HDTenEightyP/NetNews huggingface dataset:
Organization: Middle East Technical University - Computer Center
Date: Monday, 25 Jan 1993 14:09:41 TUR
From: Melih Sener <E62802@TRMETU.BITNET>
Newsgroups: sci.math
Subject:    Frobenius Thm. on real dision algebras


  As far as I know there is a theorem due to Frobenius, which
states that the only associative divison algebras over real numbers
are complex numbers and quaternions (if you drop the requirement
of associativity octonions are also added to this list.)

 Here are my questions...
1- Where can I find an explicit proof of this and related theorems?
(In Porteus' (Topological Geometry) , there is some info about the subject
but if there other sources, I'd like to know them.)

2- Is this theorem valid only for finite dimensional case?
(i.e. Is there an infinite dimensional real divison algebra?)

Thanks for any information ....

Melih Sener<e62802 at trmetu.bitnet>
'
Newsgroups: sci.math
From: fulk@cs.rochester.edu (Mark Fulk)
Subject: NCTM math teaching standards
Reply-To: fulk@cs.rochester.edu
Organization: University of Rochester Computer Science Department
Date: Thu, 21 Jan 1993 20:09:07 GMT

Does anyone know where I can pick up a copy of the NCTM(*) standards,
and the related materials?  I understand that Houghton-Mifflin has
published NCTM-based text books; if anyone knows the titles, etc,
could they please post or email that also?

(*) National Council of Teachers of Mathematics

Mark
-- 
Mark A. Fulk			University of Rochester
Computer Science Department	fulk@cs.rochester.edu
From: unicef@epilogue.mcl.ucsb.edu (Joel Rising)
Newsgroups: sci.math
Subject: Why Algebra...Important
Date: 23 Jan 93 01:23:26 GMT

In article <190744.12287mccarthy@washpost.com>

>The failure of people to use mathematics intelligently is, IMO, due to 
>this failure to use symbols.  It is similar to the problems in using
>natural languages to communicate

Certainly true.

Look what language has done for us.  Not only allowed us to communicate,  
share, work together on problems.  It's allowed us to codify objects and  
experiences, thereby allowing us to see relationships between them,  
perhaps juxtapose them so that we can see new relationships, ones we  
otherwise might not have uncovered thru experience.

Math is a language, but a far more powerful one.  To convince youself,  
write out some equation, and then try to describe all the relationships it  
embodies.  It's not just "x=ky" but also "x is proportional to y" or "as x  
goes up one, y goes up by some factor k."  Relate the variables to some  
real-world quantity, and the equation becomes even more rich with  
information.  Perhaps a whole paragraph could be gleaned from "x=ky."

The point is, whereas language allowed us to see relationships between  
words and sentences, Math allows us to see relationships between  
paragraphs, pages, perhaps whole chapters of information.  And so we can  
begin to see relationships we otherwise wouldn't have.

Imagine if we could agree on some standard symbology, and then use it to  
codify some of the world's truly huge ideas.  What new relationships might  
we see?  Could we find some way to model the process of evolution?  Could  
the causes of world poverty, hunger, disease be parameterized, and thereby  
avoided?

Of course great minds are out there working on these things.  But society  
in general is not yet capable of this next level of manipulation.  And it  
never will be if kids don't learn some algebra, or some other type of  
symbolic manipulation.

Just another undergrad,
unicef@next.mcl.ucsb.edu  
Newsgroups: sci.math
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: Job Discrimination
Organization: Department of Chemistry, University of Toronto
Distribution: sci
Date: Mon, 25 Jan 1993 15:53:36 GMT

In article <ARA.93Jan24165321@camelot.ai.mit.edu> ara@zurich.ai.mit.edu
(Allan Adler) writes:
>Many math departments place advertisements in which they specify that
>they want to hire someone having a particular nominal specialty
>and that others need not apply. [...]
>What one is actually paid to do is to teach.

     Teaching includes both graduate seminars and the supervision of graduate
students.  Since the line between teaching and research is nebulous in this
area, it strikes me that a department is fully justified in choosing its
new faculty at least partly on the basis of research field.  It wouldn't
be fair to incoming graduate students (and it would quickly prove
destructive to the department) if a cross-section of research interests
were not represented.
     Maybe I'm just missing Allan's point.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
Newsgroups: sci.math
From: rairan@ecf.toronto.edu (RAI Ranjan)
Subject: Matrix Problem
Organization: University of Toronto, Engineering Computing Facility
Date: Thu, 28 Jan 1993 16:18:59 GMT

I remember a result from first year linear algebra that said that the
eigenvectors of AB are the same as the eigenvectors of BA where A and B
are nxn real matrices.  I don't know how to prove this.  Any pointers or
references to the proof?

