mm-4519
===
Subject: Re: Textbook comments request (Hungerford's Algebra)
Has the expected level of competence at the undergraduate level 
decreased? I was not a mathematics major, but took algebra out of 
Herstein, and considered it par for the course, as did everyone 
else.  
By the way, it was one of the best elective classes I ever took 
for the short and long term benefits conferred. As a programmer I 
was always puzzled at the antipathy to mathematics manifested by 
other programmers.
-- 
Michael Press
===
Subject: On the level of undergraduate training on mathematics (was: Re: 
Textbook
 comments request (Hungerford's Algebra))
I don't know if it has decreased or not, but one thing that was mentioned by 

a 
friend of mine that has taught at the University of Ohio and University of 
Tennessee is that while our (brazilian) undergraduate courses cover deeper 
aspects than what is covered by undergraduate courses in the US, people 
usually 
make graduate students sweat a lot to get their degree, basically nullifying 

the 
difference in the degrees obtained at a Ph.D. level.
Oh, BTW, one cultural difference that I see is that a Master's degree in the 

US 
is mostly taken as a consolation prize for those that can't get a Ph.D. 
degree. Is that impression of mine correct?
Here, a Master's degree is almost *required* to enter a Doctorate level 
program 
and going the Doctorate level is really not the norm here (quite a few 
exceptions I'd add) and it can even touch quite a bit of research (at least, 

mine did).
Indeed, I'd say that Abstract Algebra is absolutely essential for developing 

the 
formal, *mathematical thinking* that one should have for writing elegant 
programs.
You can't really imagine how many headaches I get when I try to give a 
stronger 
mathematical bias when I'm teaching Analysis of Algorithms or Elementary 
Graph 
Theory.
And that ruins all the beauty of intelligent, elegantly devised algorithms. 

:-(
-- 
Rog.8erio Brito : rbrito@ime.usp.br : http://www.ime.usp.br/~rbrito
Homepage of the algorithms package : http://algorithms.berlios.de
Homepage on freshmeat:  http://freshmeat.net/projects/algorithms/
===
Subject: Re: IM style (off topic)
and built it into the program . SAVED (dot saved), a kind of shell.
It built on supervisor primitives provided by Bob Fenichel; we
provided the user interface.  (The SDC timesharing system had a
similar feature allowing communication between the user and operator
but I don't know if it worked for user to user.)  We had abbreviation
conventions, nothing like ROFL, but people would say (over) to
indicate they were waiting for a reply.  later this was shortened to
-o- or similar, and o/o meant over and out as in radio.
===
Subject: Re: Estimating the number of great white sharks
Given any value of n, it is taken that the sum of probabilities 
(expected value) is equal to one when a tagged shark is caught. Of 
course this is the theoretical mean of a probability distribution.
For example: say n = 7.
Then 0/N + 1/N + 2/N + 3/N + 4/N + 5/N + 6/N = 1
21/N = 1
N = 21
This is equal the sum of the numerators of the progression which can be 
written as Sum = 7^2/2 - 7/2 = 24.5 - 3.5 = 21
Hence N = n^2/2 - n/2 seems to work fine.
Phil H
===
Subject: Re: Reciprocals of the natural numbers
Yeah, that's my proof too, but a tad messy. I was looking for a neat
-- if slightly sophisticated -- proof.
===
Subject: Re: Reciprocals of the natural numbers
With H n := 1 + 1/2 + 1/3 + ... 1/n, write
          2*3...n + 1*3...n + 1*2*4...n + 1*2...(n-1)
   H n =  -------------------------------------------
                             n!
Let p be the largest prime less than or equal to n.  Then p divides n!
and also every term in the numerator with the single exception of
 
===
Subject: Re: Reciprocals of the natural numbers
Yeah, Betrand's postulate does give a proof.(the desired p lies
between N and N/2) But again, Bertrand's postulate is proved rather
computationally. I'm looking for a proof that's algebraic, maybe
something using arithmetic functions or even something sophisticated
like group theory but at any rate avoiding the use of the order
property. The first proof given also depends on the fact that 2 is the
smallest prime. I want to avoid using the order property.
===
Subject: Re: Reciprocals of the natural numbers
[ ... ]
[ ... ]
I thought the basic idea of the proof can be expressed as: 
If the set {1,2,...,n} contains two numbers divisible by 2^k, 
then it contains a number divisible by 2^(k+1); 
with conclusion that given n, there is an exponent k 
such that exactly one of the numbers {1,2,...,n} is divisible by 2^k. 
I'd say, this proof does not rely on the order property, 
but rather on the fact that 1+1=2. (Really!) 
===
Subject: Re: Reciprocals of the natural numbers
Okay -- the way I interpreted it when I proved it was that if 2^k
divides  another number in the given range the number is of the form
a*(2^k)where a is at least 2. Thus the number is not in the given
range, i.e between 2^k and 2^(k+1). Actually the proof works for any
prime<n. For any prime, the number of multiples of p^r strictly less
than p^(r+1) is less than p. The other details are a simple exercise
in finite field theory.  But anyway, when I said algebraic proof I
meant something somewhat multiplicative rather than additive, which
doesn't depend on size or order, maybe something using arithmetic
functions, group representations, Galois theory, even combinatorics,
something that is not so ...elementary number theoretic, but at the
same time isn't analytic computational -- a proof that Jean Pierre
Serre might give (his Course in Arithmetic (algebraic part) is full of
proofs of the sort I have in mind -- consider his proof that sigma(phi
(d) ) as d ranges over the divisors of n is n.) I don't know why I
think there should be such a proof, but I do.
===
Subject: Re: Reciprocals of the natural numbers
That shows that you have fewer than p numbers in the numerator which
are not divisible by p. Proving that their sum is not divisible by p
seems difficult. Actually, take n = 6. LCM (1, 2, 3, 4, 5, 6) = 60.
Take p = 3. 60/3 = 20, 60/6 = 10, 20 + 10 is divisible by 3, so it is
wrong.
===
Subject: Re: Reciprocals of the natural numbers
Yeah, you're right. I must have calculated on the non-p component of
the lcm remaining constant in the numerator. But it doesn't. You have
to take 2  as the prime.
===
Subject: Re: Reciprocals of the natural numbers
You've got the wrong r. If you're looking at 60, then r=3.
     
However, the fact that 1+2=3 means that p=3 fails to provide 
proof anyway. 1+2+3+4=2*5 kills 5 similarly. You need to make p 
Phil
.
===
Subject: Re: Are L^p spaces separable?
You mean trigonometric polynomials?
How can we take countable polynomials?
===
Subject: Re: Are L^p spaces separable?
Use rational coefficients.
===
Subject: Re: Are L^p spaces separable?
===
Subject: Re: Why I seldom reply to Sci Math
$#it & flies, well that's one way to put it I suppose.
It would be fine if the twits did get rid of only themselves, but in case 
you are not from this planet, the suicide bombers in Iraq are killing 
thousands of innocents along with themselves like that Cho demon at Virginia 

Tech did.
===
Subject: Re: Why I seldom reply to Sci Math
I thought you were all about flying saucers, anti-gravuty, etc.
When did you suddenly become interested in the real world?
===
Subject: Re: Why I seldom reply to Sci Math
Look you little smarty pants wipe the snot from your nose and tell Mama to 
change your diaper. There are more things in heaven and earth than are 
dream't of in your philofawzy Holmes. Wake up and smell the coffee and don't 

impose your Liliputian narrow-minded Philistinisms on one greater more 
experienced and much better educated than you are. Try to learn something of 

value. You 'thought? That's a joke. You have not yet even learned how to 
think.
===
Subject: Re: Why I seldom reply to Sci Math
Ever heard the story of how I got promoted from
the 2 of Clubs
to the Ace of Clubs? By getting two Internet cranks
to foam at the mouth on the same day? One of them
was Tom Potter. Getting him to put down his rubber
stamp and reply is quite an accomplishment. Is he
one of your crackpot friends like Beckwith? Any other
criminals you hang with? Do you crackpots have a
club like the BigIQ guys? Or maybe the BigIQ club
IS where you all get to know each other?
===
Subject: A Harried Potter
I have not heard any stories about you nor am I interested in hearing any. 
You have a small mean-spirited mind and are obviously quite ignorant of 
mathematics and physics. I never heard of the fellow you mentioned 
Potter? Isn't he a magician in some novel or other? - and I certainly 
would never join any Club that invited me. ;-) (Attributed to Groucho 
Marx and also Woody Allen).
===
Subject: Re: A Harried Potter
If you don't read sci.math, why do you
cross-post your prattle here? No one
invited you to this Club but you took
it upon yourself to join anyway.
===
Subject: Re: A Harried Potter
Sci Math is an open forum. It's not your private club. You are a 
mean-spirited fool a know-nothing who gets off on committing near hate 
crimes 
on the web. You are a Troll. You have nothing original or creative to say in 

math or in anything. You have a miserable life where all you can do is smear 

creative people who dare to venture out of the box with educated disciplined 

thinking. You think because you do not understand what you read that there 
is 
nothing to understand. You are a creep who hides under an alias. What 
degrees 
do you hold in math or in anything? You are a poseur a complete phony. Crawl 

back under your rock. Change crawl to slither.
===
Subject: Re: A Harried Potter
Nevertheless, crackpot physics is off-topic here.
Nevertheless, you are unwelcome here.
Is that what you call it? Why don't you add terrorist also?
Ok, I admit I don't suffer fools gladly.
How would you know? You don't read sci.math, you just cross-post
your prattle here.
Is that how crackpots view themselves?
But OTOH, just because I think that way doesn't mean there IS
something
to understand. What were your flying saucers powered by before you
heard
about dark energy? You must have been wrong back then, eh?
I already told you I'm Canaan Banana, not hiding at all.
Degrees aren't necessary, math truth is self-evident.
But I'm not a sociopath like your friend Beckwith.
Go back to sci,physics where you belong.
===
Subject: Re: A Harried Potter
Look you pretentious poseur. How dare you label my work crackpot? You 
hide behind an alias. You're a creep. I am having real conversations here on 

the physics with at least two intelligent people who actually know something 

and are not limited to the kind of flaming which is all you are capable of. 

This is an open forum last I heard and you are out of line. You admit you 
have no degrees in math or physics. You are what you accuse me of. Stay 
under 
your rock and continue to hide your ID like the coward you are.
===
Subject: Re: A Harried Potter
What is it you think I'm pretending to be?
I never said I was a mathematician.
I never falsely claimed to have a math degree.
These would appear to be delusions on your part.
There's no other way to describe History of discovery of flying
suacer
zero point energy warp drive, is there?
You only think that because you're too lazy to look.
Which doesn't affect anything I said, does it?
Are you really that stupid that you can't tell they're stringing you
along?
And I thought _I_ was cruel.
You heard wrong.
It's not open to crackpot physics.
You didn't mention engineering.
As I said, I don't need a degree in math. To sociopaths like Beckwith,
a physics degree is just a license to lie and cheat. What's your
degree?
That doesn't change _your_ problem, does it?
If I stay under a rock, what's the point of hiding my ID?
Of course, not being a mathematician, you don't have a
clue about basic logic, do you?
===
Subject: Re: A Harried Potter
you have pretended you are good at
   getting Internet cranks 
you aren't
that's a great example!
so
  other than the provocative title
did you have objections to the concept of casimir drives?
i actually have some concerns about such a programme
  based on some symmetry arguments
that are therefore model-dependent and don't apply in some of the
torsion models
but what about yourself?
i noticed that jack was actually asking for  authenticated
documentation 
  on several claims made
and generally just discussed physical models in that thread
did you not read past the title?
you said something relevant
i don't know the referent to  they 
  but i am not stringing jack along
i have followed jack's work for some time
  ever since my own interest in foundations began intersecting
  some of those he researches and who likewise research him
also
  i have known of non-technical references going back to the 70's
  including a well-known author that recently passed away
who spoke vehemently against the growing fundamentalism in science and
society
sarfatti has a very wide view of foundational and mathematical physics
  and anyone sincerely interested in such things
should at least follow his reference-graph
of course he makes wild speculation
  and of course there are many differences between what i see as
interesting paths
  and what he sees as interesting paths
that is what it means to do original research
disagreement
debate
and one's own direction
well
  not necessarily open-minded
but no one can stop anyone from posting here
unless physical force and the law are involved
that statement of yours does go straight to dishonesty claims...
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
===
Subject: Re: A Harried Potter
Yes, Galathaea has it pretty much right. He is in balance. In any case 
people who are not interested are not forced to read messages.
Fact of the matter is very powerful people track my thoughts and are 
interested in my opinions which in the past have affected major policy 
decisions at the White House level.
All of these exchanges are tracked by intelligence agents from several 
nations.
I am paid to think outside the box.
Disciplined speculation is part of my job.
On UFOs & paranormal there are a lot of nuts, kooks & frauds to be sure, but 

there is a core of serious scientists as well and a good fraction of them 
are 
involved in national security issues.
UFOs and the paranormal have to do with fundamental unsolved problems in the 

foundations of physics.
I do not present my physics ideas as some kind of religious revelation of 
absolute truth like many real crackpots do.
Sometimes I am wrong, and sometimes worse I am not even wrong. I have been 
right on some major physics issues such as the prediction of supersolid 
helium that I did in 1969 in a peer reviewed physic journal months before 
Tony Leggett's paper. All this is in my book Super Cosmos (on Amazon) 
including a photostat of the original paper with comments by some well known 

mainstream physicists.
Part of the reason I post to these forums is to ID talent that the national 

security apparatus may be interested in  using. One never knows what 
Schrodinger's Cat may drag in from Cyberspace.
===
Subject: Re: A Harried Potter
Managed to get a hair up Sarfatti's ass, though.
No.
Not my field.
Except when he said: essential to how the alien ET flying saucers
work!
What makes you think I haven't?
The two intelligent people.
Maybe you're not one of them.
Who's funding your work?
Is that what you call it? I call it intolerance of crackpots.
Don't make me laugh.
So you agree he's a crackpot.
Too bad truth is one of those paths.
No, it doesn't. Original crap is still crap.
Tell me about it.
It says right in the listing that sci.math is for
Mathematical discussions and pursuits.
No flying saucers.
No zero point energy.
No casimir drives.
No aliens.
Which one am I speaking to?
===
Subject: Re: A Harried Potter
mensanator :
you just proved to the world what a complete crackpot you are
you don't even understand basic quantum mechanics
  and yet you feel qualified to pass judgement here
you are a very sad person
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
===
Subject: Ignore the Talentless Trolls
I played along to see if Menstruator had any real intelligence. He doesn't 
so from now on I will ignore him. Best not to get sucked into his 
negativity. 
He only feels alive when he attacks creative people since he has no good 
original ideas of his own that the best and the brightest would find 
interesting. So this is the last I will comment on silly provocations from 
talentless Trolls.
===
Subject: Re: A Harried Potter
Really? What did I say that was wrong?
No need to.
I'm not passing judgement, I'm telling you to take it to sci.physics
where it belongs.
Doesn't anybody here understand English?
===
Subject: Re: A Harried Potter
Look Genius US Government is very interested in saucers. There are a lot 
of people working on the problem. You are an ignorant know it all. No one 
cares what you think about this. It makes no difference. If you ever have 
anything intelligent to say then say it. Otherwise get lost and keep you 
hostility to yourself. 
Frankly I am not interested enough in you to bother to find out who you are. 

You are like an annoying mosquito buzzing around. I do not spend a lot of 
time reading your insults. You seem to be some self-taught computer nerd who 

thinks he is smarter than he or she really is and does not have a good sense 

of what is important to serious people with a lot of power and money who 
control your destiny whether you like it or not.
You are not qualified to judge what is crackpot physics. I am licensed 
to do physics from State of California - PhD from University of California 
and you are the charlatan the imposter here. You are out of line.
If there is something specific in the physics messages I post then say 
something to the point, otherwise keep your narrow minded verbal abuses to 
yourself as they border on hate-crime when not intended humorously.
===
Subject: Re: A Harried Potter
Sure, the US Government is interested in all sorts of ways to
steal tax money and funnel it to Republican businessmen.
At least with saucer research, no one has to actually have
a working product like the weapon designers do. What a cushy
gig. So why are you working so hard to publicise this scam?
Don't the saucer researchers want you to shut up and quit
focusing attention on their crimes?
Who's paying them?
That's an oxymoron. Perhaps you meant someone who _thinks_
he's a know it all when actually ignorant. Your degree wasn't in
English, eh?
Like anyone cares what _you_ think.
That's for sure.
Why? This is fun.
Ooga-booga-boo!
Fine. Then shut the  up about it.
You wouldn't know it from this thread. What's the matter, today a slow
day amongst your serious correspondents?
Not only thinks, but is.
Uh, that doesn't include you, does it?
Except in your case.
Do you also have a flying saucer driver's license?
You keep saying that. What have I claimed that's untrue?
In what way? Do you see me over in sci.physics? No, I only post
to sci.math, rec.puzzles, comp.programming, comp.lang.python,
alt.math, alt.math.recreational and alt.folklore.computers where
I am always on-topic. You can't make such a claim, can you?
I did. I replied to the post where you called everyone
mean-spirited cowardly midget-minds.
That was physics, wasn't it? I wouldn't know, I don't have a physics
degree.
You know that saying midget makes you guilty of a hate crime, don't
you?
Ha ha ha ha ha ha ha ha ha!
===
Subject: Re: Probably haven't seen this one, but...
Ah. You were talking about the peaks of |sin(Mx)/sin(x)|, and so of course,
as you say, parity of M doesn't matter.
But Matt had mentioned the first extreme value of U_m(x) after x=0 and
so I had mistakenly thought that you too were talking about the extrema
of U_M(x).
David
===
Subject: Re: a square?
For a and b integers, a*b is a square for any of the following:
a = b
a = 0
b = 0
Therefore in your case:
Hence the solution is m = {-7, -2, 2, 3}.
HTH
Antonio
===
Subject: Re: a square?
that is the case, only if a and b are coprimes, for other non coprime
ordered pairs, it must not be valid.
example- 3 x 12 =36
===
Subject: Re: a square?
Hi Divij,
as already pointed out above, the solution that I proposed is not
general enough for non coprime factors. I mistakenly assumed that the
OP was asking a middle/high school question for a quadratic equation
problem and provided an answer accordingly. I realized that making
this assumption was wrong after I took a look at Kent's other
questions in sci.math. I came back to this thread but sttscitrans had
already provided a proper solution. :)
Antonio
===
Subject: Re: a square?
What about a = c and b = c*d^2, in which case a*b = (c*d)^2?
Requiring that either a = b or one of them is zero is too
restrictive.
- MO
===
Subject: Re: a square?
Yes, but you really only need to consider the cases
GCD[(-4m+17),(m^2-4) ] =1
so (-4m+17) = x^2, (m^2-4) =y^2
and
so (-4m+17) = kx^2, (m^2-4) =ky^2
as some prime divides k this implies
1) -4m+17  == 0 mod p
2) m^2-4 == 0 mod p
Substitute in original and use fact that
 finite number of solutions.
===
Subject: Re: Equivalence between the geometric and analytic definitions of 
cosine
===
Subject: Algebra help in a diffy-q
Is this correct?
1. dP/dt=.05P
2. dP/P=.05dt
3. ln P=.05t+C
4. P=e^(.05t)+e^C
5. P=Ce^(.05t)
===
Subject: Re: Algebra help in a diffy-q
Your problem is the step from 3 to 4.
Given ln(P)  = .05*t+C
one's next equations is P = e^( .05*t + C ) = e^C * e^(.05*t)
But e^C is a constant, which one can call, say, C_1.
===
Subject: Re: Algebra help in a diffy-q
===
Subject: Re: Reversing a helmholtz formula
According to the Wikipedia page
http://en.wikipedia.org/wiki/Helmholtz_resonance ,
the resonant frequency is given by:
Frequency = Sqrt(Area/(Volume*Length))*(Sound/(Pi*2)) ,
which seems to agree with your
    Volume = (Area/Length)*(Sound/((Pi*2)*Frequency))^2  'Reversed
David Bernier
===
Subject: Re: Reversing a helmholtz formula
Which, I guess means good news and bad news.
Good news, I did get the actual formula figured out...
Bad news, I did something else to make my answers fail to match.
===
Subject: Re: Reversing a helmholtz formula
I'm getting yet a third answer to this, so I wanted to re-appeal for
help.
===
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===
Subject: Serially Factoring large prime numbers --- Shor's algorithm
 modification
I'm sorry I got carried away.
I believe Shor's algorithm uses a quantum computer to factor large prime 
numbers product.  To crack the RSA algorithm you need to factor the product 

of two large prime numbers.
Now for that you do not need a large number of qubits quantum computer.
Dwave Systems (http://www.dwavesys.com) claims it has a 16 bit quantum 
computer.
How does one use that 16 bit quantum computer to factor large prime numbers 

to crack the RSA algorithm (or indeed even a small number of bits quantum 
computer which has say 10^300 states which is larger than the number of 
protons in the entire known Universe).
You can get Shor's algorithm from Wikipedia or arxiv.org
Take a look at Grover's algorithm too.
1. Use a recursive, output-feedforward algorithm as below.
1. Feed the problem into the X qubit quantum computer.
2. When the X qubits settle down, you have obtained the first X bits of the 

solution.
RECURSION, FEED-FORWARD
1A. Feed the problem into the X qubit quantum computer along with the 
first X bits of the solution.
1B. When the X qubits settle down you have obtained the second X qubits of 
the solution.
RECURSION, Feed-forward
1C. Feed the problem into the X qubit quantum computer along with the 
first X qubits of the solution and the second X qubits of the solution.
2C. When the X qubits settle down you have obtained the third X qubits of 
the solution.
Repeat the recursion and feedforward above until the entire solution is 
obtained.
Erach
===
Subject: Re: I don't mind the Axiom of Choice.
I like the axiom of choice as a friend.
===
Subject: Re: I don't mind the Axiom of Choice.
Story of my life.
===
Subject: Re: I don't mind the Axiom of Choice.
I probably have always misunderstood the axiom but I just
don't see all the fuss. It's obvious to me [ ((: ] that any
time you create a set you know what's in it (you have a
list)--if so, it should be easy (in principle) to tag each
member with a yellow sticky note, and write an identifying
integer on it. Then it's a simple matter to choose how to
order the elements, i.e., numerically. Could I possibly be
wrong? :)        ...tonyC
===
Subject: Re: I don't mind the Axiom of Choice.
That is true only for finite  sets. Let us assume all our sets are
finite for convenience.
)--if so, it should be easy (in principle) to tag each
For any finite set there are many injections from the set to N.
Assuming your strategy for the choice function is to take for each set
injection, first that involves a choice of f for each S andf or
arbitrarily many Ss this assumes the axiom of choice. The real problem
with the axiom of choice is that there may be arbitrarily many -- read
uncountably many --sets. The cardinality of the individual sets is not
a problem so long as they are non-empty.  The axiom of countable
choice, i.e for countably many sets is as far as we can go without
needing a specific axiom.
===
Subject: Re: I don't mind the Axiom of Choice.
.  The axiom of countable
Actually, I'm not sure the axiom of countable choice is a theorem in
the ZF axioms. Is it?
===
Subject: Re: I don't mind the Axiom of Choice.
|Actually, I'm not sure the axiom of countable choice is a theorem in
|the ZF axioms. Is it?
As you indicated, choice for a finite family of nonempty sets
is provable in ZF. (It's provable by induction on the number
of sets.) But countable choice isn't.
In one way, CC is much less of an assumption because it's
constructive (at least by many people's notion of constructive). A
constructive proof that each of X0, X1, ... has an element in it gives
you a way to construct an element of X_n for each n, which is what
a constructive proof of the existence of a choice sequence
x0, x1,... is.
The reason why the usual axiom of choice is nonconstructive is that
there can be distinct ways of representing the sets in the family, and
no method of reducing them to a canonical representation. A
constructive proof that the members of the family have elements gives
you a way of finding an element in each one, but if you are given two
representations of the same set in the family, there's no guarantee
that the elements you construct in it are going to be the same. In the
case of CC or DC, this problem doesn't arise, because each member of
the family X_n has a canonical label, n. If you want a choice function
f such that for each nonempty set of reals S, f(S) is a member of S,
it's a different story entirely. There seems to be no good reason to
expect that such a function is definable in the usual language of
set theory. If ZFC is consistent, then it's consistent that there is
such
a definition, but if I remember correctly, with somewhat stronger
assumptions commonly liked by set theorists, one can prove there
isn't one.
Keith Ramsay
===
Subject: Re: I don't mind the Axiom of Choice.
Assuming you are serious, yes.
If you have a list - or can tag each member with a unique positive integer - 

then its a countable set, and you don't need the Axiom of Choice. You just 
choose the first item in the list, or the one with the lowest number. 
That 
is an explicit choice function, so you don't need the Axiom of Choice.
But how are you going to form a list of the elements of R, or tag them all 
with a unique integer?
(BTW, ordering the elements isn't enough to provide choice. The set of Reals 

(0,1] is easily ordered, but has no smallest element. You need a 
well-ordering, ie one where every non-empty subset has a smallest element).
===
Subject: Re: I don't mind the Axiom of Choice.
How do you feel about Grothendieck's universe axiom?
===
Subject: Re: I don't mind the Axiom of Choice.
For what it's worth, I'm happy with any number of small large cardinal 
axioms.
-- 
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
Wovon man nicht sprechen kann, daruber muss man schweigen
 - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
===
Subject: Re: Proving an Ellipse can be Parameterized
Cc:  drmwecker@gmail.com
Try this argument...
First, you want 2 pi, not pi.
usual.
Second, yes, it is true.
Given any point (x, y) on ellipse x^2/a^2 + y^2/b^2 = 1, you seek the
preimage value t that yields (x, y).
If a = b, then t equals in measure the central angle of the circle
that you would have.
Because abs(x) <= a, the number x/a satisfies -1 <= x/a <= 1.
Therefore, we may write x/a = cos(t) for some t to be determined.
Now, t is either arccos(x/a), or arccos(x/a) + pi, depending on
quadrant.
In either case, there will be two values for y=a*sin(t) (unless we're
at a vertex).
One of the two is the required y.
Mike
Dr. Michael W. Ecker
Associate Professor of Mathematics
Pennsylvania State University
Wilkes-Barre Campus
Lehman, PA 18627
===
Subject: Re: Proving an Ellipse can be Parameterized
Are you suggesting that there is an assumption that my parameter should
pi - arctan(x/a,y/b) works without the extra step of determining the
quadrant. 
The way I see it, there are two values of y for each x, but that really
doesn't come into play, because we assume we have a solution set for F(x,y)
= x^2/a^2 + y^2/b^2 - 1 = 0, before we try to prove the curve defined by
F(x,y) = 0 can be parameterized by S(t) = (a sin t, b cos t).  Going the
other way, evaluating S(t) will always provide a unique ordered pair from
the domain of F.  I am, of course, assuming that it is meaningful to talk
about the domain of F as a set of ordered pairs.
 
