Newsgroup sci.math 152163

Directory

In article <1996Nov13.010634.14542@lafn.org>
ba137@lafn.org (Brian Hutchings) writes:
> 
> I don't get it; what is the equation supposed to "do" ??
> 
The equation represents the surface of the rounded cube, but its real
value is as a line of conversation you might want to use in meeting and
talking with women. For example, consider the hypothetical meeting
between he and She:
he: hi there! my name is ________, are you into surfaces, like
mathematical surfaces? Well you probably know the equation of the
surface of a sphere, right?
She: nods in agreement
he: well check this surface equation out
he: scribbles the equation x^4+y^4+z^4=1 on a drink napkin...
She: smiles and looks with affection at him....????????
She: f the equation, lets dance!
She : puts in a quarter and selects "Jail House Rock".......
Works vice versa for women.

George Weisz wrote:
> 
> Hi...
> Could somebody please help.
> 
> I am looking for the rotation matrix R derived from a quaternion
> q()
> 
> 
> d = 2acos(q0)
> 
>          d            q1          q2           q3
> s = sin ---     zx = ---    zy = ---     zz = ---
>          2            s           s            s
> 
>     +-            -+
>     |  ?   ?   zx  |
> R = |  ?   ?   zy  |
>     |  ?   ?   zz  |
>     +-            -+
> 
> Any help or pointer will be much appreciated.
> 
> Thanks
> 
> George
George, the fragment of the rotation matrix you gave isn't correct.  
Here's the general form of the matrix:
 [a^2-b^2-c^2+d^2     2(ab-cd)         2(ac+bd)      ]
 [  2(ab+cd)      -a^2+b^2-c^2+d^2     2(bc-ad)      ]
 [  2(ac-bd)          2(bc+ad)     -a^2-b^2+c^2+d^2  ]
Better check the signs, but I think I got it right.
In your notation, q1=a, q2=b, q3=c, q0=d
Jack

             Tips For A Roach Free Apartment.
             --------------------------------
	Apartments can be roach free, until one day the wrong 
neighbor moves next door or a current neighbor gets 
careless. Below are ways to eliminate roaches completely.
Seal Roach Routes:
------------------
	When roaches walk in under the front door, 2 inch wide 
plastic tape (like duct tape) can build a seal under and 
onto the door. The seal can be built up in layers until the 
gaps are paper thin. Plastic straws may be taped over to 
fill gaps but aren't necessary. 
	Also check the space seal at the side and top of the 
front door. How many pages of stacked paper can be pushed 
into the apartment at once? Here (if needed) taped over 
plastic straws may be helpful in creating a tight seal.
	In spring or summer, roaches can walk in through 
windows from roach infested neighboring apartments. Two inch
wide transparent tape can seal windows or screens if they 
are a roach access route.
	Taping can also be done over any existing cracks at 
points of access to the apartment for TV cable, phones lines
and water, heat, gas or electrical pipes.
Mechanically Remove Roaches:
----------------------------
	Once an apartment is sealed from roach access, an 
ongoing effort to remove or crush roaches will eventually 
eliminate the entire roach population. All it takes is some 
effort each day to eliminate some of the roaches from the 
apartment.
	For example, whenever the light is put on during the 
night, whether on entering the apartment, or on going to the
bathroom, do it carefully without wind or noise and be ready
to act to catch or crush roaches where they congregate. 
	Always be ready to act by having coarse paper towels 
folded into quarters as a convenient crushing tool, or a 
transparent plastic container with seals, if catching them.
Starve and Poison Roaches:
--------------------------
	Keep a clean dry apartment. Cover and remove garbage. 
Wipe up water. Then roaches can be caught looking for water 
or food. Roach motels can locate and catch roaches also.
	Boric acid powder sprinkled careful against the walls 
where roaches walk is highly effective for complete roach 
elimination. But it may take a month or two. Boric acid is a
cumulative poison, so don't breath it in or get it on cuts. 
Roaches that walk in it will lick their feet and poison 
themselves. Those with pets should not use this method.
	Closed container poisons can aid also toward a roach 
free apartment.  Where there is a will, there is a way.
------------------------------------------------------------
By David Kaufman, Nov. 12, 1996.  Share this leaflet freely.
         Be Good, Do Good, Be One, and Then Go Jolly.
                 What else is there to do? 
-- 
                                             davk@netcom.com

(Again, apologies if this posting appears more than once due to server problems.)
Yes, I think you took my meaning correctly -- even though I had excluded them,
we can now include the cases p=0 and p=1 if the limits are handled with care:
I was considering an infinite sequence X_1, X_2,... of i.i.d. random variables, each 
of which is 0 or 1, with fixed pr(X_i=1)=p, and I asked for the c.d.f. F(t;p) of the 
random variable X = 0.X_1X_2... = sum[k=1,2,...](X_k)*2^(-k).
Of course, the cases you first mention (p=0,1,and 0.5) are quite obvious, and other 
cases are, as you say, less so.  However, here is something that I find interesting:
Claim:  For any t and p in [0,1],  F(t/2^m;p) = F(t;p)*[(1-p)]^m;  m=0,1,2,...
[Write the binary expansion of t=t_1t_2... and note that 
F(t/2;p)=pr(0.X_1X_2X_3... <= 0.0t_1t_2t_3...)
=pr(X_1=0)*pr(0.0X_2X_3...<=0.0t_1t_2t_3...) (independence)
=(1-p)*pr(0.X_2X_3...<=0.t_1t_2...)
=(1-p)*pr(0.X_1X_2...<=0.t_1t_2...)(identically distributed)
=(1-p)*F(t;p)
and the claim follows by iteration.]
The following c.d.f. has the property claimed for F(t;p): 
    G(t;p)=t^a, with a=-log2(1-p).
Indeed, F(.;p)=G(.;p) in the special cases p=0, 1, 0.5.
So, here's a question:
If, as you say, F(t;p) is not continuous in t, is there, nevertheless,
some nice connection between F(t;p) & G(t;p) for general t and p in [0,1]?
Thanks for the reference on this topic -- perhaps it will address 
this question also. 
Robert E Sawyer (soen@pacbell.net)

roberts@ucunix.san.uc.edu (Michael A. Roberts) wrote:
>In article <56ae9e$556@niamh.indigo.ie>, Gerry Quinn  wrote:
>>rpatt@tva.gov (Russell W. Patterson at T.V.A.) wrote:
>>>
>>>If the platter turned at constant speed how would you calculate the time it 
>>>takes for the needle to travel from the beginning of the first groove to the 
>>>end of the record?
>>Just the number of grooves divided by the r.p.m.! Of course, it may start to 
>>skip before it reaches the end...
>No, I don't think so.
>How many grooves are on one side of the record? I've considered the
>problem carefully, and conclude that there is only ONE.
True.  However, you could consider an "apparent" number  of grooves.
That is, imagine a line radiating from the center.  As the table turns
the needle crosses that line at the same rate; the r.p.m. of the
turntable.  Use this and the "apparent" number of grooves (crossing
the line twice is equal to two turns,as if there were two grooves
counted.)

Fredrik Sandstrom  wrote:
>I've got a simple(?) question.  I came to think of it one day, and I
>can't come to a conclusion.  What is
> lim    0/x         ?
>x -> 0
>One possible answer would perhaps be that lim_(x->0+) 0/x = 1 and
>lim_(x->0-) 0/x = -1.  Other possibilites are +/- infinity, or perhaps
>0.  What do you think?
I think that you should read the MANY past comments on this topic
(already beaten to death) and reach your own conclusion.

