HDTenEightyP/NetNews huggingface dataset:
From: mkrogers@unix.amherst.edu (MICHAEL K ROGERS)
Subject: Re: Univariate polynomial equations and the FAQ
Organization: Amherst College
X-Newsreader: TIN [version 1.1 PL6]
Date: Fri, 6 Nov 1992 21:34:16 GMT

Eugen W. Schmidt (gsmith@clio.uucp) wrote:
: In article <1d72mnINNq2p@mozz.unh.edu> dvf@kepler.unh.edu (David V Feldman) writes:
: 
: >Fix an integer m.  Let K be the extension of Q obtained by adjoining
: >all roots of all polynomials of the form
: >       n     m    
: >	  x + a x + ... a
: >		   m         0
: 
: >where the coefficients are rational.
: 
: This sounds like the algebraic closure of Q, Q-bar.
: 
:   Let s(m) be the smallest degree of a 
: >polynomial with rational coefficients which does not have any root in K.
: >So s(0)=5, by Galois theory.  What is known about the function s(m)?
: 
: This is false for Q-bar.  If your original field extension was the
: maximal solvable extension in Q-bar, then we could try to figure out
: the answer to your question, if we could figure out the question,
: which I still can't do!

I'm not sure what the problem is either.  It seems like we want
to consider the field K(m) obtained by adjoining the roots of all
polynomials over Q of all degrees which have the following property:

	The coefficient of x^k is zero if x^k is not the
	leading term and k > m.

The claim s(0)=5 seems false then because the roots of cubic
polynomials often are of the form sqrt(a + cubert(b))  (or is
it cubert(a + sqrt(b))?).  These roots are not the linear
combination of square roots and cube roots of rational numbers.

So I suspect the original poster had a different idea in mind.
Newsgroups: sci.math
From: neil@progress.COM (Neil Galarneau)
Subject: What is catastrophe theory?
Organization: Progress Software Corp.
Date: Wed, 11 Nov 1992 18:05:52 GMT

I have heard of something called catastrophe theory.

I am looking for recommendations on articles/books (in English!) readable by a
non-math major.


Thanks!

Neil
neil@progress.com
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: definition of topological space
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Fri, 6 Nov 92 01:54:06 GMT

In article <1992Nov5.211426.3699@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:

>A function f from one topological space X to another Y is defined to be
>continuous if given any open set O in Y, f^{-1}O is open in X.  Here
>f^{-1}O means the set of all points in X which are sent by f to
points... in O!

(correcting a typo)
Xref: sparky sci.math:14918 sci.physics:18827
From: bennett@math.ksu.edu (Andy Bennett)
Newsgroups: sci.math,sci.physics
Subject: Re: Three-sided coin
Date: 13 Nov 92 04:21:51 GMT
Article-I.D.: hilbert.1e0kmvINNo79
Organization: Dept. of Mathematics, Kansas State University
NNTP-Posting-Host: hilbert.math.ksu.edu

gmortens@rodan.acs.syr.edu (Gerald E Mortensen) writes:
]my view of the problem is that:
]1. the only random variable is the angle between the coin face outward
]normal and the ground outward normal.
]2. the soft landing assumption is fair (otherwise you've got to consider
]the bounce dynamics... yuck)
]3.if the coin lands at angle 0 or 90 it will stick on the face or edge 
]respectively. otherwise, a "corner" hits first. 
]4. draw a plane through the contact point, normal to the ground and normal
]to the plane defined by the ground and coin normals.
]5. the coin will topple onto a face iff the forces (due to gravity
]acting on the coin mass) on the face side 
]outweigh the forces on the edge side of the plane.