My question was more about proving that the solution set for F(x,y)=0 is 
a
curve which can be parameterized.  Perhaps it is the inverse function
theorem I am after?  In that case, I probably have to treat the x
intercepts differently than the other points.  I think that what am really
after (now that I have refined my thinking a bit) is whether using the
inverse function theorem is necessary and sufficient to demonstrate the
solution set can be parameterized.
Now, /that/ may require me to treat y as a function of x and to write
something such as f(x) = b sqrt(1 - x^2/a^2) and g(x) = - f(x). Then prove
each is continuously differentiable for -a<x<a, and then argue symmetry for
the two cases where f(x) = g(x).
-- 
http://www.dailymotion.com/video/x1ek5w_wtc7-the-smoking-gun-of-911-updated
http://911research.wtc7.net
http://vehme.blogspot.com
Virtus Tutissima Cassis
===
Subject: Re: Proving an Ellipse can be Parameterized
For the ellipse your parametrization works fine.
For parametrizing the hyperbola use hyperbolic functions instead of trig 
functions
===
Subject: Re: On dreamin
the trolls don't even know themselves anymore
there was a time when the usenet trolls were intended
  young little punks trying to get their laughs
with cheap mindgames and transparent provocations
now the trolls think they are the antitrolls
they subscribe to whatever ideas are popular enough to be safe
  and spend their days mindlessly attacking
anyone that dares think independently
they build personal myths
  that they are somehow saving something precious
  as they work against any real insight
they don't dream
  because they don't want the responsibility of speculation
  the framework building and mathematical modelling
this neoteny of usenet
  a degeneration into infantilism
  and appeals to authority
as an avoidance of the complexities of the world around them
inertia is something general relativity deals with
  so it can't possibly have any connection to the zero-point
right?
general relativity is torsion free
right?
aspect and bell disproved any ability to give
right?
lorentz covariance shows there is no faster than light
right?
that desperation to be right
leads them to mock easily attackable charicatures
  so they can stay safely cocooned in their reality-tunnels
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
===
Excessive crossposting.
===
Subject: Integration of inverse!
f(x)=x+sin(x)
g(x)= inverse function of f(x)
Integrate (g(x), 0, Pi)???
===
Subject: Re: Integration of inverse!
Hint: Spivak, Calculus, page 256:
suppose f is increasing on [a,b]. Then if g=f^{-1} is the inverse of f:
Int(g(y),y=a..b)=b*g(b)-a*g(a)-Int(f(x),x=g(a)..g(b))
Applying the above lemma, you get immediately:
Int(g(y),y=0..Pi)=Pi*g(Pi)-0*g(0)-Int(x+sin(x),x=g(0)..g(Pi)).
All you need now are g(Pi) and g(0), which can both be evaluated by 
inspection
in one second.
-- 
I.N. Galidakis --- http://ioannis.virtualcomposer2000.com/
----------------------------------------------------------
There's ALWAYS a mistake somewhere
===
Subject: Re: Integration of inverse!
What have you done so far? What do you know about integrating inverses
of functions that you know how to integrate?
Jose Carlos Santos
===
Subject: Re: An exact simplification challenge - 14
It should be noted that this code produces the expression given :
P1 := proc()
local x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15,
x16, x17, x18, x19, x20, x21, x22, x23, x24;
    x1 := 2^(1/4);
    x2 := x1^2;
    x3 := 1/2*x2;
    x4 := 1/x3;
    x5 := ln(2)*(x3 - 1/2)^(1/2);
    x6 := sin(x5);
    x7 := cos(x5);
    x8 := arctan(x6/x7);
    x9 := ln((x7^2 + x6^2)*2^(2*(x3 + 1/2)^(1/2)));
    x10 := x4*(1/2*x8 + 1/4*x9);
    x11 := cos(x10);
    x12 := sin(x10);
    x13 := 1/4*ln((x11^2 + x12^2)*exp(- x4*(x8 - 1/2*x9)));
    x14 := arctan(x12/x11);
    x15 := x4*(- 1/2*x14 + x13);
    x16 := cos(x15);
    x17 := sin(x15);
    x18 := - 1/4*arctan(x17/x16);
    x19 := x1*x2;
    x20 := (-x4 + 2)^(1/2);
    x21 := (x4 + 2)^(1/2);
    x22 := ln((x16^2 + x17^2)*exp(2*x4*(1/2*x14 + x13)));
    x23 := (x21*x18 - 1/8*x22*x20)*x19;
    x24 := (cos(x23) + I*sin(x23))*exp((1/8*x22*x21 + x20*x18)*x19)
end;
P1():
or 
P2 := proc()
local x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15,
x16, x17, x18, x19, x20, x21, x22, x23, x24;
    x1 := 2^(1/4);
    x2 := x1^2;
    x3 := 1/2*x2;
    x4 := (2 + 2*x2)^(1/2);
    x5 := x2 + 1;
    x6 := 1/2*ln(2)*(-x4 + 2*x5^(1/2));
    x7 := cos(x6);
    x8 := sin(x6);
    x9 := ln((x7^2 + x8^2)*2^x4);
    x10 := arctan(x8/x7);
    x11 := 1/4*x2*(2*x10 + x9);
    x12 := cos(x11);
    x13 := sin(x11);
    x14 := 1/2*ln((x13^2 + x12^2)*exp((-2*x10 + x9)*x3));
    x15 := arctan(x13/x12);
    x16 := (-x15 + x14)*x3;
    x17 := cos(x16);
    x18 := sin(x16);
    x19 := arctan(x18/x17);
    x20 := ln((x18^2 + x17^2)*exp(x2*(x15 + x14))) + 2*x19;
    x21 := x2*x19;
    x22 := 1/8*(-2*x2 + 4)^(1/2)*x1;
    x23 := (2*x21 + x20)*x22;
    x24 := exp(x5*(-2*x21 + x20)*x22)*(cos(x23) - I*sin(x23))
end:
P2();
Simplify the trigs and arctrigs to obtain :
A:=exp(-1/8*ln(2)*(-2*2^(1/2)+4)^(1/2)*2^(1/4)*(-2*I*2^(1/2)*(2^(1/2)+1)^(1/

2)+I*2^(1/2)*(2+2*2^(1/2))^(1/2)-2^(1/2)*(2+2*2^(1/2))^(1/2)-2*(2^(1/2)+1)^(

1
/2)-2*I*(2^(1/2)+1)^(1/2)+2*I*(2+2*2^(1/2))^(1/2)));
(eval@applyop)(radnormal,1,A);
                                  2
Chris
===
Subject: Re: 1927: realism and phenomenalism in math and the sciences
< You're correct in what you deny but mistaken in what you implicitly
affirm.
I'm not sure what you think I am implicitly affirming, can you be a
little more specific?
< Perception is indeed unreliable, but not because the phenomena of
perception
< are unreliable. It is unreliable because perception is an elaborate
construct
< of phenomena and belief, and the beliefs are unreliable. That will
remain the
< case if even current beliefs are replaced by new beliefs.
That is exactly the manner in which I was implying that perception is
unreliable. Sorry for not specifying the details.
< Perception is not a window onto reality.
That was just a metaphor and not a strict definition.
< Whatever we see in the window is
< the only reality we will ever have.
It is the only reality that the mind has access to. The ego is a
thought construct within the mind. Whilst ever we are identified with
the ego we are bound to operate only within the mind. Also if we are
attached to intellectual knowledge we are also bound to operate only
within the mind.
Well, this is a bit of an assumption.
A word of warning: This following discussion may not seem like science
to some because it is not traditional empirical science, but it
conforms to the general approach of science. It rationally and
skeptically questions the beliefs that underly the empiricist
approach.
According to the traditional empiricist/materialist belief system you
are correct; there is no door. But if you think about it, beneath all
our perceptions and ideas there is 'something' that is real. In some
way we are a part of that something. When another 'something'
interacts with ourselves it manifests objects of perception within our
minds and we normally just accept those objects as being the actual
reality (commonsense realism). This is biologically programmed into us
and it is adequate for animal survival but it is not representative of
the ontological reality. By confusing the modifications of our minds
with the idea of external objects we build within our minds the
belief in a world of objects in space-time. But all we really know is
that we exist in some way, that something else exists in some way and
when these two resonate there arises phenomena within consciousness,
which we interpret as portraying a world of objects in space-time. If
one remains skeptical and does not resort to belief then one cannot
begin to talk about a physical universe. First we must reslove the
deeper issues of what is the something, what is consciousness and what
is the relationship between the something, consciousness and the world
that we experience.
ontologically real 'something' and the phenomena of the mind. If you
are identified with the mind or the ego then you are unaware of the
underlying reality that is the real you, because the mind cannot
directly grasp reality, it can only reflect it in distorted ways.
So to step through the door is to return to your Self through growing
self-awareness and the overcoming of the mind made reflections that we
so often confuse for reality. We ARE the reality so by knowing
ourselves we can know reality. This isn't a mind based intellectual
knowing, because the mind cannot go there, it is a direct knowing
through awareness and personal experience. This can later be expressed
in words and ideas but these are just cognitive reflections of
reality. It is only through pure awareness that reality can be
directly known.
The ego and vanity in man often stand in the way of his acceptance of
the position that super-ordinary consciousness, to which he is a total
stranger, can be possible for some members of the species to which he
belongs. This frame of mind is often pronounced in scholars who fondly
believe that more and more extensive knowledge of the world and its
infinitely varied phenomena provided by poring over vast libraries of
books, is the only expansion and advancement possible to the human
mind. It cannot but be repugnant to a polymath to be told that there
is a learning beyond his grasp, that the very nature of the mind can
change and can soar to normally super-sensible planes of being, which
are inaccessible to the keenest intellect, however well informed and
penetrating it might be.  (Gopi Krishna from 'The Wonder Of The
Brain')
< The best
< we can do is refurbush or reconstruct our percepts, by modifying
the
< structure of beliefs embedded in them, so that the changing scene in
the
< window becomes more predictable.
That is the first step. It clarifies illusions and confusions that
keep us looking in the wrong direction; outward into the objects of
sense perception rather than inward into the actual process of
perception and experience. To look outward is to be aware only of the
contents of consciousness and to believe that those contents are the
reality. To look inward is to clarify and develop consciousness
itself.
The first step in this clarification process is to question and
challenge naive realism or commonsense realism. To stop confusing the
objects of perception with the idea of ontologically real objects.
This is simply overcoming a biologically programmed belief as a
precondition for being able to think about things without constantly
slipping back into a naive realist, empiricist and materialist belief
system. This frees you to think clearly and skeptically about things.
There are many illusions that we succumb to because of the fundamental
constraints of our situation, because of biological evolution and
because of the historical evolution of ideas and beliefs. The process
of clarifying false ideas is the level that I mostly work on; using
skeptical intellectual analyses to clarify illusions and comprehend
the deeper nature of ourselves, the universe and existence in
general.
I cover such a vast territory that my writings are a little difficult
to approach, they don't fit neatly into any particular domain. But if
you are game, check out:
http://www.anandavala.info
: general collection of ideas to explore in your own way
http://www.anandavala.info/TASTMOTNOR/InformationSystemAnalysis.html
: a single structured discussion that leads you through the ideas
And also do a search for 'Anandavala' on usenet to see what
discussions there are...
Best Wishes :)
John Ringland
===
Subject: Re: 8-bits mantissa and 5 bits exponent
Sorry for the double post; it seems that Google was playing some
tricks on me...
F. Berisha
===
Subject: Book - Hadamard transform etc.
===
Subject: Re: I'm study numerical analysis,can anyone recommend some books?
This book is for you:
Numerical Methods that Work by Forman S. Acton. He covers various 
methods, but more importantly he conveys how to approach a problem 
and talks much good sense.
-- 
Michael Press
===
Subject: Help! What is meant by Linear? and is   e^x + e^y=0  linear ?
Hi there
Like what the subject says:
(1) What is meant by Linear?
(2) Is   e^x + e^y=0  Linear ?
cheers
Ben
===
Subject: Re: Help! What is meant by Linear? and is e^x + e^y=0 linear ?
People have replied with the definition of a linear function.
An equation is said to be linear if the set of its solutions is closed
under addition and scalar multiplication.  So the question is the
following:
Is it the case that, whenever e^x1 + e^y1 = 0 and e^x2 + e^y2 = 0 and
a,b are real numbers, that e^(ax1+bx2) + e^(ay1+by2) = 0?
That is, if (x1,y1) and (x2,y2) are solutions of the equation you
give, is a(x1,y1)+b(x2,y2) = (ax1+bx2, ay1+by2) always a solution as
well?
I think you can figure out the answer for yourself.  (Pick a few
values for x1,x2,y1,y2,a,b and see if they work.)
===
Subject: Re: Help! What is meant by Linear? and is e^x + e^y=0 linear ?
The word linear comes from the Latin word linearis, which means
created by lines. Linear is a property of some functions. In
mathematics, a linear function f(x) is one which satisfies the
following two properties:
    * Additivity property (also called the superposition property):
f(x + y) = f(x) + f(y).
    * Homogeneity property: f(.83Ëx) = 
.83Ëf(x) for all .83Ë.
In this definition, x is not necessarily a real number, but can in
general be a member of any vector space.
Taken from http://en.wikipedia.org/wiki/Linear
Shubee
===
Subject: Re: Help! What is meant by Linear? and is e^x + e^y=0 linear ?
However, a function such as f(x) = a + b*x is customarily called
linear, even though it fails to satisfy both of these conditions.
Of course, affine would be a better word in this case, but it is
rarely used, at least in applied fields.
R.G. Vickson
===
Subject: Re: Help! What is meant by Linear? and is   e^x + e^y=0  linear ?
The precise meaning of linear varies somewhat with the context, but 
roughly speaking, a function f(x) is linear in x if a change delta in 
the value of x produces a change c*delta in the value of f(x), where c 
is a constant.  Clearly e^x is not linear.
===
Subject: Re: why IT is an automorphism?
I'd like to thank You both for your help. Now I understand much more
from the first nontrivial example of Godbillon-Vey class (given by
Roussarie - according to Tondeur's book).
m.zych
===
Subject: convex combination of matrices
I have the following conjecture:
The inverse of the sum of a diagonal matrix (positive definite) and a
positive definite matrix A can be represented as the linear
combination of the inverse matrices of principal submatricesof the
latter matrix.
I could prove that this is indeed true for very small dimensions, but
then the wealth of the terms becomes so rich that a proof can be
hardly be given. Also ideas such as using von
Neumann series or the look at special matrix classes were not
successful. Counterexamples could not be found yet.
Any help or direction to go would be helpful.
I asked this question before and there were some answers, I
checked these answers carefully but in my case unfortunately they are
not helpful, so I'm writing again the same question hoping that to
get
now a useful answer now.
===
Subject: Re: convex combination of matrices
I don't understand this statement: if A is an nxn matrix, then its
principal submatrices and their inverses will be of dimension (n-1)x(n-1)
or lower, and so will their linear combinations.  How exactly can we
recover an nxn matrix from these submatrices?
--
Daniel Mayost
 
===
Subject: Re: convex combination of matrices
After taking inverses, the matrix filled with 0's to fit the
dimension.
===
Subject: Re: convex combination of matrices
So let's say A is a 3x3 matrix, and the matrix:
  [ 1 2 ]
  [ 3 8 ]
is an inverse of one of its principal submatrices.  Would you turn this
into:
  [ 0 1 2 ]
  [ 3 0 0 ]
  [ 0 0 8 ]
to fill the dimension?
--
Daniel Mayost
===
Subject: Re: convex combination of matrices
No, let me write the complete case for 3x3:
The inverses of principal submatrices and how they filled with 0's:
 [a 11 0 0]
[0 0 0]
[0 0 0]
[0 0 0]
[0 a 22 0]
[0 0 0]
[0 0 0 ]
[0 0 0]
[0 0 a 33]
[0 0 0]
[0 a 33 a 23]
[0 a 23 a 22]
[a 33 0 a 13]
[0 0 0]
[a 13 0 a 11]
[a 22 a 12 0]
[a 12 a 11 0]
[0 0 0 ]
and the inverse of the matrix itself.
I just used the notations for numbers, they are not actual inverses,
just to show how to fill with zeros.
Daniel Mayost- Al[CapitalYAcute]nt[CapitalYAcute]y[CapitalYAcute] gizle 
-
===
Subject: Re: convex combination of matrices
With great good luck, which is presumably why it was posed as a conjecture.
After all, though non-generic situations are (by definition) rare, they
*do* occur, and often they occur for deep and interesting reasons.
===
By the way--given the Subject: header, I wonder if the conjecture was 
supposed to have convex where linear appears.
Further by the way, I have no idea about the answer to the conjecture.
That it's true for small n (I don't know, or have forgotten, whether or
not atezel said exactly how large small was) is, even more in this
case than others, perhaps, not all that encouraging; there's quite a
few pleasant facts about positive-definite matrices of size 4 or smaller
that break down for larger sizes.
Lee Rudolph
===
Subject: Re: convex combination of matrices
After taking inverses, the matrix filled with 0's to fit the
dimension.
convex combination
by small I meant for q=1, q=2 it was proved and for q=3 in all the
examples studied so far it was true.
help to go in which direction.
===
Subject: Re: Solution Manual to Modern Control Engineering 4th Edition by 
K.Ogata
On Apr 27, 1:53 pm, Jos.8e Pedro Pinto Teixeira Marques (FEUP)
===
Subject: Re: Electrolysis of THERMATE - secrets
 
===
Subject: Can someone summarize the Cantor Confusion thread
in a few lines, for the benefit of those too busy to plough through
over 7000 posts?
In particular, has it spawned any interesting sub-topics? I can't
believe _all_ those posts just reiterate the same old arguments
to some blockhead who can't or won't accept them.
John R Ramsden
===
Subject: Re: Can someone summarize the Cantor Confusion thread
If you have trouble believing that Usenet is probably not the right place
for you.
-- 
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
Wovon man nicht sprechen kann, daruber muss man schweigen
 - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
===
Subject: can someone summarize the Can someone summarize the Cantor 
Confusion thread?
BEFORE it gets to 7000+ messages?
===
Subject: Re: can someone summarize the Can someone summarize the Cantor 
Confusion thread?
Too late - According to Google groups it is already 7150 and
counting ...
===
Subject: Re: can someone summarize the Can someone summarize the Cantor 
Confusion thread?
I meant before THIS thread gets to 7000+ messages.
===
Subject: Re: Can someone summarize the Cantor Confusion thread
Well it's true, whether you believe it or not. (This is a lot like
the situation in that thread - the reals are really uncountable,
and the diagonal proof is both simple and correct, in spite
of the fact that a lot of people don't believe it...)
************************
David C. Ullrich
===
Subject: Re: Can someone summarize the Cantor Confusion thread
Hi Dave,
What do you mean a lot of people don't believe the antidiagonal
argument's implications?
Presumably, you mean a lot of people don't.  I wonder then what they
expect to use instead.
That the reals are really uncountable from my perspective seems a
reference to the recent Skolem paradox thread, that in each model
the reals are countable somewhere.  Sets are defined by their
elements, so if no model of ZF contains all the real numbers, then, it
does not seem a reasonable foundation of them.
Have you heard of this funny constant in optics that is like
1.444... or 1.555... or so?  It's 1.444... or 1.555...?
Ross
--
Finlayson Consulting
===
Subject: simple proof that reals are uncountable
1)The interval between 0 and 1 is of length 1.  
2)Any countable collection of numbers (for example rationals between 0 and 
1) can be contained in intervals, whose lengths can be summed to a total as 

small as we want.  
3)Therefore the number of numbers between 0 and 1 is uncountable.
----------------------------------
Proof of 2)
List countable set, cover first point by interval of length x/2, second 
point by interval of length x/4, third point by interval of length x/8, etc. 

 
All intervals add up to length x - overlaps would make actual total evan 
smaller.  x can be made arbitrarily small.
===
Subject: Re: Can someone summarize the Cantor Confusion thread
Cantor's theorems are the most counter-intuitive mathematical results 
accessible to people untrained in math. Therefore they generate a lot of 
meaningless controversy on this newsgroup. You can safely skip the 
7000+ posts in that thread. Way more heat than light.
===
Subject: Re: Can someone summarize the Cantor Confusion thread
I always found it much more counter-intuitive that the rational
numbers should be countable.
===
Subject: Re: Can someone summarize the Cantor Confusion thread
Near the end, tt seems to be a lot of ruminations on the infinite
balanced, rooted, binary tree.  If it's infinitely deep, it has 2 to
the infinity leaves at that level, where it has 2^n nodes at level n.
Conway's surreal numbers on day Omega generate irrationals, and after
that still generate rationals as well, if I recall correctly.  If the
tree was completed somehow, there would be some completed infinity
with a maximal element.  Were there something like that, then each of
the terminal leaves would identify a unique path from the root to the
leaf, and each path to that level of the tree would be so identified,
at each level there are only countably many leaves.
Basically it's about the fact that transfinite cardinals are one of
the few disputed areas in mathematics.
Now having rescanned the first four or five hundred posts on the
thread, where I stopped reading that thread where the last several
thousand posts are Mueckenheim and Virgil at brickbats, one finitist,
the other, loon, there are definitely other threads with much more
substantive content about transfinite cardinals, in particular
disputed points about them, than Cantor Confusion.
Is there anything to note in there?
Cantor's results are basically an escapism from the nature of infinity
as it is seen in the number systems, source of some of the most
counterintuitive results to those quite well trained and able in
mathematics.  (The rationals and irrationals are each NCD2 sets in the
reals.)  There is no set of cardinals in ZF.  For some, there's not
even a set of real numbers with their concomitant properties of the
continuum, in ZF.  There's certainly no universe in ZF, unless
quantification over sets allows comprehension of them.
In the post-Cantorian framework, it's possible to consider why
integration is the sum of infinitesimals, in what used to be called
the infinitesimal analysis.  Some see the axiomatization of infinity
as a well-founded/regular set as a false axiom.
Model theory posits a maximal element, or there is no model of ZF, at
least not in ZF.  Models are to theories as classes are to sets.
Modern physics over time finds more use for application of infinities
and infinitesimals and no applicaiton of transfinite cardinals.  (The
physical universe is a counterexample to uncountability.)
Half of the integers are even.
Ross
--
Finlayson Consulting
===
Subject: Re: Can someone summarize the Cantor Confusion thread
Ross himself is as much loon as anyone he accuses of being one.
WM claims complete infinite binary trees have properties they cannot 
have in any internally consistent system. I only claim they have 
properties I can prove they have, at least in ZF.
===
Subject: Re: Can someone summarize the Cantor Confusion thread
Ah, Virgil my good man.  It seems that's the first you've replied to
me in some years, I don't follow your posts.  Similarly to the last
time I said, your overgeneralizations are generally wrong. A loon is a
loon.
In ZF, it is, that I hope to explain to you where I see
inconsistencies, if not internally to ZF, worse (for ZF), externally
to ZF.  In a more naive set theory without regularity, there is seen
the Russell paradox.  Then, the Russell set of that paradox happens to
be what is deemed the universe of ZF, where each set of ZF is in that
set.  Where that is so, there is as well an irregular set, so, then in
that set there is an irregular set, yet, that violates the very
regularity ZF's regularity axiom _tried_ to impose, it is decideable
in less axioms that statement about those sets and that set.
Then, in the post-Cantorian and post-Goedelian, there is reexamination
of not just the Cantorian and Goedelian results, which are assumed to
hold as much as they can, obviously, but also of the continuum,
towards re-Vitali-ization, like someone would think the real number
line is a line of points, obviously defining points and lines in terms
of each other.
I don't care whether you get it.  I _do_ explain why it is so.
Where functions between physical objects are physical objects the
universe is infinite and infinite sets are equivalent, including
itself.
A question:  why is the universe of ZF not the Russell set?
Typically, I don't give you a question you can answer.
There's A theory with no axioms, consistent with surviving ancient
philosophies.  A theory of everything is the theory of everything.
There is a universe in ZF.
Ross
--
Finlayson Consulting
===
Subject: Re: Can someone summarize the Cantor Confusion thread
Believe it.
F.
-- 
===
Subject: Re: Can someone summarize the Cantor Confusion thread
No, I just can't.
On second thoughts, yes I can.
John R Ramsden
===
Subject: Re: Can someone summarize the Cantor Confusion thread
Ramsden:
===
Subject: Re: Need you help!
Sad. If you can't do enough of the exercises by yourself, how do you
ever expect to get thru graduate school? After all, in the end you
are supposed have created something nobody else ever has. You cannot
achieve that goal by resorting to other people's work. You might get
a passing grade in this particular course with tactics like this, but
unless you realize the futility of such an approach, my honest advice
is for you to try another career.
Jyrki
===
Subject: another formulation for the same problem (convex combination of 
matrices)
The problem :
The inverse of the sum of a diagonal matrix (positive definite) and a
positive definite matrix A can be represented as the convex
combination of the inverse matrices of principal submatricesof the
latter matrix.
Based on eigenvalue decomposition:
 inv(D+A)=inv D * inv (I+A*inv D) =sum tau_k S_k where S_k's ar the
inverses of principal submatrices of A (filled with 0's to fit the
dimension).
Let V^T* L*V be the eigenvalue decomposition of A* inv D.
Then, we have to show that (after taking D and V's to the other side)
inv(I+L)=V^T*sumtau_k*D*S_k*V
            =D*sum tau_k*V^T*S_k*V
L=diag lambda_i is the diagonal matrix with eigenvalues of A*inv D,
so if we can show that the eigenvalues of A*inv D added by 1 and take
reciprocal (1/(lambda_i+1)) can be written as convex combination of
right hand side, then we are done?
Here the basic question is, what we can write about sum D*
tau_k*V^T*S_k*V?
V is the matrix of eigenvectors of A*inv D, and S_k's are the inverses
principal submatrices of A (filled with 0's after taking inverses).
Any help would be great.
===
Subject: Quasiconformal map characterization
I have the following problem:
Let f be a homeomorphism from C to C. Prove that f is K-quasiconformal
iff
d( [a,b,c,d] , [f(a),f(b),f(c),f(d)]) <= log K.    (*)
I think i know how to prove the result in one direction, namely that
for any K-quasiconformal f (*) holds. My idea was approximately the
following : wlog we can assume that (a,b,c,d) = (e_1,e_2,e_3,oo) and
[a,b,c,d] = (e_3 - e_1)/(e_3 - e_2) = ro (t), ro is a modular
function, t = w_2/w_1 for appropriate choice of the lattice L =
{w_1,w_2} in C.
Then a domain D = C  {e_1, e_2, e_3} we consider a closed curve C_1,
which lifts to a curve connecting z to z+w_1 in the covering C
(m*w_1/2 +n*w_2/2)  (using Weierstrass p-function)and use the fact
that extremela length of C_1 is 2/Im(t) (t = w_2/w_1).
quasiconformal, then the above fact
about extremal length implies that Im (af(t)+b / cf(t)+d ) <= K Im (at
+b / c+d ) for any unimodular transformation with a,b,c,d. Now this
result leads us to d_H(t,f(t)) <= log K, where d_H is the hyperbolic
distance on the upper-half plane H, which implies by Schwarz theorem
that
d( [a,b,c,d] , [f(a),f(b),f(c),f(d)])  = d_C{e_1,e_2,e_3}] (ro(t),
ro(f(t))) <= log K and we are done with (8).
This is quite brief desription, but i can't apply these ideas to the
converse case.
Do you have any ideas? I would be grateful for any of them.
===
Subject: Re: Quasiconformal map characterization
Quite an advanced question for this newsgroup, I think (unless things
have changed since I last looked, which admittedly was a while ago).
But I think we need some more information. For example, what is the
definition of a quasiconformal homeomorphism? I am assuming that it is
some variant of the geometric definition, as it would probably be
difficult to prove this just from the analytical definition. However,
there are still several versions of the geometric definition of a
quasiconformal map; e.g. involving moduli of quadrilaterals or annuli,
local or global definitions etc.
One that might be useful here is the following. f is K-quasiconformal
if the following holds. For every point z_0, take the image of a
circle of radius r around z_0. If the ratio between the inner and the
outer radius of this image is asymptotically bounded by K as r gets
small, then f is K-qc.
===
Subject: Re: Quasiconformal map characterization
Any of the geomoetric definitions which you want,assuming that i have
a book, where i can find a proof of their equivalences.
mod (A) < mod (f(A)) < K mod A for any annulus A in U.(mod means here
a modulus of an annulus).
===
Subject: Re: Quasiconformal map characterization
I would have thought all of this is somewhere in Lehto-Virtanen. Did
you look there?
===
Subject: Re: Great news! (And yet another Maple bug the long-liver (int))
Vadimir, I am relatively new to Maple (a few months) and I am trying
to put your very technical posts into context.  My impression is that
you have an automated system for hunting CAS bugs.  I went to your
site Maples bugs encyclopaedia and found a lot of stuff under
construction and some sort of report that I started to down load but
stoped because it would take quite some time.  Also, there were a lot
of words about something called GEMM?  So I am a bit confused and a
few brief non-technical sentences would be appreciated.
1.  Do you hunt for bugs or just investigate those reported?
2.  Do you make a similiar effort to determine bugs in Mathematica?
3.  Does Maple investigate and take corrective action on all, most,
some, or none of the bugs your report and is corrective action taken
in a timely manner, ie., days, months, verses years?
4.  With the proliferation of Maple and Mathematica versions, is each
new version better than previous versions bug-wise, or worse because
of the new features added?
5.  Have you posted a short, understandable, easy to read, relatively
non-technical paragraph or two on how Maple and Mathematica compare
bug-wise?
6.  How are your efforts funded?  Are you selling something?  If so,
what is it?
7.  Of the thousands of bugs reported what percentage are down to
earth problems that would affect the typical user verses very rare
situations the the typical user will never run into in his or her
lifetime?
8.  The point of using a CAS is to avoid the labor of doing provlems
by hand with a pencil and paper but if the answers cannot be trusted
and must be verified, perhaps by hand, what good is a cas?
9.  Lastly and most importantly, could you give a simple example of
how to use your bug reports to avoid wrong answers for a simple math
problem?
others understand your work, it's value, and how to use the
information.
===
Subject: Re: Ring without zero divisors
Ok. For integral domain it is easy. The problem here is exactly
noncommutativity.
Note, that this condition (*) holds in all division rings.
===
Subject: Cubes
Can anyone show the values of  a and b needed , such that :
(a-b)(a^2 + b^2 + ab )  is a cube .
===
Subject: Re: Cubes
On 5 May 2007 08:04:06 -0700, jiahao_anti-addictgamer@hotmail.com
a = 0, b any integer
b = 0, a any integer
Remove del for email
===
Subject: Re: Cubes
Special case of FLT in (poor) disguise
---
J K Haugland
http://home.no.net/zamunda
===
Subject: Re: Weird math questions
Did he just give you these questions to figure out what you would do
with them, or did you learn anything that should have helped you to
solve them?
===
Subject: All Subjects' solutions manuals in Pdf format
All Subjects' solutions manuals in Pdf format
All solutions manuals are in pdf format or Microsoft Word format.
I have tried my best to put up with the collections of my solutions manual.
Here is the list that only part of my collections:
I will put some time to make up the full list daily.
If you cant find the solution manual listed below, don't give up, feel free 

to email me
To get the solutions manual, just email me with a price you want to get the 

solutions manual you want.
To see samples, just email me.
 
My email is edisonee(at)gmail.com
Solutions Manuals
NET 2.0 Interoperability Recipes by Bruce Bukovics
A Course in Game Theory by Martin J. Osborne and Ariel Rubinstein
A First Course In Probability 7th Ed by Sheldon Ross
Adaptive Control 2nd Ed. by Karl.J.Astrom
Advanced Engineering Marhematics ERWIN KREYSZIG 9E
Advanced Engineering Mathematics 8Ed Erwin Kreyszig
Advanced Engineering Mathematics 8Ed Erwin Kreyszig in korean (all even and 

odd no.)
Advanced Macroeconomics by Jeffery Rohaly 
Advanced Modern Engineering Mathematics 3rd Ed. by Glyn James
Analog Integrated Circuit Design by David Johns, Ken Martin
Analysis and Design of Analog Intergrated Circuits 4th Ed. by Paul R. Gray
Analytical Mechanics 7th Ed. by Fowles
Antenna for all application 3rd Ed.by John D. Kraus (Instructor's Manual)
Antenna Theory 2nd Ed. by balanis
Applied Linear Statistical Models 5th Ed. by MichaelH.Kutner
Applied Numerical Analysis 7th Ed. by Curtis F. Gerald, Patrick O. Wheatley
Applied Numerical Methods with Matlab for Engineers and Scientists 2nd Ed. 
by Chapra
Applied Statistics Probability for Engineers 3rd ed Montogomery (selected 
problems)
Applied Strength of Materials 4th Ed. by Robert L. Mott
Automatic Control Systems 8th Ed. Kuo and Golnaraghi
Basic Engineering Circuit Analysis 7th Ed. by Irwin
Basic Principles and Calculations in Chemical Engineering 6th Ed. by David 
M. Himmeblau
Biochemistry 2nd Ed. by Philip W. Kuchel, Gregory B. Rakston
Bioprocess Engineering Principles by Pauline M. Doran
Business Statistics A Decision-Making Approach 6th Ed. by Groebner
C++ How to Program 3rd ed. Deitel, Deitel & Nieto (Instructor's Manual)
Calculus 4th Ed. by James Stewart (Complete Instructors manual)
Calculus 5th Ed. by James Stewart (Complete Instructors Solutions)
Calculus by Jerrold Marsden & Alan Weinstein Vol 1
Calculus Early Transcendentals 5th Ed. by James Stewart
Calculus of Variations by Russak(book and solutions manual)
Calculus: One and Several Variables 8th Ed. by Salas, Hille and Etgen
Chemical And Engineering Thermodynamics 3Ed by Wiley
Chemical Engineering Solutions to the Problems in Volume 1 by J R Backhurst
Classical Dynamics 5th Ed. by Thornton
Classical Electrodynamics 3rd Ed. by J.D. Jackon
CMOS Analog Circuit Design 2nd Ed. by P.E. Allen
Communication Systems 4th Ed. by Simon Haykin
Communication Systems Engineering 2nd Ed. by Proakis J.
Communication Systems: An Introduction to Signals and Noise in Electrical 
Communication 4th. Ed. by Bruce Carlson 
Computational Techniques for Fluid Dynamics by K. Srinivas and 
C.A.J.Fletcher 
Computer Architecture Design and Performance 2nd Ed. by Barry Wilkinson
Computer Networking A top-down approach 3rd Ed. by James F. Jurose
Computer Networking: A Top-Down Approach Featuring the Internet 2nd ed. by 
Jim Kurose and Keith Ross
Computer Networks 4th Ed. by Andrew.S.Tanenbaum
Computer Networks: A Systems Approach 3rd Ed. by larry L. Peterson and Bruce 

S. Davie
Computer Organization And Design - The Hardware Software Interface 3rd Ed.
Computer Systems Organization and Architecture by John D. Carpinell
Control Systems Engineering 3rd Ed. by Norman S. Nise
Control Systems Engineering by Nise
Design and Analysis of Experiments 6th Ed. by Montgomery
Design Of Analog Cmos Integrated Circuits by Razavi
Design with Operational Amplifiers and Analog Integrated Circuits 3rd Ed. by 

Franco, Sergio
Device Electronics for Integrated Circuits 3rd Ed. by Muller and Kamins
Differential Equations & Linear Algebra by C. Henry
Differential Equations with Boundary-Value Problems 5th Ed. by Zill and 
Cullen
Digital communication: Fundamentals and Applications 2nd Ed. by Bernard 
Sklar
Digital communications 4th Ed. John Proakis with ebook
Digital Image Processing 2nd Ed. by Gonzalez (Instructor's Manual)
Digital Integrated Circuits by Rabaey 2nd Ed. (selected problems)
Digital signal processing A Computer-Based Approach 1st Ed. by Sanjit K. 
Mitra
Digital Signal Processing by Thomas J. Cavicchi
Digital Signal Processing: Principles, Algorithms, and Applications, 3rd Ed. 

by Proakis & Manolakis
Digital Signals and Filter by S. J. Orfanidis (selected solutions)
Discrete-Time Signal Processing 2nd Ed. by Oppenheim, R.W. Schafer and J. R. 

