HDTenEightyP/NetNews huggingface dataset:
From: smith@metatron.harvard.edu (Steven Smith)
Subject: Parallel Translation on the Stiefel Manifold
Originator: dan@symcom.math.uiuc.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Harvard Robotics Lab, Harvard University
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Mon, 14 Dec 1992 17:44:51 GMT

I wish to compute the formula for parallel translation along geodesics
in the (compact) Stiefel manifold V(n,k) = O(n)/O(n-k), relative to
its natural invariant connection.

As discussed below, this problem can be solved by computing a formula
for either (i) the geodesic symmetry of V(n,k), or (ii) an involutive
automorphism of O(n) that fixes O(n-k).


The compact Stiefel manifold V(n,k) is the set of orthogonal k-frames
in R^n.  V(n,k) is a Riemannian symmetric space; its group of
isometries G := I(V(n,k)) is the group O(n) of n-by-n orthogonal
matrices, and the isotropy group K at p in V(n,k) is the group

        {   ( I 0 )  -1               }                     ( I )
        { g (     ) g   : Q in O(n-k) }  where p = g.o, o = (   ).
        {   ( 0 Q )                   }                     ( 0 )

Note that o in an n-by-k matrix whose columns lie in V(n,k).
Therefore, V(n,k) = G/K.

Let X, Y in T_p.  Denote the point exp_p(tX) by p_t.  Let s_t be the
geodesic symmetry at p_t in V(n,k).

The parallel translation tau_t of Y along the geodesic t -> exp_p(tX)
is induced by the isometry T_t = s_(t/2)s_0, i.e.,

        tau_t(Y) = (T_t) (Y).
                        *

Therefore, a formula for the geodesic symmetry s_p (at any point p)
provides a formula for parallel translation.


Alternatively, given an involutive automorphism sigma (sigma: G -> G,
sigma^2 = id) that fixes K, the following diagram commutes,

               sigma
            G -------> G
            |          |
         pi |          | pi
            V          V
           G/K -----> G/K
                s_o

and we may use sigma to determine a formula for s_o, and hence for
parallel translation.


I would appreciate any help computing a formula for the geodesic
symmetry of V(n,k), an involutive automorphism of O(n) that fixes
O(n-k), or a reference to a paper or book that discusses these ideas
in the case of Stiefel manifolds.

Steven Smith

Newsgroups: sci.math.research
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Subject: Difference Geometry
Originator: dan@symcom.math.uiuc.edu
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Followup-To: poster
X-Submissions-To: sci-math-research@uiuc.edu
Organization: The Wistar Institute of Anatomy and Biology
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Tue, 15 Dec 1992 17:03:13 GMT


Are there any coherent writeups on discrete analogues of differential
geometry?  I have L Blumenthal THEORY AND APPLICATIONS OF DISTANCE
GEOMETRY (Chelsea, 1970)--I'm more interested in the numerical analysis.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)

Newsgroups: sci.math.research
From: Leif Johansson  <leifj@matematik.su.se>
Subject: A question about inf-categories
Originator: dan@symcom.math.uiuc.edu
Followup-To: poster
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Illinois at Urbana
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 11 Dec 1992 08:33:50 GMT

I would very much appreciate any info on inifinity-categories that
are also "triangulated" - what is the correct notion anyway? Any
standard references are wellcomed. Reply through email to
leifj@matematik.su.se

For those not familiar with \inf-categories, here's the definition:
A \inf-category is a class A of morphisms such that there for all integers n
is a subclass of A denoted A_n with Ob A_n \subset Ob A_{n+1} and the structure
of a category on A_n with compatibility conditions on these category structures
making A into a Kan-komplex with the added condition that the completion of
n+1 compatible n-faces to an n+1 face is unique (which is not always the case
with Kan-komplexes). Compatible in the above is like in the picture below:

	|
	|
	|
	--------

to be completed to

	|\
	| \	
	|  \
     	|   \
        -----

(sorry for the angle mismatch..) A good ref. for the definition is: "The
equivalence of \inf-groupoids and crossed complexes." by Brown and Higgins in
Cah. de Top. et Geom. Diff. Vol 22 1981.

Thanx in advance.