Actually, it is fairly easy to solve this directly. One of my graduate students
got interested in this problem one time, solved it explicitly, and then created
a three sided coin out of wood (despite his tendency to spend time on these
sorts of games, he's actually finishing this year with a nice thesis). We went
outside to start flipping the coin and see if it would work as predicted. It
didn't, the critique about the edge having a different potential energy than
the sides turns out to be extremely important. If the coin landed on its
side all was well and good. But if it landed on its edge it would roll away.
There was always some spin on the coin to get it rolling. And after rolling
for a while, it would hit some irregularity on the sidewalk and fall over to
one side or the other. Of course, the soft landing assumption can be made to
take care of this, but then you have an assumption that is not at all like what
our experiments showed the real world is like.
-- 
Andrew G. Bennett         bennett@math.ksu.edu         If you count too
Dept. of Mathematics      Voice: (913) 532-6750        much you turn
Kansas State University   Fax:   (913) 532-7004        purple.  -  SARAH
Manhattan, KS 66502       STRICTLY MY OWN OPINIONS                    
Xref: sparky sci.math:14515 misc.education:4163
From: dlhanson@nap.amoco.com (David L. Hanson )
Newsgroups: sci.math,misc.education
Subject: Re: Is Math Hard?
Date: 5 Nov 92 23:04:08 GMT
Organization: These are my opinions.

In article <1992Nov5.184239.21050@cbfsb.cb.att.com> dal3@cbnewsg.cb.att.com (dale.e.parson) writes:
>
>I believe home based learning can be economically feasible for most U.S.
>families right now, & could be made economically feasible for many others.
>I have no doubt that it is intellectually and spiritually superior (and no,
>I am not a fundamentalist Christian) to any institutional based education.
>The major impediment is a mind set that equates learning with confinement
>that has been foisted upon the current generations of humans on this planet
>to such an extent that they cannot even imagine genuine alternatives.
>Good luck figuring out the proper way to build the cages.
>

Well, as most of the readers know I am a fundamentalist Christian and I
agree with Mr. Parsons.  I have access to a K-12 academy at our church which
I can afford and we still choose to homeschool.  We can fit the education
to meet the needs of each of our children which no institution can do. 
My wife and I determine the curriculum and books we use to fit our children
and our family.  While we are more rigid than the unschoolers we are not
tied down to any clock or calendar.  We can forget about math for a few
days and concentrate on science or literature or whatever else is 
interesting to the children (and we think is fruitful).  It is time consuming
and takes a lot of energy (it is 5:00 PM CST and I am about to leave to go
home and eat; and then teach math, science, and Bible), but IT IS WORTH IT.
(Not to slight the large effort my wife puts in all day.)
The boys love their school, they love to learn, and our family is close to
each other and happy.

Signature follows:

Proverbs 22:6 "Train a child in the way he should go, and when he is old
he will not turn from it."
=========================================================================
David L. Hanson       Internet --> dlhanson@nap.amoco.com
Amoco Corporation     X.400    --> A=attmail,P=amoco,S=Hanson,G=David,I=L
Any opinions expressed are my own!
From: rmb@psg.npl.co.uk (Robin Barker)
Newsgroups: sci.math
Subject: Re: Univariate polynomial equations and the FAQ
Summary: Restatement of problem?
Keywords: polynomials, radicals
Date: 11 Nov 92 10:40:23 GMT
Organization: National Physical Laboratory, UK


Let's have another go at stating the problem.

It is known that polynomials of degree <= 4 can be solved by
REPEATEDLY taking roots of polynomials of the form x^n + a.
i.e. x^n + polynomial of degree 0.

It is also true (?) that polynomials of degree 5 can be solved
by repeatedly taking roots of polynomials of the form x^n + a 
and x^5 + x + a, which are  x^n + polynomials of degree <= 1.

So consider a (fixed) natural number m.

K_0(m) = Q, the field of rationals.

K_r+1(m) = K_r(m) extended by all the roots of all the
                  polynomials of the form x^n + P(x),
           where n is a natural number and P is a polynomial 
           of degree <= m with coefficient in K_r(m)

K(m) = U K_r(m), the union (direct limit) of the fields K_r.


Let S(m) = minimum degree of a polymonial which does not split
           in K(m).  Is this the same with `does not split'
           replaced by `does not have a root' ?

