^a_1
b_0 = b_1 ^2  b^a_0

rose@fsu1.cc.fsu.edu          To be sure I see your response, use e-mail.
-----------------------------------------------------------------------
Be of good cheer, for it is much more fun than being depressed.
Newsgroups: sci.math
From: chepan@gsusgi1.gsu.edu (Parthasarathy Nambi)
Subject: A puzzle!
Summary: A puzzle!!
Keywords: Math, puzzle
Organization: Georgia State University
Date: Fri, 24 Jul 1992 21:04:27 GMT



 Here is something for puzzle lovers:

 Below is a sequence of numbers, can you find the next two numbers and 
 the general formula for generating numbers in this sequence:

 The numbers are:

 4, 72, 21600, 190512000, 58090919040000,   etc 


 If you know the answer please post a response in this group.


 P.Nambi

Newsgroups: sci.math
From: ycchin@tartarus.uwa.edu.au (Chin Yih Chong)
Subject: Help needed for a Proof
Summary: The proof of a determinant formula
Keywords: Help
Organization: University of Western Australia
Date: Sat, 25 Jul 1992 06:24:01 GMT

Recently, I came across a very useful formula for finding determinant,
and It goes something like this:

Given an n*n square matrix    |  A   B  |
                              |  C   D  |

where A is of dimension r*r and D is of dimension s*s, such that 
r>0,s>0 and r + s = n, then

	det | A  B |  =  det(D)*det(A - B*R*C) , where R = inverse of D
            | C  D |

Can anyone enlighten me on the proof of this formula.....
Any help is greatly appreciated.


   ^  ^
   O  O
    ^^
   \__/
   CHIN       Thank you in advance!

email address: ycchin@tartarus.uwa.edu.au
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.math
Subject: Logic and set theory
Date: 23 Jul 92 18:06:28 GMT
Organization: Purdue University Statistics Department

In article <1992Jul23.042250.10738@mixcom.com> ttyytt@mixcom.com (Adam Costello) writes:
>In article <1992Jul20.173716.6310@galois.mit.edu> tycchow@riesz.mit.edu (Timothy Y. Chow) writes:

>>But this is precisely the point!  Consider the "REAL" integers:  every
>>set of axioms and syntactic rules that the "REAL" integers satisfies
>>also admits nonstandard models.  How then do you propose to "define" the
>>REAL integers with a fixed set of axioms and syntactic rules?

>I'm sorry if I begin to sound like a broken record, but please remember
>that this is only true if you restrict your axioms to first-order
>languages.  The REAL integers _can_ be defined (to within isomorphism)
>in a second-order language.  Of course, this still doesn't get you a
>complete number theory.  Also, using a second-order language requires
>that one already knows what sets are.  If these still have to be defined,
>then we're back to the same problem.  It's inescapable.  Set theory is
>built on logic, but logic is defined in terms of sets.  People obviously
                 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>knew and understood both concepts well, before either was formalized.

This is definitely not so.  At least very much of logic does not require
sets.  The logic needed in Godel's proof is only part of first-order
intuitionistic logic, and requires no set theory at all.

The sentencial calculus was fairly well understood by Boole, etc., but
that is about all that can be said about understanding either of these
well, at least having an understanding which can be conveyed to others.
There is much better understanding of logic than of set theory.  As
someone who has worked with the objects of set theory, it is clear that
much of the power of the field is due to the fact that one works with
them, and knows how to, but they are quite vague.  The independence 
makes it clear that we will never really see a well-ordering of the 
reals, for example.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)
From: ajtd@st-andrews.ac.uk (Antony J. T. Davie)
Newsgroups: sci.math
Subject: Journal Expense
Date: 21 Jul 92 15:33:45 GMT
Followup-To: Why are Some Journals so Expensive?
Organization: St. Andrews University, Scotland.

I understand some of the remarks about profit making vs. non-profit making
journals. Nevertheless the price of some journals is OBSCENE. One such is

Theoretical Computer Science

published by Elsevier. This now costs in the region of 900 pounds sterling
in the UK which is more than that of the ENTIRE PACKAGE of journals that
one can buy from the ACM including JACM, CACM, Computer Surveys, SIGPLAN
notices, etc. etc.

We have had to cancel our subscription to TCS. May I urge as many of you
as have the authority to do so to follow our example. Maybe a mass desertion
might persuade the publishers to bring down their prices (their other journals
also seem to be sky high).

Tony Davie
From: bumby@no.rutgers.edu (Richard Bumby)
Newsgroups: sci.math
Subject: Re: Computational aids. Was: Re: An interesting limit problem.
Date: 29 Jul 92 17:47:47 GMT
Organization: Rutgers Univ., New Brunswick, N.J.

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

>In article <1992Jul29.000223.27339@massey.ac.nz> news@massey.ac.nz
>(USENET News System) writes:

...[introduction and other quotes deleted]...