In article 
darla@accessone.com (Darla) writes:
> Sweetie---
> 
> You cannot judge the importance or the value of a thing by the number and
> weight of the tools needed to produce or complete it.  It takes a lot of
> heavy equipment to haul garbage, but only a heart to fall in love.  And
> which is the greater endeavor? Which has more directly enhanced the lives
> of men and the survival of the planet?
> 
> By the way...without logic to show man how to think and reason, the
> chemists and physicists would be sitting around looking at one another
> wondering how to begin.
> 
> 
> Darla
  And you believe that the atoms in a tool such as a hammer knows that
they are tool atoms. And that atoms in something that you yourself do
not think is a tool are nontool atoms. That atoms somehow talk to each
other and say "sweetie, we are tool atoms".
   You have failed to see my point and my message. The point is, again,
that if you seek to understand the world around you and you do so by
only pen and paper on your laziness and talking with someone such as a
math proof, that understanding can never be as important as another
person who draws into his quest for understanding of the world by
encompassing vast number and large part of his surroundings. Everytime
the double slit experiment is performed, it draws in so much more of
the world than someone who is proving FLT with pen and paper.
  If your son spends 4 years at a school pushing pen and paper, no
matter how cute and heavy. That is never worth the same son who
afterwards spends 4 years in the actual work a day world of the
profession that he studied for in his 4 years of pen and paper
preparing him for. You can say that mathematics, all of it is a phsyics
warm-up experiment. Math people like to tell you that once a math proof
is given , then it is proved in eternity. Physicists are not so
arrogant and have a better mind, for they tell you that a physics
experiment can be falsified. There might have been something overlooked
and perhaps in the case of the 1003 experiment of the same test it is
found that the experiment was wrong. But this is the case for
mathematics also when you accept that a mathematics proof is merely a
physics experiment that uses little physics equipment or apparatuses,
usually only pen and paper.
  My advice to you is to open your mind. Recognize that there are
people in the world who are thousands of times smarter than you and
that when you read my posts, don't jump the gun and think that you are
correct and I am wrong. Say to yourself, I am reading AP and I can
learn something new today.

In article 
Dan Razvan Ghica  writes:
> I don't really see how the way we write a number is important. If
> "...9998" and "-2" are equivalent I would naively go for the "-2" notation
> just because it lacks the confusing "..." at the left end. Just like I
> prefer "2.0" to "1.999...". But I might be wrong. 
> 
  There is more to a number than how it is written. And I should have
not thrown in that equivalency for I opened a huge can of worms. For me
to talk about 'equality' and 'equivalency' there distinction and
perhaps there illusion would be a whole subject in itself. The Real
Numbers 2.0... and 1.999... are one and the same and are equal. There
is no difference between 2.00... and Real two and 1.999... and the
Whole Real after 1.00... This is a matter of writing a number. But
equivalency is much different because we do not say 1/2 is equal to
2/4. We know that if you have a team composed of 1 male and 1 female
and another team of 2 males and 2 females, we know those are not the
same thing.
  And here is another case where physics overpowers mathematics. In
physics we can have equality for photons or the more general bosons are
indistinguishable. In fact, bosons are the only pieces of reality that
are indistinguishable and everything else is distinguishable. And so ,
in the future the mathematicians will eventually come around to basing
their definition, and their entire understanding of equality and
equivalency-- all around boson and fermion characteristics. But this
other triumph of phsyics over mathematics will wait. First of
importance is for physics to clear out the dead wood of Finite Integers
and replace them with Infinite Integers (p-adics).
> It would be interesting if Archimedes Plutonium would steer his postings
> away from anti-mathematical-establishment conspiration-theory-esque
> rantings and tell us more about these mysterious p-adics, their fine
> properties and their potential impact on life from mathematics and physics
> to, say, accounting. 
> 
  To you and most everyone reading my Vietmath posts will look at them
as anti math establishment with touches of hollering of conspiracy. I
have never admired conspiracy theories. 
  To the world 50 years from now, they will see that I did what I had
to do. And as they read my posts they will be on my side, even 110%
percent. History is kind to those who could see the truth 50 years in
advance, and history is very unkind to those who thwarted and ignored.
Remember those two English mathematicians that ignored Ramanujan. And
Hardy would have been a mere footnote if not for Ramanujan. But those
two darkhorses are now written into the black pages of history. 
  Every prominent mathematician out there now who ignores me will be
written off and into the dark pages of history. Andy Wiles, Gerd
Faltings, Paul Erdos will be written into the comic book history of
mathematics, simply because they ignored me.
> I need more background before I start fighting the VietMath war.
> 
  I do not have time for a dialogue concerning p-adics. I have often
posted in the past that a Schaum's type of outline for elementary
p-adics should be written. Some workbook that even a good High School
student can operate on p-adics. When the world recognizes that physics
is written in p-adics and not the fictional Finite Integers then
virtually all mathematics textbooks become instantly obsolete. And book
publishers will be forced to write elementary p-adics books and
outlines.
  When p-adics replaces finite integers there will have to be a meeting
all over the world in education to decide what year to introduce
p-adics to math majors. Everyone who is not majoring in physics or
mathematics can use the false integers of finite because they never
need to worry about any integer that does not repeat in zeros leftward.
Just like anyone not wanting to major in physics can get by amiably
with Newtonian Mechanics.
> Regards,
> DRG
> 
Sorry, I do not have the time for a p-adic dialogue. About the best I
can do is to repost my own personal dialogue on p-adics that occurred
on the Net in 1993-1994. And come to think of it, I ought to keep that
dialogue in my website and to the questions of "let's have a p-adic
dialogue" I can refer the reader to a specific web page.
  The mathematics literature even up to this date, is horribly lacking
in any elementary discussions of p-adics, what they are, how to
multiply and divide with them. There strange characteristics. Why this
lack? The answer is that noone but me ever thought they were anything
more than a extension. I am the first to realize that they are the
Naturals themselves, and that the Finite Integers were a field of
ghosts, or angels that fit on the end of a needle.
> --
>  ghica@qucis.queensu.ca **** http://www.qucis.queensu.ca/home/ghica/info.html
> Many vast and imposing philosophies are based on stupid and trivial confusions.
>                                                                Bertrand Russell

Doug Craigen (dcc@cyberspc.mb.ca) wrote:
: "According to this model, which has been experimentally confirmed, a 
: ferromagnetic material (such as cobalt, nickel, and iron) is composed of 
: many small domains, their linear dimensions ranging from a few microns to 
: about 1 mm.  Thes domains, each containin about 10^15 or 10^16 atoms, are 
: fully magnetized in the sense ..."
: source: Field and Wave Electromagnetics, Second Editions. David K. Cheng. 
: p.258 (publisher, Addison Wesley)
Just for consistancies sake and clarity.
A mm = 1E-3 meters (m)
A few microns = about 3E-6 m
An average atom = about 3E-10 m
Therefore, a small domain contains (10^4)^3 = about 10^12 atoms.
           a mm domain contains (10^7)^3 = about 10^21 atoms.
1E-4 m = about a speck or 1/10 of a dime's thickness.
1E-5 m = about a 1/10 of a speck. 
This is the domain size that contains about 10^15 atoms 
or 10^5 atoms in diameter.
Thanks for the information.
-- 
                                             davk@netcom.com

In article <56b0t4$4ed@dartvax.dartmouth.edu>
Archimedes.Plutonium@dartmouth.edu (Archimedes Plutonium) writes:
>   My advice to you is to open your mind. Recognize that there are
> people in the world who are thousands of times smarter than you and
> that when you read my posts, don't jump the gun and think that you are
> correct and I am wrong. Say to yourself, I am reading AP and I can
> learn something new today.
We are feeling more humble then usual tonight %^)

Richard Gain wrote:
>   1)   What is the angle between two adjacent faces?
> 
>   2)  What is the relationship between edge length of the pentagonal faces and diameter (face to face or vertex to vertex, whichever is easier) of the dodecahedron?
1) 116,57 degrees
2) face to face: 2,270 times the edge length
I have extracted this from information given in various handbooks. If
you want to check, good luck!

In article  Le Compte de
Beaudrap  writes:
>        Now why didn't I think of this? Arch, would it be possible to 
> please talk more about p-adics and less about how they will cause the 
> collapse of mathematics? Serious request, here: I don't mean to be snide 
> or sarcastic. Tell us about them.
>
> Niel de Beaudrap
Sorry but my agenda is so loaded that I even parcel out my
entertainment time. I even told a pretty redhead (potential date) that
my schedule was completely full until next May for me to even consider.
 I just do not have the time to dialogue. What I can do is repost my
old 1993-1994 dialogue. Some 1,000 posts on p-adics a dialogue which
had many math experts talking about p-adics. If you want I can post
about 5 dialogues to some of these VietMath War posts. I think this may
be a good idea.
If you have ever done a patent, you would know that I have no time for
a dialogue. I have a patent due at the end of Dec 96. Then another due
in April 97. Then another due midyear 97 and another due in November
97. Some are over 100 pages long. A dialogue on p-adics is far down on
my list of priorities. Besides what would a "great dialogue" on p-adics
accomplish for me? That I learn some more about p-adics that I did not
already know, when the major theme is that the p-adics are the Natural
numbers. 
No, genius is mostly knowing your priorities. Besides, how do I know
that your questions is genuine. I suspect people who want to get me
into a dialogue which has no direction in sight. I ask myself are these
Socratic method persons who would fish for a dialogue sucker? Are they
really genuine in their questions or are they panning for being correct
and me being shown wrong. I have seen a few  on the Net who chase after
posters and try to engage them in some dull, stultifying dialogue. 
Something about their psychology that they need a Socratic dialogue.
Perhaps they stay awake at night dreaming of scoring a victory on the
Net over someone in a Socratic dialogue and the Net is their avenue of
accomplishing this rum-dummy effort. I usually can smell people out
before they even utter their first rum dummy lines.
  I am not accusing you Niel of any rum. But I notice no technical talk
of p-adics on your part. The best I can do is to repost my 1993-1994
dialogue on p-adics under a Vietmath title.