MVH leifj

Newsgroups: sci.math.research
From: kuplinsk@math.rutgers.edu (Julio Kuplinsky)
Subject: tangent plane
Originator: dan@symcom.math.uiuc.edu
Followup-To: ru.nb.math.general
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Rutgers Univ., New Brunswick, N.J.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 18 Dec 1992 16:34:48 GMT



Can anyone point me to a source that discusses this problem (which
should be well known, I guess)?

Let f:R^2 ---> R be a function of type C1 with a local minimum at
(0,0) and f(0,0)=0. Suppose that you start pouring water right above
0, and at some point the water starts to spill, say when the depth of
the water is h. Is it true that there is a point (x,y) with f(x,y) =h 
where the tangent plane to f is horizontal? 

J. Kuplinsky

Newsgroups: sci.math.research
From: Berni@nw42.wiwi.uni-bielefeld.de (B. Strohmeier)
Subject: Inequality question
Originator: dan@symcom.math.uiuc.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Fakultaet fuer Wirtschaftswissenschaften, Uni Bielefeld, Germany
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Thu, 17 Dec 1992 10:03:01 GMT

Can the following theorem be easily proofed?

Theorem:
Let 
    1. p_1\geq p_2\geq\ldots\geq p_n and q_1\geq q_2\geq\ldots\geq q_n
       with 0\leq p_i\leq 1 and 0\leq q_i\leq 1 \forall 1\leq i\leq n
    2. \sum_{i=1}^np_i=\sum_{i=1}^nq_i=1
       (imagine p_i and q_i as probabilities in decreasing order)       
    3. \sum_{i=1}^kp_i\geq\sum_{i=1}^kq_i \forall 1\leq k\leq n
       (the cumulated sum of p_i is always greater or equal than the 
        cumulated sum of q_i)
Then
    \sum_{i=1}^np_i(1-q_i)^\alpha\leq\sum_{i=1}^nq_i(1-p_i)^\alpha
    \forall real \alpha\geq 1 

If this is true, it follows that a weaker expert can better predict a
stronger expert than vice versa.
Thanks in advance. 		  

Bernhard Strohmeier
bstrohm@erasmus.hrz.uni-bielefeld.de


Newsgroups: sci.math.research
From: Allan Adler <ara@zurich.ai.mit.edu>
Subject: Index theory
Originator: dan@symcom.math.uiuc.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: M.I.T. Artificial Intelligence Lab.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Wed, 16 Dec 1992 09:22:25 GMT


I have an elliptic complex E on a smooth projective variety X and an 
automorphism T of X of finite order which lifts to an action on the elliptic 
complex. I don't want to assume that T has only isolated fixed points.

Can someone point me to contemporary discussions of the Lefschetz number
of the map with respect to E and of the index theorem in this equivariant
setting?

If they are easy to read, that is fine with me. Honest.

Allan Adler
ara@altdorf.ai.mit.edu


Newsgroups: sci.math.research
From: moskowit@itd.nrl.navy.mil (Ira Moskowitz,b16/r139,47310,)
Subject: Dirichlet series
Originator: dan@symcom.math.uiuc.edu
Reply-To: moskowit@itd.nrl.navy.mil
Followup-To: Poster
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Information Technology Division, Naval Research Laboratory
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Tue, 15 Dec 1992 14:09:42 GMT

I am looking through the book by S. Mandelbrot "Dirichlet Series".  On the
first page he defines a quantity called D the upper density of a strictly
increasing sequence of positive numbers. In the next paragraph he uses the
notation

	$D^{.}$

which I have given in TeX notation.  Unfortuantely he never defines $D^{.}$
Dirichlet series are not my area and I cannot decipher the meaning form the
text.  If anyone could help me out I would apprecite it.  Thank you.