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

>I must concur.  There is no evidence whatever that learning to compute
>gives any understanding of what the computation does, and why it is done.

This reminds me of the Applied Linear Algebra course (beginning
graduate level) that I am teaching right now.  While doing homework
exercises designed to aid understanding of concepts just introduced,
the students frequently make arithmetic errors leading to
qualitatively different results than they have been told to expect.
Frequently this discrepancy is clear at an early stage of the work,
yet calculation continues.  I still have the rest of this week to try
to teach them the right answer to the question:  "Which do you trust
more: the theoretical principle we proved two days ago or your
ability to perform the arithmetic you learned in grade school?"

>A six-year-old can understand the Peano postulates with little difficulty;
>they do not mention anything except counting.  Then the understanding of
>what the arithmetic operations mean can be taught.  Those who have
>manipulative ability will learn the time-saving mechanics, and those
>who do not are far better served by using calculators.

>.... [remainder of article deleted]

I know that my own school training suffered from an emphasis on
manipulation over understanding, and things seem to be getting worse.
We have ample evidence of the major pitfalls in our approach to the
basic operations on numbers, and have successfully taught tiny chips
of silicon to avoid them.  However, the schools persist in advancing
students whose future learning will suffer because of a lack of
understanding of these concepts.
-- 
R. T. Bumby **  Rutgers Math ||   Amer. Math. Monthly Problems Editor
bumby@math.rutgers.edu       || P.O. Box 10971 New Brunswick, NJ08906-0971
bumby@dimacs.rutgers.edu     || Phone: [USA] 908 932 0277 * FAX 908 932 5530
From: johnk@jhunix.hcf.jhu.edu (John J Kuszewski)
Newsgroups: sci.math
Subject: distance geometry in 2-D
Date: 31 Jul 92 20:17:45 GMT
Organization: HAC - Johns Hopkins University, Baltimore

Given 5 points in a plane A, B, C, D, & E and the distances between
all pairs of points except D & E, can you give me a general means of 
determining the distance between D & E?  Can it be done without using 
transcendental functions?  I need to be able to compute this quickly.


-- 
John Kuszewski
johnk@jhunix.hcf.jhu.edu
I'm not an idiot, but I play one on USENET
Newsgroups: sci.math
From: tycchow@riesz.mit.edu (Timothy Y. Chow)
Subject: Re: You know, the integers (was: Re: Stupid question about FLT)
Organization: None.  This saves me from writing a disclaimer.
Date: Thu, 23 Jul 92 03:37:20 GMT

In article <11667.Jul2300.06.3692@virtualnews.nyu.edu> brnstnd@nyu.edu (Dan Bernstein) writes:

>You're equating the mathematical term ``the sets'' with some particular
>collection which you think of as modelling the sets. What I am saying is
>that the word ``set,'' for all mathematical purposes, is a purely
>syntactic object which we manipulate according to certain rules.

Aha!  The WORD "set" is a syntactic object.  There is a world of difference
between the word "set" and a set.  Similarly there is a difference between
the phrase "the integers" and the integers.  If you alter your claims about
the integers to be claims about the phrase "the integers" then I will have
no objection to what you say.
-- 
Tim Chow     tycchow@math.mit.edu
Where a calculator on the ENIAC is equipped with 18,000 vacuum tubes and weighs
30 tons, computers in the future may have only 1,000 vacuum tubes and weigh
only 1 1/2 tons.                               ---Popular Mechanics, March 1949
Newsgroups: sci.math
From: dzk@cs.brown.edu (Danny Keren)
Subject: Square roots of polynomials
Organization: Brown University Department of Computer Science
Date: Mon, 27 Jul 1992 18:56:17 GMT

I am looking for

1) An algorithm that can decide whether a polynomial in one variable
   (over the integers or reals) has a square root.

2) An algorithm to compute such roots.

Thanks,

-Danny Keren.

Newsgroups: sci.aeronautics
From: Michael F. Kamprath <kamprath@engin.umich.edu>
Subject: Re: Please send me all known info on Aurora!!!!
Date: Thu, 30 Jul 92 16:52:05 EDT
Organization: University of Michigan, Aerospace Engineering
X-Useragent: Nuntius v1.1

Subject: Please send me all known info on Aurora!!!!
From: Michael A. Kopack, kopackm@lonex.rl.af.mil
In article <1992Jul30.181034.23409@lonex.rl.af.mil> Michael A. Kopack,
kopackm@lonex.rl.af.mil writes:
>
>So, could somebody please send me any info that you have on the project.
>Please, nothing too secretive. I am in AFROTC and really don't want to
get
>booted for knowing too much about an Ultra Secret project. But, any
decent
>info will be appreciated. If I get enough info, I will post the results.
> 
>
>Thanks in advance,
>
>--Mike Kopack
>


Do you honestly think someone would tell you secret or even classified
stuff
over the internet?  And do you really think you'd get booted from AFROTC
because _they_ did?
Newsgroups: sci.aeronautics