***********************************************************************
This works, I did it and have already received $420.00 in the past week.
************************************************************************
Hello! I've got some awesome news that I think you need to take two
minutes to read if you have ever thought "How could I make some
serious cash in a hurry???" , or been in serious debt,  ready to do
almost anything to get the money needed to pay off those bill
collectors. So grab a snack, a warm cup of coffee, or a glass of your
favorite beverage, get comfortable and listen to this interesting,
exciting find!
   Let me start by saying that I FINALLY FOUND IT! That's right!. I
found it! And I HATE GET RICH QUICK SCHEMES!! I hate those schemes
like multi-level marketing, mail-order schemes, envelope stuffing
scams, 900 number scams... the list goes on forever. I have tried
every darn get rich quick scheme out there over the past 12 years. I
somehow got on mailing lists for people looking to make money (more
like 'desperate stupid people who will try anything for money!').
Well,  when I was a teenager,  these claims to 'get me rich quick'
sounded irresistible! I would shell out $14.95 here, $29.95 there,
$24.95 here, and another $49.95 there.  I had maxed out my new Circuit
City Card AND my Visa...I was desperate for money!!  So, I gave them
all a chance but failed at every one of them! Maybe they worked for
some people, but not for me.  Eventually, I just tossed that JUNK MAIL
in the trash when I got the mail.  I recognized it right away.  I can
smell a money scam from a mile away these days,  SO I THOUGHT....
I thought I could sniff out a scam easily.  WAS I WRONG!!  ....I LOVE
THE INTERNET!!!
   I was scanning thru a NEWSGROUP and saw an article stating to
GET CASH FAST!!  I thought..."Here on the Internet??  Well, I'll just
have to see what schemes could possibly be on the internet." The
article described a way to MAIL A ONE DOLLAR BILL TO ONLY FIVE PEOPLE
AND MAKE $50, 0000 IN CASH WITHIN 4 WEEKS!  Well, the more I thought
about it, the more I became very curious. Why? Because of the way it
worked AND BECAUSE IT WOULD ONLY COST ME FIVE DOLLARS (AND FIVE
STAMPS), THAT'S ALL I EVER PAY....EVER!!
   Ok, so the $50,000 in cash was maybe a tough amount to reach, but
it was possible.  I knew that I could at least get a return of $1,000
or so.  So I did it!! As per the instructions in the article, I mailed
out ('snail mail'for you e-mail fanatics) a single dollar bill to each
of the five people on the list that was contained in the article.  I
included a small note, with the dollar, that stated "Please Add Me To
Your List."  I then removed the first position name of the five names
listed and moved everyone up one position, and I put my name in
position five of the list.  This is how the money starts rolling in!
I then took this revised article now with my name on the list and
REPOSTED IT ON AS MANY NEWSGROUPS AND LOCAL BULLETIN BOARD
MESSAGE AREAS THAT I KNEW.  I then waited to watch the money come
in...prepared to maybe receive about $1000 to $1500 in cash or so....
But what a welcome surprise when those envelopes kept coming in!!!  I
knew what they were as soon as I saw the return addresses from people
all over the world-Most from the U.S., but some from Canada, even some
from Australia!  I tell you, THAT WAS EXCITING!!  So how much did I
get in total return?  $1000? $5000? Not even!!! I received a total of
$23,343!!!  I couldn't believe it!!
   I now have a brand new black Acura Integra to speak for, due to
this!! Now after almost 8 months, I am ready to do it again!!! So
maybe it was possible to get $50,000 in cash, I don't know, but  IT
COMPLETELY DEPENDS ON YOU, THE INDIVIDUAL!  You must follow through
and repost this article everywhere you can think of!  The more
postings you achieve will determine how much cash will arrive in your
very own mailbox!!  It's just too easy to pass up!!!
   Let's review the reasons why you should do this:  The only cost
factors are for the five stamps, the 5 envelopes and the 5 one dollar
bills that you send out to the listed names by snail mail (US Postal
Service Mail).  Then just simply repost the article (WITH YOUR NAME
ADDED) to all the newsgroups and local BBS's you can.  Then sit back
and, (ironically), enjoy walking (you can run if you like! :o  ) down
your driveway to your mailbox and scoop up your rewards!!  We all have
five dollars to put into such an easy effortless investment with
SPECTACULAR REALISTIC RETURNS OF $15,000 to $25,000 in about 3-5
weeks!  So HOLD OFF ON THOSE LOTTERY NUMBERS FOR TODAY,EAT AT HOME
TONIGHT INSTEAD OF TAKEOUT FROM McDONALDS AND INVEST FIVE  DOLLARS IN
THIS AMAZING MONEY MAKING SYSTEM NOW!!! YOU CAN'T LOSE!!
   So how do you do it exactly, you ask?  I have carefully provided
the mostdetailed, yet straightforward instructions on how to easily
get this underway and get your cash on its way. SO, ARE YOU READY TO
MAKE SOME CASH!!!?? HERE WE GO!!!
*** THE LIST OF NAMES IS AT THE END OF THIS ARTICLE. ***
OK,  Read this carefully.  Get a printout of this information, if you
like, so you can easily refer to it as often as needed.
INSTRUCTIONS:
1.  Take a sheet of paper and write on it the following:
"Please add my name to your list".  This creates a service out of this
money making system and thus making it completely legal. You are not
just randomly sending a dollar to someone, you are paying one dollar
for a legitimate service.  Make sure  you include your name and
address.  I assure you that,  again,  this is completely legal!  For a
neat little twist, also write what slot their name was in: "You were
in slot 3",  Just to add a little fun!  This is all about having fun
and making money at the same time!
2.  Now fold this sheet of paper around a dollar bill ,(no checks or
money orders), and put them into an envelope and send it on its way to
the five people listed.  The folding of the paper around the bill will
insure its arrival to its recipient. THIS STEP IS IMPORTANT!!
3.  Now listen carefully, here's where you get YOUR MONEY COMING TO
YOUR MAILBOX.   Look at the list of five people;  remove the first
name from position one and move everyone on the list up slot one on
the list.  Position 2 name will now move to the position 1 slot ,
position 3 will now become position 2, 4 will be be 3, 5 wil be 4.
Now put your name, address, zipcode AND COUNTRY in position 5, the
bottom position on the list.
4.  Now upload this updated file to as many newsgroups and local
bulletin boards' message areas & file section as possible.  Give a
catchy description of the file so it gets noticed!!  Such as:
"NEED FAST CASH?, HERE IT IS!" or "NEED CASH TO PAY OFF
YOUR DEBTS??",  etc.  And the more uploads, the more money you will
make, and of course, the more money the others on the list will make
too.  LET'S ALL TAKE CARE OF EACH OTHER BY BEING HONEST AND BY PUTTING
FORTH 120 PERCENT INTO THIS PROFITABLE & AMAZING SYSTEM!!! You'll reap
the benefits, believe me!!! Set a goal for the number of total uploads
you'll post, such as 15-20 postings or more!  Always have a goal in
mind!!! If you can UUE encode the file when uploading,  that will make
it easier for the people to receive it and have it downloaded to their
hard drive.  That way they get a copy of the article right on their
computer without hassles of viewing and then saving the article from
the File menu. Don't alter the file type, leave it as an MS-DOS Text
file. The best test is to be able to view this file using Microsoft's
Notepad for Windows 3.x or WordPad for Windows '95. If the margins
look right without making the screen slide left or right when at the
ends of the sentences, you're in business!
5.  If you need help uploading, simply ask the sysop of the BBS, or
"POST" a message on a newsgroup asking how to post a file, tell them
who your Internet provider is and PEOPLE WILL ALWAYS BE GLAD TO HELP.
I would try to describe how to do it but there are simply too many
internet software packages with slightly different yet relatively
simple ways to post or upload a file.  Just ask for help or look in
the help section for 'posting'. I do know that for GNN, you simply
select 'POST' then enter a catchy description under the subject box,
choose 'ATTACH', selecting 'UUE' and NOT 'TXT', then choose 'Browse'
to go look for the file. Find your text file CASH.TXT and click on it
and choose 'OK'.  Place a one line statement in the main body section
of the message post screen. Something like "Download this to read how
to get cash arriving in your mailbox with no paybacks!" or whatever.
Just make sure it represents its true feasibility, NOT something
like..."Get one million dollars flooding in your mailbox in two days!"
You'll never get ANY responses!
6.  And this is the step I like.  JUST SIT BACK AND ENJOY LIFE BECAUSE
CASH IS ON THE WAY!!  Expect to see a little money start to
trickle in around 2 weeks, but AT ABOUT WEEKS 3 & 4, THE MONEY STORM
WILL HIT YOUR MAILBOX!! All you have to do is take it out of the
mailbox and try not to scream too loud (outside anyway) when you
realize YOU HIT THE BIG TIME AT LAST!!
7.  So go PAY OFF YOUR BILLS AND DEBTS and then get that something
special you always wanted or buy that special person in your life (or
the one you want in your life)  a gift they'll never forget.  ENJOY
LIFE!
8.  Now when you get low on this money supply,  simply re-activate
this file again; Reposting it in the old places where you originally
posted and possibly some new places you now know of. Don't ever lose
this file, always keep a copy at your reach for when you ever need
cash.  THIS IS AN INCREDIBLE TOOL THAT YOU CAN ALWAYS RE-USE TIME AND
TIME AGAIN WHEN CASH IS NEEDED!
9.  (This step added by Charles Reiley).  Hello, This is exciting,
isn't it?! While I'm on the list, just add a note saying "Please
include extra money tips" with your name & E-MAIL address, and I will
(FOR FREE) send you some neat methods to increase the money you will
receive with this plan. Why?... Why not? I'm not a selfish jerk...I
like helping out others. E-mail just makes it a touch easier and
cheaper, too!  After I drop off the list, I can no longer offer you
this advice, obviously, but maybe someone else who gets my tips will
offer and simply replace my name on this step number 9. Good luck and
give this plan your all, it will definitely pay off! Like Mike said,
HAVE FUN WITH IT!!!
10. (This comment added by Mike Lorincz) Hell dude, this is great, just
send the money and wait like 1 week, then all of a sudden, BOOOOOOM!
Mail flood full of dollar bills. Hahahah its great
******************************************************************
******************************************************************
THE NAMES LIST       THE NAMES LIST      THE NAME LIST
******************************************************************
*     HONESTY IS WHAT MAKES THIS PROGRAM SUCCESSFUL!!!
*
*
*
*
*  #1      C. PRUETT
         PO BOX 1047
         ANOKA MN. 55303- 
 #2      SUZIE COOK
         1820 west sahuaro #110
         phoenix az. 85029 
 #3      JEWELL E. SIMPSON
         10120 NORTH 96TH DRIVE
         PEORIA AZ. 85345  
 #4      W. PRUETT
         368 E. SCHOOL ST. #2
         OWATONNA MN. 55060 
#5       DONNA GLENN
         308 3RD AVE EAST
         JEROME, ID 83338
***********************************************************************
This works, I did it and have already received $420.00 in the past week.
************************************************************************