S(0) = 5  (some quintics are not soluable by radicals),
S(1) > 5  (all quintics are soluable by radicals and
           ultraradicals - roots of x^5 + x + a).

To repeat the original poster, what is known about S(m) ?
Newsgroups: sci.math
From: brennan@tfs.com (Brennan Hildebrand)
Subject: Has anybody heard of maple?
Organization: TRW Financial Systems
Date: Fri, 13 Nov 1992 06:59:38 GMT

If so, what is it, and where can it be found?  does xmaple come with it?


Thanks
-brennan

brennan@tfs.com
-- 
+------------------------------------------------------------------------------+
| Brennan Hildebrand                                              oo           |
| brennan@tfs.com                                            o oooooooo        |
|                                                   oooo  ooooooooooooooooo    |
Newsgroups: sci.math
From: lombardo@ghost.dsi.unimi.it (franco lombardo)
Subject: Re: Functions for n-valued logic
Keywords: n-valued logic
Organization: Computer Science Dep. - Milan University
Date: Fri, 13 Nov 1992 10:21:50 GMT

I haven't understood your method (I am not a mathematician).
The elements of the lattice you talk about are the elements
of {0,1/2,1}^3, but which is the order relationship of
this lattice, and what do you mean with "variations"?
Thank you very much!
			Franco Lombardo



Newsgroups: sci.math
From: Jim_Treloar@mindlink.bc.ca (Jim Treloar)
Subject: centrifugal force
Organization: MIND LINK! - British Columbia, Canada
Date: Sat, 7 Nov 1992 06:56:02 GMT

Can anyone give me a formula for estimating the centrifugal force at distance
x for various rpms. Please KIS I am not a mathematician. Jacktar

--
Jim Treloar alias Jacktar
Newsgroups: sci.math
From: dob@ccr-p6.ccr.jussieu.fr (Dominique BERNARDI p3512)
Subject: La Vie, Mode d'Emploi (Was: math in non-fiction)
Summary: Perec not guilty.
Organization: Universites P. & M. Curie / D. Diderot
Date: Mon, 9 Nov 1992 14:28:35 GMT

In article <Bwt3AM.8Gs@unix.amherst.edu> mkrogers@unix.amherst.edu (MICHAEL K ROGERS) writes:
>In "La vie, mode d'emploi" by Georges Perec there is a proof
>(of sorts) that the degree of the composition of two homogenous
>maps is the product of the degrees of the two maps.  The
>symbol for composition is a zero (0) and not a little circle.
>So is it that the narrator mistakes the small circle for
>a zero or is it the author's own ignorance?  Not that it matters....

I just checked my copy of the book, and the error
is not there. So I suppose the ignorance is not
the author's or the character's, but the publisher's.

Dominique Bernardi.
Xref: sparky sci.math:14637 misc.education:4210
From: cyeomans@ms.uky.edu (Charles Yeomans)
Newsgroups: sci.math,misc.education
Subject: Re: Is Math Hard?
Date: 9 Nov 92 14:07:57 GMT
Organization: University Of Kentucky, Dept. of Math Sciences

In article <ccDyTB3w164w@allen.com> carolyn@allen.com (Carolyn Allen) writes:
>
>Necessity is the mother of invention...no one said that money inspires 
>creativity, self-discipline or intelligence. You're facing necessity, so 
>count your blessings and cut the jealousy. You have been given a 
>background that can motivate you to great heights if you appreciate it 
>for the kick in the behind it is.

I thought laziness was the mother of invention.