---
Ira Moskowitz
moskowit@itd.nrl.navy.mil
From: frandag@math.ksu.edu (Francis Fung)
Newsgroups: sci.math
Subject: Ref. for existence of universal objects?
Date: 17 Dec 1992 13:09:02 -0600
Organization: Dept. of Mathematics, Kansas State University
Distribution: world
NNTP-Posting-Host: hilbert.math.ksu.edu


I was just wondering if anyone knew of a comprehensible reference
for a proof that there exist universal objects in categories satisfying
certain conditions, which I don't really understand. The reference
in Massey's Alg. Top.: An Intro. was to Bourbaki's Theory of Sets, 
but the terminology is essentially impenetrable for me. Perhaps there
is a more modern treatment somewhere. Any input is welcomed!
Francis Fung
From: rags@triples.math.mcgill.ca (Robert A. G. Seely)
Newsgroups: sci.math
Subject: Re: Philosophy of Pi
Date: 14 Dec 92 14:49:54 GMT
Organization: /etc/organization

In article <1gi1bmINNsou@function.mps.ohio-state.edu> edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:
>>YESSSSS!!!!!  exp(i*Pi) + 1 = 0
>>is perhaps the most beautiful identity in mathematics,
>
>I disagree.  The beautiful identity is exp(ix) = cos x + i sin x.
>Unlike the previous one, it is even useful...
>-- 
>  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
>  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
>  The Ohio State University      telephone: 614-292-0395 (Office)
>  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)


But this is just a matter of preferring the general to the particular
instance - many might prefer the instance as a beautiful representative of 
the general equation, understanding that the instance also encompasses the 
general by implication.

-rags
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: Philosophy of Pi
Date: 14 Dec 1992 08:14:30 -0500
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu

>YESSSSS!!!!!  exp(i*Pi) + 1 = 0
>is perhaps the most beautiful identity in mathematics,

I disagree.  The beautiful identity is exp(ix) = cos x + i sin x.
Unlike the previous one, it is even useful...
-- 
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
Xref: sparky sci.math:16984 rec.puzzles:7953 alt.usage.english:9559
From: J.Theodore.Schuerzinger@dartmouth.edu (J. Theodore Schuerzinger)
Newsgroups: sci.math,rec.puzzles,alt.usage.english
Subject: Re: Naming Large Numbers (Re: Negative Zero)
Date: 15 Dec 92 21:50:22 GMT
 <Dec.15.05.12.50.1992.13518@romulus.rutgers.edu> 
 <1992Dec15.162324.28405@dartvax.dartmouth.edu>  
 <1992Dec15.210004.2556@hobbes.kzoo.edu>
Organization: Dartmouth College, Hanover, NH
X-Posted-From: InterNews1.0b1@newshost.dartmouth.edu

In article <1992Dec15.210004.2556@hobbes.kzoo.edu>
k044477@hobbes.kzoo.edu (Jamie R. McCarthy) writes:

> J.Theodore.Schuerzinger@dartmouth.edu (J. Theodore Schuerzinger) writes:
> >clong@romulus.rutgers.edu (Chris Long) writes:
> >
> >> Eckler, R. "The Only Man Infinity Fears", _Word Ways_ Vol. 19,
> >>   Num. 4 (Nov. 1986) p. 252-254
> >> 
> >>   The largest number given is millitwoillimillionillion, which
> >>   can't be written down in standard notation.
> >
> >Why can't it be written down in standard notation?  Unless it's
> >irrational or transcendental, one should be able to write it down.
> 
> This mathematical hypothesis of yours is as false as your
> linguistic hypotheses.

No smileys?
> 
> I submit that one cannot write down, in scientific notation, the number
> x, such that x is the integer component of pi times n, where n is
> sufficiently large.  (Take n to be ten to the power of the number of
> atoms in the universe, for instance.)

I'm not certain exactly what you mean by "integer component", unless
you just mean to drop everything after the decimal, but in this
example, assuming there are 10^126 atoms in the universe, wouldn't the
answer be:

3.14159 ... * 10^1 000 000 000 000 000 000 000 000 000 000 000 000 000
000- 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000- 000 000 000 000 000 000 000 000 000?