Mark Leung (mleung@silver.ucs.indiana.edu) wrote:
: Does anyone know if there is any computer package for running
: kernel regression (or parzen window estimation)?
: Thanks.
: Mark
I am also interested in this.  Please forward info to
my email address also.
finasc@ccunix.ccu.edu.tw
thanks in advance.

In article  Le Compte de
Beaudrap  writes:
>
>        As soon as chemistry stopped being alchemy, it was a branch of 
>physics. It happened in the late 19th, not the early 20th, century. To 
>quote Rutherford: "All science is either physics or stamp collecting."
>That was from long before the full glory of Quantum Physics.
>
  I'll buy that. I think most chemists innately know that they are a
specialized area of physics. 
>
>        As well, how can physics ever subsume math!? That's impossible! 
>While findings in physics may force math to change, it is the laws of 
>physics that are expressed in math, NOT the laws of math expressed in 
>physics. I defy you to, using Maxwell's equations, prove that 1+1=2, 
>without depending on the proof asked for to accomplish it.
>
 Nay, your above is your accepted brainwash. Look, try to imagine a
world in which it has no indivisible parts-- no atoms. This is very
difficult and shows the degree of assumptions people carry with them.
You see, the only reason we have numbers in the first place is because
atoms are numerous.
 To show your above beliefs are wrong, I need not prove via Maxwell
Equations that 1+1 = 2. All I need to show you and the myriad others is
to consider this.
Consider humans inside of the 5f6 establishing a mathematics and they
come to the moment in history when they seek that special number that
relates how many diameters make a circle. We know that special number
to be 3.14.... Could that number be different to another advanced
lifeform somewhere else in the universe? The answer is yes. The answer
is that life, intelligent life can have different pi depending on where
that advanced life is located.
  You see, Niel, to your education and brainwashing you think that pi
is an absolute.
  But if you consider that pi and e come from the physical world itself
and that we discover pi as 3.14... in this corner of the universe but
that pi and e can change and have been different in the past and will
be different in the future. 
  You see, 5f6 of 231 plutonium has in the collapsed waveform
(collapsed wavefunction reverts to rational numbers and uncollapsed are
transcendental numbers) . But the diameter to the circumference of 5f6
of plutonium is 22 subshells divided by 7 shells. The girth, the
circumference of plutonium is 22 subshells inside of a diameter a 7
shells.
  The reason all math people find that the ratio of circumference to
diameter is a number in rational form of 22/7 and for e , 19/7  (19
occupied* subshells in 7 shells) is because the Maker of everything has
a belt, a girth of 22, and occupied 19 subshells in 7 shells.
  Every mathematician before me has never answered why 3.14... (whether
rational or transcendental form) has ever answered why these two
numbers. Why not a whole 3 and a whole 2. The answer could never be
given by math people but the answer has to be given by the "experience
of the whole world". Physics has to answer why pi is 3.14... and not 3
and why e is 2.71... and not 2 or 2.50...
  Once physics has answered that, then it implies that in the future
when the universe is a different atom totality such as a element 150,
then the pi and e for those advanced lifeforms inside that element 150
outer electron space, their pi and e will be different from our pi and
e inside the 5f6 of plutonium.
  Physics is tops, is pinnacle and all other subjects are dressing for
physics.
>        If physics predicts a mathematical property, THEN has physics 
>subsumed math. You state that physics CONTRADICTS math, or shows that 
>math is insufficient; that means that the laws of mathematics do not form 
>a proper base as defined.
>
   You got that partially correct. My attack on mathematics goes like
this.
  If a branch of physics or even a tiny spot of physics finds p-adics
essential. Essential and where the Finite Integers are inadequate. What
that discovery means is that Finite Integers as counting numbers were
as fake, as a mere crude approximation of what the genuine and true
integers were. This usurpment is similar to the usurping of Newtonian
Mechanics by Quantum Mechanics.
  Thus my attack on mathematics is merely a search for physics , some
spot in physics where p-adics are essential and where Finite Integers
just fail to describe that physics. My guess is that the Quantum Hall
Effect numbers are p-adic numbers and that they look strange and
bizarre because they are seen as rational numbers and Finite Integers.
But if they are seen as just 7-adics and that they are 1,2,3,4,.... in
7-adics but oddball numbers otherwise. Well, physics subsumes
mathematics, swallows it forevermore in that one experiment.
>
>
>        Excuse me, but are you not also being a mathematician in 
>contributing to mathematics? (Are you not also acting like a High Priest 
>impersonator by writing this article? "The end of the finite integers is
>a'comin, and all of the unbeleivin' mathematicians of the world will be 
>thrown into the fires of hell!")
   Yes I am a mathematician when it is proved that physics is written
in p-adics and not Finite Integers. I have to come down hard on math
people to let them know. It was not by coincidence that I used the
Vietnam war to run a harangue on the math community. Consider: how far
would the Vietnam war protestors have gotten if they wrote to the
president Dear LBJ, please stop the Vietnam war. Those protesters did
the best thing possible to turn the attitude of that war. I have 2
proofs of the Riemann Hypothesis. If my name was Andy Wiles and had
control of Annals of Mathematics the way Andy has control of that
magazine, then the world would have had 2 accepted proofs of the
Riemann Hypothesis in 1993. 
   I can no longer ask "please Mr. Edwards will you look at my 2 proofs
of the Riemann Hypothesis". Instead I have to call out these buffoons
and wait for my day in the sun. When my day comes then I will change
the crooked and self-serving way that mathematics is run.
>
>        As well, where does the impression of mathematicians feeling 
>superior to scientists arise? I never heard of this, and many 
>mathematicians were also physicists. Were you scared by a 
>mathematician in your childhood?
>
  It is obvious, just look at all the replies to my saying that
mathematics is a subdepartment of physics. Only I have supported this
claim and all the other posts have opposed this claim. Even you Niel
are opposed to this claim. And the reason you are opposed, I can only
guess is that everyone has read in this arrogant books that math is
great and tops. But now in a newer day where there is an Atom Totality
theory, that older claim of math is tops really has not much support. 
>        As an aside, I take opposition to your calling me a birdbrain, 
>despite the fact that I haven't  breathed a word against p-adics 
>themselves yet. And until I have sufficient reason, I won't.
>
>
  I do that as a price that the lethargic math community will pay. The
day when p-adics are found essential in physics and that Naturals =
p-adics is confirmed then the math people who had responsibility to
consider Naturals = p-adics but who ignored it, heckled it, jeered it.
Well, then they pay the price for their obtuseness and their ignoring
it. I want accountability in mathematics and the sciences. In the old
days we were not as open nor had free access to the press and world as