Thanks.

-- 
Ranjan Rai                             <rairan@ecf.toronto.edu> 
Engineering Science 9T3                <rr@odin.control.toronto.edu> 
University of Toronto                    
Newsgroups: sci.math
From: rgep@emu.pmms.cam.ac.uk (Richard Pinch)
Subject: Re: Can Anyone Solve this?????
Organization: Department of Pure Mathematics, University of Cambridge
Date: Mon, 25 Jan 1993 10:44:44 GMT

In article <1993Jan23.210732.19327@magnus.acs.ohio-state.edu> mfreiman@magnus.acs.ohio-state.edu (Mark R Freiman) writes:
>
>             If W={f such that f"-2f'+f=0}
>               What is the dimension? and what is a Basis?
>
>I know the answer for the dimension is 2, and a basis is
>               x          x
>              e  and    xe
>
>             but how would one go about obtaining these answers?

Assume that the solution exists and can be represented by a power series
in x, and that differentiation of the power series term-by-term is valid
(these are not trivial assumptions).  Suppose that f = \sum_n a_n x^n;
then equating coefficients of power of x in the equation gives

          2.1.a_2 + 1.a_1 + a_0 = 0    ... coefficient of x^0

          3.2.a_3 + 2.a_2 + a_1 = 0    ... coefficient of x^1

etc

          (n+2)(n+1)a_n+2 + (n+1)a_n+1 + a_n = 0 ...      x^n

and it is clear that the a_n for n >= 2 depend only on the values
of a_0 and a_1, which can be chosen freely.  Choosing a_0 = a_1 = 1
gives a_n = 1/n! and choosing a+0 = 1, a_1 = 1/2 gives a_n = 1/(n+1)!
and so these two solutions span the two-dimensional vector space of
possible sequences of coefficients a_n.  Since the first corresponds
to the function e^x, and the second to the function xe^x, and since
these two functions do indeed satisfy the original equation (this _has_
to be verified) then they forms a basis for the two-dimensional space
of solutions.

Richard Pinch

Newsgroups: sci.math
From: burbank@fraser.sfu.ca (Max Burbank)
Subject: Theory of a game
Organization: Simon Fraser University, Burnaby, B.C., Canada
Date: Tue, 26 Jan 1993 23:06:43 GMT

Here is a game:
There are two countries. Each country has different number of cities and
ONE traveller. Each traveller only travels  within his own country. The
path  between two cities can be two  way, one way or "conditional", for  
instance, traveller A can travel from his city 1 to city 2 only if traveller
B is in city 5 of the other country. Given such two countries with cities,
roads, and conditions defined, also given the initial position of the two 
travellers, here is the question:
Which cities are reachable? or pick one city and ask if it is reachable?
Are there some theory dealing with this kind of problem? The number of  
countries can be greater than 2. Travellers can move simultaneously or
one at a time. The path condition is always defined in terms of other
traveller's positions  at that time. The travelling between two cityes
takes no time.  
Newsgroups: sci.aeronautics
From: szopinsk@picard.med.ge.com (Jerry Szopinski Mfg 4-6983)
Subject: Re: V/STOL fighters
Organization: GE Medical Systems, Magnetic Resonance
Date: Mon, 25 Jan 93 10:16:11 GMT

                  (text deleted)

: >this is where the missiles will most likely hit.  With the engines amidships 
: >(around the CG), even a relatively small blast, such as that of a shoulder-
: >launched SAM, will cause catastrophic engine, control and structural damage.  
: >A larger missile like the Sidewinder will cut the plane in half.  (All right, 

                   (text deleted)
: 
: >Chad Wemyss
: >Worcester Polytechnic Institute
: 
: 	Wouldn't the four nozzles of a non-afterburning turbofan have a
: much smaller IR signature than two nozzles of a twin engined
: afterburning plane? The exhaust of the Harrier would have greater
: diffusion and for much of the upper hemisphere, the nozzles are hidden
: by the wing.
: 	If there is a direct strike by an AAM, there would be alot of
: catastrophic damage anyway whereever the engine is located. Most missile
: hits would be proximity blasts(?) in a manoeuvering engagement.(This is
: conjecture on my part). 
: 	Most of the designs for ASTOVL planes are high(by jet fighter
: terms) bypass turbofans so the IR signature of these engines should be
: inherrently less than the current generation of low-bypass engines.{I
: think the pegaseus has bypass ratio of 1.2 compared to the f100 of the
: f15 ratio 0.7}
: 
: 
: 					Daniel Oi
: 					University of Wesyern Australia