Charles Yeomans
cyeomans@ms.uky.edu
yeomans@austin.onu.edu
Newsgroups: sci.math,misc.education
From: dlevy@viper.engin.umich.edu (David W Levy)
Subject: Re: DATCOM
Date: Fri, 06 Nov 92 09:45:55 EST
Organization: University of Michigan Aerospace Engineering, Ann Arbor, MI
Originator: dlevy@viper.engin.umich.edu


In article <seyJ3cq00WB7MavKAe@andrew.cmu.edu>, lc2b+@andrew.cmu.edu (Lawrence Curcio) writes:
> Could someone give me a reference for the details of the DATCOM method,
> or for other semi-empirical methods of drag coefficient determination. 
> 
> Thanks,
> -Larry
Here ya go:

Hoak, D.E., et al.,
USAF Stability and Control DATCOM,
Global Engineering Documents, Clayton, MO, 1978.

Hoerner, S.F.,
Fluid-Dynamic Drag,
Hoerner Fluid Dynamics, Bricktown, NJ, 1965.

Roskam, J.,
Airplane Design,
Roskam Aviation and Engineering Corp., Ottowa, KS, 1989


The DATCOM is your basic cookbook, and leads you through step by step.
Many of the methods come from Hoerner.  Lately, it has been difficult
to get a hold of new copies of Hoerner's book; hopefully it's in your
library.  The DATCOM probably isn't.

Roskam's book gives a good summary of the DATCOM methods for fairly
conventional airplane configurations in subsonic flight.

Newsgroups: sci.aeronautics
From: gerard@galaxy.nsc.com (Gerry Dowling x3188)
Subject: Re: Questions
Organization: National Semiconductor, Santa Clara
Date: Thu, 12 Nov 1992 17:24:04 GMT

In article <19921103.002048.710@almaden.ibm.com> GORDON@UKCEVM1.VNET.IBM.COM writes:
> I have three questions where someone on the net may be able to help...
>
> 2) At 'The Last Moffet' show, there was a two seat A7 in the static
>    park. It had the refuelling probe extended, NAWC on the tail and
>    a red star on the intake cover. The serial number is so low-viz
>    that I can not decipher it, does anyone know what it is/was?
>
>    Help on any of the above would be most appreciated....
>  Cheers, Gordon
>Disclaimer: Any opinion detected in this posting is not that of IBM.
>
I'm not sure if the a/c was an A7 but I have a photo of a two seater plane 
parked in the static area with a red star on the fuselage and tail.If this 
is the same a/c then the number 143 appears on the nose,23143 on 
the tail and N143SG on the fuselage just underneath the elevator.
From: jmn@crown.berkeley.edu (J. Mark Noworolski)
Newsgroups: sci.aeronautics
Subject: Re: How accurate can I make a homebrew altimeter? - more Q's
Date: 9 Nov 1992 21:36:05 GMT
Organization: University of California, Berkeley
NNTP-Posting-Host: crown.berkeley.edu

drchambe@tekig5.pen.tek.com (Dennis Chamberlin) (and many others) write:

>The biggie of error sources is barometric pressure variation, as you said.
>This correction is made manually, using sea-level corrected barometric
>pressure reported by widely-distributed locations on an hourly basis. These 
>figures are available from NWS offices and FAA flight service stations.
>The pressure is manually entered into the altimeter whenever accuracy is 
>deemed important, such as prior to an approach.

Can anybody explain how this works in some more detail?
I'd like to know how this is/can be implemented mathematically.


As far as I can gather from the responses I have received the following is/are
true:

1. Altimeter readings are based on standard atmosphere- they use the pressure
reading exclusively to show the equivalent height above sea level- ASSUMING
a standard atmosphere.

2. If they are temperature compensated this means that any errors introduced
by the pressure transducer over a temperature range are compensated. ie. the 
pressure transducer mechanism is made linear over a wide temperature range.
ie. temperature compensated does not mean that temperature readings are 
somehow used to give a better estimate of the height, just that we are 
correcting for inaccuracies in the instrument over temperature.

thanks
mark
Newsgroups: sci.aeronautics
From: sherwood@space.ualberta.ca (Sherwood Botsford)
Subject: Re: How accurate can I make a homebrew altimeter?
Organization: University Of Alberta, Edmonton Canada
Date: Thu, 5 Nov 1992 19:48:16 GMT