Buck
Distributed Systems Principles and Paradigms by Andrew S. Tanenbaum and 
Maarten Van Steen
Econometric Analysis 5th Ed. by William H. Greene
Econometric Analysis of Cross Section and Panel Data by Jeffrey M. 
Wooldridge
Electric Circuits 7th Ed. by Nilsson
Electric Machinery 6th Ed. by Fitzgerald, Kingsley, Uman
Electric Machinery and Power System Fundamentals 1st Ed. by Stephen J. 
Chapman (Instructor's Manual)
Electric Machinery Fundamentals 4th Ed. by Stephen J Chapma 
(Instructor's_Manual)
Electrical Engineering Principles And Applications 4th Edition by Giorgio 
Rizzoni
Electrical Engineering Principles And Applications by Hambley
Electronic Circuit Analysis and Design 2nd Ed. by Donald A. Neamen
Electronic Physics by Strabman
Electronics 2nd Ed. by Allan R. Hambley
Element of Electromagnetic by Sadiku
Elementary Differential Equations and Boundary Value problems 7th Ed. by 
Boyce, DiPrima (book and solutions)
Elementary Differential Equations and Boundary Value Problems 8th Ed.
Elementary Linear Algebra by K. R. Matthews (book and solution manuals)
Elementary Mechanics and Thermodynamics by John W. Norbury
Elements of Chemical Reaction Engineering 3rd Ed. by Timothy Hubbard, 
Jessica hamman and David Johnson
Elements of Information Theory by Thomas M. Cover
Engineering Biomechanics: Statics by Angela Matos, Eladio Pereira, Juan 
Uribe and Elisandra Valentin
Engineering Circuit Analysis 6th Ed. by Hayt
Engineering Electromagnetics 6th Ed. by William H. Hayt, Jr. and Hohn A. 
Buck 
Engineering Fluid Mechanics 7th Ed. by Crowe
Engineering Mathematics 4th Ed. by John Bird
Engineering Mechanics Dynamics 10th edition by Hibbeler
Engineering Mechanics Dynamics 11th edition by Hibbeler
Engineering Mechanics Dynamics 3rd Ed. by Hibbeler
Engineering Mechanics Dynamics 5th Ed. by Meriam
Engineering Mechanics Dynamics by Bedford and Fowler
Engineering Mechanics statics 10th edition by Hibbeler
Engineering Mechanics statics 11th edition by Hibbeler
Engineering Mechanics Statics 4th Ed. Bedford
Engineering Mechanics Statics by Meriam
Feedback Control of Dynamic Systems 4th Ed. by G. F. Franklin, J. D. Powell, 

A. Emami
Fluid mechanics 5th Ed. by White 
Fourier and Laplace transforms by Antwoorden (selected solutions) 
Fractal Geometry: Mathematical Foundations and Applications by Kenneth 
Falconer
Fundamentals of Aerodynamics 2nd Ed. by John D. Anderson
Fundamentals Of Aerodynamics 3rd Ed. by Anderson (Instructor's Solutions 
Manual)
Fundamentals of Applied Electromagenetics  5th Ed+
Fundamentals of Differential Equations by Nagle Saff Snider
Fundamentals of Digital Logic with Verilog Design 1st Ed. by S. Brown, Z. 
Vranesic
Fundamentals of Digital Logic with VHDL Design 1st Ed. by S. Brown, Z. 
Vranesic
Fundamentals of Electric Circuits 2nd Ed. by C.K.Alexander M.N.O.Sadiku
Fundamentals of Engineering Thermodynamics 5th ed (M. J. Moran & H. N. 
Shapiro) 
Fundamentals of Financial Management With Infotrac Concise 4th Ed. by Eugene 

Brigham
Fundamentals of Fluid Mechanics 3th Ed. by Munson (Student solution manual)
Fundamentals of Fluid Mechanics 4th Ed. by Munson
Fundamentals of Fluid Mechanics 5th Ed. by Munson
Fundamentals of Heat and Mass Transfer 5th Ed. Incropera
Fundamentals of Logic Design 5th Ed. by  Charles Roth
Fundamentals of Machine Component Design 3rd Ed. by Juvinall and Marshek
Fundamentals of Machine Component Design 4th Ed. by Juvinall
Fundamentals of Phsics 6th ed. by Halliday, Resnick (instructor's manual)
Fundamentals of phsics 7th ed. by David Halliday, Robert Resnick, and Jearl 

Walker (instructor's manual)
Fundamentals of Thermal-Fluid Sciences by Cengal
Fundamentals of Thermodynamics 6th Ed. Richard E. Sonntag, Claus Borgnakke, 

Gordon J. Van Wylen
Guide to Energy Management 5th Ed. by Klaus-Dieter E. Pawlik
Heat Transfer 2nd Ed. by Cengel
Hydraulics in Civil and Environmental Engineering 4th Ed. by Andrew Chawick
Introduction To Algorithms 2nd Ed. by Philip Bille (selected problems)
Introduction To Algorithms 2nd Ed. by Thomas H. Cormen, Charles E.Leiserson, 

Ronald L. Rivest, Clifford Stein
Introduction to Antenna Theory by Palacios
Introduction to electric circuits 6th Ed. by Dorf-Svaboda 
Introduction to electrodynamics 3rd Ed. by David Griffiths
Introduction to Fluid Mechanics 5ed. by Fox
Introduction to Fluid Mechanics 6th Ed. by Fox
Introduction to Linear Algebra 3th Ed. by Gilbert Strang
Introduction to Probability by Charles M. Grinstead and J. laurie Snell
Introduction to Quantum Mechanics 2ed Griffiths, David J.
Introduction to Software Engineering by R. Mall
Introduction to VLSI circuits and Systems by John P. Uyemura
Introduction to Wireless Systems by P. M. Shankar
Investment Analysis and Portfolio Management by Reilly Brown
Linear Algebra and its Applications  3rd Ed.  by Lay
Linear Algebra by Jim Hefferon
Linear circuit analysis by R. A. DeCarlo and P. Lin 
Linear Systems and Signals by B P Lathi
Logic Computer Design Fundamentals 2th Ed. by Morris Mano (selected 
problems)
Managerial Accounting 11th Ed.
Material Science and Engineering an Introduction 5th Ed. by Callister
Material Science and Engineering an Introduction 6th Ed. by Callister
Materials & Processing in Manufacturing 9th Ed. by Demargo
Mathematical Methods for Physics and Engineering 3rd Ed. by 
K.F.RileyandM.P.Hobson
Mathematics for Economics by Simon and Blume
Matrix Analysis And Applied Linear Algebra by Carl D. Meyer
Mechanical Engineering Design 7th Ed. Shigley
Mechanics of Fluids 4th Ed. by I. H. Shames
Mechanics of Fluids 8th Ed. by Bernard Massey
Mechanics of Materials 3rd Ed. Elsevier by S. Nemat-Nasser
Mechanics of Materials 5th 6th Ed. by Gere
Mechanics of materials Hibbeler 6th
Mechanics Of Materials(3rd Ed , By Beer, Johnston, & Dewolf)
Microeconomic Analysis 3rd Ed. by Hal R. Varian
Microeconomic Theory by Andreu Mas-Colell, Jerry R. Green, Michael Dennis 
Whinston
Microelectronic Circuits 4th Ed. by Sedra, Smith
Microelectronic circuits 5th Ed. Sedra
Microelectronics Digital and Analog Circuits and Systems by Millman
Microwave and rf design of wireless systems by Pozar
Microwave Engineering 2nd Ed. David M Pozar
Microwave Engineering 3rd Ed. David M Pozar
Microwave Transistor Amplifiers Analysis and Design 2nd Ed. by Guillermo 
Gonzalez
Modern Control Engineering 3rd Ed. by K.OGATA 
Modern Digital and Analog Communications Systems by B P Lathi
Modern Quantum Mechanics Revised Ed. by J.J. Sakurai (solutions and book)
Multi Variable Calculus 5th Ed.
Numerical Methods for Engineers by Steven C. Chapra and Raymond P. Canale
Operating System Concepts 6th Ed. by Abraham Silberschatz
Operating System Concepts 7th Ed. by Abraham Silberschatz
Operating Systems:Internals and Design Principles 4th Ed. by William 
Stallings
Options, Futures, & Other Derivatives 4th Ed. by John C. Hull
Organic Chemistry 5th Ed. by Atkins and Carey
Physical Chemistry 7th. Ed. by Peter Atkins & Julio de Paula
Physics for Scientists & Engineers (a strategic approach) by Randall D 
Knight
Physics for Scientists & Engineers by Tipler & Mosca 5th Edition
Physics For Scientists And Engineers 3rd Ed. by Douglas C. Giancoli
Physics for Scientists and Engineers 5th Extended Version by Serway and 
Faughn
Physics Volume 2 5th Ed. by Halliday, Resnick and Krane
Power System Analysis by John J. Grainger & William D. Stevenson, Jr
Principles of Communication 5th Ed. by R. E. Ziemer, William H. Tranter
Principles of Physics 4th Ed. Calculus Based by Serway, Raymond A. and John 

W. Jewett
Principles with Applications BY Giancoli 6TH Edition
Probability and Statistics for Engineering and the_Sciences 6th Ed.
Probability and Statistics for Engineers and Scientists (selected problems)
Probability Random Variables and Stochastic Processes 4th Ed. by Papoulis
Process Systems Analysis and Control by Donald R.coughanowr(selected 
problems)
Quantum mechanics by Kyriakos Tamvakis
Quantum Mechanics by P. Saltsidis
Recursive Macroeconomic Theory by Lars Ljungqvist and Thomas J. Sargent
Recursive Methods in Economic Dynamics by Wright
RF circuit Design Theory and Application by Ludwig bretchko
Sears and Zemansky's University Physics 11th Ed.
Semiconductor Device Fundamentals 1st Ed. by Robert F. Pierret
Semiconductor Devices Physics and Technology 2nd Ed. by S. M. Sze
Semiconductor Physics and Devices 3rd Ed. by Neamen
Serway and Jewett's Physics for Scientists and Engineers 6th ed. by McGrew 
and Currie
Signal Processing and Linear Systems by B P Lathi
Signals And Systems 2nd Ed. by Haykin
Signals And Systems 2nd Ed. by Oppenheim
Signals, Systems and Transforms 3rd Ed. by Oppenheim
Soil Mechanics: concepts and applications 2ed William Powrie
Solid State Electronic Device 5th Ed. by Ben Streetman (Instructor's 
Manual)
Strengths of Materials by Beer, Johnston, Dewolf
Structural Analysis by R.C. Hibbeler 
System Dynamics by Ogata (B problems only)
The C Programming Language 2nd Ed. by Kernighan and Ritchie 
The Econometrics of Financial Markets by Petr Adamek
The Science and Engineering of Materials 4th Ed. by Donald R. Askeland 
Pradeep P. Phule (Instructor's Manual)
Theory and Applications of OFDM and CDMA Wideband Wireless Communications 
(2005)
Thermodynamic 5th ed. Cengal
Thermodynamics of Turbomachinery 5th Ed.
Thermodynamics: An Engineering Approach 5th Ed. by Cengel Boles 
(Instructor's Solutions Manual)
Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas  Vol 1
Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas  Vol 2
Transport Phenomena 2nd Ed. by Bird and Stewart(to class 1 and class 2 
problems)
Undergraduate Econometrics by Hill, Judge and Griffiths
University Physics with Modern Physics (11th) by  Hugh D. Young and Roger A. 

Freedman.
Vector Calculus 3rd Ed. by Susan Jane Colley
Vector Mechanics for engineers dynamics by beer 6th edition
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Wireless Communications principles and practice 2nd Ed. by Theodore 
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Applied mathematics and Modeling for Chemical Engineers by Rice and Do
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Applied Numerical Methods Using Matlab by Yamg, cao, Chung and Morris
Applied Statistics Probability for Engineers 3rd Ed. by Montogomery
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dsSa
Business Analysis And Valuation Using Financial Statements - Text And Cases
C++ How to Program 5th Ed. by H. M. Deitel, P. J. Deitel
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Computational Fluid Mechanics and Heat Transfer 2nd Ed. by Tannehill, 
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Computer Organization and Design: The Hardware-Software Interface
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DWDM Network Designs and Engineering Solutions by Astwin Gumaste and Tony 
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Elements of Electromagnetics 3rd Ed. by Sadiku
Elements of The Theory of Computation 2nd Ed. by Lewis and Papadimitriou
Financial Accounting McGraw-Hill
Fluid Mechanics 2nd Ed. by Rjucsh K. Kundu and Ira M. Cohen
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Fundamentals of Aerodynamics by Anderson
Fundamentals of Gas Dynamics 2nd Ed. by Zucker R D , Biblarz
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Imperfect C++ Practical Solutions for Real-Life Programming by Matthew 
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Introduction to Thermal Systems Engineering: Thermodynamics, fluid 
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Linear Algebra And Its Applications by David C Lay
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Whinston
Modern Control Engineeing 3rd Ed. by Katsuhiko Ogata
Modern Operating Systems 2nd Ed. By Tanenbaum
Modern Wireless Communications by Simon Hatkin and Michael Moher
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Physics for Scientists and Engineers 6th Ed. by Serway Jewett
Principles and applications of Electrical Engineering by Giorgio Rizzoni
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Probability, Random Variables, and Random Signal Principles 2nd Ed. by 
Peyton Z. Peebles, Jr. 
Rules Of Thumb For Chemical Engineers A Manual Of Quick, Accurate Solutions 

To Everyday Process Engineering Problems 3rd Ed. by carl Branan
Schaum's Outline of College Physics by Fredrick J. Bueche and Eugene Hecht
Scientific Computing An Introductory Survey by Michael T. Heath
Signals And Systems by Oppenheim
Thermal Physics 2nd Ed. by Kittel
Vector Mechanics for engineers statics 7th. Ed. by Ferdinand P. Beer
Wireless Communications by Andrea Goldsmith
===
Subject: Chinese symbol for pi an the root
I'm looking for the symbol, Chinese mathematician used for the ratio of the
circumference and the diameter of a circle, before they have been influenced 

by
western mathematic.
I'm also looking for the symbol, Chinese Mathematican used to descr.92be 
the (n-th) root of
a number, before they have been influenced by western mathematic.
Berthold Heinrich
Germany
===
Subject: Countable dense set.
What dose it mean : countable dense set. Give me some examples, please.
===
Subject: Re: Countable dense set.
Ok, I understend in: for example set of rational numbers is countable
dense set in real numbers.
===
Subject: Re: Countable dense set.
In sci.math, Nik
on 5 May 2007 10:09:01 -0700
Indeed; that's an excellent example of a set that is
both dense everywhere (for every pair of points in the
set there's at least one other between) and countable
(a bijective mapping exists between the candidate set and
the set of natural numbers).
However, it is not the only one.  The following describes
a series of sets which are also countable and dense everywhere:
t_b = {n / b^i : n, i in J}
all finite b-ary expansions.
The set of all real roots of f(x) = 0, where f() is a polynomial in
Z[x], is also dense everywhere and countable, since the set of all f()
is countable.
-- 
#191, ewill3@earthlink.net
Useless C++ Programming Idea #23291:
void f(item *p) { if(p != 0) delete p; }
-- 
===
Subject: Re: Countable dense set.
There's a difference between a set being dense in itself
(what you defined) and a set being dense in another
set. In fact, the Cantor set is dense in itself, but it's
_nowhere_dense_ in the real numbers.
Dave L. Renfro
===
Subject: Re: Countable dense set.
of what you defined with dense in itself. However, I note
that any singleton set in the reals is dense using your
definition and nowhere dense in the reals.
Dave L. Renfro
===
Subject: mixing binary and continuous variables in discriminant analysis
Is it generally OK to mix binary (e.g., discrete indicator) variables
with continuous variables in discriminant analysis?  I having in mind
financial applications like credit scoring or bankruptcy prediction.
===
Subject: Re: mixing binary and continuous variables in discriminant 
analysis
Some statisticians quibble about this, but my results mixing continuous and
categorical variables have been good.  Don't forget that you have to 
convert
the categories of categorical variables into a set of 0/1 binary variables
(many software programs do this for you automatically).
You might want to consider other types of models. Decision trees are a 
natural
choice for categorical variables.
-- 
Phil Sherrod
(PhilSherrod 'at' comcast.net)
http://www.dtreg.com  (Decision trees, Neural networks and SVM modeling)
http://www.nlreg.com  (Nonlinear Regression)
===
Subject: Re: mixing binary and continuous variables in discriminant 
analysis
Yes. Just don't interpret the p-values etc too closely.
You might be better off switching to logistic regression.
===
Subject: exponential / factorial
I'm working through a computer science textbook on my own, for fun.
Some of the problems are really too hard for me to figure out -- in
that case, I look at the answers. However, sometimes even *the
answers* are too hard for me to figure out. Basically, I need to know
why
    exponent(n, n) / factorial(n) = product[k=1; k=n-1]( exponent( ( (k
+1) / k ), k) )
I'm sorry if that's a little confusing -- I've posted a PDF and
TeXmacs file at
    https://svn.j-s-n.org/writing/math/knuth_problems/1.2.5-24/
If that helps any.
===
Subject: Re: exponential / factorial
Why not use standard notation?  Instead of writing exponent(a,b), just
write a^b ('a to the power b'). Anyway, just write out in detail the
right-hand side. Try it first for some small values of n, such as n =
2 or 3. Then use induction.
R.G. Vickson
===
Subject: Re: exponential / factorial
I write:
  exponent(n, n) as n^n
  factorial(n)  as n!
  product[k=1; k=n-1]( exponent( ( (k+1) / k ), k) )
     as PROD( ((k+1)/k)^k )  , k=1..n-1 implicit
Then
  PROD( (k+1)^k ) = PROD( (k+1)^(k+1) ) / PROD( (k+1) ) / PROD( k^k )
But
  PROD( (k+1)^(k+1) ) / PROD( k^k )  = n^n
and
  PROD( (k+1) ) = n!
Eduardo.
===
Subject: Re: exponential / factorial
PROD( k^k )
Grrr  errata
.. Then
..  PROD( ((k+1)/k)^k ) = PROD( (k+1)^(k+1) ) / PROD( (k+1) ) /
PROD( k^k )
===
Subject: Re: exponential / factorial
What is the standard way to write out a product or sum in plain text?
===
Subject: Re: exponential / factorial
Just as product or sum. It was the 'exponent statement I was
objecting to, as I thought my post made clear enough.
R.G. Vickson
===
Subject: Re: Definition of finite.
 All versions of set theory of which I am aware have an
 axiom which guarantees an infinite set.  
.................
Not all set theories has such an axiom, take for example
Kripke-Platek set theory with urelements.
Now it would be interesting to see how one can define
natural number in Z-I-R
I propose the following definition of x is a natural number in Z-I-R
I think this would do the job.
However in this theory there is no need to define x is finite, since
every x in Z-I-R is finite.
Zuhair
===
Subject: Re: Definition of finite.
We don't need axioms to make these definitions. I keep explaining that
we don't even have to mention omega to define 'natural number'.
where 'finite' is defined as any of the equivalents of 'well ordered
by an R and its converse', and 'ordinal' is defined as 'well ordered
by epsilon and is epsilon-transitive'.
That's IDIOTIC.
Are you thinking that because Z-R-I can't prove the existence of an
infinite set (thus, a fortiori, of an infinite ordinal) it follows
that we might as well take the naturals to be the ordinals?
If that's what you're thinking, it's IDIOTIC and you are RELAPSING
into illogical thinking that we ALREADY have been through with you.
What I thought you finally understood by this time is that even though
a theory might not prove the existence of objects having a certain
property, it doesn't follow that the theory RULES OUT that there are
such objects. Even though Z-R-I doesn't prove the existence of any
infinite ordinals, it still doesn't RULE OUT that they exist. So the
definition of 'natural number' still must be stated so as to rule out
that a natural number could be an infinite ordinal, otherwise it is
left UNdetermined whether there are natural numbers that are infinite
when what we WANT to do is make it DETERMINED that there are NOT
natural numbers that infinite.
NO!!! NO!!! NO!!!
We went through that with you about a year ago!!!
In Z-I-R it is UNDETERMINED whether every set is finite. In Z-I-R it
is NOT determined that every set is finite.
A theory that DOES determine that every set is finite is Z-R-I + ~I.
That is, Z-R-I plus the NEGATION of the axiom of infinity. There, yes,
all sets are finite. But in just Z-R-I, it is UNDETERMINED whether
there are infinite sets, thus UNDETERMINED whether all sets are
finite.
Come on, zuhair, we spent a lot of work a year ago to finally get you
to understand that but now you're repeating your old misconceptions
again.
MoeBlee
===
Subject: Re: Definition of finite.
Oops, yes that is true, what you said is true, actually I know that,
but it is due to my poor practice in this field that I sometimes keep
doing the same mistake again and again?
But Moe I have an argument behind all of that. You didn't see it.
What I want to do is to see weather Tarski's definition of
x is finite in terms of x is natural, is workable in Z-I-R.
y equinumerous to x)
My point is that If I want to use the above definition of x is finite
then I cannot say that in Z-I-R  a natural number is a finite ordinal.
Why?
& x is finite)
then I can't use Tarski's definition without circularity, since if I
use it, the definition would be:
x)
which is clearly circular.
However there is a way around that!
I can't get Supp's now so I will make a primitive try, and I am
looking forwards for you assisting me in that.
In Z-I-R :
Ez( zex & zu{z}=y) ) ).
In words, in Z without infinity and without regularity: any x is said
to be a natural number if and only if x is an ordinal in which every
member y other than 0, has an immediate predecessor z in x.
of course 'immediate predecessor' is the converse of ' immediate
successor'.
Now we can proceed and define x is finite in Z-I-R
Now these formulae that I gave, are really independable of Infinity,
they are the same formulae used in Z-R and in Z-R-I, and are not
circular.
And they are better than the definition mentioned by Rubin which is
since this formula requires axiom of infinity, since the existence of
Omega 'w' is not garanteed without infinity, and so this formula
doesn't work in Z-R-I, since w is not defined to exist in Z-R-I.
So in summary:
In Z-I-R or Z-R.
Ez( zex & zu{z}=y) ) ).
Am I right this time?
Zuhair
===
Subject: Re: Definition of finite.
Yes, I've answered that several times already. The answer is YES.
I've alreay addressed this.
If we define
then of course we can't define 'natural number' as 'finite ordinal'.
But then we will define 'natural number' in some way so that we PROVE,
not define, that x is a natural number iff x is a finite ordinal.
Again, the formulas and all of that are in, e.g., Suppes's book.
Of course there is. I've mentioned it already.
I hope I can help you with studying the book. I can't help you to get
the book. But it's widely available at a very cheap price.
That doesn't work, since you need to stipulate that z is also an
ordinal. This works:
ordinal &  (y=0 v Ez(z is an ordinal & y=zu{z}))))).
Change that to: x is an ordinal in which every member other than 0 is
a successor ordinal.
Yes, we already knew that.
Again, your notion of defintions being independent of axioms is not
precise. However,I do understand your point in a general sense, and I
too prefer to define 'finite' and 'natural number' without mentioning
'w'.
It's not as simple as you state it. I addressed this technical point
already.
MoeBlee
===
Subject: Re: Definition of finite.
No wait, we're BOTH wrong.
You are right about not having to mention 'y is an ordinal' since yex
entails y is an ordinal (my only excuse for overlooking that is that
I'm posting while I'm very very hungry as I keep putting off going out
for a bite to eat and thus I can really only think about food, not
sets, right now!).
But the formula should be:
The way we had it, omega would qualify to be a natural number. What I
added to correct that is the 'y=x' clause. I.e., x itself must also be
either 0 or a successor, and not just a set whose members are all
either 0 or a successor.
I think it's right now. (I'll check it again when I come back from
getting some food!) And I think it can be simplified too.
MoeBlee
===
Subject: Re: Definition of finite.
I think I have it cleared up now. Check this out as a simplification
and see if it's correct:
v Ez n=zu{z}))
That should be equivalent to:
v n is a successor ordinal))
And both should be equivalent to the correction I offered in my
previous post.
MoeBlee
===
Subject: Re: Definition of finite.
You should define clearly ' x is a successor ordinal'
I think you mean
Yes, I think your correction works.
It is a nice definition.
Still I think my definition works to
I think we both corrected our definitions right!
You definition is equivalent to mine.
Zuhair
===
Subject: Re: Definition of finite.
Although both of your and my definitions are correct and equivalent,
but I still think that mine is better. Because your definition states
frankly that 0 is a natural number, while mine implies that, I mean in
your definition 0 is fixed to be a natural number, your definition
doesn't explain why 0 is a natural number, it orders zero to be a
natural number, while mine do explain why?
So though the two definitions are equivalent yet I think mine is more
meaningful.
Zuhair
===
Subject: Re: Definition of finite.
Pshaw. Your definition has the clause:
which is equivalent to
x=0 v x e Ux
just as mine also treated x=0 as part of a disjunction.
There's no substantive difference there. It's just a matter of which
sentential equivalent we chose.
Your continual claims of better, simpler, more intuitive, etc.,
now more meaningful about your various proposals are irritating,
especially when they so often turn out not to be the case.
MoeBlee
===
Subject: Re: Definition of finite.
hahaha............, I was just jocking here.
I know that they are equivalent!
===
Subject: Re: Definition of finite.
I will check them. But both of these corrections are complex formulae.
The one I gave is much simpler than both of these.
===
Subject: Re: Definition of finite.
I was wrong, but I corrected my definition. The corrected definition
of mine is not wrong.
This is complex, my formula is simpler.
I don't see how can that be???
I defined x is natural in the following manner ( the corrected
definition ):
Now with this definition , how can Omega satisfy it??
The union of Omega is not in Omega, because the union of Omega IS
Omega itself, and since every ordinal is not in itself, then we have
~Uwew, and so we have ~ w is a natural number.
This corrected formula of mine, is a simple formula, and it is simpler
than the one you gave.
Zuhair
===
Subject: Re: Definition of finite.
Your correction:
That can be simplified:
I think that works as follows:
Suppose x is a finite ordinal. Then the only thing that it isn't
obvious (or that we haven't already established) as holding on the
right hand side of the biconditional in the definition is:
But we can show that as follows (though maybe there's an easier way?):
If x is a finite ordinal, then Ux is a finite ordinal.
If x is a finite ordinal and ~x=0, then ~ x subset of Ux as follows by
induction on x:
If x=1 then ~x subset of Ux.
Suppose ~x subset of Ux. Show ~ xu{x} subset of U(x u {x}).
U(x u {x}) = Ux u x. So we must show ~ xu{x} subset of Ux u x.
x e xu{x}. But if x e Ux u x, then x e Ux (since ~xex).
But if x e Ux, then, since Ux is an ordinal, we have  x subset of Ux,
which contradicts the inductive hypothesis.
So ~x subset of Ux.
So, by trichotomy of ordinals, Ux is a proper subset of x.
So Ux e x.
To show the right hand side of the biconditional in the definition
entails that x is a finite ordinal, it suffices to show that x is not
a limit ordinal. And we have that since if x is a limit ordinal then
~x=0 and ~ x e Ux.
Look at the old formulation, and you will see that w satisfies the
definition.
Right, with the CORRECTED version, w does not satisfy it. But with the
version BEFORE the corrected version (wihch is what I was talking
about), w satisfies it.
Simpler doesn't have a formal determination, but look at how we
simple it is to read one of the versions I gave:
x is 0 or (x is a sucessor ordinal and every member of x is either 0
or a successor).
That's surely no more complicated than your:
x is an ordinal and if x is not 0 then the union of x is a member of
x, and every member of x that is not 0 is equal to the successor of
some member of x.
MoeBlee
===
Subject: Re: Definition of finite.
Sorry Moe, the formula that I have presented was actually incomplete:
What I meant was this:
This was my formula, but I missed mentioning the union part of it, I
am not concentrating these days , I have a lot of work, anyhow.
About z we don't need to mention that z is an ordinal, since every
member of an ordinal is an ordinal.
I am sure that this formula works.
that any x that is ordinal and who's union is a member of it , then
and only then this x is a last membered ordinal ( which might be
finite or infinite of course ).
every member in x other than 0 should have an immediate predecessor z
that is in x, and of course z would be an ordinal since every member
of an ordinal is an ordinal.
So in words this definition is saying.
A natural number x is a last membered ordinal in which every member y
has an immediate predecessor z in x.
I think that this definition works.
Zuhair
===
Subject: Re: Definition of finite.
How a subset-maximal element is defined in first order logic?
Can you write this definition in first order logic, please.
The formula please.
This is Dedekind's finite.
5 is actually my definition that I have presented in this thread and
that many people in this group say that they prove that it is
equivalent to 4 ( i.e. Dedekind's ).
You say they are distinct, then the definition I gave at this thread
which was said to be equivalent to Dedekind's is in reality not!
I have always been suspecious regarding this 'equivalence'.
===
Subject: Re: Definition of finite.
of x)
Get Suppes's set theory book.
Here's Tarksi's definition ['P' stands for 'power set of']:
element of S)
Get Suppes's set theory book. There's a bunch of this stuff in there.
Just get a good set theory textbook.
In Z set theories:
The Tarski definition I just gave is equivalent to the 'well ordered
by an R and its converse' definition.
The Dedekind definition is equivalent to the 'incremental'
definition.
The Tarski condition entails the Dedekind condition ('not equinumerous
with a proper subset of itself') (indeed, this is called the
'pigeonhole principle') but the Dedekind condition does not entail the
Tarski condition.
Adding the axiom of choice (even just the axiom of countable choice),
the Dedekind condition entails the Tarski condition so that with the
axiom of choice (or even just the axiom of countable choice), the
Tarski and Dedekind definitions are equivalent.
MoeBlee
===
Subject: Re: Definition of finite.
Hey Moe, tell me in Z-I-R, how x is a natural number is defined?
Zuhair
===
Subject: Re: Definition of finite.
I ALREADY mentioned:
And there are other equivalent definitions. I strongly suggest you get
Suppes's set theory book, which as a Dover paperback, and especially
as a used copy, can be purchased for literally just a few dollars.
MoeBlee
===
Subject: Re: Definition of finite.
Yes of course I am ignorant regarding this.
However my argument is perfectly clear.
I prefer defining the class of finite sets ( which is a proper class
by the way) first, and after that I go define the set of natural
numbers as a proper subset of the class of finite sets using
separation with property_ ordinal.
It is easier to define the class first and then you go define a
subclass of it using separation.
To do the opposite i.e to define the proper class of finite sets after
a proper subset of it that is the set of the natural numbers, even if
the last set is defined independently of finitude as to avoid
circularity; looks to me as an upside down approach.
I know that both approaches are equivalent, but I prefer defining
'finite'
first , then we define ' ordinal ' , and after that we define natural
number as
a finite ordinal.
Zuhair
===
Subject: Re: Definition of finite.
It is clear what you prefer in one definition over another; and I
SHARE with you that preference. But what was wrong wa your
mathematical and historical characterizations of the matter.
Now you're in a class theory. That's okay too. Either in, say, Z or in
NBG, yes, we know that we can first define 'finite' and 'ordinal'
without mentioning the axiom of infinity or omega. I already
recommended Suppes's set theory textbook to see how he does that and
how he proves equivalences along the way (actually, some of it is in
exercises that I even worked out with the help of other posters in
sci.logic and sci.math).
So do I. But you need to be more careful about what you say about the
mathematics, metamathematics and the history of it.
MoeBlee
===
Subject: Re: Definition of finite.
Any definition of a class in terms of a proper subset of it, would
give an impression that the defining subset has some kind of
importance over all other sets in this class. I think one shouldn't
use such an approach unless he outlines why this defining set is so
important.
In a thoery which defines finite cardinals and finite ordinals , as
natural numbers , it is clear that Tarski's approach of defining x is
since the finitude of all sets is meansured after that of these
natural numbers.
However I still don't  like it.
The easier way is to define x is finite , then define x is ordinal and
then go define x is natural number.
Zuhair
===
Subject: The surprising Truth
http://www.newsonfocus.com/index.php?option=com_content&task=view&id=587&Ite