Sorry I can't be any more accurate, but right now I don't have an
approximation of pi to that many places handy!  :-)


--Ted Schuerzinger
email: .zed@Dartmouth.EDU
"I should have known it would be bad vodka when all the label said was
'Russian Vodka'."
Xref: sparky sci.math:17140 rec.puzzles:8035 alt.usage.english:9686
From: wilcox@vax.oxford.ac.uk
Newsgroups: sci.math,rec.puzzles,alt.usage.english
Subject: Re: Naming Large Numbers (Re: Negative Zero)
Date: 17 Dec 92 14:43:06 GMT
Organization: Oxford University VAX 6620

In article <1992Dec15.210004.2556@hobbes.kzoo.edu>, k044477@hobbes.kzoo.edu (Jamie R. McCarthy) writes:
> I submit that one cannot write down, in scientific notation, the number
> x, such that x is the integer component of pi times n, where n is
> sufficiently large.  (Take n to be ten to the power of the number of
> atoms in the universe, for instance.)

Practically speaking, one cannot. Theoretically speaking, one can. Assuming one
can write down pi primitive recursively (I think one can) one can even write
your number down primitive recursively, which is as near practicality as
mathematicians ever get.
-- 

Stephen Wilcox             |   For Sale: Posts in British Government. Suit
wilcox@vax.oxford.ac.uk    |   outgoing American. Highest bids accepted.
Newsgroups: sci.math
From: leemike@eecg.toronto.edu (Michael Lee)
Subject: Re: need proof:  (1 + 1/n)^n ==> e
Organization: CSRI, University of Toronto
Date: 16 Dec 92 07:35:20 GMT

In article <1glt0lINNquc@news.aero.org> doner@Aero.org (John Doner) writes:
>In article <1glr2qINN2vg@usenet.INS.CWRU.Edu>, fau@po.CWRU.Edu (Francis A. Uy) writes:
>|> 
>|> I can't believe I forgot the proof of this one.
>|>  Subject line says it all.
>
>First tell us what you want to use for a definition of e.

First show that (1 + 1/n)^n <= e <= (1 + 1/n)^(n+1).
                            b
                           |\  
Let Integ[a, b, f(t) dt] = |  f(t) dt
                          \|
                            a
n is a positive Integer.

log(1 + 1/n) = Integ[1, 1+1/n, dt/t]

Since 1 > 1/t in the interval of t, 
   Integ[1, 1+1/n, dt/t] <= Integ[1, 1+1/n, dt],
   Integ[1, 1+1/n, dt] = 1/n.

Since 1/(1+1/n) => 1/t in the interval of t,
   Integ[1, 1+1/n, dt/t] => Integ[1, 1+1/n, dt/(1+1/n)],
   Integ[1, 1+1/n, dt/(1+1/n)] = 1/(1+n).

Therefore,
   1/(n+1) <= log(1+1/n) <= 1/n.

From the right inequality,
   1 + 1/n <= e^(1/n);
thus,
   (1 + 1/n)^n <= e.
From the left inequality,
   e^(1/(1+n)) <= 1 + 1/n;
thus,
   e <= (1 + 1/n)^(n+1).

Therefore,
   (1+1/n)^n <= e <= (1+1/n)^(n+1)

Divide the right inequality by 1+1/n,
   e/(1+1/n) <= (1+1/n)^n.
Combine the above with the left inequality
   e/(1+1/n) <= (1+1/n)^n <= e.
As n approaches infinity, e/(1+1/n) -> e.

Therefore, using the pinching theorem of limits,
   (1+1/n)^n -> e.

regards,
  Michael Lee
Newsgroups: sci.math
Subject: Re: GRAVITY-NEUTRALIZING AIR/SPACECRAFT
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 9 Dec 92 20:59:43 GMT
Organization: Beckman Instruments, Inc.

In <1992Dec8.172135.2714@cnsvax.uwec.edu> mcelwre@cnsvax.uwec.edu writes:

>    

>                       Gravity-NEUTRALIZING Air/Spacecraft
>                         or ZERO/REDUCED-Gravity Chamber

(1) What is this doing on sci.math?

(2) Has this mcelwre@cnsvax.uwec.edu being posting messages with high
bogosity indicies for a while?  The name looks familiar, but I can't find
any others in the current news spool.