J. Mark Noworolski writes
> I am working on building an electronic altimeter and vario  
combination
> (basically the plan is to use a pressure sensor, some electronics and  
an LCD
> display).
> 
> I'm not sure what claims, if any, I will be able to make about  
accuracy.
> It seems to me that a height measurement based on pressure is very  
difficult
> to do - since it is impossible to know the exact distribution of  
temperature
> throughout the atmosphere.
> 
> My question basically is:
> How accurate are airplane altimeters and how do they compensate for
> weather fluctuations?
> 
> Also, depending on how high we are above sea level to start with, a  
different
> pressure variation will be observed per metre of height increment-  
how
> do you take this into account?
> 
> thanks,
> mark

What you measure is atmospheric pressure.  Every airplane altimeter  
I've seen had a knob to set barometric pressure.  Since barometric  
pressure is always referenced to sea level equivalent, by setting the  
barometric pressure to that of the nearest airfield, your altimeter  
will give a reasonable value. 

Off hand from the altimeters I've seen, +- 50 feet is as good as you're  
going to get.  But I wouldn't bet my life on it.

If you need more accurate altitude measurement to keep from bumping the  
ground, consider making a radar altimeter.
From: drchambe@tekig5.pen.tek.com (Dennis Chamberlin)
Newsgroups: sci.aeronautics
Subject: Re: How accurate can I make a homebrew altimeter?
Date: 9 Nov 92 18:46:25 GMT
Article-I.D.: tekig7.7521
Reply-To: drchambe@tekig5.pen.tek.com
Organization: Tektronix, Inc., Beaverton,  OR.

In article <1d8nd2INNnba@agate.berkeley.edu> jmn@crown.berkeley.edu (J. Mark Noworolski) writes:
>I am working on building an electronic altimeter and vario combination
>
>It seems to me that a height measurement based on pressure is very difficult
>to do - since it is impossible to know the exact distribution of temperature
>throughout the atmosphere.
>
>My question basically is:
>How accurate are airplane altimeters and how do they compensate for
>weather fluctuations?
>
>Also, depending on how high we are above sea level to start with, a different
>pressure variation will be observed per metre of height increment- how
>do you take this into account?
>
I believe aircraft altimeters assume a standard lapse rate for temperature. I 
don't know the magnitude of errors that result, but it seems to be good enough
for air traffic control. This is perhaps partly due to the fact that aircraft 
at similar altitudes are subject to the same error. 

Some altimeter designs, particularly those using solid-state pressure 
transducers, produce an error due to instrument temperature. On my Casio 
altimeter-watch I would estimate the magnitude of this to be in the neighborhood of minus 20 or 30 feet per degree F temperature change, but I'm sure the 
manufacturer would have a spec on it. For enhanced accuracy, you might 
want to consider a temperature sensor and correction scheme.

The biggie of error sources is barometric pressure variation, as you said.
This correction is made manually, using sea-level corrected barometric
pressure reported by widely-distributed locations on an hourly basis. These 
figures are available from NWS offices and FAA flight service stations.
The pressure is manually entered into the altimeter whenever accuracy is 
deemed important, such as prior to an approach.
Newsgroups: sci.aeronautics
From: wd@cs.tu-berlin.de (Wolfgang Diestelkamp)
Subject: Re: How accurate can I make a homebrew altimeter? - more Q's
Organization: Technical University of Berlin, Germany
	<1dmlk5INN8pm@agate.berkeley.edu>
Date: Tue, 10 Nov 1992 12:28:07 GMT

In article <1dmlk5INN8pm@agate.berkeley.edu> jmn@crown.berkeley.edu (J. Mark Noworolski) writes:

> As far as I can gather from the responses I have received the following is/are
> true:
> 
> 1. Altimeter readings are based on standard atmosphere- they use the pressure
> reading exclusively to show the equivalent height above sea level- ASSUMING
> a standard atmosphere.