mid=13
===
Subject: Code for computing cubic spline coefficients
Does anyone know where I can get C code for computing the coefs of a
best fit cubic spline for some sample data I have?
B
===
Subject: Re: Code for computing cubic spline coefficients
I recently asked a similar question, and Dave Eberly pointed me at the 
BSplineFitDiscrete sample code on his http://www.geometrictools.com 
website.  As I recall, it's C++ code rather than C, but the algorithm is 
of course useful, and there's also a nice PDF document explaining the 
mathematics.
- Brooks
-- 
===
Subject: Re: Code for computing cubic spline coefficients
Regardless, you will learn the best if you gave it a shot yourself
first (if you had spare time).
Good luck,
P.
===
Subject: Re: Code for computing cubic spline coefficients
is what I am trying to do, and any advise on if the approach is right
or wrong would help.  I have a bunch of 2D datapoints which I can plot
along the X-Y axis.  I am trying to find a best fit curve for those
data points.
I have been using this tool
http://www.mathpad.com/public/htmls/new/applets/CurveFitApplet.html
And it shows that a cubic spline best fits my data.
What I would like to find out are what the coefficients of the spline
were.  I would like to know this, so I can use this to compress my
data.
Few questions I have are
1. How does one find the best fit cureve here... trial and error?
2. Do I need to do some sort of pattern matching?
As long as I can save just the coefficients, I can then save the
deltas between the spline Y coordinates and my data set and this
should compress better than the original data... as long as there
arent too many coefficients.
B
===
Subject: Re: Code for computing cubic spline coefficients
Is this for a homework assignment? If it is, you might be surprised to
know that many faculty members are also members of this group;-)
Regardless, you will learn the best if you gave it a shot yourself
first.
Good luck,
P.
===
Subject: Re: Measure termnology
I have heard the term K-finite used for this property.  I think
Folland's analysis text uses it, but I can't find my copy at the
moment.
===
Subject: Re: What is the Automorphism Group of SL(2,5)?
|
|Even when G does not have trivial center, G/Z(G) embeds in the
|automorphism group of G. If G <= H then sometimes that embedding lifts
|to one of H/Z(H) into Aut(G).  In the case of G=SL(2,5), it is
|contained in H=GL(2,5) and the embedding lifts.  A natural description
|is that the automorphism group looks like the group of all invertible
|matrices, but where you consider two matrices the same if they are
|scalar multiples of each other.
|
|The elements of H=GL(2,5) act as conjugation still, but of course
|C_H(G) acts trivially.  Since C_H(G) = Z(H) is just the scalar
|matrices, H/Z(H) acts faithfully on G.  In fact H/Z(H) = PGL(2,5) is
|the entire automorphism group.
|
|The slightly more general construction is that for G <= H, N_H(G) acts
|via conjugation as automorphisms of G, but C_H(G) acts trivially, so
|N_H(G) / C_H(G) embeds into the automorphism group of G.  Choosing H
|wisely so that N_H(G) is big (like all of H) and C_H(G) is small, lets
|you understand the automorphism group.
|
|For perfect groups there is a very close relationship between Aut(G)
|and Aut(G/Z(G)).  You may want to consult Aschbacher's Finite Group
|Theory text, especially the chapter on perfect central extensions (my
|copy is out at the moment).  This should explain why PGL(2,5) and S_5
|are isomorphic, and so the automorphism group did not change.
I spoke with my thesis advisor, and he states that this group, SL(2,5), 
is very relevant as a special case for my thesis.
SL(2,5) is isomorphic to the binary icosahedral group, 2I, 
120 elements, not the 108 I claimed in a previous post) and has a finite 
presentation given by generators and relators as <s,t| (st)^2 = s^3 = 
My new question is, does anyone know an example of two explicit matrices 
A and B in SL(2,5) which satisfy the above relations?
The Wikipedia page lists two elements in mathbb{H}, the quaternions, 
which satify the relation, so that will allow me to use quaternions to 
do calculations; however, I know Aut(2I) realized as PGL(2,5), not as an 
automorphism group of the quaternions.
I could write a C program to check all 120 choose 2 = 7,140 pairs of 
matrices in SL(2,5) to see which satisfy the relations, but if someone 
just knows and could post the answer, it would save me some time.
Also, since Aut(SL(2,5)), which is PGL(2,5) by the above post, is 
isomorphic to S_5, could someone post an explicit isomorphism between 
them? Since I know generators and relators for S_5 are <a,b| a^2, b^3, 
PGL(2,5). (I don't know if I will need this, but it might be nice to 
know.)
-- 
Jeffrey Rolland 
===
Subject: Re: What is the Automorphism Group of SL(2,5)?
The matrices s=[1,-1;1,0], t=[-1,0;-1,-1] satisfy (st)^2 = s^3 = -1,
and t^5 is equivalent to -1 mod 5, so these matrices with entries in
the field with five elements satisfy the relations.  If you look at
other fields of prime order, these will still be decent matrices to
look at.
the group A_5, not S_5.
PGL(2,5) is generated by the (equivalence classes of scalar multiples
of the) matrices s,t and u=[2,0;0,1].
A presentation for GL(2,5) is given by
  < S,T,U | S^3 = T^5 = (S*T)^2, U^4 = 1, S*U =  U*(T^2*S*T^-2*S^-1),
where this is just the presentation for SL(2,5) with an extra
generator U corresponding to u, its order, and its action on SL(2,5).
The corresponding presentation for PGL(2,5) is
  < s, t, u | sss = t^5 = stst, uuuu = 1, su = utts*t^-2*s^-1, tu =
where the last relation is the only different one, and simply
specifies the scalar matrix 2 is equivalent to the identity.
An isomorphism from PGL(2,5) to S_5 is given by sending s to (2,5,3),
t to (1,2,3,4,5), and u to (1,4,5,2).
GAP is a nice tool for working with groups in a computational manner.
If you decide to keep working with groups in a hands on manner, it
might be very useful.  The website http://www.gap-system.org/ has
downloads, documentation, and tutorials.
GAP has a simple interface to an algorithm called coset enumeration
that lets you check your finite presentations are complete.  After
you discovered some elements of your group that satisfy the relations,
it is nice to know you do in fact have the largest group satisfying
those relationships.  Coset enumeration is a process to find the order
of a finite group from a presentation.  Once you define a finitely
presented group, the output of the algorithm can be accessed by simply
calling the Size() function on the group.
If you have interest in computational algebra, coset enumeration is
relatively easy to understand and for presentations of this size can
be programmed fairly easily in javascript to make a little interactive
version which outputs a proof along with the size.
GAP also has a simple interface to an algorithm similar to your try
all pairs idea, but which more efficiently discards sections of the
search space.  Once you have defined two groups you can ask for an
isomorphism between them, using IsomorphismGroups().  To prove
correctness merely requires having a presentation of one of the groups.
===
Subject: Re: What is the Automorphism Group of SL(2,5)?
|The matrices s=[1,-1;1,0], t=[-1,0;-1,-1] satisfy (st)^2 = s^3 = -1,
|and t^5 is equivalent to -1 mod 5, so these matrices with entries in
|the field with five elements satisfy the relations.  If you look at
|other fields of prime order, these will still be decent matrices to
|look at.
|
|the group A_5, not S_5.
|
|PGL(2,5) is generated by the (equivalence classes of scalar multiples
|of the) matrices s,t and u=[2,0;0,1].
|
|A presentation for GL(2,5) is given by
|  < S,T,U | S^3 = T^5 = (S*T)^2, U^4 = 1, S*U =  U*(T^2*S*T^-2*S^-1),
|where this is just the presentation for SL(2,5) with an extra
|generator U corresponding to u, its order, and its action on SL(2,5).
|
|The corresponding presentation for PGL(2,5) is
|  < s, t, u | sss = t^5 = stst, uuuu = 1, su = utts*t^-2*s^-1, tu =
|where the last relation is the only different one, and simply
|specifies the scalar matrix 2 is equivalent to the identity.
|
|An isomorphism from PGL(2,5) to S_5 is given by sending s to (2,5,3),
|t to (1,2,3,4,5), and u to (1,4,5,2).
|
|
|GAP is a nice tool for working with groups in a computational manner.
|If you decide to keep working with groups in a hands on manner, it
|might be very useful.  The website http://www.gap-system.org/ has
|downloads, documentation, and tutorials.
|
|GAP has a simple interface to an algorithm called coset enumeration
|that lets you check your finite presentations are complete.  After
|you discovered some elements of your group that satisfy the relations,
|it is nice to know you do in fact have the largest group satisfying
|those relationships.  Coset enumeration is a process to find the order
|of a finite group from a presentation.  Once you define a finitely
|presented group, the output of the algorithm can be accessed by simply
|calling the Size() function on the group.
|
|If you have interest in computational algebra, coset enumeration is
|relatively easy to understand and for presentations of this size can
|be programmed fairly easily in javascript to make a little interactive
|version which outputs a proof along with the size.
|
|GAP also has a simple interface to an algorithm similar to your try
|all pairs idea, but which more efficiently discards sections of the
|search space.  Once you have defined two groups you can ask for an
|isomorphism between them, using IsomorphismGroups().  To prove
|correctness merely requires having a presentation of one of the groups.
THANK YOU SO MUCH! I was just logging into the 'net at home on Saturday 
night to email my advisor that I was going to have to write a program 
and that writing, debugging, and running the program could conceivably 
take a couple of days, when I read your post. I wasn't at my computer to 
post a reply, and I was out of town at a First Communion all day 
yesterday, so I didn't post a reply before this.
on 5/5, but wasn't willing to go through the learning curve for it, as I 
wasn't sure it was what I needed. Since you recommend it, I will take a 
closer look.
-- 
Jeffrey Rolland 
===
Subject: Missouri State Problem Corner (New Address)
Belatedly, the new problems have been posted at
http://faculty.missouristate.edu/l/lesreid/POTW.html
===
Subject: Pull back map.
I'm not sure if I fully understand what a pull back map is.
I have a definition in my notes that states:
V, W be vector spaces.
and similary for W*.
Then we have (in a diagram which is a triangle)
The pull back map T* is given by
T*(f)(v) =(foT)(v)
This has left me slightly confused. I'm not wholly sure what the pull
back map exactly is. and the notation T*(f)(v) has me slightly
a w? If anyone could give me a pointer, it would be much appreciated.
===
Subject: Re: Pull back map.
The idea is this: you have a function T that lets you go from V to
W. If you have a map f going from W to somewhere else, then you can
use the function T to go from V to wherever f goes: just take a v in V,
send it to W via T, and then apply f to go from W to somewhere
else. 
T* is a map from W* to V*. Thus, the inputs to T* are elements of W*,
and the outputs are elements of V*.
But what kind of animal are the elements of W*? They are functions,
which go from W to R; while the elements of V* are functions as well,
mapping from V to R.
Thus, to define T*, we need to say what T*(f) is for any function
element of V*, that is, a FUNCTION, whose domain is V and whose
codomain is R.
function? One way is to say what it does to any given element of its
domain.
So let v in V. Then T*(f), which is a function from V to R, is defined
at v. We need to say what T*(f) is when you evaluate it at v. That is,
we need to say what [T*(f)](v) is. And the definition is that it is
the element f(T(v)).
Now, does that make sense? Yes: v is in V, so T(v) is a vector in
W. And since f is a function from W to R, we can evaluate f(T(v)),
T*(f)(v) be equal to f(T(v)) will indeed give you a (set theoretic)
map from V to R.
That is, the map T* is defined by pre-composing with T: given any
function f with domain W, you can compose T with f, and that is what
T*(f) is: the function foT (f composed with T).
You need to make sure that T*(f) is indeed a linear transformation,
but that follows because it is the composition of the linear
transformation T and the linear transformation f, so that's not a
problem. For each f, the map T*(f) is indeed an element of V*. 
And you need to make sure that T* is indeed a linear
tranformation. But again, that's not too hard, because if f,g are
elements of W*, and a is any scalar, then T*(f+ag) is the composition
of T with f+ag, and composition distributes over sums and scalar
products of linear transformations; that is,
  (f+ag)oT = (foT) + a(goT) = T*(f) + aT*(g).
-- 
It's not denial. I'm just very selective about
 what I accept as reality.
    --- Calvin (Calvin and Hobbes by Bill Watterson)
Arturo Magidin
magidin-at-member-ams-org
===
Subject: Re: Pull back map.
If I were You I'd hope that someone else will answer too ;)... but
I'll do my best.
transformation T* acting on W* assigning to each element of it an
element of V* obtained by composition. So You should now look at T*(f)
as on element of V* which itself is a function from V to R and thus it
takes elements of V as arguments.
katastrofa_nadfioletu
===
Subject: Re: Pull back map.
answer so soon!
Sorry to be pedantic, but why does it seem trivial that f is an
element of W* ?
Following the arguements that have been presented to me, i understand
that T*(f) should be thought of as an element of V*, its just i feel
inclined to say that T*(f)(v) is from V* to R ?
How should one intuitively of a pull back map?
===
Subject: Re: Pull back map.
I feel asked to reply so I'll do it concisely  keping in mind the fact
that You already have answers for Your questions in Arturo Magidin's
great post.
You have written that it is defined as such an animal ;):
Hmmm.... T*(f) is from V* what means that it takes v's from V to r's
from R and is linear. All Things Bright and Beautifull concerning
details are already covered by A.Magidin.
(We all know there is thought (sic!) missing ;))
Well if the direction forward is given by T - so it is from V to W
than T* works 'backward': it goes from W* BACK to V*. In my opinion it
is much more word play than sth. serious.
katastrofa_nadfioletu
===
Subject: Re: Pull back map.
            days. My association with the Department is that of an alumnus.
The point is: you are trying to describe what a function from W* to V*
is going to be. To describe it, you explain what it does to an
arbitrary element of W*. 
that, it is implicit that you are saying: if x is any element of the
domain, then this is what you do in order to figure out what the
output of the function f is when the input is that given x.
Likewise, above, the phrasing makes it clear that f is meant to be an
element of the domain of T*, i.e., an element of W*.
No, it is not. T*(f)(v) is an element of R. It's not a function from
anywhere to anywhere.
Intuitively what? 
Again: the following works for ANY functions and sets: if you have a
from Y to Z. This is called pre-composing with T. That's what the
pull-back map is. 
-- 
It's not denial. I'm just very selective about
 what I accept as reality.
    --- Calvin (Calvin and Hobbes by Bill Watterson)
Arturo Magidin
magidin-at-member-ams-org
===
Subject: Re: Pull back map.
read your message. You've clearly explained what T* is, and that was
appreciated.
===
Subject: Re: Pull back map.
            days. My association with the Department is that of an alumnus.
   [...]
You are welcome!
In case you are wondering why it is called pullback (the name has
other meanings, by the way, particularly in Category Theory, but you
do not need to worry about that), the reason is this: you have a map T
that you picture as:
      T
and you have maps from W down to the field R:
      T
           |
           |  f
          |/
           R
The map T* allows you to pull back the arrow f so that you get an
arrow going from V to W:
      T
         |
         |   f
T*(f)    |
      | |/
      -   R
So it's as if you took the top end of the arrow f, and pulled it
back so that it is now at V instead of at W.
-- 
It's not denial. I'm just very selective about
 what I accept as reality.
    --- Calvin (Calvin and Hobbes by Bill Watterson)
Arturo Magidin
magidin-at-member-ams-org
===
Subject: Re: Pull back map.
Perhaps it is clearer if you rewrite the definition as
T*(f) =  f o T
Not at all.
Marc
===
Subject: Re: Pull back map.
For me T* is the dual of T, pull-back is a 'base change':
is a kind of 'extending coefficients'
===
Subject: Re: Subsets and intersection graphs
Sorry, small typo: the second type of swap should read:
(ii) choose some subset in G and swap the state of all of its elements in 
states B and C, i.e. those in state B change to state C and vice versa but 
those in state A remained unchanged.
===
Subject: Math overview book
Does anyone know any good books that give an overview of different
topics in mathematics and then talk about applications that the
different fields of mathematics have. I am a year away from getting a
math major, and I am interested in knowing what the use of different
fields of mathematics are.
-cjkogan111
===
Subject: Re: Math overview book
It sounds like you are looking for ideas of where mathematics is applied 
in various careers.  Check out the Mathematical Association of America 
(www.maa.org) and the American Mathematical Society (www.ams.org) for 
resources.  In particular, see
http://www.ams.org/bookstore?co1=AND&co2=AND&co3=AND&d=BOOK&f=G&fn=105&l=100

&op1=AND&op2=AND&op3=AND&p=1&pg1=&pg2=&pg3=ALLF&r=5&s1=&s2=&s3=Careers&subje

c
t=genint&u=
(I don't know if that is the whole link:  Search for careers at 
http://www.ams.org/bookstore .)
http://www.maa.org/students/undergrad/career.html
-- 
Stephen J. Herschkorn                        sjherschko@netscape.net
Math Tutor on the Internet and in Central New Jersey and Manhattan
===
Subject: Re: Math overview book
Courant and Robbins, What is Mathematics?
===
Subject: Re: Math overview book
I second the recommendation of this as a good introductory survey of a
significant part of pure mathematics. For applications to physics,
engineering, economics, operations researcxh, and heaven knows what
else - I'm not sure I know of a similarly good title.  But check books
by John L. Casti.
-- 
Chris Henrich
http://www.mathinteract.com
God just doesn't fit inside a single religion.
===
Subject: Re: Math overview book
Agreed - but for somebody a year away from a maths major?
===
Subject: Re: Math overview book
I guess really what I am looking for is the applications of
mathematics.
Something to help me say - if I have a problem like this, then I need
to look into that branch of mathematics.
Finally, if there isn't a book that is all encompassing, I would be
more interested in focusing on statistical mathematics. In this case,
I would also be interested in a book that talked about what types of
problems can be solved by different branches.
-cjkogan111
===
Subject: Re: The similitude group
Dilations sounds right to me.
Don't know, sorry.
On real normed spaces (including Euclidean space) it appears to follow
from the Mazur-Ulam theorem that such maps must be affine.  This
theorem says that any bijective isometry between real normed spaces is
affine.  If f is considered as a map from (X,||.||) to (X, ||.||/c_f),
it will be a bijective isometry and thus affine.  It follows that f is
this case I suppose the group of dilations of X is some semidirect
product of R, Aut(X) and X.
Wikipedia has a proof of the Mazur-Ulam theorem:
http://en.wikipedia.org/wiki/Mazur-Ulam_theorem .
Hope this helps.
===
Subject: Re: The similitude group
===
Subject: Re: Poincare inequality
I was thinking in the calculus of variation direction and have 
misinterpreted your hint.
===
Subject: Re: Challenge
On 18 Apr 2007 18:27:46 -0700, Fausto Stangler
Take a 2 digit number 10a+b, reverse it to get 10b+a, subtract the
second from the first to get 9a-9b = 9(a-b) which is obviously a
multiple of 9.
Use induction to convince yourself it will be true regardless of the
number of digits in the number.
Remove del for email
===
Subject: Re: An exact simplification challenge - 9
These substitiutions work best :
 A:=6*sin(Pi/14)*(1+sqrt(14-3*sqrt(21))
 *cos(arccot(3*sqrt(3))/6)-sqrt(14+3*sqrt(21))
 *sin(arccot(3*sqrt(3))/6))/(15+2*sqrt(14-3*sqrt(21))
 *cos(arccot(3*sqrt(3))/6)-3*sqrt(21)
 *cos(arccot(3*sqrt(3))/3)-2*sqrt(14+3*sqrt(21))
 *sin(arccot(3*sqrt(3))/6)-sqrt(7)
 *sin(arccot(3*sqrt(3))/3));
 sub := {7^(1/2) = r1, sin(1/3*arccot(3*3^(1/2))) = -1/14*r1+3/7*r1*r3,
(14-3*21^(1/2))^(1/2) = r2, sin(1/14*Pi) = r3,
cos(1/3*arccot(3*3^(1/2))) = 3/14*r4+1/7*r4*r3-4/7*r4*r3^2, 21^(1/2) =
r4, (14+3*21^(1/2))^(1/2) = 2*r1*r2+3/7*r4*r1*r2,
cos(1/6*arccot(3*3^(1/2))) =
13/14*r2-4/7*r4*r3^2*r2+1/7*r4*r2*r3+6/7*r2*r3-18/7*r3^2*r2+3/14*r4*r2,
sin(1/6*arccot(3*3^(1/2))) =
1/14*r1*r2-4/49*r1*r4*r3*r2-2/49*r1*r4*r3^2*r2-3/7*r1*r3*r2+3/98*r4*r1*r2},
[r1 = RootOf(_Z^2-7), r2 = RootOf(_Z^2-14+3*RootOf(_Z^2-21)), r3 =
RootOf(8*_Z^3-4*_Z^2-4*_Z+1,.2225209340), r4 = RootOf(_Z^2-21)];
 (evala@Expand@subs)(sub,A);
A :=
6*sin(1/14*Pi)*(1+(14-3*21^(1/2))^(1/2)*cos(1/6*arccot(3*3^(1/2)))-(14+3*21^

(1/2))^(1/2)*sin(1/6*arccot(3*3^(1/2))))/(15+2*(14-3*21^(1/2))^(1/2)*cos(1/6

*
arccot(3*3^(1/2)))-3*21^(1/2)*cos(1/3*arccot(3*3^(1/2)))-2*(14+3*21^(1/2))^(

1
/2)*sin(1/6*arccot(3*3^(1/2)))-7^(1/2)*sin(1/3*arccot(3*3^(1/2))))
sub := {7^(1/2) = r1, sin(1/3*arccot(3*3^(1/2))) = -1/14*r1+3/7*r1*r3,
(14-3*21^(1/2))^(1/2) = r2, sin(1/14*Pi) = r3,
cos(1/3*arccot(3*3^(1/2))) = 3/14*r4+1/7*r4*r3-4/7*r4*r3^2, 21^(1/2) =
r4, (14+3*21^(1/2))^(1/2) = 2*r1*r2+3/7*r4*r1*r2,
cos(1/6*arccot(3*3^(1/2))) =
13/14*r2-4/7*r4*r3^2*r2+1/7*r4*r2*r3+6/7*r2*r3-18/7*r3^2*r2+3/14*r4*r2,
sin(1/6*arccot(3*3^(1/2))) =
1/14*r1*r2-4/49*r1*r4*r3*r2-2/49*r1*r4*r3^2*r2-3/7*r1*r3*r2+3/98*r4*r1*r2},
[r1 = RootOf(_Z^2-7), r2 = RootOf(_Z^2-14+3*RootOf(_Z^2-21)), r3 =
RootOf(8*_Z^3-4*_Z^2-4*_Z+1,.2225209340), r4 = RootOf(_Z^2-21)]
1
Chris
===
Subject: Re: An exact simplification challenge - 9
[ ... ]
[ ... ]
Why so complicated?? 
  simplify(combine(%)); 
is more than sufficient. - Result:  1  
It is only a pity that  this way 
one cannot see that the formula rests 
on the fact that sin(Pi/14) is the root of a cubic equation 
and on a solution formula for such equations. 
===
Subject: Re: An exact simplification challenge - 9
That code produces no simplifications of Maple V R4...
Converting to algebraic field extension does however.
Chris
===
Subject: A bit scared but I dare to...
I'd like to invite You to speak Your mind on the following idea  of
constructing a Klein Bottle:
 lets start with an ordinary torus
T^2={(exp(iu),exp(iv)); u,v belng to [-.b9,.b9]}
and define a right action of a cyclic group Z 2={e,a} (e being
neutral element) on it by:
(exp(iu),exp(iv))*e=(exp(iu),exp(iv))
(exp(iu),exp(iv))*a=(exp(iu),exp(-iv))
Now take Aut(S^1) - the group of all automorphisms of S^1 and define a
left action of Z 2 on this group by simply combinig elements. I mean,
if g is an automorphism from Aut(S^1) than  (eg)()=g() and
(ag)=a(g()).
In the product T^2 x Aut(S^1) we find equivalence classes:
(t,g).81¤(t*z,zg) where I've put t for an arbitrary element of T^2 

and 
z
for an arbitrary element of Z 2. It means that each class consists of
two elements of the product:
[(exp(iu),exp(iv)),g] = {(exp(iu),exp(iv)),g), (exp(iu),exp(-iv)),ag)}
What we eventually got is a torus with  proper points on its fibres
identified (thus giving a Klein Bottle) and suitably modified group of
its fibres automorphisms.
Is such a construction correct?
katastrofa nadfioletu
===
Subject: Re: A bit scared but I dare to...
Well, maybe I failed to explain this line:
Transformation g is acting on an elements of S^1 and gives obviously
also elements of S^1. Element e acts on this group as an identity.
Element a acts on element g from Aut(S^1) and gives some g' which act
as follows:
(lets put exp(im) as an arbitrary element of S^1)
g'(exp(im))=a(g(exp(im))=a(exp(im'))=exp(-im')
I hope that now someone will drop a line
k_n
===
Subject: Re: Easy puzzle
Another way to express essentially the same answer-- if R is a ring then in 

R[x] we have
(x^4 + 1)(x^2 - 2) = (x - x^3)^2 - 2
so if x is a fourth root of -1 (or if x is a square root of 2) then x-x^3 is 

a square root of 2. 
===
Subject: Re: Jack Sarfatti bio
You really provoked me.
James tried modifying his document three times, after
three consecutive rejections. 
The document in question was reject three times, consecutively. 
The journal submissions were made one after the other, after each rejection. 