we do with the Internet. And so accountability now plays a major role
in science and math.
  If I am found wrong and that the p-adics are not the Naturals and
that no place in physics are p-adics essential, then I pay the price
and eat crow and be historically blacklisted or made a clown of. But I
believe I am correct and if it takes calling Gerd Faltings a worthless
math birdbrain that he may go into action and consider that equation of
Naturals = INfinite Integers, and that he will go down into infamy in 
math history if I am found correct. Then it was good that I put a
bunsen burner under his stupid and lazy ass.
>
>        Maybe. As Quantum Physics has "classical" and "renormalised" 
>versions of theories, so may mathematics under p-adics. (What does 
>"p-adic" stand for, anyway? Just curious.)
>
  I have often stated that mathematics has rarely had any revolutions.
About the only real revolution was the introduction of nonEuclidean
geometries. But mathematics is ripe for a real, apple cart upsetting
revolution. A revolution that will make obsolete almost all the math
textbooks of present. Such a revolution would be Naturals = p-adics =
Infinite INtegers. And I have likened that revolution to the Quantum
physics revolution over the old Newtonian Mechanics. I have often
implied that Naturals = Finite Integers is Newtonian Mechanics and that
Naturals = Infinite Integers is the Quantum Mechanics of mathematics.
>
>        Firstly, I agree that physics EXPERIMENTS have more basis in 
>reality than math: math is a formal system which seems to work, and 
>physics experiments are measurements of reality itself. However, 
>THEORETICAL physics depends on math intimately. Physics theory without 
>math boils down to: "light is very very very very fast."
>
  All theoretical phsyics is hogwash unless it has experiments behind
it. And thanks for you above for the bells are ringing. Mathematics =
Theoretical Physics which has no experimental evidence.  Pure
theoretical physics is phsyics experiments that use only pen and paper.
>        Secondly, how did you "derive" (for lack of a better word) 
>p-adics? Are p-adics a consequence of observation, as the existance of
>the neucleus of an atom is? Or are p-adics the only way math and physics 
>able to coexist? If the latter, I submit that you have found a math that 
>is better for a basis of physics. P-adics are a part of physics (as 
>opposed to math) IF AND ONLY IF p-adics exist by the observations of 
>physics. Have you observed a 2 today? Not two objects, not ink in the 
>symbolic representation of "2", but an actual 2? No such thing exists, 
>one cannot "observe" a number, nor can one observe a class of numbers. 
>Thusly, p-adics are a part of MATH, NOT PHYSICS.
>
  If this world had no atoms , but something else, something continuous
perhaps then mathematics created in such a world would be numberless
and be based on whatever that stuff of that universe was.
  I did not found p-adics, Kurt Hensel did that at the turn of the 20th
century. I independantly discovered Infinite Integers and then later
found out that p-adics cover the Infinite Integers. This often happens
in science or math. That you work on something and think you have
discovered something totally new and find out that someone else worked
it out 100 years earlier than you.
>
>
>        Ah, so then you did not observe a p-adic, you merely concluded 
>that to use a p-adic instead of a finite integer solved your problems. 
>Your problems of reconciliation of THEORETICAL PHYSICS with EXPERIMENTAL 
>PHYSICS, not PHYSICS with MATH. By improving math, you makephysics 
>consistent. If p-adics are indeed an improvement, I applaud your efforts.
>However, in trying to convince (convert?) others to see things your way, 
>you have begun to sound more like a fanatical Nazi than a rational 
>philosopher of any type.
>
>        P-adics are math. New math, math brought about due to problems in
>physics, but math nonetheless. By insulting math, you insult yourself. 
>Whether you are aware of it or not, you are a mathematician, and are 
>trying to bring about a mathematical, and not a physical, revolution. 
>Physics will not envelop math, as you envision: math will not be whipped, 
>kiss physics' feet, or be put into concentration camps. Theoretical 
>physics will still be the middle man between experimental physics and 
>math, trying to predict the former by use of the latter. It will merely 
>be the first time that an inadequacy in physics will necessitate a change 
>in math, is all, just as inadequacies have necessitated better 
>experimental procedures all these centuries.
>
>        I put it to you that you are either a physicist who has been 
>either abused, teased, or put down by mathematical peers, and that you 
>are trying to insult them by saying that physics is infinitely superior 
>to math. In that, you are gravely mistaken. All quests for truth are 
>equally valid, and while some may be based on others (ie, just as PHYSICS 
>is based on MATH and observation), all searches for truth are noble, and 
>light up our world with their insights.
>
  No, I have my work and ideas before the eyes of the world. If any of
my theories are found correct, such as the Atom Totality, then all of
those that ignored or denied or the many that persecuted me will pay
their price.
  The Net has changed the playing field of science in publishing. No
longer can a professor from Princeton who has his hand on the journals
gets published. If Wiles is awarded the Wolfskehl prize for FLT and 10
or 50 years later my Naturals = P-adics is finally admitted as true and
that Wiles FLT was another scam just as Kempe's scam of the 4 - Color
Mapping. Well, it was all on record and I ask that Wiles and the
Goettingen Academy of Sciences go down in history , in infamy , as the
darkhorse persecutors and con-artists and buffoons that they were.
   The way we publish science and math must change. The old clubhouse,
inner circle are held accountable if they ignore a genius of the
subject.
>        This has been my humble opinion, amplified by way of reaction to 
>extreme comments about math. (Newton's 3rd law: For every action, there 
>is an equal but opposite reaction...a qualitative law of physics, which 
>needs math to be of any concrete use.) I neither oppose nor promote 
>p-adics, but I do oppose the way that the promoter(s) of p-adics seem to 
>go to great lengths put math down, especially with shock tactics like 
>"Physics Envelops Math" and "Math forced to grub, grub, grub". Let 
>us discuss things, and think things out, like reasoning beings: That's Why 
>God Gave Us Brains.
>
>        Math a branch of Physics? IMHO, impossible. P-adics valid? No 
>comment. After all, I haven't enough of a basis to have an opinion. If 
>only all people were like that, all the time...
>
  You really have not been open minded in your above.
>
>Niel de Beaudrap
 Math cannot even begin to describe quantum mechanics in its strange
logic, in its breaking of causality. Even a piece of biology is bigger
than is the whole subject of mathematics. Take the human brain and
mind, it fits mathematics into a tiny corner of that biological brain,
and yet the brain is just a composition of atoms and what the atoms do
is the subject of physics, is it not.
  So try to be a little more open minded

  Hello.
  I've heard of three algorithms that make easier finding
polynom null-points. The three algorithms supposedly help
finding integer, rational and imaginary null-points. Can
someone give me an example and an explanation of those
algorithms?
  Thanks in advance...