The major threat to a VSTOL aircraft like the AV-8A Harrier would be AAA
and SAMs (including the shoulder-launced variety commonly used by today's
ground forces).  The threat from above would be minimal because the attack-
ing pilot would be firing a heat-seeking missile roughly toward the ground.
The IR sensor would have a hard time picking the harrier's exhaust out from
all the heat coming up from the ground.  With SAMs or shoulder-launched
missiles the Harrier would be silohetted(sp.?) against the cool sky, making
it much easier for the IR sensor to lock on.

On the AV-8A the larger pair of the four exhaust nozzles are located in the
same area as the engine; this is the most likely the area that a heat-  
seeking missile would lock on to.  A hit in this area would be very serious.
If just the nozzles were damaged you'd lose half your thrust/lift, depending
on what mode you were in at the time.


Jerry

"It riles them to believe that you perceive the web they weave and keep on
thinking free!"  --  Moody Blues



:
From: dianysos@raphael.u.washington.edu (Benjamin Andrews)
Newsgroups: sci.aeronautics
Subject: Re: NACA airfoil data request
Date: 26 Jan 93 16:59:34 GMT
Organization: University of Washington
NNTP-Posting-Host: 128.95.56.203

Try a book called: Theory of Wing Sections, it just may have what you need
From: kshan@pepper.rutgers.edu (Kyungsook Han)
Newsgroups: sci.aeronautics
Subject: program for aerodynamics problems
Date: 26 Jan 93 00:49:01 GMT
Organization: Rutgers Univ., New Brunswick, N.J.


Does anybody know of a program which solves aerodynamics problems?
I am particularly interested in NASA public domain programs and programs 
which implement lifting-line theory. 
Any pointers would be appreciated.

Kyungsook Han
Department of Computer Science
Rutgers University
Newsgroups: sci.aeronautics
From: edhresko@hresko.eos.ncsu.edu (ERIC DAVID HRESKO)
Subject: Re: NACA 0012 - Definition ?
Originator: edhresko@c00553-1403br.eos.ncsu.edu
Reply-To: edhresko@eos.ncsu.edu
Organization: Techno-Geeks Inc.
Date: Thu, 21 Jan 1993 15:45:12 GMT



	I don't have the book with me, but Abbot and Von Den Hoff's Theory of
Wing Sections has the formula for the NACA 4 series wings.  We used it last
semester to do some stuff in my aero classes with it...
-- 


Eric

******************************************************************************
Eric Hresko		* Mail:  edhresko@eos.ncsu.edu                        
Kanki House of Steaks   * Voice: (why would you want to call?) 1-919-821-5168
Dishwasher 2nd Class    * HK Rules!!! (But a FAL will do in a pinch)         
DISCLAIMER:  I don't wear sandals, eat granola, or tiptoe thru the Tulips    
                                                                             
At what temp will a frog become a superconductor?                             
				-Me at 3 a.m.                                
******************************************************************************
Newsgroups: sci.aeronautics,sci.research.careers,sci.space,soc.college.grad
From: abbasi@star.enet.dec.com (My name is Nasser Abbasi)
Subject: Re: Orbital Mechanics--Careers?
Organization: Digital Equipment Corporation
Distribution: usa
Date: Wed, 27 Jan 1993 07:02:42 GMT


In article <1jqitsINN48q@geraldo.cc.utexas.edu>, mjones@ccwf.cc.utexas.edu (mark jones) writes...
> 
>After u.g. major in math with lots of physics I'm trying to decide on 
>masters/Ph.d in math or orbital mechanics.  What are the opportunities 
>in orbital mechanics and will they still be there in 5 or 6 years.  
>Any advice is greatly appreciated.  Reply via net or directly 
>mjones@ccwf.cc.utexas.edu

since defense and aerospace are not doing too well, one would think
OM area might not be too hot. is there actually an MS in OM? or is
OM studied under control engineering? or mechanical engineering?

if however you study physics, you can do both, OM and math and many other 
things too ;-)

\nasser


Newsgroups: sci.aeronautics
From: bowers@rigel.dfrf.nasa.gov (Al Bowers)
Subject: Re: Aerodynamic centers of various airfoils
Organization: NASA Dryden, Edwards, Cal.
	<1993Jan20.232439.14173@bmerh85.bnr.ca>
Distribution: sci.aeronautics
Date: Thu, 21 Jan 1993 19:34:20 GMT

In article <1993Jan20.232439.14173@bmerh85.bnr.ca> mkfeil@bcrki9.bnr.ca (Max Feil) writes:

>As I understand it, the aerodynamic center of all airfoils is very
>close to the 25% chord point when operated subsonically. My question
>is: Just how far does it vary for the different kinds of airfoil
>sections, eg. conventional; flat (sometimes used for fins/stabs);
>reflexed; laminar flow (high point at 50%); etc.