The paper was judged as either a trivial point, not worth a paper, or else 
completely wrong.
Afterwards, I told James it was time to get a PhD in math or to go into 
physics and stop hitting his head against the wall.
He would not listen.
There was NO multiple submission of his paper to journals at the same time.
He could not respond to criticism of his document, so the entire process 
became a dialogue of the deaf
I have asked Jack Sarfatti not to foward to me any further messages from 
this forum to me.
You who have made such accusations against me are contemptible and I will 
not reply any further to what you write.
Good by and good riddance
Andrew Beckwith, PhD
===
Subject: Re: Jack Sarfatti bio
Who's you? How come someone with a BigIQ can't figure
out a simple thing like Usenet? Such as quoting the post
you're replying to or learning what the return key is for?
I notice you and Sarfatti both have the same problem.
What do you suppose the problem is? Are you guys just
too lazy? Maybe you can blame it on Dark Energy?
And you kept putting your name on it.
And rightly so, I hear.
Or all three.
Funny the kind of kooks you run into in a BigIQ club, eh?
Who said there was?
I could have told you that.
Wanna bet Jack doesn't listen?
Still don't know who you is. It can't be me because what I
said wasn't an accusation. It was an admission of fraud on
your part, so you must be refering to someone else.
Don't let the door hit you in the ass on the way out.
===
Subject: Re: Jack Sarfatti bio
I think that both are posting through mathforum where posts are viewed
as threaded. The message to which you are replying, however, appears
to be a reply to Dr. Sarfatti's original post, so I'm as confused as
you are as to whom he is addressing.
Dr.'s Sarfatti and Beckwith: if you are reading this, could you get
into the habit of including some text from the posts to which you are
replying, for the benefit of those reading through Google Groups?
===
Subject: Re: Jack Sarfatti bio
how many googoltudes of self-colliding Deloreans are needed
to condense a black hole -- more or less than one?
on a scale of minus ten to minus nine Deloreans,
what is the 2-adic valuation of CO2 hedges,
last year, on a per trade basis?
thus:
I thought it was going to be an insurmountable puzzle,
til I realized, we're *all* a strange loop.  as
Houdini proved, you're only in the straitjacket
*as long as* you think you are;
it's not an acceptable costume *by itself*,
so, you have to change out of it, which won't be
that diffcult, since you put it on by yourself
with a couple of shoehorns (one for each shoe;
don't even *try* to remove the shoehorns .-)
thus:
that's art.  on the other hand,
have you put in a bid for refurbishing Epcot?
Randomecile;
just when you thought,
It/is/safe/to come/in/out/of the/rain!
(tm/patentpretending)
thus:
phase.  The set of these is just the Riemann sphere!
thus:
the famous result by what-is-his-**** also generates negative values,
which are either composite, or not necessarily prime
(I forgot .-)...
I think, it was a formula in 26 variables and 25 degrees i.e.,
usually given as multinomial factors, as part of a result,
proving that there is no formula to solve any Diophantine eq.
... correct?
thus:
yeah, all you world patriots & matriots;
just sit on your hands, while Dick goes ape
in Sudan, Iran and possibly all other once and
future British quagmires....  Belize, Canada, Trinidad
AND Tobago; the list goeth on.
thus:
look, up in the sky -- it's Googoltude (TM) ?!?
http://www.ldeo.columbia.edu/LCSN/Eq/20010911_WTC/WTC_LDEO_KIM.pdf
--nnerfmann!
===
Subject: Re: Jack Sarfatti bio
I am not replying to any more of your accusations or
innuendo.
Go away. I am finished with you.
===
===
Subject: Brian Quincy Hutchings
Who let this nut out of his strait jacket? ;-)
===
Subject: Re: Brian Quincy Hutchings
I thought it was going to be an insurmountable puzzle,
til I realized, we're *all* a strange loop.
Houdini proved,
you're only in the straitjacket *as long as*
you think you are;
it's not an acceptable costume *by itself*,
so, you have to change out of it, which won't be
that diffcult, since you put it on by yourself
with a couple of shoehorns (one for each shoe;
don't even *try* to remove the shoehorns .-)
thus:
that's art.  on the other hand,
have you put in a bid for refurbishing Epcot?
Randomecile;
just when you thought,
It/is/safe/to come/in/out/of the/rain!
(tm/patentpretending)
thus:
This octahedron is a discrete version of the Bloch ball describing
you don't know about that, I should remind you:
phase.  The set of these is just the Riemann sphere!
thus:
did the OP prove that this algorithm always makes primes?
the famous result by what-is-his-**** also generates negative values,
which are either composite, or not necessarily prime
(I forgot .-)
I think, it was a formula in 26 variables and 25 degrees i.e.,
usually given as multinomial factors, as part of a result,
proving that there is no formula to solve any Diophantine eq.
... correct?
thus:
yeah, all you world patriots & matriots;
just sit on your hands, while Dick goes ape
in Sudan, Iran and possibly all other once and
future British quagmires.
Belize, Canada, Trinidad AND Tobago;
the list goeth on.
tudy_says_oil_reliance_strains_military?mode=PF
thus:
the report quoted below, as the sole reference
for the original posting, herein, says soem thing
of significance about the magnitudes of energy,
directly at the top of page 5.
look, up in the sky -- it's Googoltude (TM) ?!?
http://www.ldeo.columbia.edu/LCSN/Eq/20010911_WTC/WTC_LDEO_KIM.pdf
--nnerfmann!
===
Subject: Strange Loop
Doug Hofstadter has a new book Strange Loop.
My physics is based on that general idea.
===
Subject: Re: Jack Sarfatti bio
Just plain drop dead.
I could care less what you say about me. 
I tried to help James Harria out. It failed.
Just go to hell. You are despicable.
===
Subject: Re: Jack Sarfatti bio
1. I dropped trying to help James Harris after he wanted to start suing 
people. That was several months ago. I blocked his e mail.
After all of efforts failed, I drew the conclusion James was unreasonable 
and would not learn
4. I urged James to get a PhD. He refused to enroll in any institution of 
higher learning for this endeavor.
Tarring me with guilt by association over James, is over the top. 
In a word, drop it. Find some other issue to hit me with. The James Harris 
saga is old hat and I am tired of it.
Andrew Beckwith, PhD
===
Subject: Re: Jack Sarfatti bio
Were you a contributing author?  If so, you contributed to something 
completely bogus.  If not, you did something that is clearly unethical. 
  Either way it doesn't look good.
===
Subject: Re: Jack Sarfatti bio
That's fraud.
But doesn't James have a BigIQ, just like you do?
Are you trying to imply a BigIQ ain't worth  without
an education?
No, you tarred yourself.
I didn't see any hint of an apology in the above,
so why should it be dropped?
People in Hell want ice water.
===
Subject: JHS issue
Are you trying to imply a BigIQ ain't worth  without
an education?
In your case education has obviously been wasted or missed no matter what 
your IQ. ;-)
===
Subject: Re: JHS issue
Better to not have it than have it and squander it
like you and Beckwith.
===
Subject: Re: JHS issue
Look you fool. You know nothing about me an Beckwith. You have no basis to 
say we squandered anything. Even if we did, what business is it of yours? 
You seem to live only to stalk creative people on the WEB with vicious 
annoying allegations. You are a minor demon from Hell.
===
Subject: Re: Jack Sarfatti bio
===
Subject: Re: Jack Sarfatti bio
Well in light of your explanation I guess that could be true, though I
hope you can at least appreciate why people would jump to conclusions
about you when your name appears on APF. Sorry if you have explained
this before, I'm relatively new here.
Consider it dropped.
===
Subject: Re: Jack Sarfatti bio
===
Subject: Re: Jack Sarfatti bio
It was indeed me. You can see Andy writing about his friend JSH here:
The paper he co-authored with JSH may be read here:
I did not intend to insult you with my original post. If anything you
should consider it a friendly warning; if I were in your position, be
that the position of a crank or misunderstood genius (I don't claim to
know which you are) then Dr. Beckwith is the last person I would want
in my corner. Have a look at the paper and, if you have time, the many
other threads in which Harris defends its conclusions in the face of
simple counterexamples, and you should hopefully see why.
===
Subject: Re: Jack Sarfatti bio
===
Subject: Re: Jack Sarfatti bio
I'm not a mathematician but an amateur who has learnt a bit of maths,
and that is more than enough to be able to claim with complete
confidence that James' work is bogus.
Could, but doesn't. He is one of those people who thinks that
ignorance is somehow an asset.
It is a characteristic of much of JSH's work that it looks like real
maths from a distance. The nonsense becomes apparent upon close
inspection.
On the subject of your own work, do you have some references where I
can read your theories in detail? I'm afraid I can never make head or
tail of the summaries you post.
===
Subject: Re: Jack Sarfatti bio
I should have written above: actually I do not believe that Dr.
as a co-author to it in a bid to enhance Harris' credibility. Again, I
have no idea whether you are a crank or not, but James Harris
certainly is.
===
Subject: Re: Jack Sarfatti bio
Well I will ask Andy if I remember to. It's not pressing. I did try to read 

that URL and I could not make head or tail of it, but I did not try that 
hard 
and looked at it quickly, and frankly number theory sort of stuff makes my 
eyes glaze over - it's not my thing. I am interested in using physics to 
explain and predict actual phenomena and to keep the excess math baggage to 

a 
minimum when possible. My main interest these days is in cosmology - dark 
energy and dark matter with applications including military.
===
Subject: Did you read about that?
you can take a look for this web sites
http://www.imanway.com/vb/forumdisplay.php?f=90
http://www.geocities.com/islamone l/index.htm
or read this
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What is Islam?
The name of this religion is Islam, the root of which is S-L-M, which
means peace. The word Salam, derived from the same root, may also
mean greeting one another with peace.
One of the beautiful names of God is that He is Peace. But Islam means
more than that: it means submission to the One God, and it means
living in peace with the Creator -- peace within one's self, peace
with other people, and peace with the environment.
Thus, Islam is a total system of living. A Muslim is supposed to live
in peace and harmony with all these segments. It follows that a Muslim
is any person, anywhere in the world, whose obedience, allegiance, and
loyalty are to God, the Lord of the Universe.
The followers of Islam are called Muslims. Muslims are not to be
confused with Arabs.
Muslims may be Arabs, Turks, Persians, Indians, Pakistanis,
Malaysians, Indonesians, Europeans, Africans, Americans, Chinese, or
other nationalities.
An Arab could be a Muslim, a Christian, a Jew or an atheist. Any
person who adopts the Arabic language is called an Arab.
The language of the Qur'an (the Holy Book of Islam) is Arabic. Muslims
all over the world try to learn or improve their Arabic, so that they
may be able to read the Qur'an and understand its meaning. They pray
in the language of the Qur'an, Arabic. Islamic supplications to God
could be (and are) delivered in any language.
There are one billion Muslims in the world; there are about 200
million Arabs. Among those two hundred million Arabs, approximately
ten percent are not Muslims. Thus Arab Muslims constitute only about
twenty percent of the Muslim population of the world.
[Hyphen]
ALLAH THE ONE AND THE ONLY GOD
Allah was the Arabic word for God long before the birth of Muhammad,
peace be upon him.
Muslims believe that Allah is the name of the One and Only God. He is
the Creator of all human beings. He is the God for the Christians, the
Jews, the Muslims, the Buddhists, the Hindus, the atheists, and all
others. Muslims worship God, whose name is Allah. They put their trust
in Him and they seek His help and His guidance.
Muhammad was chosen by God to deliver His Message of Peace, namely
Islam. He was born in 570 C.E. (Common Era) in Makkah, Arabia. He was
entrusted with the Message of Islam when he was at the age of forty
years. The revelation that he received is called the Qur'an, while the
message is called Islam.
Muhammad is the very last Prophet of God to mankind. He is the final
Messenger of God. His message was and is still to the Christians, the
Jews and the rest of mankind. He was sent to those religious people to
inform them about the true mission of Jesus, Moses, Jacob, Isaac, and
Abraham.
Muhammad is considered to be the summation and the culmination of all
the prophets and messengers that came before him. He purified the
previous messages from adulteration and completed the Message of God
for all humanity. He was entrusted with the power of explaining,
interpreting and living the teaching of the Qur'an.
Muslims are required to respect all those who are faithful and God
conscious people, namely those who received messages. Christians and
Jews are called People of the Book. Muslims are asked to call upon the
People of the Book for common terms, namely, to worship One God, and
to work together for the solutions of the many problems in the
society.
Christians and Jews lived peacefully with Muslims throughout centuries
in the Middle East and other Asian and African countries. The second
Caliph, Umar, chose not to pray in the church in Jerusalem, so as not
to give later Muslims an excuse to take it over. Christians entrusted
the Muslims, and as such the key of the Church in Jerusalem is still
in the hands of the Muslims.
When Jews fled from Spain during the Inquisition, they were welcomed
by the Muslims. They settled in the heart of the Islamic Caliphate.
They enjoyed positions of power and authority. Throughout the Muslim
world, churches, synagogues and missionary schools were built within
the Muslim neighborhoods. These places were protected by Muslims
during bad times and good, and have continued to receive this
protection during the contemporary crises in the Middle East
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What is the Qur'.89n?
The Qur'.89n is the name given to Allah's speech that He revealed to His
servant and Messenger Muhammad (peace be upon him); speech that is
recited as an act of worship, is miraculous, and cannot be imitated by
man. It is the name of Allah's Book, and no other book is called by
this name.
The connection between the Creator and his Creation is by way of His
Messengers, and these Messengers only know what Allah wants from them
by way of revelation, either directly or indirectly. The rational mind
cannot dismiss the possibility of revelation, since nothing is
difficult for the all-powerful Creator
revelation is a communication between two beings: one that speaks,
commands, and gives, and another who is addressed, commanded, and
receives. Prophet Muhammad (peace be upon him) - as with every Prophet
- never confused himself with the One who gave the revelation to him.
As a human being, he felt his weakness before Allah, feared Allah's
wrath if he should disobey, and hoped for Allah's mercy.
1. No matter how brilliant or insightful a person might be, there is
no way that he could discuss the happenings of nations lost to
antiquity, issues of belief and Divine Law, the rewards and
punishments of Heaven and Hell, and future events, all in such great
detail without any contradiction and with a most perfect style and
literary form. The Prophet (peace be upon him) had never once read a
book nor met with any historian
2. The Qur'.89n makes to the disbelievers a stern challenge that they
will never be able to produce a chapter similar to it. Such a
challenge would never have come from the Messenger (peace be upon him)
3. The Qur'.89n, in some places, sternly rebukes Muhammad (peace be upon
him) where he acted upon his own judgment in something and did not
decide on what is best. The Qur'.89n clarified the truth and showed the
error of the Prophet (peace be upon him).
4. Many verses of the Qur'.89n begin with the imperative verb Say! As
a matter of fact, this occurs more than three hundred times,
addressing Muhammad (peace be upon him) and directing him with respect
to what he should say. He, thus, did not follow his own desires; he
followed only what was revealed to him.
5. Complete harmony exists between what the Qur'.89n says regarding the
physical world and what has been discovered by modern science. This
has been a source of amazement for a number of contemporary western
researchers.
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Who was Muhammad?
Muhammad (peace be upon him) was born in Makkah in the year 570,
during the period of history Europeans called the Middle Ages.
Muhammad was the son of Aamenah and Abdullah, from the tribe of
Quraysh. He was a direct descendant of Ishmael, the eldest son of
prophet Abraham. Muhammad's father died just before he was born, and
his mother passed away when he was six. He was raised by this
grandfather, the chief of Makkah; and upon his grandfather's death,
Muhammad came under the care of his uncle, Abu Talib.
Muhammad was a shepherd in his youth. As he grew up, he became known
for his truthfulness, generosity, and sincerity; earning the title of
al Amin, the trustworthy one. Muhammad was frequently called upon to
arbitrate disputes and counsel his fellow Makkans.
At age 25, Muhammad married Khadijah, an honorable and successful
businesswoman. They were blessed with two sons and four daughters. It
was an ideal marriage and they lived a happy family life.
Muhammad was of a contemplative nature and had long detested the
decadence and cruelty of his society. It became his habit to meditate
from time to time in the cave of Hira' near the summit of Jabal an-
Nur, the Mountain of Light on the outskirts of Makkah.
How did Muhammad become a Messenger of God?
At the age of 40, while engaged in a meditative retreat, Muhammad
received his first revelation from God through the Archangel Gabriel.
This revelation, which continued for twenty three years, is known as
the Qur'an
Muhammad began to share the revelations he received from God with the
people of Makkah. They were idol worshippers, and rejected Muhammad's
call to worship only One God. They opposed Muhammad and his small
group of followers in every way. These early Muslims suffered bitter
persecution.
In 622, God gave the Muslim community the command to emigrate. This
event, the hijrah or migration, in which they left Makkah for the city
of Madinah, some 260 miles to the North, marks the beginning of the
Muslim calendar.
Madinah provided Muhammad and the Muslims a safe and nurturing haven
in which the Muslim community grew. After several years, the Prophet
and his followers returned to Makkah and forgave their enemies. Then,
turning their attention to the Ka'bah (the sanctuary that Abraham
built), they removed the idols and rededicated it to the worship of
the One God. Before the Prophet died at the age of 63, most of the
people of Arabia had embraced his message. In less than a century,
Islam had spread to Spain in the west, as far east as China.
===
Subject: half angle tangent identity
Given tan(x / 2) = sin x/(1 + cos x)
What identity can be applied to sin x
and which one can be applied to
(1 + cos x) so that we can derive tan ( x / 2)
to establish that they are equal?
--
conrad
===
Subject: Re: half angle tangent identity
If you *must* proceed in the way your question specifies,
   sin x/(1 + cos x)
 = sqrt[ (sin x)^2 / (1 + cos x)^2 ]
 = sqrt[ { 1 - (cos x)^2 } / (1 + cos x)^2 ]
With a bit of algebra, this can be written as
 = sqrt[ ( 1 - cos x) / 2 ] / sqrt[ ( 1 + cos x) / 2 ]
Using the half-angle identities, this is
 = sin(x/2) / cos(x/2) = tan(x/2)
But it's simpler to verify your identity
   tan(x / 2) = sin x/(1 + cos x)   (*)
by making the substitution  x = 2y, giving
   tan(y)  =  sin(2y) / [ 1 + cos(2y) ]   (**)
Using the double-angle identities, this is
   =  2 sin(y) cos(y) / [ 2 (cos y)^2 ]
   =  sin(y) / cos(y)  =  tan(y)
This verifies (**), hence also (*).
 
===
Subject: Re: half angle tangent identity
Uhhh.. You're GIVEN that they're equal...Your very words...
(1 + cos x) then ...
Just a general hint... I find it easier to remember the double angle
formulas, so rewrite your identity to be proved as:
tan y = sin(2y)/(1+cos(2y) )
If you use the cos(2y) identity that has a -1 in it, you should be
well on your way...
===
Subject: DataQ Data Acquisition Custom Software
Biopotential Biofeedback Data Acquisition
DataQ Data Acquisition Custom Software
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(Preprogrammed Port and Drivers)
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0-15 Plot bits + Analog
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Record WaveForms for later Study.
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Visit DataQ Home site
www.dataq.com
Or there support forum
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===
Subject: Re: Gerald t' Hooft
Apparently not.  All's well with the world after all.
===
Subject: Out of the mouths of idiots
Hey Gibberish Boogie Man
Why don't you keep silent until you have something that is is not trite, 
that is interesting and intelligent to say? You are living proof that God 
makes mistakes.
===
Subject: Re: Out of the mouths of idiots
Here's something definitely trite, not very intelligent, but possibly
mildly
interesting. I like the way 't Hooft's name is spelled in his book 50
years
of Yang-Mills Theory - Gerardus 't Hooft. Makes him sound like some
medievil monk:
http://www.amazon.ca/Years-Yang-Mills-Theory-Gerardust-Hooft/dp/9812560076/r

ef=sr_1_10/702-5521257-6164827?ie=UTF8&s=books&qid=1178457461&sr=1-10
John R Ramsden
===
Subject: Re: Out of the mouths of idiots
It is or was common in the Netherlands to give children a latin name,
but call them by the colloquial version of it.
Victor.
-- 
Victor Eijkhout -- eijkhout at tacc utexas edu
===
Subject: Geradus t'Hooft
===
Subject: Error in t'Hooft's Nobel Lecture?
My point is especially clear in Bohm's pilot wave-hidden variable 
interpretation. It is less clear in other interpretations.
===
Subject: Quark force and NASA Pioneer Anomaly Analogy
G. t'Hooft Nobel Lecture Rev Mod Phys 2000 on the quark forces:
Note these forces obtain a constant strength at arbitrarily large 
distances for quarks.
A formally similar phenomenon seems to be measured in the anomalous motions 

of the 2 NASA Pioneer space vehicles at outer regions of our solar system 
beyond Saturn with an attractive g-force = cH with H = Hubble parameter.
OK why the asymptotic Hubble parameter? Well it is related to the local dark 

energy density
a(t) ~ e^Ht
Dark energy density ~ /zpf ~ 1/(Hubble radius)^2 ~ 1/(Area of future 
deSitter horizon).
One must multiply by c^4/G = superstring tension to get conventional units
Hubble radius ~ 10^28 cm ~ 13.7 billion light years
Hubble radius is c/H.
/zpf(cosmic dark energy) ~ (H/c)^2
A digression on NASA Pioneer anomaly
the g-force (per unit test mass) is
g = - dV(dark matter)/dr =  +2c^2/(clumped dark matter)r = -c^2|/(dark 
matter)|r
where / < 0 dark matter of negative zero point energy density with 
equal and opposite positive quantum exotic vacuum pressure.
Let r = 0 be the position of our Sun.
Granted this is adhoc, but if we suppose
/(clumped dark matter) = (H/c)(1/r)
i.e., a dark matter solar halo hollow shell concentric with Sun's center 
(blown out from Sun?)
g = cH with fits the actual observation.
Curious.
Similarly for quark confinement force as a strong ZPF induced gravity 
force - a dark matter bag / ~ 1/(length scale)r.
Back to large-scale cosmology:
In terms of Bekenstein's horizon information theory & world hologram our 
pocket universe on the cosmic landscape is an IT FROM BIT simulation VALIS 
holographic image projected back FROM the future retrocausally worth ~ 
10^122 c-BITS
http://qedcorp.com/APS/ureye.gif
?
Eye at future deSitter 2D horizon (anyonic Star Maker intelligence?) 
sends advanced signals back in time to trigger inflation from the false 
vacuum retrocausing low entropy of early universe relative to late universe 

in a Novikov loop in time.
My point is especially clear in Bohm's pilot wave-hidden variable 
interpretation. It is less clear in other interpretations.
Jack Sarfatti
sarfatti@pacbell.net
If we knew what it was we were doing, it would not be called research, 
would it?
- Albert Einstein
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
http://lifeboat.com/ex/bios.jack.sarfatti
http://qedcorp.com/APS/Dec122006.ppt
http://www.flickr.com/photos/lub/sets/72157594439814784
===
Subject: Re: Gerald t' Hooft
It's a troll, I think.  Not even Sarfatti would mistake
Gerard t'Hooft for Gerald.
Tom
===
Subject: Re: Gerald t' Hooft
05/05/2007
But would he mistake 't Hooft for t'Hooft?
-- 
Unsolicited bulk E-mail subject to legal action.  I reserve the
right to publicly post or ridicule any abusive E-mail.  Reply to
domain Patriot dot net user shmuel+news to contact me.  Do not
===
Subject: Shmuel Shmutz
My God a Jew with a trite mind? I'm shocked. Shmuel you are a disgrace to 
the race and I descend from Rabbi Rashi 1040-1105 AKA Solomon ha-Zarfati. 
See 
my book Destiny Matrix. How dare you descend to the level of the Trolls?
===
Subject: Re: Shmuel Shmutz
Change I descend to I ascend from. But in Shmuel Putz's case the correct 
word is descend to the Trolls. ;-)
===
Subject: More inanities from morons
How trivial your mind's are. Many smart people are dyslexic. For example 
Lenny Susskind could hardly spell when I met him at Cornell in 1963 yet he 
is 
a top physics professor at Stanford. You idiots are anal compulsive without 

a 
creative thought in your midget minds. Yes, I made all those hasty errors. 
So 
what? You are HACK MINDS, what Ayn Rand calls Second Handers. like that 
Digital Maoist Calton Bolick over at the Wicked Pedio Files. Go split your 
inane hairs over at Wiki. You have the mentality of a bureaucrat in a novel 

by Kafka. You are so stupid that the physics ideas of great elegance and 
beauty pass over your head and all you can think of is Gerald or where to 
place the ' in tHooft.
===
Subject: Re: More inanities from morons
Change How trivial your mind's are to
How trivial your minds are.
And I send messages from different locations. You would cool guys like you 
could figure that one out.
===
Subject: Retro-causal signal nonlocality
Evidence for the violation of retarded causality violating micro-quantum 
theory.
Do some of us avoid tragedy by foreseeing it? Some scientists nowbelieve 
that the brain really CAN predict events before they happen
Professor Dick Bierman sits hunched over his computer in a darkened room. 
The gentle whirring of machinery can be heard faintly in the background.
He smiles and presses a grubby-looking red button.
In the next room, a patient slips slowly inside a hospital brain scanner. If 

it wasn't for the strange smiles and grimaces that flicker across the 
woman's 
face, you could be forgiven for thinking this was just a normal health 
check.
But this scanner is engaged in one of the most profound paranormal 
experiments of all time, one that may well prove whether or not it is 
possible to predict the future.
For the results - released exclusively to the Daily Mail - suggest that 
ordinary people really do have a sixth sense that can help them 'see' the 
future.
Such amazing studies - if verified - might help explain the predictive 
powers of mediums and a range of other psychic phenomena such Extra Sensory 

Perception, deja vu and clairvoyance. On a more mundane level, it may 
account 
for 'gut feelings' and instinct.
The man behind the experiments is certainly convinced. We're satisfied 
that people can sense the future before it happens, says Professor Bierman, 

a psychologist at the University of Amsterdam.
We'd now like to move on and see what kind of person is particularly good 
at it.
And Bierman is not alone: his findings mirror the data gathered by other 
scientists and paranormal researchers both here and abroad.
Professor Brian Josephson, a Nobel Prize-winning physicist from Cambridge 
University, says: So far, the evidence seems compelling. What seems to be 
happening is that information is coming from the future.
In fact, it's not clear in physics why you can't see the future. In 
physics, you certainly cannot completely rule out this effect.
Virtually all the great scientific formulae which explain how the world 
works allow information to flow backwards and forwards through time - they 
can work either way, regardless.
Shortly after 9/11, strange stories began circulating about the lucky few 
who had escaped the outrage.
It transpired that many of the survivors had changed their plans at the last 

minute after vague feelings of unease.
It was a subtle, gnawing feeling that 'something' was not right. Nobody 
vocalised it but shortly before the attacks, people started altering their 
plans out of an unspoken instinct.
One woman suffered crippling stomach pain while queuing for one of the 
ill-fated planes which flew into the World Trade Center.
She made her way to the lavatory only to recover spontaneously. She missed 
her flight but survived the day. Amid the collective outpouring of grief and 

horror it was easy to overlook such stories or write them off as 
coincidences.
But in fact, these kind of stories point to an interesting and deeper truth 

for those willing to look.
If, for example, fewer people decided to fly on aircraft that subsequently 
crashed, then that would suggest a subconscious ability to divine the 
future. 
Well, strange as it seems, that's just what happens.
The aircraft which flew into the Twin Towers on 9/11 were unusually empty. 
All the hijacked planes were carrying only half the usual number of 
passengers. Perhaps one unusually empty plane could be explained away, but 
all four?
And it wasn't just on 9/11 that people subconsciously seemed to avoid 
disaster. The scientist Ed Cox found that trains 'destined' to crash carried 

far fewer people than they did normally.
Dr Jessica Utts, a statistician at the University of California, found 
exactly the same bizarre effect.
If it was possible to divine the future, you might expect those at the sharp 

end, such as pilots, to have the most finely tuned instincts of all. And 
again, that's just what you see.
When the Air France Concorde crashed in 2000, it wasn't long before the 
colleagues of those killed in the crash spoke about a sense of foreboding 
that had gripped the crew and flight engineers before the accident.
Speaking anonymously to the French newspaper Le Parisien, one spoke of a 
'morbid expectation of an accident'.
I had this sense that we were going to bump into the scenery, he said.
The atmosphere on the Concorde team for the last few months, if one has 
the guts to admit it, had been one of morbid expectation of an accident. It 

was as if I was waiting for something to happen.
All of these stories suggest that we can pick up premonitions of events that 

are yet to be.
Although these premonitions are not in glorious Technicolor, they are often 

emotionally powerful enough for us to act upon them.
In technical parlance it is known as 'presentiment' because emotional 
feelings are being received from the future, not hard facts or information.
The military has long been fascinated by such phenomena. For many years the 

US military (and latterly the CIA) funded a secretive programme known as 
Stargate, which set out to investigate premonitions and the ability of 
mediums to predict the future.
Dr Dean Radin worked on the Stargate programme and became fascinated by the 

ability of 'lucky' soldiers to forecast the future.
These are the ones who survived battles against seemingly impossible odds. 
Radin became convinced that thoughts and feelings - and occasionally-actual 

glimpses of the future - could flow backwards in time to guide soldiers.
It helped them make life-saving decisions, often on the basis of a hunch.
He devised an experiment to test these ideas. He hooked up volunteers to a 
modified lie detector, which measured an electrical current across the 
surface of the skin.
This current changes when a person reacts to an event such as seeing an 
extremely violent picture or video. It's the electrical equivalent of a 
wince.
Radin showed sexually explicit, violent or soothing images to volunteers in 

a random sequence determined by computer.
And he soon discovered that people began reacting to the pictures before 
they saw them. It was unmistakable. They began to 'wince' a few seconds 
before they actually saw the image.
And it happened time and time again, way beyond what chance alone would 
allow.
So impressive were Radin's results that Dr Kary Mullis, a Nobel Prizewinning 

chemist, took an interest. He was hooked up to Radin's machine and shown the 

emotionally charged images.
It's spooky, he says I could see about three seconds into the future. 
You shouldn't be able to do that.
Other researchers from around the world, from Edinburgh University to 
Cornell in the US, rushed to duplicate Radin's experiment and improve on it. 