Concerning an infinite sequence of iid 0/1 random variables
X_1, X_2,... , with fixed pr(X_i=1), the following comments 
have appeared in this thread.
Alan Douglas wrote:

>... one can easily imagine an infinity
> of sequences whose relative frequencies never converge.
G. A. Edgar wrote:

>Sure.  Such a sequence is no less likely (or more likely) 
>than any given sequence whose frequencies do converge.
I haven't thought about this in a long time, but something 
is wrong here, I think.  *All* binary sequences have 
*convergent* relative frequencies, so convergence is 
not only "almost sure", but "sure". 
(The questions concern not *whether* there is convergence, 
but rather the *values* to which there is convergence.)
Denote by R_n the (random) relative frequency of "1" among 
X_1, X_2, ..., X_n: R_n = (X_1+...+X_n)/n; n=1,2,... 
and let non-random values be denoted by corresponding
lower-case symbols.
Claim:
*Every* binary sequence has a convergent relative frequency.
(It suffices to look at the non-random case, just noting
r_n = r_(n-1) + (x_n - r_(n-1))/n, hence 
|r_n - r_(n-1)| <= 1/n -> 0.)
It follows trivially that for infinite *random* sequences, 
pr("R_n converges")=pr({(x_1, x_2, ...): r_n converges})=1, 
since *every* (x_1, x_2, ...) is such that r_n converges.
Lastly, as a consequence of the Law of Large Numbers,
pr("R_n converges to t")=1 if and only if t=pr(X_i=1).
Robert E Sawyer (soen@pacbell.net)
_____________________________

Anthony Potts wrote:
> 
> On 7 Nov 1996, David L Evens wrote:
> I am doing it for my reasons. I am not leaving any failures behind me.
> After this work, it would not be any harder to work in any other field of
> research. Again, I picked HEP because of its reputation, and I am not
> about to drop down to something which I do not find as interesting.
> 
> So, people may think of me what they like. The only people I have to think
> about are myself and my fiancee. If I have a lot of people calling me a
> wanker behind my back, or a failure, or whatever, it doesn't matter.
> 
> I have done what I came to do, and now am moving on, and that's all there
> is to it.
> 
> Anthony Potts
> 
> CERN, Geneva
Take a break from it all. Spend the needed time for yourself and your
fiancee. We all must do this in our own way. When your are ready,
Science will be here for you. You will be able to start with a new vigor 
and drive. There are things on the horizon that are beyond ones wildest
dreams. Dreams are what we all are made of. We will look for your
return.
Warren York

  Hi!
  I need help with the following problem:
     I have this matrix "A"
          __          __
         |  1  3  1  4  |
     A = |  2  4  1  1  |
         |  3  5  4  2  |
         |  a  b  c  2  |
          --          --
      and it's characteristic polynom which is:
        x^4 - 11x^3 + 7x^2 + 72x - 93
   Now, what I need are the unknown matrix elements a, b and c.
  Can anyone recommend the fastest way to go about solving this
problem?
  Regards,
          Oleh.

  Hello to all of you math adorers.
  I need someone to teach me solving systems described in subject.
As the best practice is through examples, here's one:
  dx/dt - 2dy/dt + 7dx/dt = -2x + y - z
  -3dx/dt - 2dy/dt + 6x = 3x + y - 7dx/dt
  5dx/dt - 3y + 7dx/dt = -2x + 4dy/dt - z
  I'm aware of the fact that this kind of equations are solved by
integrating, but I've never met with such complicated problem as
this one (mostly I solved single equations, not systems). I guess
the first step would be changing sides for some members in the
2nd and 3rd equation (dx, dy & dt to the left), but what then?
   Stay beatiful!

If i plug Iain Mains book twenty more times he said he might get me a
free copy (not).
In Iain Main's book "Vibration and Waves in Physics" he considers the
physics of the anchored string. Now what gives me goosebumps about this
system is that it has the same frequency wavelength relationship as a
massive quanta in one dimension!
(children and mental midgets are easily impressed)
A while back i asked the readers of sci.physics to come up with a
physical system which has the same frequency wavelength relationship as
a massive quanta in 3 dimensions. Well either no one cared about my
question or they did not see it (i've been kilefiled?) ?
I think i have something now that works ?
Consider an infinite 3 dimensional system of masses and springs such
that each mass has six springs attached to it in a symmetric fashion,
and all the masses are hooked toghther by the springs and form a cubic
array. This is the system one considers as a simple model of vibrations
in solids?
Now transform the above system:
1) replace each spring with an inductor and capacitor in series,
2) each mass is replaced with one end of a capacitor and the other end
of the capacitor is grounded.
Now perturb the system at some small region (apply an oscillating
voltage at a point where one of the masses once was) for a long time
with less than some critical frequency and energy is not absorbed after
steady state is reached, but increase the frequency above the critical
value and energy propagates out of the small region?
Thanks for any help!
Homework, come up with a physical system which models (some, not all
aspects of the):
1) electron field (include spin)
2) electron-photon field (spinless electron)
3) electron-photon field (include spin)
and for extra credit,
4) quark field with and without spin.
Have fun!

In article <56c3ou$sng@r02n01.cac.psu.edu>
ale2@psu.edu (ale2) writes:
> 
> Homework, come up with a physical system which models (some, not all
> aspects of the):
> 
> 1) electron field (include spin)
> 
> 2) electron-photon field (spinless electron)
> 
> 3) electron-photon field (include spin)
> 
> and for extra credit,
> 
> 4) quark field with and without spin.
> 
> Have fun!
for extra extra credit come up with a physical system which models
(some, not all aspects of):
5) spacetime, include all fields, photon, electron, quark, weak boson,
graivton, gluon......

In article <56b965$27f@dartvax.dartmouth.edu>
Archimedes.Plutonium@dartmouth.edu (Archimedes Plutonium) writes:
> 
>  Math cannot even begin to describe quantum mechanics
i'm guessing your guess is a bad one 
> in its strange
> logic, in its breaking of causality. Even a piece of biology is bigger
> than is the whole subject of mathematics.
Were you raped by a bunch of Mathematicians late in life ?

Octavio Hector Juarez Espinosa (oj22+@andrew.cmu.edu) wrote:
: I would like to know if there are some routines in "C" or any language
: to read a matrix from disk.
: I am reading element by element (519 by 519) and delays 11 minutes.
Are you obligued to use a given format in that the matrix is stored
on disk? If not, check if your matrices are "sparse", i.e. most
entries are zero. In this case, you only have to write the
non-zero elements to disk, together with their position, i.e. you
have to write (and later to read) a sequence of triplets (i,j,a).
So writing and reading a matrix should be much faster.
: In a PC with visual basic delays 35 minutes. I would like to know if there
: are ways to speed up the process?
I'd suggest using a _programming language_ instead of VB ;->
(Forgive me, but I couldn't resist giving this silly remark ;-)
Greetings,
                                       Andreas Jung.
--
Andreas Gisbert Jung     DL9AAI Tel:0381/498-3364 Fax:0381/498-3366
Theoretische Informatik  mailto:ajung@informatik.uni-rostock.de
Universitaet Rostock     http://www.informatik.uni-rostock.de/~ajung/
PGP fingerprint =  8A 0B 05 CA EE AB 7B 01  D9 07 6A D0 84 38 BB 82

Does any one out there know about the mathematical systems used in India, 
which were replaced by current systems? I have been pointed in the 
non-western direction and know nothing. I am paricularly interested in 
their number systems and the ways in which they represented or modelled 
influence. Although they were not successful they were trying to achieve 
something and represent their beliefs - anyone know what they were?
The systems developed in the west clearly worked on the range of 
problems of contemporary interest and found a niche. And 
subsequently overshadowed all other approaches, which died off. What were 
they? Now mathematics needs to move into new areas, and the PC allows new 
approaches. I may like to take up were the East left off.
As I know nothing, any view or reference is appreciated. Please pass the 
message on to anyone interested in history of mathematics, or eastern 
mathematics.
thanks 
Trevor