I believe that this is a result of lifting lione theory, that the AC
will always be at 25% chord.

>As an example, in data I have the a.c. of NACA 2412 ranges between
>23.9% and 24.7% at reynold's numbers between 3.1E6 and 8.9E6 (this is
>a semi-symmetrical airfoil). All the other airfoil's that I have data
>for are also within a percent or two of 25%, but none of these are
>exotic.

Even the more exotic airfoils (eg. supercriticals, GAWs, Eppler,
Wortman, Liebeck, Drela types, etc) behave in this way.  I think as
long as you maintain reasonably attached flow on the airfoil, it
should hold.  If you do something stupid, like a cusp on the trailing
edge that is so strong that it never attaches the flow, then I'd
expect it to not be well behaved.

>Another question: In supersonic flow the a.c. is at 50% chord, as a
>result of (as I understand it) fairly equivalent shock wave effects at
>the leading and trailing edge. How far does this vary among airfoils?
>What does the transition (trans-sonic) area look like when comparing
>the a.c.'s of different airfoils?

I think this is explained by Busemann's theory.  And in most of the
cases I have seen, it behaves very close to the theory as well.  This
was the idea behind unstable aircraft.

If you make the CG farther back so that the aircraft has a negative
static margin subsonically, then supersonically, the static margin
will be less positive than if you has a subsonically stable aircraft.
This should reduce your transonic trim drag and give better supersonic
performance.  Unfortunately, you also incur problems with high alpha
recovery and trim drag at subsonic conditions.

--
Al Bowers                       bowers@rigel.dfrf.nasa.gov
NASA F-18 High Alpha Research Vehicle, Lead Aero
NASA, Dryden Flight Research Facility, Edwards, California
From: Michael F. Kamprath <kamprath@space-grant.sprl.umich.edu>
Newsgroups: sci.aeronautics,sci.research.careers,sci.space,soc.college.grad
Subject: Re: Orbital Mechanics--Careers?
Date: 27 Jan 1993 20:01:52 GMT
Organization: University of Michigan, Aerospace Engineering
Distribution: world
NNTP-Posting-Host: sprl-mac2016.sprl.umich.edu
X-UserAgent: Nuntius v1.1.1d12
X-XXMessage-ID: <A78C554F2B01C4FC@sprl-mac2016.sprl.umich.edu>
X-XXDate: Wed, 27 Jan 93 21:05:51 GMT

In article <1993Jan27.070433.3488@nntpd.lkg.dec.com> My name is Nasser
Abbasi, abbasi@star.enet.dec.com writes:
>In article <1jqitsINN48q@geraldo.cc.utexas.edu>, mjones@ccwf.cc.utexas.edu

>(mark jones) writes...
>> 
>>After u.g. major in math with lots of physics I'm trying to decide on 
>>masters/Ph.d in math or orbital mechanics.  What are the opportunities 
>>in orbital mechanics and will they still be there in 5 or 6 years.  
>>Any advice is greatly appreciated.  Reply via net or directly 
>>mjones@ccwf.cc.utexas.edu
>
>since defense and aerospace are not doing too well, one would think
>OM area might not be too hot. is there actually an MS in OM? or is
>OM studied under control engineering? or mechanical engineering?
>
>if however you study physics, you can do both, OM and math and many other 
>things too ;-)
>
>\nasser

Here at U-M's Aerospace deptartment, I am getting my MSE (Aerospace) with a
concentration in flight dynamics, and personally, I am concentrating in orbital
mechanics.  It is not "official," i guess, but I would say I was getting my
degree in orbital mechanics. But then again, an MSE can almost be considered
a specialized BSE. 

======================================================================
|Michael F. Kamprath                   | The University of Michigan  |
|  kamprath@space-grant.sprl.umich.edu |      Aerospace Engineering  |
|  kamprath@engin.umich.edu            |      Graduate Student       |
======================================================================
From: gt6192a@prism.gatech.EDU (Scott Turney)
Newsgroups: sci.aeronautics
Subject: Re: NACA 0012 - Definition ?
Date: 21 Jan 93 19:07:39 GMT
Organization: Georgia Institute of Technology

Strangely enough, I was just assigned the task of writing some panel code
for a NACA 0012 in my CFD class this morning.