And they got similar results.
It was soon discovered that gamblers began reacting subconsciously shortly 
before they won or lost. The same effect was seen in those terrified of 
animals, moments before they were shown the creatures.
The odds against all of these trials being wrong are literally millions to 
one against.
Professor Dick Bierman decided to take this work even further. He is a 
psychologist who has become convinced that time as we understand it is an 
illusion. He could see no reason why people could not see into the future 
just as easily as we dip into memories of our past.
He's in good company. Einstein described the distinction between the past, 
present and future as 'a stubbornly persistent illusion'.
To prove Einstein's point, Bierman looked inside the brains of volunteers 
using a hospital MRI scanner while he repeated Dr Radin's experiments.
These scanners show which parts of the brain are active when we do certain 
tasks or experience specific emotions.
Although extremely complex, and with each analysis taking weeks of computing 

time, he has run the experiments twice involving more than 20 volunteers.
And the results suggest quite clearly that seemingly ordinary people are 
capable of sensing the future on a fairly consistent basis. Bierman 
emphasises that people are receiving feelings from the future rather than 
specific 'visions'.
It's clear, though, that if ordinary people can receive feelings from the 
future then perhaps the especially gifted may receive visions of things yet 

to be.
It's also clear that many paranormal phenomena such as ESP and clairvoyance 

could have their roots in presentiment.
After all, if you can see a few seconds into the future, why not a few days 

or even years? And surely if you could look through time, why not across 
great distances?It's a concept that ties the mind in knots, unless you're a 

physicist.
I believe that we can 'sense' the future, says the Nobel Prizewinning 
physicist Brian Josephson.
We just haven't yet established the mechanism allowing it to happen.
People have had so called 'paranormal' or 'transcendental' experiences 
along these lines. Bierman's work is another piece of the jigsaw. The fact 
that we don't understand something does not mean that it doesn't happen.'
If we are all regularly sensing the future or occasionally receiving 
glimpses of it, as some mediums claim to do, then doesn't that mean we can 
change the future and render the 'prediction' obsolete?
Or perhaps we were meant to receive the premonition and act upon it? Such 
paradoxes could go on for ever, providing a rich seam of material for films 

such as Minority Report - based on a short story of the same name - in which 

a special police department is able to foresee and prevent crimes before 
they 
have even taken place.
Could such science fiction have a grain of truth in it after all? The 
emerging view, Bierman explains, is that 'the future has implications for 
the 
past'.
This phenomena allows you to make a decision on the basis of what will 
happen in the future. Does that restrain our free will? That's up to the 
philosophers. I'm far too shallow a person to worry about that.
The problem with presentiment is that it appears so nebulous that you can't 

rely on it to make reliable decisions. That may be the case, but there are 
plenty of instances where people wished they had listened to their 
premonitions or feelings of presentiment.
One of the saddest involves the Aberfan disaster. This occurred in 1966 when 

a coal tip collapsed and swept through a Welsh school killing 144 people, 
including 116 children. It turned out that 24 people had received 
premonitions of the tragedy.
One involved a little girl who was killed. She told her mother shortly 
before she was taken to school: I dreamed I went to school and there was no 

school there. Something black had come down all over it.
So should we listen to our instincts, hunches and dreams? Some experts 
believe we may already be using them in our everyday lives to a surprising 
degree.
Dr Jessica Utts at the University of California, who has worked for the US 
military and CIA as an independent auditor of its paranormal research, 
believes we are constantly sampling the future and using the knowledge to 
help us make better decisions.
I think we're doing it all the time, she says. We've looked at the 
data and it does seem to happen.
So perhaps the Queen in Through The Looking Glass was right: It's a poor 
sort of memory that only works backwards.
from London Evening Standard May 5, 2007
===
Subject: Re: Retro-causal signal nonlocality
How's the time machine coming along?
===
Subject: Time Machine for Trolls
We plan to round up all The Trolls, the usual suspects and put them back in 

time as food for sabre tooth tigers and the like.
===
Subject: Re: More inanities from morons
That's you would think cool guys like you could figure that one out.
===
Subject: Re: Gerald t' Hooft
===
Subject: Re: Gerald t' Hooft
That's just the thing, Sarfatti Lite.  While I have known
the real Jack Sarfatti to be a little nuts and a little
full of himself, I have never known him to be hastily
careless (or is that carelessly hasty?).  You've had
plenty of time, also, to correct the spelling 'tHooft.
Anyway, Jack is also way too bright to engage in a tit
for tat where nothing is to be gained.  And three:  
when you do mention physical theories in this troll,
they are empty of the logical content that Jack strives
for in his hit and run postings.  You wouldn't be
capable of sustaining a dialogue on that level.
Pretty good troll, though.
Tom
===
Subject: Re: Gerald t' Hooft
Look Mr Smarty Pants, although I am a Virgo and like to get things right 
especially spelling and grammar unlike you I am not the perfect genius and 
especially in silly e-mails like this am prone to make mistakes. One mistake 

I characteristically make when I am in a rush and do not bother to read the 

rough draft before sending is to forget to use question marks where they 
belong. I also sometimes misuse it's and its and more rarely misuse 
their and there. I am not good at spelling other people's names. So, 
yes, it's me, The One And Only who can write for example
M^a^b = dTheta^a/Phi^b - Theta^a/dPhi^b
Meantime in your trite obsessions over spelling t'Hooft's first name you 
miss the interesting physics about the dimensions of coupling constants 
needed for a renormalizable sensible quantum field theory in Section 4 of 
t'Hooft's lectures on the subject. Of course none of you really understand 
what this is all about do you?
Step right up. Let's see if the Trolls know anything.
Sarfatti's Homework Problem Set #1
1. Define field.
2. How does a classical field differ from a quantum field?
3. What is the relationship between Feynman's path integral formulation of 
quantum field theory and traditional quantum field theory?
4. What does symmetry mean in field theory?
5. What does it mean to localize a global symmetry?
Start there.
The Real Sarfatti who mis-spelled t'Hooft's first name - oooh what a Mortal 

Sin!
===
Subject: Re: Gerald t' Hooft
These are pretty basic questions, Jack.
A classical field is a map from spacetime to some target space, which
may satisfy additional requirements (for example it may be smooth or
may be a section of a bundle over spacetime).
A quantum field is what you get when you quantise a classical field,
for example by canonical quantisation.
Although path integrals have not been rigorously defined in general,
in simple cases they can be defined and shown to be equivalent to
canonical quantisation. In such cases different choices of path
integral correspond to different choices in canonical quantisation
such as operator orderings.
A symmetry in classical field theory is an of automorphism of the
spacetime and of the target space which leave the action invariant. In
quantum field theory a symmetry is a map on the Hilbert space which
preserves transition probabilities. Such maps are known to be either
linear and unitary or antilinear and antiunitary due to Wigner's
theorem.
If the action of a classical field theory is invariant under
multiplication of the fields by constant elements of a symmetry Lie
group G then one may define a new theory that is invariant under
multiplication of the fields by spacetime-dependent elements of G by
incorporating a new field into the theory called a gauge field. If the
matter field is a section of a vector bundle associated to some
principal G-bundle then the gauge field is described by a connection
on the latter.
Now that I've answered your questions could you answer mine? When I
asked you before for a reference where I may read about your work you
provided a link to some elementary QFT notes written by somebody else
together with a vague reference to your own work. You can't expect
people to be able to evaluate your stuff if they can't see it!
===
Subject: Re: Gerald t' Hooft
Basic questions yes. But from the idiocies of some of the Trolls my 
expectations are low.
1 OK as far as it goes. Written like a mathematician not a physicist but we 

won't hold that against you.
2.Needs more details.
3. Good.
4. Good. Again a bit too formal for a physicist's taste - but basically 
correct.
5. Good.
OK you get an A on this first one.
Now that I've answered your questions could you answer mine? When I asked 
you before for a reference where I may read about your work you provided a 
link to some elementary QFT notes written by somebody else together with a 
vague reference to your own work. You can't expect
people to be able to evaluate your stuff if they can't see it!
You obviously missed a message. I gave a reference to my book Super 
Cosmos that you can order from Amazon. It's not expensive. I also told you 
I had an archive paper you can download from 2006. Just Google I forget the 

exact URL. I plan to revise the paper. Also I have jillions of messages on 
what I am thinking all over the WEB - go to my Blog Destiny Matrix, or join 

Sarfatti_Physics_Seminars at Yahoo Groups (300 members) or go to Discussion 

Group at http://stardrive.org
Now understand this
1. I am no longer in academia.
2. I am not subject to publish or perish.
3. I am financially independent of the system.
Hence I do what I please. WYSIWYG. I am leaving my thoughts all over the WEB 

for posterity. I do give some technical talks. I gave 2 at Pacific Coast 
Gravity meeting 2007, 2006. I am giving one at STAIF 2008 for DOD types to 
be 
published at AIP. If you go to Wiki you will see some references to my work 

but not complete.
===
Subject: Re: Gerald t' Hooft
I have developed a preference for the way mathematicians do physics of
late.
Come off it, it was a vague question. There are lots of distinctions
between CFT and QFT and I wasn't going to list them all.
Indeed I did miss it; it's possible that it didn't make it to Google
Groups (that happened to me a few times when I used to post from
mathforum). I will have a look at your references when I find the
time, thank you.
===
Subject: Re: G. t' Hooft
If I write something you don't understand then ask me to explain it. I 
prefer the conversation on the web. Formal papers are obsolete. Who resds 
them? I don't have to play by the rules of academia to keep my job and 
advance. I prefer live intelligent discussion left for posterity on the web. 

Others who need to keep jobs etc can write it up for their masters, PhDs etc 

in the history of ideas or whatever. There are dozens of smart people who 
are 
tracking my work including inside intelligence agencies. Note I am one of 
the 
architects of Reagan's SDI which helped bring the Soviet Union down in spite 

of what the lefty physicists like Sid Drell at SLAC said. It worked 
politically. I have influence in high dark places in the Military Industrial 

Complex. Many of the academics who attack me personally and never discuss my 

actual ideas are noted for their extreme left-wing politics mind you. I 
welcome constructive debate on physics ideas.
===
Subject: Basic Questions
OK 
6. if you think of the 4 tetrad 1-forms as quantum fields, do you agree they 

should have spin 1?
i.e. e^a = e^audx^u
e^au as a spin 1 vector field with a as a kind of internal index.
Yes? No? in your opinion.
7. What about the 6 tetrad 1-forms? What spin should they have?
S^a^b = - S^b^a = S^a^budx^u
Also spin 1 as quantum fields - yes? No? 
8. Note Einstein's 
ds^2 = e^aea = guvdx^udx^v
You understand?
9. e^a = I^a + A^a
I^a is for Minkowski spacetime.
A^a is dynamical spin 1 from localizing T4 in actions of all non-gravity 
source fields - analog of vector potential in EM.
So ds^2 as a quantum field, i.e. guv should have spin 0, spin 1 and spin 2 
quantum pieces - spin 2 from A^aAa
I^a is not dynamical its components are Kronecker delta for geodesic 
observers. You understand?
===
Subject: Re: Basic Questions
Note basic physical idea of emergent gravity, the tetrads and the spin 
connections of gravity are analogous to the superflow in Helium II below 
Lambda point, and to coherent distortions of a supersolid.
John A. Wheeler says
The Question is: What is The Question?
A. Zee says there are many physicists who can answer a well-posed important 

question pregnant with physical insight and consequences, but there are very 

few who can ask them. I do the latter. 
10. The torsion field is a Cartan 2-form covariant exterior derivative of 
the tetrads. Since the tetrads are analogous to the EM vector potential, the 

torsion field is analogous to the EM field tensor.
T^a = De^a = de^a + S^ac/e^c = T^auvdx^u/dx^v
S^ac is spin connection 1-form (lower tetrad indices with Minkowski metric)
In 1915 GR T^a = 0
This is when you only locally gauge T4 and you get Ricci coefficients - 
anholonomic object for S^a^b determined only from local T4 i.e.
T^a(T4) = 0 induces non-dynamical S^a^b(T4).
This gives 1915 Riemann-Christoffel curvature 2-form
R^a^b(T4) = DS^a^b(T4) = dS^a^b(T4) + S^ac(T4)/S^cb(T4)
Einstein-Hilbert action density is the 0-form
~ *[R^a^b/e^c/e^d]
* = Hodge dual
T^a(P10) =/= 0
R^a^b(P10) = R^a^b(T4) + torsion field terms
beyond Einstein's 1915 GR.
The extra 6 variable parameters suggest Calabi-Yau space fiber.
===
Subject: Re: Gerald t' Hooft
Let He and She who are without Sin and Hypocrisy cast the first judgments of 

loon, troll, crank, crackpot etc. Everyone here is obviously 
disqualified. It's a fuzzy border before one crosses the line into hate 
crime 
territory. Interesting issue but I don't want to open that can of worms, 
that 
Pandora's Box, too widely. t'Hooft's physics is more interesting to me at 
the 
moment.
Advanced Problem
I. Read through all of t'Hooft's lectures and write down some key ideas you 

find in there that you think are interesting and important that you would 
like to understand better.
A Turing Test to check reliability of your Troll judgments
===
Subject: Re: Gerald t' Hooft
as a crackpot who believes
  both general relativity and quantum mechanics
  will one day be  disproven 
( in the same way newtonian mechanics was  disproven  )
i like this test
one of the regular attacks thrown around here
  is the  word-salad  hex
a compound word used to avoid thinking about topics
  one does not have the background to understand
  http://xxx.lanl.gov/pdf/gr-qc/9805079
  the  holographic principle 
  decompactifying compactified dimension
and uses a  horizon algebra  to show
  a black hole horizon may be seen
as being composed of string bits of unit length
what interests me most about his approach
  is that it provides a natural means for quantising time
through the holographic principle
i am interested in such approaches
  as a means for developing computational approaches
to new physical theories
my background in categorial computer science
  makes me want to learn how i might be able to interpret
  time quantisations in a cartesian closed category
or some effective monoidal generalisation
now t'hooft mentions other directions for such a programme
  ( in the lakatosian meaning )
like his interesting reconciliation with cellular automata
http://www.phys.uu.nl/~thooft/gthpub/digit01.pdf
on a different track
  following work by jackiw
  and assisting work by nobbenhuis
the symmetries proposed for the cosmological constant problem
here
http://arxiv.org/pdf/gr-qc/0602076
are an interesting approach to a long-standing problem
******..*******
yes this a good exercise after all
  and a review shows many other papers of his
should be reviewed and added to my files for future reference
of course
  the paper i mentioned in a different post
http://arxiv.org/PS_cache/quant-ph/pdf/0212/0212095v1.pdf
uses terms like  beables  and  ontology 
  that only crackpots like j s bell use
of course
  usenet cops ( in troll's clothing )
use bell against any cranks using such terminology
so there is this blind cycle going on
of trolls using cranks against cranks
  ( while the cranks foolishly think they are
    simply investigating legitimate foundational issues )
..
actually
  i'm getting bitter here
  and angered at people who are too stupid to follow references
or do any research / study / follow-up
beyond what they needed to pass their classes
so i will stop
  but i still think it was a good exercise
  if for no other reason than i got to familiarise myself
he is still an important thinker
  with many stimulating ideas
thank you
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
===
Subject: Re: Gerald t' Hooft
[...]
[...]
In Section 1, 't Hooft describes a thought experiment where three
(1).  Also the z-direction is mentioned here.
Then from (3) we get a correlation if the three observers
each measure spin in the x-direction,
and from (7) that if all three observers measure the
there is no correlation.
   We now assume that our device emits them either
    with all spins up ( sigma_z^{i} = +1), or all values
    down (sigma_z^i{i} = -1 ).
I don't understand how come there is correlation in the
David Bernier
===
Subject: Re: Gerald t' Hooft
In some convenient basise.
===
Subject: Re: Gerald t' Hooft
Yes, very good comments. I am interested in discussing t'Hooft's ideas. He 
is very smart guy of course. Best to ignore the Trolls they are like ticks, 

mosquitos and fleas.
Yes horizons as strings very important. That seems natural in my theory.
I have three real Higgs scalar fields projected down to 3+1 spacetime from 
9+1 spacetime. The latter is what you need to consistently derive the 4 
tetrads and the 6 spin connections from gradients of Goldstone phases if you 

insist on stable topological defects for all 9 (possibly 10) Higgs fields.
3 real Higgs fields on 3D spacelike slice have point defects where all 3 
vanish leaving their 2 independent Goldstone phases undefined. You surround 

a 
point defect in physical space with an S2 that is a closed surface that is 
not a boundary because of the enclosed point phase singularity. The 3 Higgs 

fields have a S2 vacuum manifold of minima in their O(3) potential. 
Single-valuedness of the Higgs fields means integer wrapping numbers i.e. 
how 
many times do the Higgs field order parameters wrap around the vacuum 
manifold for one wrap around the surrounding surface S2 in physical space?
So assume one Planck area Lp^2 per enclosed node. Then we get a kind of 
Schwarzschild radial coordinate
Area(S2)~ NLp^2
N = number of point nodes inside the surrounding S2 physical surface.
r ~ N^1/2Lp
This is like a string with N^1/2 links.
Volume(S2) ~ N^3/2Lp^3
Take the future deSitter horizon of area 1//zpf
/zpf ~ dark energy density
According to Bekenstein that's
N ~ 1/Lp^2/zpf ~ 10^122 BITS = number of nodes enclosed by future & past 
deSitter horizons.
That is a volume ~ (Hubble radius)^3 BTW
i.e. (10^61)^3 Planck cubes but all the dynamics is only in the (10^61)^2 
Planck areas of the deSitter horizon i.e. world hologram.
===
Subject: Re: Gerald t' Hooft
Perhaps, but lousy spoofing. Doesn't use the same posting
host that Jack has used for ever and a day.
There's only one thing more pitiful than being a usenet 
loon, and that's _pretending_ to be a usenet loon.
Phil
-- 
Home taping is killing big business profits. We left this side blank 
so you can help. -- Dead Kennedys, written upon the B-side of tapes of
/In God We Trust, Inc./.
===
Subject: Re: Gerald t' Hooft
Agreed.
Tom
===
Subject: Trite Obsessions with Trolls and Loons
All of you drowning in the quicksand of these trite preoccupations are 
obviously projecting your own fears, your own self-loathings, that you are 
that of which you accuse others of being. Guess what?
===
Subject: Re: Gerald t' Hooft
On 06 May 2007 00:24:03 +0300, Phil Carmody
Hehe.
===
Subject: Re: G t' Hooft
Hey midget mind why are you making such a big deal of this mis-spelling. 
I'll tell you why, because it's the only idea your little mind can grasp. 
Look Shlemeil a laptop computer is mobile able to switch posting hosts like 

kleenexes. Got it Genius. Meantime you miss the message completely worrying 

about your competition from loons and trolls. If you want to see a loon and 

a 
troll simply look in the mirror Mr. Big Shot Expert in All Things Important 

and Trivial - especially the latter in your case.
===
Subject: Re: Gerald t' Hooft
You are right.  This is quite extraordinary.  Not just one reply, but 
many, all on the same day.  Maybe he's changed his medication.
===
Subject: Easy Quadratic Equation Problem
A ball is thrown from the top of a cliff and its height (h in metres)
above the ground (after t seconds) is given by the formula:
h = 20t - 5t^2 + 25
Question) At what time is the ball 40m above the ground?
===
Subject: Re: Easy Quadratic Equation Problem
So what is your problem with this problem?
===
Subject: Re: Easy Quadratic Equation Problem
I don't think this is a relevant concern.  The question deals with
one can deduce that the ball was thrown with a vertical velocity
component of 20 m/s upward, somewhere where g is 10 m/s^2 and air
friction is non-existent...
Good point.  The cliff must be 25 m above the ground.
Personally, I prefer to make the height somewhere below the level of
the cliff top.  This gives practice in solving quadratics where the
roots are of opposite sign, and also illustrates the case of a
mathematically correct but physically unaccepatable root.
function...
===
Subject: Re: Easy Quadratic Equation Problem
Well simply, what is the answer and working out to this question.
===
Subject: Re: Easy Quadratic Equation Problem
Note that the problem looks remarkably like a homework problem, so that 
most people here will help you if you show your work, but are reluctant 
to just give answers, as that defeats the learning process that homework 
is designed to foster.  
What have you tried so far?
===
Subject: Re: Easy Quadratic Equation Problem
Apparently you want to solve
   40 = 20t - 5t^2 + 25
Simplifying,
   t^2 - 4 t + 3 = 0
You can solve this using the quadratic formula, but one would think
you could factor it by inspection. 
 