Fred Galvin  writes:
>> Computer simulation, anyone? .
>
>Why? Wouldn't it be more efficient to just program your computer to
>*compute* the expected number of moves using your strategy, for each of
>the 719 nontrivial permutations? It would be somewhat harder, but still
>quite feasible (for 6 books), to compute the exact solution of the puzzle,
>i.e., the expected-number-of-moves-using-best-strategy and, of course, the
>best strategy itself. For 4 books it's a reasonable computation to do by
>hand.
My thoughts exactly.  The problem space has 720 nodes, and at each
node there are 7 arcs out (including one reflexive arc) for each of
the 6 possible choices of book, a total of 30,240 one-way arcs in all.
(In fact some of them are redundant but I suspect it's better to just
ignore that fact.)  Someone with a good head for algorithms should
easily be able to generalize Dijkstra's algorithm to find the distance
from each node to the origin (node 1-2-3-4-5-6), where "distance" is
the expected number of moves under the best strategy.  The only
complication is you have to compute the "distance" 6 times to evaluate
a single node (one for each book you might have drawn there) and take 
the arithmetic mean of these results as that node's distance.
You can then read the best strategy directly from the graph: it can be
represented as a chart with 720 (OK, 719) rows and 6 columns, one row
for each configuration you could be in and a column for each book
indicating where you should replace that book after drawing it from
that configuration (the answer will be the node that has the lowest
score of the 7 reachable nodes including the one you just came from).
Of course there could still be a little competition to see if the
table can be captured in some much more concise form, such as
maximizing the weighted score of subsequences according to some formula.
Anyone have some time to burn on this?
-- David A. Karr (dkarr@bbn.com)
   (Not necessarily representing the views of my employer)

In article <32875320.6872710@netnews.worldnet.att.net>
           draig@ix.netcom.com "Foucault" writes:
> This is a very basic, rather simple related rate problem that for some
> reason has me completely stumped.   I'm hoping that someone here might
> take a moment or so to put me on the right track.
> 
>         The problem is : A 6ft tall man walks at the rate of 5 ft/sec
> toward a 16ft high street light. At what rate is the tip of the shadow
> changing when he is 10 feet from the base of the light?
> 
>         Ok so I draw an illustration for myself.
>                 o
>                 | \
>                 |    \ 
          16ft    |       \ 
>         pole    |          \
>                 |      6ft  |\
>                 |      man  |   \
>                 |           |      \
>                 -----------------------\  <-tip of shadow
>                  10 ft.     ^
> 
>                 The mans velocity (dx/dt) is -5 ft/sec.
> 
If the man is at distance x from the bottom of the pole then
by considering the similar triangles the tip of his shadow is
at x*16/10 from the bottom of the pole. So if the man is
moving towards the pole at 5ft/sec the tip of the shadow is
moving at 5*16/10 = 8ft/sec. The fact that he is 10ft from 
the pole does not affect the answer.
Or have I missed something.
-- 
John R Guppy

In article <327FB411.167E@sgi.com> John Wilkinson  writes:
>Eric Burke wrote:
>> Solve n(n+1)/2 = N for n.
In fact you really need the least integer n such that n(n+1)/2 >= N.
>> 
>> n^2 + n - 2N = 0
>> 
>> n = floor((-1 + sqrt(1+4N)) / 2)
>>                      ^^^^
>
>
>The expression inside the sqrt should be 1+8N.
Right, and the "floor" should be a "ceil".  You need to round *up*
whenever 1+8N is not a perfect square.
ObPuzzle: Suppose you don't want to do all this math.  What's a
sure-fire algorithm that will allow you to stack the cans correctly
without any extra calculation, and without any risk that you'll have
to move a can that you've already placed because you were wrong about
needing it there?  (That is, ensure that if you have, say, only 55
cans, you don't foolishly put 11 cans in the bottom row.)
-- David A. Karr (dkarr@bbn.com)
   (Not necessarily representing the views of my employer)

Peter Jackson  writes:
> Q.  What do you get if you cross an elephant with a fridge ?
> 
> A.  Elephant fridge sin(theta).
Wrong.  Wrong wrong wrong.  You mix up vectors, their lengths and
scalars horrible, so as to make the joke rather pointless.
-- 
David Kastrup                                     Phone: +49-234-700-5570
Email: dak@neuroinformatik.ruhr-uni-bochum.de       Fax: +49-234-709-4209
Institut f=FCr Neuroinformatik, Universit=E4tsstr. 150, 44780 Bochum, Germa=
ny

Le Compte de Beaudrap  writes:
> On Fri, 8 Nov 1996, Lyle VonSpreckelsen wrote:
@> 
@> > Solve this
@> > 
@> > Three Pipes supply an oil storage tank.  The tank can be filled by
@> > pipes  A and B running for 10 hours, by pipes B and C running for 15
@> > hours, or by pipes A and C running for 20 hours.  How long does it
@> > take to fill the tank if all three pipes run?
@> > 
@> > Got my andvanced math teacher (MR. V.) stumped 
@> > 
@> > J.D
@> 
@> =09What I am about to write may look long and inelegant, but it 
@> really isn't. Read on.
@> ______________________________________________________________
@> 
@> Let       V =3D volume of tank,
@>     a, b, c =3D the "flow rates" of pipes A, B, C
@> 
@> Therefore, 10(a + b + 0) =3D V {eqn1}
@>            15(0 + b + c) =3D V {eqn2}
@>            20(a + 0 + c) =3D V {eqn3}
@> 
@> {eqn2} - {eqn1} gives:  -10a + 5b + 15c =3D 0
@>                    or        (b + 3c)/2 =3D a 
@> 
@> Substitute this into {eqn3} to get:  10(b + 3c) - 20c =3D V
@>                                 or          10b + 10c =3D V.
@> 
@> 
@> But from {eqn1}:  10a + 10b =3D V
@>   We have found:  10c + 10b =3D V
@> 
@> Therefore:  10a =3D 10c
@>        or     a =3D c.
@> 
@> Now, {eqn3} states that 20a + 20c =3D V
@>               Therefore       40a =3D V
@>                                 a =3D V/40
@>                                 c =3D V/40
@> 
@> {eqn1} states that 10a + 10b =3D V
@>          Therefore       10b =3D 3V/4
@>                            b =3D 3V/40.
@> 
@> Now that a, b, and c are known, what is the time "t" such that (a+b+c)t =
=3D V?
@> The question is now very straightforward. (5V/40)t =3D V,
@>                                                  t =3D 40/5 =3D 8.
@> 
@> Combined, the pipes fill the tank in 8h.
@> This is the most straightforward (ie, direct) way of solving the problem.
@> No more direct way can be found (please hit me if I'm wrong).
I feel free to hit you.  If I fill the tank with the three
combinations A+B, A+C *and* B+C at once, after one hour it will be
filled to 1/10 + 1/15 + 1/20 =3D 13/60.  Having only A+B+C available,
however, it will be filled half of that, 13/120.  So it will take
120/13 hours to fill it, 9 3/13 hours.
You not only get the answer wrong (if, as you claimed a=3Dc, then the
combination A+B should fill the tank in the same time as B+C, which it
doesn't), you make it *really* complicated as well.
-- 
David Kastrup                                     Phone: +49-234-700-5570
Email: dak@neuroinformatik.ruhr-uni-bochum.de       Fax: +49-234-709-4209
Institut f=FCr Neuroinformatik, Universit=E4tsstr. 150, 44780 Bochum, Germa=
ny

Judson McClendon  writes:
> Christianity is receiving Jesus as Savior and Lord. There's nothing
> about turning off your brain.
In general, many scientists are offended by the assumption present in
any spiritualism that there are things you cannot deduce with your
brain alone.
In short, they hear a constant calling: "I am the Lord, the mind.
Thou shalt have none other beside me."
Usually the zeal with which people claim that the scientific mind is
omniscient and omnipotent decreases with the level they advance to
scientifically.  They have enough work to do not care about using
science as a sort of substitute for religion, as they find they get
far less usefully and convincingly done when using science for that
than what it is good at.  Of course it is amazing what the human mind
can do, but that is a far call from claiming it is omnipotent.
-- 
David Kastrup                                     Phone: +49-234-700-5570
Email: dak@neuroinformatik.ruhr-uni-bochum.de       Fax: +49-234-709-4209
Institut f=FCr Neuroinformatik, Universit=E4tsstr. 150, 44780 Bochum, Germa=
ny

"6pt@qlink.queensu.ca" <6pt@qlink.queensu.ca> writes:
> > You are an alien life form, or you would not have been able to survive
> > in absolute vacuum.  For you the problem might be that easy, but the
> > average golfer has to fight something like "air resistance" which will
> > let the average golfball not fly perfect parabolas.
> > 
> > --
> > David Kastrup                                   
> Eat a dick, asshole.
Good lord, a *hostile* alien life form!
-- 
David Kastrup                                     Phone: +49-234-700-5570
Email: dak@neuroinformatik.ruhr-uni-bochum.de       Fax: +49-234-709-4209
Institut f=FCr Neuroinformatik, Universit=E4tsstr. 150, 44780 Bochum, Germa=
ny

Do any one know if there is a C program can
do Fixed-Point Sqrt() ?
Thank you in advance.       