The NACA 0012 can be expressed by

y= 0.6(0.2969x^.5 - 0.1260x - 0.3516x^2 + 0.2843x^3 - 0.1015x^4)


Or this is the approximation we are using at least.

The point (0,0) is the leading edge.

X goes from 0 to 1


-- 
Scott Turney
Newsgroups: sci.aeronautics
From: drela@athena.mit.edu (Mark Drela)
Subject: Re: ***Help w/ aero HW(hodograph problem)***
Organization: Massachusetts Institute of Technology
Date: Wed, 27 Jan 1993 23:51:21 GMT

In article <1993Jan27.042024.17478@magnus.acs.ohio-state.edu>, bphillip@magnus.acs.ohio-state.edu (Brent R Phillips) writes:
|> Here's the problem
|> I have a high aspect ratio, high altitude, powered sailplane.  I need to
|> construct a Hodograph(Vv vs. Vh).  I am given that the THP = 600 HP at
|> 50,000ft.  The problem I am running into is that I have a equation to use for
|> lbs. of thrust but, none for THP.  I do not know a V(infinity) for a
|> convertion. Nor do I know enough about the A/C to calculate R/C(max) for a
|> given V(infinity).

potential energy increase rate = excess thrust power

  mgV  =  V (T - D)
     v     

mg = weight     T = thrust     D = drag
                                                                        2    2
V  = vertical velocity   V  = horizontal velocity     V = speed = sqrt(V  + V )
 v                        h                                             v    h



If the flight path angle is shallow, i.e.  V  << V  , you can approximate
                                            v     h
Lift = mg   and   V = V  ,  so 
                       h

   V  =  V (T/mg  -  D/L)
    v     h


  Mark Drela                          First Law of Aviation:
  MIT Aero & Astro          "Takeoff is optional, landing is compulsory"
From: herrickd@iccgcc.decnet.ab.com (daniel lance herrick)
Newsgroups: sci.aeronautics
Subject: Re: Wind Tunnel Smoke
Date: 26 Jan 93 21:27:46 GMT

In article <1993Jan18.191838.21869@cbnewse.cb.att.com>, mckiou@cbnewse.cb.att.com (kevin.w.mckiou) writes:
> So..what is commonly used to generate smoke in wind tunnel testing?
> Any suggestions for my little tunnel?

There are several low tech possibilities in the incense section of
a store that carries such things.  I would try a punk stick first.
If your wind is low enough it doesn't fan the stick into flame it 
would give a single localized stream of smoke that is relatively
easy to move from one place to another.  And the turbulence from
the stick should settle out in a reasonably short distance.

dan
Newsgroups: sci.aeronautics
From: P.J.Plane@massey.ac.nz (Philip Plane)
Subject: Re: Want information of Foward swept wing
Organization: School of Maths & Info. Sci., Massey University, Palmerston North, NZ
Date: Fri, 29 Jan 93 02:01:35 GMT

In article <1k91qjINN7fp@bigboote.WPI.EDU> chadwemy@wpi.WPI.EDU (Chad Barret Wemyss) writes:
>
>Another advantage of Forward-Swept Wings (FSW) is that it makes the aircraft 
bla bla stuff deleted...

An advantage that no-one has mentioned is that in very light aricraft forward
swept wings are used to reduce the effect of crew weight on the C of G, allowing
a wider range of crew weights. Many two seat gliders demonstrate this.




-- 
Philip Plane          _|_   P.J.Plane@massey.ac.nz
----------------------(_)----------------------
Glider pilots have no visible means of support
Newsgroups: sci.aeronautics
From: hausner@qucis.queensu.ca (Alejo Hausner)
Subject: Re: Rumors......rumors!
Organization: M.Sc, C.S, Queen's, Kingston, Canada.
Date: Thu, 21 Jan 1993 19:33:57 GMT

In article <1jimbtINNdgk@usenet.INS.CWRU.Edu> ak336@cleveland.Freenet.Edu (John Dill) writes:
>
>I have spent alot of time digging up info about the super-secret
>"Arora" spy plane...and still don't have a clue! All you other hi-tech-
>nophopes....let's hear any rumors or speculation you've run across!
>

There is a mailing list that discusses stuff like this.  It's
called skunk-works.  There is a digest available.  Here's the
info:

Alejo Hausner (hausner@qucis.queensu.ca)

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