===
Subject: differentiation question
  I got stumped at a follwing question.
Find the slope of
9x - 4x ln y = 3  at ( 1/3, 1)
a. 9 - 4 ln 3
b. 5
c. 6
d. 27/4
e. 9 + 4 ln 3
Any help is appreciated
===
Subject: Re: differentiation question
is this correct?
9x - 4x ln y = 3
-4x ln y = 3 - 9x
ln y =  - 3/4x  +  9x/4x
ln y =  - 3/4x  +  9/4
y' /y = - 3/4
y' = -3/4 y
??
===
Subject: Re: differentiation question
As others have pointed out, you treat -3/4x as -3/(4x) when solving the
equation (some people allow this meaning, although I think it's poor
form), then treat it as (-3/4)x when differentiating.
So far, the other posts have missed the fact that this is not an
implicit differentiation problem at ALL.  Namely,
   ln y = -3/(4x) + 9/4
is exactly solvable as
   y = exp(-3/(4x) + 9/4).
-- 
Ron Bruck
===
Subject: Re: differentiation question
Sure, explicit is better (y' depends only on x), but given that values
for both and x and y were specified, implicit differentiation is a
little easier and gets the same answer.
Also, the very fact that values for x and y were _both_ given strongly
suggests that the intent was to provide an opportunity for the student
to use implicit differentiation.
quasi
===
Subject: Re: differentiation question
Exactly: the wording of the question suggests an intended method, 
hence my hint. Virgil already indicated the long-winded direct 
approach, which somehow misses the point. 
-- 
rusty
===
Subject: Re: differentiation question
No, the derivative of -3/(4x) is not -3/4.
If you differentiate correctly, you can make it work, but the
preferred way to do this problem is to by implicit differentiation.
Read the discussion in your text where implicit differentiation is
introduced. Study the worked examples. Then retry this problem.
quasi
===
Subject: Re: differentiation question
No, the above line should be
   ln y = -3/(4x) + 9/4
===
Subject: Re: differentiation question
Hint: (ln y)' = y'/y.
-- 
rusty
===
Subject: Re: differentiation question
Or solve for y in terms of x first, then find dy/dx, then substitute 1/3 
for x.
===
Subject: Three parallels do not cut - one should assume, shouldn't one?
Discussing geometry with a pure mathematician is really difficult, as
they use - when they follow Hilbert - ,,straight line,  ,,plane  and
,,euclidian geometry  differently to the followers of the  geometry of
Euclid. There is (or was) an intention behind this.
The space, where we do our empirical observations in and where we live
in, was modelled into a static geometry of three dimensions and this
is used by the modern mathematicians too to give us visualisations of
simple, trivial and mostly well-known facts, especially about geodesic
lines.
Lines are a very general concept with some properties, f.e. that any
two points of a line are connected with a path in this line. More
special are lines without kinks, even more special are smooth lines
Here we can talk of curvature and torsion, with  the example of  a
helix (screw).
Under oh so many kinds of surfaces we again can restrict here to
smooth surfaces. Euler already analyzed the curvatures of smooth
surfaces into a formula, and he and his colleagues (Bernoulli) found
the expressions for geodesics, or one kind of isoperimetric lines in
the most general sense, as they were called then, the one of the
shortest length in a surface, without any objection to Euclids axioms,
without changing the fifth postulate(axiom) or adding a new one.
At the other end of specialisation we find straight lines and circle-
lines, plane and spherical surfaces,  elements of Euklids
Elements  (and solids too). They are posessing so many properties,
that i barely will name a small part of these, like being either
finite or not, enclosing an area or volume and separating a surface or
the whole space into two regions, a straight line is not intersecting
itself, or  a straight line can be the invariant of a rotation ( it's
axis).
A straight line is always the shortest path between any two points of
it. This property is generalized into the concept of the shortest path
in a surface, visualized by a taut string on every smooth surface. So
a  straight line is a geodesic too, just as parts of a great circle of
a sphere are geodesic. Three points of a geodesic often form a
triangle in space, so in these cases geodesics are not straight lines.
A straight line  is a line of zero curvature, and this property can
not be generalized - of course in this 3D-space we are considering
here. It is a defining property. A geodesic can be of zero curvature
too, but then it is a straight line.There are  different definitions
of a geodesic, like a line being piecewise or locally  the shortest
path, but not neceassarily between any two points in it ( i will come
back to it in another letter)
An example of a curved surfaces is  a hyperbolic paraboloid:
http://xahlee.org/surface/gallery_o.html
When modern mathematicians (of the last century)  call a geodesic line
by the name of a ,,straight line, one has no means to differ between
the straight lines (being geodesic in this surface) and the curved
geodesics. In fact, this surface can be generated by moving straight
lines, it is a ruled surface. Another ruled surface is the hyperboloid
of one sheet, in which we find for every straight line in this surface
a parallel straight line in this surface (okay, an anticipation to
parallels, which will turn up later on). Some of the geodesics in
these visualisations are circles, missing the property of straight
lines, that one of three points is in between the other two, and
differ in that circles have a finite length and that two antipodal
points do not define exact one geodesic (20 000 km gone from Your
place in any direction on earth along a geodesic path will always end
up at the same spot).
A plane has become very important to the scientists, as they do their
lectures on blackboards, their communication with sheets of paper and
flatscreens. Ask a german mathematician about a classification of
figures of straight lines with four edges ( ,,Vier-eck), very often he
will not mention the tetrahedron. This seems to influence the thoughts
of Hilbert too. He divides the geometry into three types, his
,,hilbertized euclidian, for which we are given the example of a plane
(which is of overall (Euler) main-curvatures zero), and the ,,non-
euclidian, for which they show us spheres and ellipsoids ( of
positive Gauss-curvature) and the hyperbolic surfaces ( of negative
Gauss-curvature), all being called with the name of ,,plane. So
Hilbert seperates the whole of geometry into three classes, which
originates in the difference  of three types of  smooth 2D-surfaces.
As some pure mathematicians don't admit reality to their math, the
closest they can get to it, is the geometry, which they are using in
their visualisations.In calling it ,,flat they express how they
percieve this 3D-space.
An illustration to the three types of surfaces is given by Tim Golden
here
http://bandtechnology.com/tmp/conicals.jpg
He cuts from a flat piece of paper a sector and joins the ends with
the result of a cone-like surface. And by inserting this sector into
the cut of another plane he gets a wavy surface, which can not be
ironed out into a flat, planar surface without folds and double
layers. He does, what is basic to every taylor working with plane
cloth as a basic material. These surfaces are not smooth, so a better
picture is found in thinking of felt, which we can  shrink to a bowler
Eulers mathematical description of these surfaces through the main
curvatures in every point Gauss proceeded to an intrinsic look at
them, that is, without resorting to the space these surfaces are in.
He measures the curvature around a point with a closed line of equal
distance, all measured in the surface, bringing the proportion of
curve length to distance in the surface to a limit.
In between the plane and it's scaling deformations by stretching and
shrinking are the bending of the plane along a parabel or to a
cylinder - developable surfaces, as they are called. Either these fall
into the category of euclidian planes - then Hilbert do not
distinguish them from the planar plane of overall curvature zero, or
he just forgot to include them in the axioms of  (his) geometry.
And where is here an undulated surface , created with the rotation of
a sin-function, where the torus  with negative Gauss-curvature on the
surface part facing to the rotational axis, two rings of zero Gauss-
curvature and positive Gauss-curvature on the outer rest of the
surface,  and  where are the simple deformations of a plane with
preserving mesh coordinates, where are the not smooth surfaces?
There is nothing wrong in somehow being a mathematical taylor or doing
surgery on skins ( i personally like this way of associative
comprehension) - only  basic geometric objects like solids don't seem
to be popular.
forth some beautiful surfaces and more and  this could be much
improved in knowing each others dialect.
.
,,One should always be able to talk in place of 'points, straight
lines, planes' of ,,tables, benches, beer-mugs'.
... we could be better off in talking to each other about 'geodesics,
surfaces and Hilbert's euclidian geometry'. And it would help to
restrict the usage of straight line to a  line of curvature zero and
planes to surfaces of overall curvature zero.
Now let's look at parallels:
Definition 23
Parallel straight lines are straight lines which, being in the same
plane and being produced infinitely in both directions, do not meet
one another in either direction.
Postulate 5.
That, if a straight line falling on two straight lines makes the
interior angles on the same side less than two right angles, the two
straight lines, if produced infinitely, meet on that side on which are
the angles less than the two right angles.
(Heath translates Euclid's word into indefinitely, the german
translation of Helmuth Gericke has here the word ins unendliche).
With these two, and may be the other Postulates of Euklid one can
derive a lot of properties of parallels. Remember, Euclid is  talking
only about straight lines having the property of being parallel.
Some properties of parallels:
they are straight lines (thus they have all properties of them)
they can be produced infinitely
they do not cut or intersect
They keep equal distance to each other(Posidonius 100 bc)
This property is often used in everyday life and generalized to other
lines as well. One example are latitudes on earth. They are not
straight, they don't lie in a plane and they can not be produced
without end, but they do not cut.
By just defining a more general parallelism  as equidistant lines, one
would find the helix equidistant-parallel to it's axis, leaving an
somehow uneasy feeling about a definition of equal distance. I leave
this to You. In another posting i can give a bit more about this.
Being parallel is a symmetric relation
Now a generalisation to geodesics
Geodesics in the same smooth surface, which do not meet each other in
either direction, can be called geodesic-parallel or not-cutting
geodesics.
Besides this 'not intersecting' from all the other other properties
mentioned so far, only the symmetrie is kept.
And there is a nice property of parallels ( of course straight line
parallels) given by Euklid in
Proposition 30.
Straight lines parallel to the same straight line are also parallel to
one another.
There is transitivity between parallels. Being parallel is a
equivalence relation of straight lines, it is reflexiv, symmetric and
transitiv.And this gives a partition of all straight lines  into
equivalence classes (into shares).
The more recent concept of an arrow-vector (together with scaling and
addition) expresses this as a direction in space. A straight line can
be characterized by a point and a direction (and opposite
direction).Parallel lines share a direction. Two intersecting straight
lines differ in direction - measured as an angle. ( And of course not
intersecting straight lines in space either are parallel or skew. And
not to forget, there are plenty of lines, which are not straight and
not geodesic).
Now a highlight of a hyperbolic surface ( a smooth surface of negative
Gauss curvature) is, that given a geodesic BC and a point A, one can
draw more than one geodesic through this point, and these don't
intersect with the first. A sketch ( the lines should be interpreted
as geodesics, not necessarily as straight ones):
             |         )           |
             |       /             |
   G'   D |      / F           |C
             |    /                |
             |  )                  |
          A|(                    |B
             /|                    |
           /  |                    |
         (    |                    )
       /      |     )              |
 F'/        |        G         |
All geodesics between AG and AF, like AD, should not intersect BC, all
lines prolonged.
Now take point F . AF is still not intersecting BC, but again, also
through F can be found another geodesic, which will not cut BC. This
one cuts AB in T.
So now we have two geodesics not cutting BC, one through A and one
through T  - but these two AF and FT of course intersect in F.
             |        )           |
             |      /             |
   G'   D |     / F          |C
             |    /               |
             |  )                 |
          A|(        T         |B
             /|                   |
           /  |                   |
         (    |                   )
       /      |     )             |
 F'/        |        G        |
Somehow clumsy ( but a simpler demonstration would not be understood
so easily) - anyhow:
geodesic parallelism doesn't always hold for three geodesics  or
Two geodesics, being geodesic-parallel to a third, are not necessarily
geodesic-parallel to each other.
With friendly greetings
Hero
===
Subject: Re: Fermat's Last theorem short proof
Yes of course, but the question is not at all about the existence of the 
real P that satisfies the equation
The question is about the EXACT value of P
The question is about the type and the nature of the real number P
The question is much far behind the existence of P
Bassam Karzeddin
Al Hussein bin Talal University
JORDAN
===
Subject: Re: Solution manual of textbooks in ebook format! Get it in hours!
All Subjects' solutions manuals in Pdf format
All solutions manuals are in pdf format or Microsoft Word format.
I have tried my best to put up with the collections of my solutions
manual.
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.NET 2.0 Interoperability Recipes by Bruce Bukovics
A Course in Game Theory by Martin J. Osborne and Ariel Rubinstein
A First Course In Probability 7th Ed by Sheldon Ross
Adaptive Control 2nd Ed. by Karl.J.Astrom
Advanced Engineering Marhematics ERWIN KREYSZIG 9E
Advanced Engineering Mathematics 8Ed Erwin Kreyszig
Advanced Engineering Mathematics 8Ed Erwin Kreyszig in korean (all
even and odd no.)
Advanced Macroeconomics by Jeffery Rohaly
Advanced Modern Engineering Mathematics 3rd Ed. by Glyn James
Analog Integrated Circuit Design by David Johns, Ken Martin
Analysis and Design of Analog Intergrated Circuits 4th Ed. by Paul R.
Gray
Analytical Mechanics 7th Ed. by Fowles
Antenna for all application 3rd Ed.by John D. Kraus (Instructor's
Manual)
Antenna Theory 2nd Ed. by balanis
Applied Linear Statistical Models 5th Ed. by MichaelH.Kutner
Applied Numerical Analysis 7th Ed. by Curtis F. Gerald, Patrick O.
Wheatley
Applied Numerical Methods with Matlab for Engineers and Scientists 2nd
Ed. by Chapra
Applied Statistics Probability for Engineers 3rd ed Montogomery
(selected problems)
Applied Strength of Materials 4th Ed. by Robert L. Mott
Automatic Control Systems 8th Ed. Kuo and Golnaraghi
Basic Engineering Circuit Analysis 7th Ed. by Irwin
Basic Principles and Calculations in Chemical Engineering 6th Ed. by
David M. Himmeblau
Biochemistry 2nd Ed. by Philip W. Kuchel, Gregory B. Rakston
Bioprocess Engineering Principles by Pauline M. Doran
Business Statistics A Decision-Making Approach 6th Ed. by Groebner
C++ How to Program 3rd ed. Deitel, Deitel & Nieto (Instructor's
Manual)
Calculus 4th Ed. by James Stewart (Complete Instructors manual)
Calculus 5th Ed. by James Stewart (Complete Instructors Solutions)
Calculus by Jerrold Marsden & Alan Weinstein Vol 1
Calculus Early Transcendentals 5th Ed. by James Stewart
Calculus of Variations by Russak(book and solutions manual)
Calculus: One and Several Variables 8th Ed. by Salas, Hille and Etgen
Chemical And Engineering Thermodynamics 3Ed by Wiley
Chemical Engineering Solutions to the Problems in Volume 1 by J R
Backhurst
Classical Dynamics 5th Ed. by Thornton
Classical Electrodynamics 3rd Ed. by J.D. Jackon
CMOS Analog Circuit Design 2nd Ed. by P.E. Allen
Communication Systems 4th Ed. by Simon Haykin
Communication Systems Engineering 2nd Ed. by Proakis J.
Communication Systems: An Introduction to Signals and Noise in
Electrical Communication 4th. Ed. by Bruce Carlson
Computational Techniques for Fluid Dynamics by K. Srinivas and
C.A.J.Fletcher
Computer Architecture Design and Performance 2nd Ed. by Barry
Wilkinson
Computer Networking A top-down approach 3rd Ed. by James F. Jurose
Computer Networking: A Top-Down Approach Featuring the Internet 2nd
ed. by Jim Kurose and Keith Ross
Computer Networks 4th Ed. by Andrew.S.Tanenbaum
Computer Networks: A Systems Approach 3rd Ed. by larry L. Peterson and
Bruce S. Davie
Computer Organization And Design - The Hardware Software Interface 3rd
Ed.
Computer Systems Organization and Architecture by John D. Carpinell
Control Systems Engineering 3rd Ed. by Norman S. Nise
Control Systems Engineering by Nise
Design and Analysis of Experiments 6th Ed. by Montgomery
Design Of Analog Cmos Integrated Circuits by Razavi
Design with Operational Amplifiers and Analog Integrated Circuits 3rd
Ed. by Franco, Sergio
Device Electronics for Integrated Circuits 3rd Ed. by Muller and
Kamins
Differential Equations & Linear Algebra by C. Henry
Differential Equations with Boundary-Value Problems 5th Ed. by Zill
and Cullen
Digital communication: Fundamentals and Applications 2nd Ed. by
Bernard Sklar
Digital communications 4th Ed. John Proakis with ebook
Digital Image Processing 2nd Ed. by Gonzalez (Instructor's Manual)
Digital Integrated Circuits by Rabaey 2nd Ed. (selected problems)
Digital signal processing A Computer-Based Approach 1st Ed. by Sanjit
K. Mitra
Digital Signal Processing by Thomas J. Cavicchi
Digital Signal Processing: Principles, Algorithms, and Applications,
3rd Ed. by Proakis & Manolakis
Digital Signals and Filter by S. J. Orfanidis (selected solutions)
Discrete-Time Signal Processing 2nd Ed. by Oppenheim, R.W. Schafer and
J. R. Buck
Distributed Systems Principles and Paradigms by Andrew S. Tanenbaum
and Maarten Van Steen
Econometric Analysis 5th Ed. by William H. Greene
Econometric Analysis of Cross Section and Panel Data by Jeffrey M.
Wooldridge
Electric Circuits 7th Ed. by Nilsson
Electric Machinery 6th Ed. by Fitzgerald, Kingsley, Uman
Electric Machinery and Power System Fundamentals 1st Ed. by Stephen J.
Chapman (Instructor's Manual)
Electric Machinery Fundamentals 4th Ed. by Stephen J Chapma
(Instructor's_Manual)
Electrical Engineering Principles And Applications 4th Edition by
Giorgio Rizzoni
Electrical Engineering Principles And Applications by Hambley
Electronic Circuit Analysis and Design 2nd Ed. by Donald A. Neamen
Electronic Physics by Strabman
Electronics 2nd Ed. by Allan R. Hambley
Element of Electromagnetic by Sadiku
Elementary Differential Equations and Boundary Value problems 7th Ed.
by Boyce, DiPrima (book and solutions)
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Elementary Linear Algebra by K. R. Matthews (book and solution
manuals)
Elementary Mechanics and Thermodynamics by John W. Norbury
Elements of Chemical Reaction Engineering 3rd Ed. by Timothy Hubbard,
Jessica hamman and David Johnson
Elements of Information Theory by Thomas M. Cover
Engineering Biomechanics: Statics by Angela Matos, Eladio Pereira,
Juan Uribe and Elisandra Valentin
Engineering Circuit Analysis 6th Ed. by Hayt
Engineering Electromagnetics 6th Ed. by William H. Hayt, Jr. and Hohn
A. Buck
Engineering Fluid Mechanics 7th Ed. by Crowe
Engineering Mathematics 4th Ed. by John Bird
Engineering Mechanics Dynamics 10th edition by Hibbeler
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Engineering Mechanics Dynamics by Bedford and Fowler
Engineering Mechanics statics 10th edition by Hibbeler
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Feedback Control of Dynamic Systems 4th Ed. by G. F. Franklin, J. D.
Powell, A. Emami
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Fractal Geometry: Mathematical Foundations and Applications by Kenneth
Falconer
Fundamentals of Aerodynamics 2nd Ed. by John D. Anderson
Fundamentals Of Aerodynamics 3rd Ed. by Anderson (Instructor's
Solutions Manual)
Fundamentals of Applied Electromagenetics  5th Ed+
Fundamentals of Differential Equations by Nagle Saff Snider
Fundamentals of Digital Logic with Verilog Design 1st Ed. by S. Brown,
Z. Vranesic
Fundamentals of Digital Logic with VHDL Design 1st Ed. by S. Brown, Z.
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Fundamentals of Electric Circuits 2nd Ed. by C.K.Alexander
M.N.O.Sadiku
Fundamentals of Engineering Thermodynamics 5th ed (M. J. Moran & H. N.
Shapiro)
Fundamentals of Financial Management With Infotrac Concise 4th Ed. by
Eugene Brigham
Fundamentals of Fluid Mechanics 3th Ed. by Munson (Student solution
manual)
Fundamentals of Fluid Mechanics 4th Ed. by Munson
Fundamentals of Fluid Mechanics 5th Ed. by Munson
Fundamentals of Heat and Mass Transfer 5th Ed. Incropera
Fundamentals of Logic Design 5th Ed. by  Charles Roth
Fundamentals of Machine Component Design 3rd Ed. by Juvinall and
Marshek
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Fundamentals of Phsics 6th ed. by Halliday, Resnick (instructor's
manual)
Fundamentals of phsics 7th ed. by David Halliday, Robert Resnick, and
Jearl Walker (instructor's manual)
Fundamentals of Thermal-Fluid Sciences by Cengal
Fundamentals of Thermodynamics 6th Ed. Richard E. Sonntag, Claus
Borgnakke, Gordon J. Van Wylen
Guide to Energy Management 5th Ed. by Klaus-Dieter E. Pawlik
Heat Transfer 2nd Ed. by Cengel
Hydraulics in Civil and Environmental Engineering 4th Ed. by Andrew
Chawick
Introduction To Algorithms 2nd Ed. by Philip Bille (selected problems)
Introduction To Algorithms 2nd Ed. by Thomas H. Cormen, Charles
E.Leiserson, Ronald L. Rivest, Clifford Stein
Introduction to Antenna Theory by Palacios
Introduction to electric circuits 6th Ed. by Dorf-Svaboda
Introduction to electrodynamics 3rd Ed. by David Griffiths
Introduction to Fluid Mechanics 5ed. by Fox
Introduction to Fluid Mechanics 6th Ed. by Fox
Introduction to Linear Algebra 3th Ed. by Gilbert Strang
Introduction to Probability by Charles M. Grinstead and J. laurie
Snell
Introduction to Quantum Mechanics 2ed Griffiths, David J.
Introduction to Software Engineering by R. Mall
Introduction to VLSI circuits and Systems by John P. Uyemura
Introduction to Wireless Systems by P. M. Shankar
Investment Analysis and Portfolio Management by Reilly Brown
Linear Algebra and its Applications  3rd Ed.  by Lay
Linear Algebra by Jim Hefferon
Linear circuit analysis by R. A. DeCarlo and P. Lin
Linear Systems and Signals by B P Lathi
Logic Computer Design Fundamentals 2th Ed. by Morris Mano (selected
problems)
Managerial Accounting 11th Ed.
Material Science and Engineering an Introduction 5th Ed. by Callister
Material Science and Engineering an Introduction 6th Ed. by Callister
Materials & Processing in Manufacturing 9th Ed. by Demargo
Mathematical Methods for Physics and Engineering 3rd Ed. by
K.F.RileyandM.P.Hobson
Mathematics for Economics by Simon and Blume
Matrix Analysis And Applied Linear Algebra by Carl D. Meyer
Mechanical Engineering Design 7th Ed. Shigley
Mechanics of Fluids 4th Ed. by I. H. Shames
Mechanics of Fluids 8th Ed. by Bernard Massey
Mechanics of Materials 3rd Ed. Elsevier by S. Nemat-Nasser
Mechanics of Materials 5th 6th Ed. by Gere
Mechanics of materials Hibbeler 6th
Mechanics Of Materials(3rd Ed , By Beer, Johnston, & Dewolf)
Microeconomic Analysis 3rd Ed. by Hal R. Varian
Microeconomic Theory by Andreu Mas-Colell, Jerry R. Green, Michael
Dennis Whinston
Microelectronic Circuits 4th Ed. by Sedra, Smith
Microelectronic circuits 5th Ed. Sedra
Microelectronics Digital and Analog Circuits and Systems by Millman
Microwave and rf design of wireless systems by Pozar
Microwave Engineering 2nd Ed. David M Pozar
Microwave Engineering 3rd Ed. David M Pozar
Microwave Transistor Amplifiers Analysis and Design 2nd Ed. by
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Modern Control Engineering 3rd Ed. by K.OGATA
Modern Digital and Analog Communications Systems by B P Lathi
Modern Quantum Mechanics Revised Ed. by J.J. Sakurai (solutions and
book)
Multi Variable Calculus 5th Ed.
Numerical Methods for Engineers by Steven C. Chapra and Raymond P.
Canale
Operating System Concepts 6th Ed. by Abraham Silberschatz
Operating System Concepts 7th Ed. by Abraham Silberschatz
Operating Systems:Internals and Design Principles 4th Ed. by William
Stallings
Options, Futures, & Other Derivatives 4th Ed. by John C. Hull
Organic Chemistry 5th Ed. by Atkins and Carey
Physical Chemistry 7th. Ed. by Peter Atkins & Julio de Paula
Physics for Scientists & Engineers (a strategic approach) by Randall D
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Physics for Scientists & Engineers by Tipler & Mosca 5th Edition
Physics For Scientists And Engineers 3rd Ed. by Douglas C. Giancoli
Physics for Scientists and Engineers 5th Extended Version by Serway
and Faughn
Physics Volume 2 5th Ed. by Halliday, Resnick and Krane
Power System Analysis by John J. Grainger & William D. Stevenson, Jr
Principles of Communication 5th Ed. by R. E. Ziemer, William H.
Tranter
Principles of Physics 4th Ed. Calculus Based by Serway, Raymond A. and
John W. Jewett
Principles with Applications BY Giancoli 6TH Edition
Probability and Statistics for Engineering and the_Sciences 6th Ed.
Probability and Statistics for Engineers and Scientists (selected
problems)
Probability Random Variables and Stochastic Processes 4th Ed. by
Papoulis
Process Systems Analysis and Control by Donald R.coughanowr(selected
problems)
Quantum mechanics by Kyriakos Tamvakis
Quantum Mechanics by P. Saltsidis
Recursive Macroeconomic Theory by Lars Ljungqvist and Thomas J.
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Recursive Methods in Economic Dynamics by Wright
RF circuit Design Theory and Application by Ludwig bretchko
Sears and Zemansky's University Physics 11th Ed.
Semiconductor Device Fundamentals 1st Ed. by Robert F. Pierret
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Serway and Jewett's Physics for Scientists and Engineers 6th ed. by
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Signal Processing and Linear Systems by B P Lathi
Signals And Systems 2nd Ed. by Haykin
Signals And Systems 2nd Ed. by Oppenheim
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Soil Mechanics: concepts and applications 2ed William Powrie
Solid State Electronic Device 5th Ed. by Ben Streetman (Instructor's
Manual)
Strengths of Materials by Beer, Johnston, Dewolf
Structural Analysis by R.C. Hibbeler
System Dynamics by Ogata (B problems only)
The C Programming Language 2nd Ed. by Kernighan and Ritchie
The Econometrics of Financial Markets by Petr Adamek
The Science and Engineering of Materials 4th Ed. by Donald R. Askeland
Pradeep P. Phule (Instructor's Manual)
Theory and Applications of OFDM and CDMA Wideband Wireless
Communications (2005)
Thermodynamic 5th ed. Cengal
Thermodynamics of Turbomachinery 5th Ed.
Thermodynamics: An Engineering Approach 5th Ed. by Cengel Boles
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Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas
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Undergraduate Econometrics by Hill, Judge and Griffiths
University Physics with Modern Physics (11th) by  Hugh D. Young and
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Vector Calculus 3rd Ed. by Susan Jane Colley
Vector Mechanics for engineers dynamics by beer 6th edition
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Wireless Communications principles and practice 2nd Ed. by Theodore
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Ebooks:
A First Course in Differential Equations by J. David Logan
Applied Cryptography by A. Menezes. P. van Oorschot and S. Vanstone
Applied mathematics and Modeling for Chemical Engineers by Rice and Do
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Applied Numerical Methods Using Matlab by Yamg, cao, Chung and Morris
Applied Statistics Probability for Engineers 3rd Ed. by Montogomery
Applied Technology and Instrumentation for Process Control by Douglas
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Business Analysis And Valuation Using Financial Statements - Text And
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C++ How to Program 5th Ed. by H. M. Deitel, P. J. Deitel
Calculus Early Transcendentals 5th Ed. by James Stewart
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Computational Fluid Dynamics: Principles and Applications by J. Blazek
Computational Fluid Mechanics and Heat Transfer 2nd Ed. by Tannehill,
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Computer Organization and Design: The Hardware-Software Interface
Cryptography and Network Security Principles and Practices 2th Ed. by
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Digital And Analog Communication Systems 5th Ed. by Leon W. Couch
Rabaey.pdf
Digital Signal Processing: A Computer-based Approach 2nd Ed. by Sanjit
K. Mitra
Discrete Mathematics: Elementary and Beyond by Loavz, Pelikan,
Vesztergombi
DWDM Network Designs and Engineering Solutions by Astwin Gumaste and
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Ebook  Wireless Communications principles and practice 1996
Elementary Applied Partial Differential Equations with Fourier Series
and Boundary Value Problems 2nd Ed. by Richard Haberman
Elementary Calculus: An Infinitesimal Approach 2nd Ed. by H. Jerome
keisler
Elements of Electromagnetics 3rd Ed. by Sadiku
Elements of The Theory of Computation 2nd Ed. by Lewis and
Papadimitriou
Financial Accounting McGraw-Hill
Fluid Mechanics 2nd Ed. by Rjucsh K. Kundu and Ira M. Cohen
Fluid Mechanics 4th Ed. by Frank M. White (With Study Guide)
Fundamentals of Aerodynamics by Anderson
Fundamentals of Gas Dynamics 2nd Ed. by Zucker R D , Biblarz
Harper s Biochemistry 26th Ed. by Murray, Granner, Mayes and Rodwell
Heat and Mass Transfer 2nd Ed. by Stephan
Imperfect C++ Practical Solutions for Real-Life Programming by Matthew
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Introduction to Thermal Systems Engineering: Thermodynamics, fluid
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Linear Algebra And Its Applications by David C Lay
Microeconomic Theory by Andreu Mas-Colell, Jerry R. Green and Michael
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Modern Control Engineeing 3rd Ed. by Katsuhiko Ogata
Modern Operating Systems 2nd Ed. By Tanenbaum
Modern Wireless Communications by Simon Hatkin and Michael Moher
Numerical Analysis by David Kincaid and Ward Cheney
Numerical Methods using MATLAB 3rd Ed. by Mathrews and Fink
Numerical Techniques In Electromagnetics 2nd Ed. by Matthew N. O.
Sadiku
Physics for Scientists and Engineers 6th Ed. by Serway Jewett
Principles and applications of Electrical Engineering by Giorgio
Rizzoni
Principles of Genetics 7th Ed. by Tamarin
Probability, Random Variables, and Random Signal Principles 2nd Ed. by
Peyton Z. Peebles, Jr.
Rules Of Thumb For Chemical Engineers A Manual Of Quick, Accurate
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Branan
Schaum's Outline of College Physics by Fredrick J. Bueche and Eugene
Hecht
Scientific Computing An Introductory Survey by Michael T. Heath
Signals And Systems by Oppenheim
Thermal Physics 2nd Ed. by Kittel
Vector Mechanics for engineers statics 7th. Ed. by Ferdinand P. Beer
Wireless Communications by Andrea Goldsmith
===
Subject: Re: Solution manual of textbooks in ebook format! Get it in hours!
All Subjects' solutions manuals in Pdf format
All solutions manuals are in pdf format or Microsoft Word format.
I have tried my best to put up with the collections of my solutions
manual.
Here is the list that only part of my collections:
I will put some time to make up the full list daily.
If you cant find the solution manual listed below, don't give up, feel
free to email me
To get the solutions manual, just email me with a price you want to
get the solutions manual you want.
To see samples, just email me.
My email is edisonee(at)gmail.com
Solutions Manuals
.NET 2.0 Interoperability Recipes by Bruce Bukovics
A Course in Game Theory by Martin J. Osborne and Ariel Rubinstein
A First Course In Probability 7th Ed by Sheldon Ross
Adaptive Control 2nd Ed. by Karl.J.Astrom
Advanced Engineering Marhematics ERWIN KREYSZIG 9E
Advanced Engineering Mathematics 8Ed Erwin Kreyszig
Advanced Engineering Mathematics 8Ed Erwin Kreyszig in korean (all
even and odd no.)
Advanced Macroeconomics by Jeffery Rohaly
Advanced Modern Engineering Mathematics 3rd Ed. by Glyn James
Analog Integrated Circuit Design by David Johns, Ken Martin
Analysis and Design of Analog Intergrated Circuits 4th Ed. by Paul R.
Gray
Analytical Mechanics 7th Ed. by Fowles
Antenna for all application 3rd Ed.by John D. Kraus (Instructor's
Manual)
Antenna Theory 2nd Ed. by balanis
Applied Linear Statistical Models 5th Ed. by MichaelH.Kutner
Applied Numerical Analysis 7th Ed. by Curtis F. Gerald, Patrick O.
Wheatley
Applied Numerical Methods with Matlab for Engineers and Scientists 2nd
Ed. by Chapra
Applied Statistics Probability for Engineers 3rd ed Montogomery
(selected problems)
Applied Strength of Materials 4th Ed. by Robert L. Mott
Automatic Control Systems 8th Ed. Kuo and Golnaraghi
Basic Engineering Circuit Analysis 7th Ed. by Irwin
Basic Principles and Calculations in Chemical Engineering 6th Ed. by
David M. Himmeblau
Biochemistry 2nd Ed. by Philip W. Kuchel, Gregory B. Rakston
Bioprocess Engineering Principles by Pauline M. Doran
Business Statistics A Decision-Making Approach 6th Ed. by Groebner
C++ How to Program 3rd ed. Deitel, Deitel & Nieto (Instructor's
Manual)
Calculus 4th Ed. by James Stewart (Complete Instructors manual)
Calculus 5th Ed. by James Stewart (Complete Instructors Solutions)
Calculus by Jerrold Marsden & Alan Weinstein Vol 1
Calculus Early Transcendentals 5th Ed. by James Stewart
Calculus of Variations by Russak(book and solutions manual)
Calculus: One and Several Variables 8th Ed. by Salas, Hille and Etgen
Chemical And Engineering Thermodynamics 3Ed by Wiley
Chemical Engineering Solutions to the Problems in Volume 1 by J R
Backhurst
Classical Dynamics 5th Ed. by Thornton
Classical Electrodynamics 3rd Ed. by J.D. Jackon
CMOS Analog Circuit Design 2nd Ed. by P.E. Allen
Communication Systems 4th Ed. by Simon Haykin
Communication Systems Engineering 2nd Ed. by Proakis J.
Communication Systems: An Introduction to Signals and Noise in
Electrical Communication 4th. Ed. by Bruce Carlson
Computational Techniques for Fluid Dynamics by K. Srinivas and
C.A.J.Fletcher
Computer Architecture Design and Performance 2nd Ed. by Barry
Wilkinson
Computer Networking A top-down approach 3rd Ed. by James F. Jurose
Computer Networking: A Top-Down Approach Featuring the Internet 2nd
ed. by Jim Kurose and Keith Ross
Computer Networks 4th Ed. by Andrew.S.Tanenbaum
Computer Networks: A Systems Approach 3rd Ed. by larry L. Peterson and
Bruce S. Davie
Computer Organization And Design - The Hardware Software Interface 3rd
Ed.
Computer Systems Organization and Architecture by John D. Carpinell
Control Systems Engineering 3rd Ed. by Norman S. Nise
Control Systems Engineering by Nise
Design and Analysis of Experiments 6th Ed. by Montgomery
Design Of Analog Cmos Integrated Circuits by Razavi
Design with Operational Amplifiers and Analog Integrated Circuits 3rd
Ed. by Franco, Sergio