--
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.
My interaction with our news system is unstable; please mail anything important.
Newsgroups: sci.math
From: idx009@cck.coventry.ac.uk (the Crisco Kid)
Subject: Re: Naming Large Numbers (Re: Negative Zero)
Organization: Eris's Restaurant
Date: Tue, 15 Dec 1992 17:23:15 GMT

In article <Dec.15.05.12.50.1992.13518@romulus.rutgers.edu> clong@romulus.rutgers.edu (Chris Long) writes:
>Eckler, R. "The Only Man Infinity Fears", _Word Ways_ Vol. 19,
>  Num. 4 (Nov. 1986) p. 252-254
>
>  The largest number given is millitwoillimillionillion, which
>  can't be written down in standard notation.

How about Graham's Number, which, if I remember rightly is an upper
bound on some value (which "everybody knows" is really... six), and
had to have a special notation of its own to be writable?

				Kay
-- 
6'2", dark short hair, blue eyes, bisexual and horny as ....
Kay Dekker, Dept of Industrial Design, Coventry University, Coventry UK
37 Old Winnings Road, Keresley Village, Coventry   |B0 f t+ g++ k++! s+ e r p!
Phone: +44 203 838668 (work) +44 203 337865 (home) |Deflowerer-of-innocents
Newsgroups: sci.math
From: orourke@sophia.smith.edu (Joseph O'Rourke)
Subject: Re: Projecting a vector onto a plane
Organization: Smith College, Northampton, MA, US
Date: Thu, 17 Dec 1992 16:15:52 GMT

In article <1992Dec17.150409.13943@bert.eecs.uic.edu> barnes@bert.eecs.uic.edu (Craig Barnes) writes:
>
>How do I project an arbitrary
>vector on to a plane defined by two other vectors?

Call the arbitrary vector V, and the two vectors in the plane A and B.
Here is one method.  Compute a normal N to the plane by crossing
A and B:  N = A x B.  Make this a unit normal n.  Project V onto this 
normal with the dot product: d = V . n.  Now your unknown vector U
plus (d n) must give V.  So U = V - d n.
Newsgroups: sci.math
From: shaw@toadflax.UCDavis.EDU (Rob Shaw)
Subject: Rounding Rules
Organization: UC Davis, EECS Division of Computer Science
Date: Sun, 20 Dec 1992 00:30:18 GMT
Reply-To: shaw@toadflax.UCDavis.EDU (Rob Shaw)
X-Posted-From: toadflax.cs.ucdavis.edu
NNTP-Posting-Host: sol.ctr.columbia.edu


What is the rationale behind the following rounding rule?

when dealing with 5's followed by all zero's, check the
next digit to the left. If it's even, round down; odd,
round up.

For example both 1.13500 and 1.14500 are 1.14 to 3 places.
What is the advantage of having the interval closed at both
ends around even digits, and open at both ends around odds?

Why the asymmetry?

Thanx.

Rob
From: ow0a+@andrew.cmu.edu (Oswald Wyler)
Newsgroups: sci.math
Subject: Re: Implication truth table ... Confusion
Date: 11 Dec 92 12:01:05 GMT
Article-I.D.: andrew.0f_EyVm00iV4A562IG
Organization: Mathematics, Carnegie Mellon, Pittsburgh, PA

Mike,
Look at it this way:  First, the truth vale (T or F) of P ==> Q is fully
determined by the truth values of P and Q.  Second, the statement
x = 3 ==> x^2 = 9  is *true*, where x is a variable.  This means that
the statement is true *no matter what value x takes*.  Do you accept
these premises?
O.K. if so, gotcha!  See what happens if you put x = -3.
Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
From: steve@fulcrum.oz.au (Steve Taylor)
Subject: Re: TIME HAS INERTIA - BASS JEALOUS AND INSECURE-ABIAN VALIDATED
Organization: The Fulcrum Consulting Group
Date: Mon, 14 Dec 1992 04:24:37 GMT

HOW do YOU feel about NEW $CIENTI$TS claim that LOONIES like to write HUGE
ARTICLES with lots AND lots of CAPITALISED words in them? Do YOU FEEL 
optimistic WHEN YOU see an ARTICLE on the NET that looks like this WITH LOTS
of EXCLAMATION POINTS!!!!!! DO you TRUST political commentary WHERE all WORD$
with THE letter S in THEM have THE letter S REPLACED!!! by $ TO show the
EVILS of capitali$m? ARE you impressed when YOU see references to PROMINENT
scientists who ARE NEVER NAMED!!! SEVERAL of this PLANETS finest SCIENTISTS
have told ME that THEY ARE IMPRESSED, but I AM NOT allowed to say WHO THEY
ARE!!!