Hitech wrote:
> 
>  e^(i pi) = - 1
> e^(2i pi) = 1
>     2i pi = ln(1)
>     2i pi = 0
>   -4 pi^2 = 0
>      pi^2 = 0
>        pi = 0
> 
> therefore,
> 
> e^(i pi) + 1 = 0   is false
> 
> Where did I go wrong?
You've only taken the real part of ln(1):
For complex z:
ln(z) = ln |z| + i arg(z)
For z = 1 
	ln(z) = ln|1| + i (2n pi) (n = ...-2, -1, 0, 1, 2...)
	      = 0     + i (2n pi)
	      = i (2n pi)
For the principal value, n = 1
Therefore 
	ln(1) = i (2 pi)
which matches the Left Hand Side
Paul Lloyd

Dino Kermelek (dkermel@antun.gtfvz.hr) wrote:
:   Hello to all of you math adorers.
:   I need someone to teach me solving systems described in subject.
: As the best practice is through examples, here's one:
:   dx/dt - 2dy/dt + 7dx/dt = -2x + y - z
:   -3dx/dt - 2dy/dt + 6x = 3x + y - 7dx/dt
:   5dx/dt - 3y + 7dx/dt = -2x + 4dy/dt - z
:   I'm aware of the fact that this kind of equations are solved by
: integrating, but I've never met with such complicated problem as
: this one (mostly I solved single equations, not systems). I guess
: the first step would be changing sides for some members in the
: 2nd and 3rd equation (dx, dy & dt to the left), but what then?
Rewrite this system as 
		  A (x',y',z') = f(x,y,z),      (*)
where A is a matrix, (x'=dx/dt and so on), f a function returning the
right hand side (which now only depends on x,y,z). 
Now check whether the matrix A is invertible or not (e.g. by computing
det(A)).
If A is invertible, you can rewrite (*) as
	       (x',y',z') = A^{-1}f(x,y,z),       (**)
(A^{-1} means the inverse matrix of A).  You can solve this system by
standard means (look for "linear systems with constant coefficients").
If A is not invertible, you will find that x,y,z on the hand side must
satisfy some condition (some linear combination of them has to be 0 --
since f will turn out to be linear) so that the equation
			 A(a,b,c) = f(x,y,z)
is solvable for (a,b,c).  [I.e. f(x,y,z) must be in the range of A.]
Find this condition, and use it to replace some of the x,y,z by an
expression involving the other(s).  Now either you have found that
there is only the trivial solution or you have reduced (*) to a system
with one or two variables/equations, with another 'A' and another 'f'.
This new 'A' should be invertible and you now are in the situation of
(**).
Best regards,
  Dirk 
--
    Dirk Alboth, Mathematics Dept., Paderborn University
    33095 Paderborn, Germany

Howdy,
	I just received a new GPS receiver, which is a box the size of a
handheld calculator which will let me know exactly where I am and what
time it is (Ain't technology great!)
	Being the curious sort, I'm trying to figure out the math involved.  I
have the basic idea, but the method for solving the system of equations
I end up with has deserted me sometime since college.
	Basics:
	24 satellites are circling the earth each broadcasting their position
and the current time.
	It supposedly takes reception from 4 satellites to derive position and
current time. More satellites can be tracked to reduce the error.
	Receiver requires an accurate clock, although not necessarily one which
has been accurately set.
	I only am interested in solving in a "generic" X,Y,Z space.  I have a
fairly good idea how to convert results to latitude/longitude and
altitude above the earth.
	Definitions:
	Da = Distance from unknown to Satellite a
	Da = sqrt( (X-Xa)^2 + (Y-Ya)^2 + (Z - Za)^2 )
	Ta = Time broadcast from Satellite a with position information
	Ra = Receiver time when broadcast from Satellite a received
	Vs = Velocity of radio signal
	It appears that once you solve X, Y, and Z that time is known, i.e.
once you know Da, Ra should equal Ta + (Da / Vs).  The difference
between actual Ra and calculated Ra is the offset for adjusting the
clock.
	I think I understand the problems with "bad" satellite geometry, let's
assume the ideal (which supposed is one satellite straight overhead,
with the remaining 3 equally spaced out around you just above the
horizon.)
	Partial Solution:
	(Da - Db) = [(Ra - Rb) - (Ta - Tb)] * Vs
	(Da - Dc) = [(Ra - Rc) - (Ta - Tc)] * Vs
	(Da - Dd) = [(Ra - Rd) - (Ta - Td)] * Vs
	for satellites a, b, c, and d.
	Once I plug in the long form of D equation, I'm stumped.  Can anyone
show me how to solve such a system of equations in terms of X, Y, and Z?
	Thanks for all the help.  E-mail replies would be appreciated, I don't
get to read the newsgroup as often as I'd like!
	Thanks again,
	Jeff
	jeffh@streek.com

Le Compte de Beaudrap wrote:
> 
> On Fri, 8 Nov 1996, JC wrote:
> 
> > Bob Silverman wrote:
> > >
> > > Juilan Au  wrote:
> > >
> > > >Hi,
> > >
> > > >Could you pleased tell me the name of a fraction of which the
> > > >numerator is greater than the denumerator? Thanks!
> > >
> > > Rational.
> > >
> > > No other name is needed. I aim this concept at elementary teachers who, for some
> > > reason, think it necessary to divide fractions into 'proper' and 'improper'.
> > > This distinction is meaningless.
> >
> > No it isn't. If it was meaningless, there wouldn't be a word
> > making the distinction. Just because you're a numerical purist
> > doesn't mean everybody has to be.
> >
> 
>         Granted that we need people who think the name "improper
> fraction" is improtant to make the world an interesting and better place ;) ,
> name one instance where it is very important that the class of
> fraction known as "improper fractions" have a name particular to
> themselves. In other words, if it is imortant that they have a name, then
> please tell us, /why/ is it important?
> 
I already have done in a previous post

Hi,
Could someone out there explain exacly what a confidence interval
mathematically measures? 
I understand what it is trying to
measure:
        the likely hood that the expectation of a random variable on the
        entire space is within
        a spcified interval.
        The specified interval is often chosen to be symmetrical about the
        expectation of a sampling of the random variable.
Please respond via email.  
Thanks so much!
--- Chris

In article <56b5lj$kvt@lyra.csx.cam.ac.uk>, I wrote
>In article <563g2p$4e6@q.seanet.com>, ksbrown@seanet.com (Kevin Brown) writes:
>[...]
>|> 
>|> In general I think these expansions can be generated from partitions
>|> of any odd abundant number. 
>
>In the nomenclature of UPiNT this conjecture is "every odd abundant number
>is pseudoperfect", or even more charmingly "there are no odd weird numbers".
>[A weird number is a primitive abundant number that is not pseudoperfect.]
>Sadly, this seems too good to be true... Counterexample, anyone?
Well, now I have UPiNT in front of me {moral: never post without it...] I
should correct this: primitiveness is not required for weirdness. Still,
"no odd primitive weird numbers" <=> "no odd weird numbers", obviously.
The existence of odd weird numbers is said to be open by UPiNT, but the
Erdos prize for settling this is a mere $10. Nothing much seems to have 
changed between the 1982 and 1994 editions, or indeed since:
  S.J. Benkoski & P. Erdos
  On weird and pseudoperfect numbers
  Math. Comp. 28 (1974) 617-623   + corrigendum 29 (1975) 673
Chris Thompson
Email: cet1@cam.ac.uk

How to calculate the dimensions of a square whose diagonal is 35mm
longer than the sides