This is only partially true; standard pressure (29.92" or 1013.25 HectoPascal)
is assumed only above a certain altitude (which varies between 2000' above
the ground and 18.000' above sea level). This is to give everyone a standardized
altitude reading for separation. Below this, proximity to the ground,
i.e. height, becomes an important factor. so the local actual pressure (QNH)
is measured by a ground station, converted to the equivalent sea level pressure
(QNH) and manually preset on the altimeter.
Temperature is a different thing; for temperature, the standard atmosphere
(ISA = international standar atmosphere) is taken as basis, which assumes
15 Celsius at sea level and 2 degree decrease every 1000 feet. Concerning operation
close to the ground, this doesn't give any error at all, because the temperature
error is linearly dependend on the vertical distance between the reference
station and the point, at which the altitude is measured. So assuming you touch
down at the airport that measures the pressure, you'll have a zero temperature
error.

> 
> 2. If they are temperature compensated this means that any errors introduced
> by the pressure transducer over a temperature range are compensated. ie. the 
> pressure transducer mechanism is made linear over a wide temperature range.
> ie. temperature compensated does not mean that temperature readings are 
> somehow used to give a better estimate of the height, just that we are 
> correcting for inaccuracies in the instrument over temperature.

This is true, what is compensated for is only the instrument error. There
can be no compensation (in the instrument) for the temperature error
due to non-ISA temp of the atmosphere.
-- 
Wolfgang Diestelkamp
wd@cs.tu-berlin.de
wolfgang@first.gmd.de
From: drchambe@tekig5.pen.tek.com (Dennis Chamberlin)
Newsgroups: sci.aeronautics
Subject: Re: How accurate can I make a homebrew altimeter? - more Q's
Date: 10 Nov 92 19:31:39 GMT
Reply-To: drchambe@tekig5.pen.tek.com
Organization: Tektronix, Inc., Beaverton,  OR.

In article <1dmlk5INN8pm@agate.berkeley.edu> jmn@crown.berkeley.edu (J. Mark Noworolski) writes:
>drchambe@tekig5.pen.tek.com (Dennis Chamberlin) (and many others) write:
>
>>The biggie of error sources is barometric pressure variation, as you said.
>>This correction is made manually, using sea-level corrected barometric
>>pressure reported by widely-distributed locations on an hourly basis. These 
>
>Can anybody explain how this works in some more detail?
>I'd like to know how this is/can be implemented mathematically.

For example:

Hillsboro airport is a weather reporting station at an elevation of 200 feet
above sea level. Upon installation, the station barometer is adjusted for
the field elevation of 200 feet. This has the effect of adding approximately 
0.20 inches to the measured pressure, thus indicating a pressure as though
the instrument was located at the bottom of a 200 foot well at that location
(sea level). The correction is approximately 1 inch per 1000 feet, but is
not linear with altitude.

Hillsboro regularly reports their *indicated* pressure to aircraft in the 
vicinity. The aircraft altimeter has an adjustment knob that is calibrated
in inches (pressure), and this adjustment directly affects the indicated 
altitude. 

If the sea-level pressure at Hillsboro is 1 inch high due to local weather,
an approaching aircraft would tend to follow his uncorrected altimeter to
an erroneously high true altitude. (Altimeter reads low, pilot reacts.)
However, Hillsboro's instrument measures a pressure of 30.72 inches:

       29.92 standard pressure
     +  1.00 local high pressure
     -  0.20 reduction due to 200 ft. field elevation
       _____
       30.72

The instrument was previously corrected for field elevation, so it indicates
30.92 and this is reported to the aircraft. The pilot dials this into his 
altimeter, hich then reads 1000 feet higher. (This example uses an absurdly
large error for illustration.) The pilot reacts to the new reading by flying
back to the correct true altitude.

It is still basically a manual system. 
Cruise missiles use separate arrangements. 

	    Aviation Weather
	    (both FAA publications, available from GPO)
	    Pressure Transducer Handbook, National Semiconductor