						
						STEVE!!! (Steve in real life)
Newsgroups: sci.math
From: news@massey.ac.nz (USENET News System)
Subject: Re: '-' operation
Organization: Massey University
Date: Wed, 16 Dec 92 03:18:20 GMT

In article <92350.145501B7D@psuvm.psu.edu>, <B7D@psuvm.psu.edu> writes:
> 
> Recently my daughter brought back Problem Set II of Wisconsin Mathematics
> Science and Engineering Talent Search, and Question 4 in it is as following:
>          Operation @ satisfies the conditions that
>                 X @ (Y @ Z) = X @ Y + Z and X @ X = 0 for any real numbers
>           X, Y, Z. Show that @ must be subtraction.

An assumption is made here, but not stated, that @ has higher priority than +.

As you showed, x@0 = x@(x@x) = x@x + x = 0 + x = x.

Now you need to show that x@y = z   <=>   x = z + y.

Now, x = x@0 = x@(y@y) = x@y + y
and if x = z + y then z = x@y and conversely.

Conversely, if y = x@z then x = y + z

Note that, you _do_ need a clear idea what you wish to prove -
in this case, because subtraction is usually defined as the
inverse of addition you need to prove the equivalence above.

Terry Moore
Newsgroups: sci.math
From: sbardhan@uncc.edu (Soumendu Bardhan)
Subject: Re: Interesting Discrete Math Question
Reply-To: sbardhan@uncc.edu
Organization: University of NC at Charlotte
Date: Wed, 16 Dec 1992 21:20:16 GMT

you can draw 51 without satisfying the condition

1, 2,3, 7, 8, 9, ....., 97, 98, 99 

Newsgroups: sci.math,sci.math.symbolic
From: jk87377@cc.tut.fi (Juhana Kouhia)
Subject: Re: SIMTEL-20 symbolic mathmatica software
Organization: Tampere University of Technology
Date: Sat, 19 Dec 92 02:59:06 GMT


In article <1992Dec17.163420.23679@austin.onu.edu>
yeomans@austin.onu.edu (Charles Yeomans) writes:
>
>I am, as far as I know, the original complainer.  I have nothing personal 
>against Huang.  What does annoy the shit out of me is that someone posted
>a request for a location for SIMTEL and this Huang replied, as he has done
>to many other posters - "I suggest you try SymbMath", followed by info about
>how to purchase it.  What he did NOT do is to answer the poster's question
>about SImtel.  Furthermore, he appears to have added several other newsgroups
>to the follow-up line for no discernible reason other than to advertise his 
>product.

Please, will you, Dr. Huang, respect the above opinions in future?
So, that we can apply the opinion below.

From: nitin@Ingres.COM (Nitin Borwankar)
>
>Let's focus on helping each other


Well, Huang, you wrote something about that you are annoyed
of commercial postings by Maple, Mathematica or such...
What you think if they all decide to always reply
to five or such groups independing on where the request
was posted?

Also, several months ago, when I complained about your postings,
I suggested to put info on your program to sci.math FAQ article.
Last I verified, your program was not mentioned in that list;
why not?


Juhana Kouhia
Newsgroups: sci.math
From: hiraga@Csli.Stanford.EDU (Yuzuru Hiraga)
Subject: Re: need proof:  (1 + 1/n)^n ==> e
Organization: Stanford University CSLI
Date: Fri, 18 Dec 1992 01:05:43 GMT

In article <1glt0lINNquc@news.aero.org> doner@Aero.org (John Doner) writes:
>In article <1glr2qINN2vg@usenet.INS.CWRU.Edu>, fau@po.CWRU.Edu (Francis A. Uy) writes:
>|> 
>|> I can't believe I forgot the proof of this one.
>|>  Subject line says it all.
>
>First tell us what you want to use for a definition of e.

Hmmm.....

Given e = (1 + 1/n)^n, prove that (e^x)' = e^x;
which boils down to lim(h->0) (e^h - 1)/h = 1.

-Yuzuru Hiraga
Newsgroups: sci.math