Device Electronics for Integrated Circuits 3rd Ed. by Muller and
Kamins
Differential Equations & Linear Algebra by C. Henry
Differential Equations with Boundary-Value Problems 5th Ed. by Zill
and Cullen
Digital communication: Fundamentals and Applications 2nd Ed. by
Bernard Sklar
Digital communications 4th Ed. John Proakis with ebook
Digital Image Processing 2nd Ed. by Gonzalez (Instructor's Manual)
Digital Integrated Circuits by Rabaey 2nd Ed. (selected problems)
Digital signal processing A Computer-Based Approach 1st Ed. by Sanjit
K. Mitra
Digital Signal Processing by Thomas J. Cavicchi
Digital Signal Processing: Principles, Algorithms, and Applications,
3rd Ed. by Proakis & Manolakis
Digital Signals and Filter by S. J. Orfanidis (selected solutions)
Discrete-Time Signal Processing 2nd Ed. by Oppenheim, R.W. Schafer and
J. R. Buck
Distributed Systems Principles and Paradigms by Andrew S. Tanenbaum
and Maarten Van Steen
Econometric Analysis 5th Ed. by William H. Greene
Econometric Analysis of Cross Section and Panel Data by Jeffrey M.
Wooldridge
Electric Circuits 7th Ed. by Nilsson
Electric Machinery 6th Ed. by Fitzgerald, Kingsley, Uman
Electric Machinery and Power System Fundamentals 1st Ed. by Stephen J.
Chapman (Instructor's Manual)
Electric Machinery Fundamentals 4th Ed. by Stephen J Chapma
(Instructor's_Manual)
Electrical Engineering Principles And Applications 4th Edition by
Giorgio Rizzoni
Electrical Engineering Principles And Applications by Hambley
Electronic Circuit Analysis and Design 2nd Ed. by Donald A. Neamen
Electronic Physics by Strabman
Electronics 2nd Ed. by Allan R. Hambley
Element of Electromagnetic by Sadiku
Elementary Differential Equations and Boundary Value problems 7th Ed.
by Boyce, DiPrima (book and solutions)
Elementary Differential Equations and Boundary Value Problems 8th Ed.
Elementary Linear Algebra by K. R. Matthews (book and solution
manuals)
Elementary Mechanics and Thermodynamics by John W. Norbury
Elements of Chemical Reaction Engineering 3rd Ed. by Timothy Hubbard,
Jessica hamman and David Johnson
Elements of Information Theory by Thomas M. Cover
Engineering Biomechanics: Statics by Angela Matos, Eladio Pereira,
Juan Uribe and Elisandra Valentin
Engineering Circuit Analysis 6th Ed. by Hayt
Engineering Electromagnetics 6th Ed. by William H. Hayt, Jr. and Hohn
A. Buck
Engineering Fluid Mechanics 7th Ed. by Crowe
Engineering Mathematics 4th Ed. by John Bird
Engineering Mechanics Dynamics 10th edition by Hibbeler
Engineering Mechanics Dynamics 11th edition by Hibbeler
Engineering Mechanics Dynamics 3rd Ed. by Hibbeler
Engineering Mechanics Dynamics 5th Ed. by Meriam
Engineering Mechanics Dynamics by Bedford and Fowler
Engineering Mechanics statics 10th edition by Hibbeler
Engineering Mechanics statics 11th edition by Hibbeler
Engineering Mechanics Statics 4th Ed. Bedford
Engineering Mechanics Statics by Meriam
Feedback Control of Dynamic Systems 4th Ed. by G. F. Franklin, J. D.
Powell, A. Emami
Fluid mechanics 5th Ed. by White
Fourier and Laplace transforms by Antwoorden (selected solutions)
Fractal Geometry: Mathematical Foundations and Applications by Kenneth
Falconer
Fundamentals of Aerodynamics 2nd Ed. by John D. Anderson
Fundamentals Of Aerodynamics 3rd Ed. by Anderson (Instructor's
Solutions Manual)
Fundamentals of Applied Electromagenetics  5th Ed+
Fundamentals of Differential Equations by Nagle Saff Snider
Fundamentals of Digital Logic with Verilog Design 1st Ed. by S. Brown,
Z. Vranesic
Fundamentals of Digital Logic with VHDL Design 1st Ed. by S. Brown, Z.
Vranesic
Fundamentals of Electric Circuits 2nd Ed. by C.K.Alexander
M.N.O.Sadiku
Fundamentals of Engineering Thermodynamics 5th ed (M. J. Moran & H. N.
Shapiro)
Fundamentals of Financial Management With Infotrac Concise 4th Ed. by
Eugene Brigham
Fundamentals of Fluid Mechanics 3th Ed. by Munson (Student solution
manual)
Fundamentals of Fluid Mechanics 4th Ed. by Munson
Fundamentals of Fluid Mechanics 5th Ed. by Munson
Fundamentals of Heat and Mass Transfer 5th Ed. Incropera
Fundamentals of Logic Design 5th Ed. by  Charles Roth
Fundamentals of Machine Component Design 3rd Ed. by Juvinall and
Marshek
Fundamentals of Machine Component Design 4th Ed. by Juvinall
Fundamentals of Phsics 6th ed. by Halliday, Resnick (instructor's
manual)
Fundamentals of phsics 7th ed. by David Halliday, Robert Resnick, and
Jearl Walker (instructor's manual)
Fundamentals of Thermal-Fluid Sciences by Cengal
Fundamentals of Thermodynamics 6th Ed. Richard E. Sonntag, Claus
Borgnakke, Gordon J. Van Wylen
Guide to Energy Management 5th Ed. by Klaus-Dieter E. Pawlik
Heat Transfer 2nd Ed. by Cengel
Hydraulics in Civil and Environmental Engineering 4th Ed. by Andrew
Chawick
Introduction To Algorithms 2nd Ed. by Philip Bille (selected problems)
Introduction To Algorithms 2nd Ed. by Thomas H. Cormen, Charles
E.Leiserson, Ronald L. Rivest, Clifford Stein
Introduction to Antenna Theory by Palacios
Introduction to electric circuits 6th Ed. by Dorf-Svaboda
Introduction to electrodynamics 3rd Ed. by David Griffiths
Introduction to Fluid Mechanics 5ed. by Fox
Introduction to Fluid Mechanics 6th Ed. by Fox
Introduction to Linear Algebra 3th Ed. by Gilbert Strang
Introduction to Probability by Charles M. Grinstead and J. laurie
Snell
Introduction to Quantum Mechanics 2ed Griffiths, David J.
Introduction to Software Engineering by R. Mall
Introduction to VLSI circuits and Systems by John P. Uyemura
Introduction to Wireless Systems by P. M. Shankar
Investment Analysis and Portfolio Management by Reilly Brown
Linear Algebra and its Applications  3rd Ed.  by Lay
Linear Algebra by Jim Hefferon
Linear circuit analysis by R. A. DeCarlo and P. Lin
Linear Systems and Signals by B P Lathi
Logic Computer Design Fundamentals 2th Ed. by Morris Mano (selected
problems)
Managerial Accounting 11th Ed.
Material Science and Engineering an Introduction 5th Ed. by Callister
Material Science and Engineering an Introduction 6th Ed. by Callister
Materials & Processing in Manufacturing 9th Ed. by Demargo
Mathematical Methods for Physics and Engineering 3rd Ed. by
K.F.RileyandM.P.Hobson
Mathematics for Economics by Simon and Blume
Matrix Analysis And Applied Linear Algebra by Carl D. Meyer
Mechanical Engineering Design 7th Ed. Shigley
Mechanics of Fluids 4th Ed. by I. H. Shames
Mechanics of Fluids 8th Ed. by Bernard Massey
Mechanics of Materials 3rd Ed. Elsevier by S. Nemat-Nasser
Mechanics of Materials 5th 6th Ed. by Gere
Mechanics of materials Hibbeler 6th
Mechanics Of Materials(3rd Ed , By Beer, Johnston, & Dewolf)
Microeconomic Analysis 3rd Ed. by Hal R. Varian
Microeconomic Theory by Andreu Mas-Colell, Jerry R. Green, Michael
Dennis Whinston
Microelectronic Circuits 4th Ed. by Sedra, Smith
Microelectronic circuits 5th Ed. Sedra
Microelectronics Digital and Analog Circuits and Systems by Millman
Microwave and rf design of wireless systems by Pozar
Microwave Engineering 2nd Ed. David M Pozar
Microwave Engineering 3rd Ed. David M Pozar
Microwave Transistor Amplifiers Analysis and Design 2nd Ed. by
Guillermo Gonzalez
Modern Control Engineering 3rd Ed. by K.OGATA
Modern Digital and Analog Communications Systems by B P Lathi
Modern Quantum Mechanics Revised Ed. by J.J. Sakurai (solutions and
book)
Multi Variable Calculus 5th Ed.
Numerical Methods for Engineers by Steven C. Chapra and Raymond P.
Canale
Operating System Concepts 6th Ed. by Abraham Silberschatz
Operating System Concepts 7th Ed. by Abraham Silberschatz
Operating Systems:Internals and Design Principles 4th Ed. by William
Stallings
Options, Futures, & Other Derivatives 4th Ed. by John C. Hull
Organic Chemistry 5th Ed. by Atkins and Carey
Physical Chemistry 7th. Ed. by Peter Atkins & Julio de Paula
Physics for Scientists & Engineers (a strategic approach) by Randall D
Knight
Physics for Scientists & Engineers by Tipler & Mosca 5th Edition
Physics For Scientists And Engineers 3rd Ed. by Douglas C. Giancoli
Physics for Scientists and Engineers 5th Extended Version by Serway
and Faughn
Physics Volume 2 5th Ed. by Halliday, Resnick and Krane
Power System Analysis by John J. Grainger & William D. Stevenson, Jr
Principles of Communication 5th Ed. by R. E. Ziemer, William H.
Tranter
Principles of Physics 4th Ed. Calculus Based by Serway, Raymond A. and
John W. Jewett
Principles with Applications BY Giancoli 6TH Edition
Probability and Statistics for Engineering and the_Sciences 6th Ed.
Probability and Statistics for Engineers and Scientists (selected
problems)
Probability Random Variables and Stochastic Processes 4th Ed. by
Papoulis
Process Systems Analysis and Control by Donald R.coughanowr(selected
problems)
Quantum mechanics by Kyriakos Tamvakis
Quantum Mechanics by P. Saltsidis
Recursive Macroeconomic Theory by Lars Ljungqvist and Thomas J.
Sargent
Recursive Methods in Economic Dynamics by Wright
RF circuit Design Theory and Application by Ludwig bretchko
Sears and Zemansky's University Physics 11th Ed.
Semiconductor Device Fundamentals 1st Ed. by Robert F. Pierret
Semiconductor Devices Physics and Technology 2nd Ed. by S. M. Sze
Semiconductor Physics and Devices 3rd Ed. by Neamen
Serway and Jewett's Physics for Scientists and Engineers 6th ed. by
McGrew and Currie
Signal Processing and Linear Systems by B P Lathi
Signals And Systems 2nd Ed. by Haykin
Signals And Systems 2nd Ed. by Oppenheim
Signals, Systems and Transforms 3rd Ed. by Oppenheim
Soil Mechanics: concepts and applications 2ed William Powrie
Solid State Electronic Device 5th Ed. by Ben Streetman (Instructor's
Manual)
Strengths of Materials by Beer, Johnston, Dewolf
Structural Analysis by R.C. Hibbeler
System Dynamics by Ogata (B problems only)
The C Programming Language 2nd Ed. by Kernighan and Ritchie
The Econometrics of Financial Markets by Petr Adamek
The Science and Engineering of Materials 4th Ed. by Donald R. Askeland
Pradeep P. Phule (Instructor's Manual)
Theory and Applications of OFDM and CDMA Wideband Wireless
Communications (2005)
Thermodynamic 5th ed. Cengal
Thermodynamics of Turbomachinery 5th Ed.
Thermodynamics: An Engineering Approach 5th Ed. by Cengel Boles
(Instructor's Solutions Manual)
Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas
Vol 1
Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas
Vol 2
Transport Phenomena 2nd Ed. by Bird and Stewart(to class 1 and class 2
problems)
Undergraduate Econometrics by Hill, Judge and Griffiths
University Physics with Modern Physics (11th) by  Hugh D. Young and
Roger A. Freedman.
Vector Calculus 3rd Ed. by Susan Jane Colley
Vector Mechanics for engineers dynamics by beer 6th edition
Vector Mechanics for engineers dynamics by beer 7th edition
Vector Mechanics for engineers statics by beer 6th edition
Vector Mechanics for engineers statics by beer 7th edition (nearly the
same with edtion 8)
Wireless Communications principles and practice 2nd Ed. by Theodore
Rappaport 1996
Ebooks:
A First Course in Differential Equations by J. David Logan
Applied Cryptography by A. Menezes. P. van Oorschot and S. Vanstone
Applied mathematics and Modeling for Chemical Engineers by Rice and Do
Applied Mathematics and Modeling for Chemical Engineers by Richard G.
Rice and Duong D. Do
Applied Numerical Methods Using Matlab by Yamg, cao, Chung and Morris
Applied Statistics Probability for Engineers 3rd Ed. by Montogomery
Applied Technology and Instrumentation for Process Control by Douglas
O.J. dsSa
Business Analysis And Valuation Using Financial Statements - Text And
Cases
C++ How to Program 5th Ed. by H. M. Deitel, P. J. Deitel
Calculus Early Transcendentals 5th Ed. by James Stewart
Calculus: Concepts and Contexts 2nd Ed. by Stewart
Computational Fluid Dynamics: Principles and Applications by J. Blazek
Computational Fluid Mechanics and Heat Transfer 2nd Ed. by Tannehill,
Anderson and Pletcher
Computer Organization and Design: The Hardware-Software Interface
Cryptography and Network Security Principles and Practices 2th Ed. by
William Stallings
Cryptography and Network Security Principles and Practices 4th Ed. by
William Stallings
Digital And Analog Communication Systems 5th Ed. by Leon W. Couch
Rabaey.pdf
Digital Signal Processing: A Computer-based Approach 2nd Ed. by Sanjit
K. Mitra
Discrete Mathematics: Elementary and Beyond by Loavz, Pelikan,
Vesztergombi
DWDM Network Designs and Engineering Solutions by Astwin Gumaste and
Tony Antony
Ebook  Wireless Communications principles and practice 1996
Elementary Applied Partial Differential Equations with Fourier Series
and Boundary Value Problems 2nd Ed. by Richard Haberman
Elementary Calculus: An Infinitesimal Approach 2nd Ed. by H. Jerome
keisler
Elements of Electromagnetics 3rd Ed. by Sadiku
Elements of The Theory of Computation 2nd Ed. by Lewis and
Papadimitriou
Financial Accounting McGraw-Hill
Fluid Mechanics 2nd Ed. by Rjucsh K. Kundu and Ira M. Cohen
Fluid Mechanics 4th Ed. by Frank M. White (With Study Guide)
Fundamentals of Aerodynamics by Anderson
Fundamentals of Gas Dynamics 2nd Ed. by Zucker R D , Biblarz
Harper s Biochemistry 26th Ed. by Murray, Granner, Mayes and Rodwell
Heat and Mass Transfer 2nd Ed. by Stephan
Imperfect C++ Practical Solutions for Real-Life Programming by Matthew
Wilson
Introduction to Thermal Systems Engineering: Thermodynamics, fluid
mechanics, and heat tranfer by Moran
Linear Algebra And Its Applications by David C Lay
Microeconomic Theory by Andreu Mas-Colell, Jerry R. Green and Michael
Dennis Whinston
Modern Control Engineeing 3rd Ed. by Katsuhiko Ogata
Modern Operating Systems 2nd Ed. By Tanenbaum
Modern Wireless Communications by Simon Hatkin and Michael Moher
Numerical Analysis by David Kincaid and Ward Cheney
Numerical Methods using MATLAB 3rd Ed. by Mathrews and Fink
Numerical Techniques In Electromagnetics 2nd Ed. by Matthew N. O.
Sadiku
Physics for Scientists and Engineers 6th Ed. by Serway Jewett
Principles and applications of Electrical Engineering by Giorgio
Rizzoni
Principles of Genetics 7th Ed. by Tamarin
Probability, Random Variables, and Random Signal Principles 2nd Ed. by
Peyton Z. Peebles, Jr.
Rules Of Thumb For Chemical Engineers A Manual Of Quick, Accurate
Solutions To Everyday Process Engineering Problems 3rd Ed. by carl
Branan
Schaum's Outline of College Physics by Fredrick J. Bueche and Eugene
Hecht
Scientific Computing An Introductory Survey by Michael T. Heath
Signals And Systems by Oppenheim
Thermal Physics 2nd Ed. by Kittel
Vector Mechanics for engineers statics 7th. Ed. by Ferdinand P. Beer
Wireless Communications by Andrea Goldsmith
===
Subject: Re: Comprehensive Solutions Manual for College Textbooks
All Subjects' solutions manuals in Pdf format
All solutions manuals are in pdf format or Microsoft Word format.
I have tried my best to put up with the collections of my solutions
manual.
Here is the list that only part of my collections:
I will put some time to make up the full list daily.
If you cant find the solution manual listed below, don't give up, feel
free to email me
To get the solutions manual, just email me with a price you want to
get the solutions manual you want.
To see samples, just email me.
My email is edisonee(at)gmail.com
Solutions Manuals
.NET 2.0 Interoperability Recipes by Bruce Bukovics
A Course in Game Theory by Martin J. Osborne and Ariel Rubinstein
A First Course In Probability 7th Ed by Sheldon Ross
Adaptive Control 2nd Ed. by Karl.J.Astrom
Advanced Engineering Marhematics ERWIN KREYSZIG 9E
Advanced Engineering Mathematics 8Ed Erwin Kreyszig
Advanced Engineering Mathematics 8Ed Erwin Kreyszig in korean (all
even and odd no.)
Advanced Macroeconomics by Jeffery Rohaly
Advanced Modern Engineering Mathematics 3rd Ed. by Glyn James
Analog Integrated Circuit Design by David Johns, Ken Martin
Analysis and Design of Analog Intergrated Circuits 4th Ed. by Paul R.
Gray
Analytical Mechanics 7th Ed. by Fowles
Antenna for all application 3rd Ed.by John D. Kraus (Instructor's
Manual)
Antenna Theory 2nd Ed. by balanis
Applied Linear Statistical Models 5th Ed. by MichaelH.Kutner
Applied Numerical Analysis 7th Ed. by Curtis F. Gerald, Patrick O.
Wheatley
Applied Numerical Methods with Matlab for Engineers and Scientists 2nd
Ed. by Chapra
Applied Statistics Probability for Engineers 3rd ed Montogomery
(selected problems)
Applied Strength of Materials 4th Ed. by Robert L. Mott
Automatic Control Systems 8th Ed. Kuo and Golnaraghi
Basic Engineering Circuit Analysis 7th Ed. by Irwin
Basic Principles and Calculations in Chemical Engineering 6th Ed. by
David M. Himmeblau
Biochemistry 2nd Ed. by Philip W. Kuchel, Gregory B. Rakston
Bioprocess Engineering Principles by Pauline M. Doran
Business Statistics A Decision-Making Approach 6th Ed. by Groebner
C++ How to Program 3rd ed. Deitel, Deitel & Nieto (Instructor's
Manual)
Calculus 4th Ed. by James Stewart (Complete Instructors manual)
Calculus 5th Ed. by James Stewart (Complete Instructors Solutions)
Calculus by Jerrold Marsden & Alan Weinstein Vol 1
Calculus Early Transcendentals 5th Ed. by James Stewart
Calculus of Variations by Russak(book and solutions manual)
Calculus: One and Several Variables 8th Ed. by Salas, Hille and Etgen
Chemical And Engineering Thermodynamics 3Ed by Wiley
Chemical Engineering Solutions to the Problems in Volume 1 by J R
Backhurst
Classical Dynamics 5th Ed. by Thornton
Classical Electrodynamics 3rd Ed. by J.D. Jackon
CMOS Analog Circuit Design 2nd Ed. by P.E. Allen
Communication Systems 4th Ed. by Simon Haykin
Communication Systems Engineering 2nd Ed. by Proakis J.
Communication Systems: An Introduction to Signals and Noise in
Electrical Communication 4th. Ed. by Bruce Carlson
Computational Techniques for Fluid Dynamics by K. Srinivas and
C.A.J.Fletcher
Computer Architecture Design and Performance 2nd Ed. by Barry
Wilkinson
Computer Networking A top-down approach 3rd Ed. by James F. Jurose
Computer Networking: A Top-Down Approach Featuring the Internet 2nd
ed. by Jim Kurose and Keith Ross
Computer Networks 4th Ed. by Andrew.S.Tanenbaum
Computer Networks: A Systems Approach 3rd Ed. by larry L. Peterson and
Bruce S. Davie
Computer Organization And Design - The Hardware Software Interface 3rd
Ed.
Computer Systems Organization and Architecture by John D. Carpinell
Control Systems Engineering 3rd Ed. by Norman S. Nise
Control Systems Engineering by Nise
Design and Analysis of Experiments 6th Ed. by Montgomery
Design Of Analog Cmos Integrated Circuits by Razavi
Design with Operational Amplifiers and Analog Integrated Circuits 3rd
Ed. by Franco, Sergio
Device Electronics for Integrated Circuits 3rd Ed. by Muller and
Kamins
Differential Equations & Linear Algebra by C. Henry
Differential Equations with Boundary-Value Problems 5th Ed. by Zill
and Cullen
Digital communication: Fundamentals and Applications 2nd Ed. by
Bernard Sklar
Digital communications 4th Ed. John Proakis with ebook
Digital Image Processing 2nd Ed. by Gonzalez (Instructor's Manual)
Digital Integrated Circuits by Rabaey 2nd Ed. (selected problems)
Digital signal processing A Computer-Based Approach 1st Ed. by Sanjit
K. Mitra
Digital Signal Processing by Thomas J. Cavicchi
Digital Signal Processing: Principles, Algorithms, and Applications,
3rd Ed. by Proakis & Manolakis
Digital Signals and Filter by S. J. Orfanidis (selected solutions)
Discrete-Time Signal Processing 2nd Ed. by Oppenheim, R.W. Schafer and
J. R. Buck
Distributed Systems Principles and Paradigms by Andrew S. Tanenbaum
and Maarten Van Steen
Econometric Analysis 5th Ed. by William H. Greene
Econometric Analysis of Cross Section and Panel Data by Jeffrey M.
Wooldridge
Electric Circuits 7th Ed. by Nilsson
Electric Machinery 6th Ed. by Fitzgerald, Kingsley, Uman
Electric Machinery and Power System Fundamentals 1st Ed. by Stephen J.
Chapman (Instructor's Manual)
Electric Machinery Fundamentals 4th Ed. by Stephen J Chapma
(Instructor's_Manual)
Electrical Engineering Principles And Applications 4th Edition by
Giorgio Rizzoni
Electrical Engineering Principles And Applications by Hambley
Electronic Circuit Analysis and Design 2nd Ed. by Donald A. Neamen
Electronic Physics by Strabman
Electronics 2nd Ed. by Allan R. Hambley
Element of Electromagnetic by Sadiku
Elementary Differential Equations and Boundary Value problems 7th Ed.
by Boyce, DiPrima (book and solutions)
Elementary Differential Equations and Boundary Value Problems 8th Ed.
Elementary Linear Algebra by K. R. Matthews (book and solution
manuals)
Elementary Mechanics and Thermodynamics by John W. Norbury
Elements of Chemical Reaction Engineering 3rd Ed. by Timothy Hubbard,
Jessica hamman and David Johnson
Elements of Information Theory by Thomas M. Cover
Engineering Biomechanics: Statics by Angela Matos, Eladio Pereira,
Juan Uribe and Elisandra Valentin
Engineering Circuit Analysis 6th Ed. by Hayt
Engineering Electromagnetics 6th Ed. by William H. Hayt, Jr. and Hohn
A. Buck
Engineering Fluid Mechanics 7th Ed. by Crowe
Engineering Mathematics 4th Ed. by John Bird
Engineering Mechanics Dynamics 10th edition by Hibbeler
Engineering Mechanics Dynamics 11th edition by Hibbeler
Engineering Mechanics Dynamics 3rd Ed. by Hibbeler
Engineering Mechanics Dynamics 5th Ed. by Meriam
Engineering Mechanics Dynamics by Bedford and Fowler
Engineering Mechanics statics 10th edition by Hibbeler
Engineering Mechanics statics 11th edition by Hibbeler
Engineering Mechanics Statics 4th Ed. Bedford
Engineering Mechanics Statics by Meriam
Feedback Control of Dynamic Systems 4th Ed. by G. F. Franklin, J. D.
Powell, A. Emami
Fluid mechanics 5th Ed. by White
Fourier and Laplace transforms by Antwoorden (selected solutions)
Fractal Geometry: Mathematical Foundations and Applications by Kenneth
Falconer
Fundamentals of Aerodynamics 2nd Ed. by John D. Anderson
Fundamentals Of Aerodynamics 3rd Ed. by Anderson (Instructor's
Solutions Manual)
Fundamentals of Applied Electromagenetics  5th Ed+
Fundamentals of Differential Equations by Nagle Saff Snider
Fundamentals of Digital Logic with Verilog Design 1st Ed. by S. Brown,
Z. Vranesic
Fundamentals of Digital Logic with VHDL Design 1st Ed. by S. Brown, Z.
Vranesic
Fundamentals of Electric Circuits 2nd Ed. by C.K.Alexander
M.N.O.Sadiku
Fundamentals of Engineering Thermodynamics 5th ed (M. J. Moran & H. N.
Shapiro)
Fundamentals of Financial Management With Infotrac Concise 4th Ed. by
Eugene Brigham
Fundamentals of Fluid Mechanics 3th Ed. by Munson (Student solution
manual)
Fundamentals of Fluid Mechanics 4th Ed. by Munson
Fundamentals of Fluid Mechanics 5th Ed. by Munson
Fundamentals of Heat and Mass Transfer 5th Ed. Incropera
Fundamentals of Logic Design 5th Ed. by  Charles Roth
Fundamentals of Machine Component Design 3rd Ed. by Juvinall and
Marshek
Fundamentals of Machine Component Design 4th Ed. by Juvinall
Fundamentals of Phsics 6th ed. by Halliday, Resnick (instructor's
manual)
Fundamentals of phsics 7th ed. by David Halliday, Robert Resnick, and
Jearl Walker (instructor's manual)
Fundamentals of Thermal-Fluid Sciences by Cengal
Fundamentals of Thermodynamics 6th Ed. Richard E. Sonntag, Claus
Borgnakke, Gordon J. Van Wylen
Guide to Energy Management 5th Ed. by Klaus-Dieter E. Pawlik
Heat Transfer 2nd Ed. by Cengel
Hydraulics in Civil and Environmental Engineering 4th Ed. by Andrew
Chawick
Introduction To Algorithms 2nd Ed. by Philip Bille (selected problems)
Introduction To Algorithms 2nd Ed. by Thomas H. Cormen, Charles
E.Leiserson, Ronald L. Rivest, Clifford Stein
Introduction to Antenna Theory by Palacios
Introduction to electric circuits 6th Ed. by Dorf-Svaboda
Introduction to electrodynamics 3rd Ed. by David Griffiths
Introduction to Fluid Mechanics 5ed. by Fox
Introduction to Fluid Mechanics 6th Ed. by Fox
Introduction to Linear Algebra 3th Ed. by Gilbert Strang
Introduction to Probability by Charles M. Grinstead and J. laurie
Snell
Introduction to Quantum Mechanics 2ed Griffiths, David J.
Introduction to Software Engineering by R. Mall
Introduction to VLSI circuits and Systems by John P. Uyemura
Introduction to Wireless Systems by P. M. Shankar
Investment Analysis and Portfolio Management by Reilly Brown
Linear Algebra and its Applications  3rd Ed.  by Lay
Linear Algebra by Jim Hefferon
Linear circuit analysis by R. A. DeCarlo and P. Lin
Linear Systems and Signals by B P Lathi
Logic Computer Design Fundamentals 2th Ed. by Morris Mano (selected
problems)
Managerial Accounting 11th Ed.
Material Science and Engineering an Introduction 5th Ed. by Callister
Material Science and Engineering an Introduction 6th Ed. by Callister
Materials & Processing in Manufacturing 9th Ed. by Demargo
Mathematical Methods for Physics and Engineering 3rd Ed. by
K.F.RileyandM.P.Hobson
Mathematics for Economics by Simon and Blume
Matrix Analysis And Applied Linear Algebra by Carl D. Meyer
Mechanical Engineering Design 7th Ed. Shigley
Mechanics of Fluids 4th Ed. by I. H. Shames
Mechanics of Fluids 8th Ed. by Bernard Massey
Mechanics of Materials 3rd Ed. Elsevier by S. Nemat-Nasser
Mechanics of Materials 5th 6th Ed. by Gere
Mechanics of materials Hibbeler 6th
Mechanics Of Materials(3rd Ed , By Beer, Johnston, & Dewolf)
Microeconomic Analysis 3rd Ed. by Hal R. Varian
Microeconomic Theory by Andreu Mas-Colell, Jerry R. Green, Michael
Dennis Whinston
Microelectronic Circuits 4th Ed. by Sedra, Smith
Microelectronic circuits 5th Ed. Sedra
Microelectronics Digital and Analog Circuits and Systems by Millman
Microwave and rf design of wireless systems by Pozar
Microwave Engineering 2nd Ed. David M Pozar
Microwave Engineering 3rd Ed. David M Pozar
Microwave Transistor Amplifiers Analysis and Design 2nd Ed. by
Guillermo Gonzalez
Modern Control Engineering 3rd Ed. by K.OGATA
Modern Digital and Analog Communications Systems by B P Lathi
Modern Quantum Mechanics Revised Ed. by J.J. Sakurai (solutions and
book)
Multi Variable Calculus 5th Ed.
Numerical Methods for Engineers by Steven C. Chapra and Raymond P.
Canale
Operating System Concepts 6th Ed. by Abraham Silberschatz
Operating System Concepts 7th Ed. by Abraham Silberschatz
Operating Systems:Internals and Design Principles 4th Ed. by William
Stallings
Options, Futures, & Other Derivatives 4th Ed. by John C. Hull
Organic Chemistry 5th Ed. by Atkins and Carey
Physical Chemistry 7th. Ed. by Peter Atkins & Julio de Paula
Physics for Scientists & Engineers (a strategic approach) by Randall D
Knight
Physics for Scientists & Engineers by Tipler & Mosca 5th Edition
Physics For Scientists And Engineers 3rd Ed. by Douglas C. Giancoli
Physics for Scientists and Engineers 5th Extended Version by Serway
and Faughn
Physics Volume 2 5th Ed. by Halliday, Resnick and Krane
Power System Analysis by John J. Grainger & William D. Stevenson, Jr
Principles of Communication 5th Ed. by R. E. Ziemer, William H.
Tranter
Principles of Physics 4th Ed. Calculus Based by Serway, Raymond A. and
John W. Jewett
Principles with Applications BY Giancoli 6TH Edition
Probability and Statistics for Engineering and the_Sciences 6th Ed.
Probability and Statistics for Engineers and Scientists (selected
problems)
Probability Random Variables and Stochastic Processes 4th Ed. by
Papoulis
Process Systems Analysis and Control by Donald R.coughanowr(selected
problems)
Quantum mechanics by Kyriakos Tamvakis
Quantum Mechanics by P. Saltsidis
Recursive Macroeconomic Theory by Lars Ljungqvist and Thomas J.
Sargent
Recursive Methods in Economic Dynamics by Wright
RF circuit Design Theory and Application by Ludwig bretchko
Sears and Zemansky's University Physics 11th Ed.
Semiconductor Device Fundamentals 1st Ed. by Robert F. Pierret
Semiconductor Devices Physics and Technology 2nd Ed. by S. M. Sze
Semiconductor Physics and Devices 3rd Ed. by Neamen
Serway and Jewett's Physics for Scientists and Engineers 6th ed. by
McGrew and Currie
Signal Processing and Linear Systems by B P Lathi
Signals And Systems 2nd Ed. by Haykin
Signals And Systems 2nd Ed. by Oppenheim
Signals, Systems and Transforms 3rd Ed. by Oppenheim
Soil Mechanics: concepts and applications 2ed William Powrie
Solid State Electronic Device 5th Ed. by Ben Streetman (Instructor's
Manual)
Strengths of Materials by Beer, Johnston, Dewolf
Structural Analysis by R.C. Hibbeler
System Dynamics by Ogata (B problems only)
The C Programming Language 2nd Ed. by Kernighan and Ritchie
The Econometrics of Financial Markets by Petr Adamek
The Science and Engineering of Materials 4th Ed. by Donald R. Askeland
Pradeep P. Phule (Instructor's Manual)
Theory and Applications of OFDM and CDMA Wideband Wireless
Communications (2005)
Thermodynamic 5th ed. Cengal
Thermodynamics of Turbomachinery 5th Ed.
Thermodynamics: An Engineering Approach 5th Ed. by Cengel Boles
(Instructor's Solutions Manual)
Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas
Vol 1
Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas
Vol 2
Transport Phenomena 2nd Ed. by Bird and Stewart(to class 1 and class 2
problems)
Undergraduate Econometrics by Hill, Judge and Griffiths
University Physics with Modern Physics (11th) by  Hugh D. Young and
Roger A. Freedman.
Vector Calculus 3rd Ed. by Susan Jane Colley
Vector Mechanics for engineers dynamics by beer 6th edition
Vector Mechanics for engineers dynamics by beer 7th edition
Vector Mechanics for engineers statics by beer 6th edition
Vector Mechanics for engineers statics by beer 7th edition (nearly the
same with edtion 8)
Wireless Communications principles and practice 2nd Ed. by Theodore
Rappaport 1996
Ebooks:
A First Course in Differential Equations by J. David Logan
Applied Cryptography by A. Menezes. P. van Oorschot and S. Vanstone
Applied mathematics and Modeling for Chemical Engineers by Rice and Do
Applied Mathematics and Modeling for Chemical Engineers by Richard G.
Rice and Duong D. Do
Applied Numerical Methods Using Matlab by Yamg, cao, Chung and Morris
Applied Statistics Probability for Engineers 3rd Ed. by Montogomery
Applied Technology and Instrumentation for Process Control by Douglas
O.J. dsSa
Business Analysis And Valuation Using Financial Statements - Text And
Cases
C++ How to Program 5th Ed. by H. M. Deitel, P. J. Deitel
Calculus Early Transcendentals 5th Ed. by James Stewart
Calculus: Concepts and Contexts 2nd Ed. by Stewart
Computational Fluid Dynamics: Principles and Applications by J. Blazek
Computational Fluid Mechanics and Heat Transfer 2nd Ed. by Tannehill,
Anderson and Pletcher
Computer Organization and Design: The Hardware-Software Interface
Cryptography and Network Security Principles and Practices 2th Ed. by
William Stallings
Cryptography and Network Security Principles and Practices 4th Ed. by
William Stallings
Digital And Analog Communication Systems 5th Ed. by Leon W. Couch
Rabaey.pdf
Digital Signal Processing: A Computer-based Approach 2nd Ed. by Sanjit
K. Mitra
Discrete Mathematics: Elementary and Beyond by Loavz, Pelikan,
Vesztergombi
DWDM Network Designs and Engineering Solutions by Astwin Gumaste and
Tony Antony
Ebook  Wireless Communications principles and practice 1996
Elementary Applied Partial Differential Equations with Fourier Series
and Boundary Value Problems 2nd Ed. by Richard Haberman
Elementary Calculus: An Infinitesimal Approach 2nd Ed. by H. Jerome
keisler
Elements of Electromagnetics 3rd Ed. by Sadiku
Elements of The Theory of Computation 2nd Ed. by Lewis and
Papadimitriou
Financial Accounting McGraw-Hill
Fluid Mechanics 2nd Ed. by Rjucsh K. Kundu and Ira M. Cohen
Fluid Mechanics 4th Ed. by Frank M. White (With Study Guide)
Fundamentals of Aerodynamics by Anderson
Fundamentals of Gas Dynamics 2nd Ed. by Zucker R D , Biblarz
Harper s Biochemistry 26th Ed. by Murray, Granner, Mayes and Rodwell
Heat and Mass Transfer 2nd Ed. by Stephan
Imperfect C++ Practical Solutions for Real-Life Programming by Matthew
Wilson
Introduction to Thermal Systems Engineering: Thermodynamics, fluid
mechanics, and heat tranfer by Moran
Linear Algebra And Its Applications by David C Lay
Microeconomic Theory by Andreu Mas-Colell, Jerry R. Green and Michael
Dennis Whinston
Modern Control Engineeing 3rd Ed. by Katsuhiko Ogata
Modern Operating Systems 2nd Ed. By Tanenbaum
Modern Wireless Communications by Simon Hatkin and Michael Moher
Numerical Analysis by David Kincaid and Ward Cheney
Numerical Methods using MATLAB 3rd Ed. by Mathrews and Fink
Numerical Techniques In Electromagnetics 2nd Ed. by Matthew N. O.
Sadiku
Physics for Scientists and Engineers 6th Ed. by Serway Jewett
Principles and applications of Electrical Engineering by Giorgio
Rizzoni
Principles of Genetics 7th Ed. by Tamarin
Probability, Random Variables, and Random Signal Principles 2nd Ed. by
Peyton Z. Peebles, Jr.
Rules Of Thumb For Chemical Engineers A Manual Of Quick, Accurate
Solutions To Everyday Process Engineering Problems 3rd Ed. by carl
Branan
Schaum's Outline of College Physics by Fredrick J. Bueche and Eugene
Hecht
Scientific Computing An Introductory Survey by Michael T. Heath
Signals And Systems by Oppenheim
Thermal Physics 2nd Ed. by Kittel
Vector Mechanics for engineers statics 7th. Ed. by Ferdinand P. Beer
Wireless Communications by Andrea Goldsmith
===
Subject: Re: Comprehensive Solutions Manual for College Textbooks
All Subjects' solutions manuals in Pdf format
All solutions manuals are in pdf format or Microsoft Word format.
I have tried my best to put up with the collections of my solutions
manual.
Here is the list that only part of my collections:
I will put some time to make up the full list daily.
If you cant find the solution manual listed below, don't give up, feel
free to email me
To get the solutions manual, just email me with a price you want to
get the solutions manual you want.
To see samples, just email me.
My email is edisonee(at)gmail.com
Solutions Manuals
.NET 2.0 Interoperability Recipes by Bruce Bukovics
A Course in Game Theory by Martin J. Osborne and Ariel Rubinstein
A First Course In Probability 7th Ed by Sheldon Ross
Adaptive Control 2nd Ed. by Karl.J.Astrom
Advanced Engineering Marhematics ERWIN KREYSZIG 9E
Advanced Engineering Mathematics 8Ed Erwin Kreyszig
Advanced Engineering Mathematics 8Ed Erwin Kreyszig in korean (all
even and odd no.)
Advanced Macroeconomics by Jeffery Rohaly
Advanced Modern Engineering Mathematics 3rd Ed. by Glyn James
Analog Integrated Circuit Design by David Johns, Ken Martin
Analysis and Design of Analog Intergrated Circuits 4th Ed. by Paul R.
Gray
Analytical Mechanics 7th Ed. by Fowles
Antenna for all application 3rd Ed.by John D. Kraus (Instructor's
Manual)
Antenna Theory 2nd Ed. by balanis
Applied Linear Statistical Models 5th Ed. by MichaelH.Kutner
Applied Numerical Analysis 7th Ed. by Curtis F. Gerald, Patrick O.
Wheatley
Applied Numerical Methods with Matlab for Engineers and Scientists 2nd
Ed. by Chapra
Applied Statistics Probability for Engineers 3rd ed Montogomery
(selected problems)
Applied Strength of Materials 4th Ed. by Robert L. Mott
Automatic Control Systems 8th Ed. Kuo and Golnaraghi
Basic Engineering Circuit Analysis 7th Ed. by Irwin
Basic Principles and Calculations in Chemical Engineering 6th Ed. by
David M. Himmeblau
Biochemistry 2nd Ed. by Philip W. Kuchel, Gregory B. Rakston
Bioprocess Engineering Principles by Pauline M. Doran
Business Statistics A Decision-Making Approach 6th Ed. by Groebner
C++ How to Program 3rd ed. Deitel, Deitel & Nieto (Instructor's
Manual)
Calculus 4th Ed. by James Stewart (Complete Instructors manual)
Calculus 5th Ed. by James Stewart (Complete Instructors Solutions)
Calculus by Jerrold Marsden & Alan Weinstein Vol 1
Calculus Early Transcendentals 5th Ed. by James Stewart
Calculus of Variations by Russak(book and solutions manual)
Calculus: One and Several Variables 8th Ed. by Salas, Hille and Etgen
Chemical And Engineering Thermodynamics 3Ed by Wiley
Chemical Engineering Solutions to the Problems in Volume 1 by J R
Backhurst
Classical Dynamics 5th Ed. by Thornton
Classical Electrodynamics 3rd Ed. by J.D. Jackon
CMOS Analog Circuit Design 2nd Ed. by P.E. Allen
Communication Systems 4th Ed. by Simon Haykin
Communication Systems Engineering 2nd Ed. by Proakis J.
Communication Systems: An Introduction to Signals and Noise in
Electrical Communication 4th. Ed. by Bruce Carlson
Computational Techniques for Fluid Dynamics by K. Srinivas and
C.A.J.Fletcher
Computer Architecture Design and Performance 2nd Ed. by Barry
Wilkinson
Computer Networking A top-down approach 3rd Ed. by James F. Jurose
Computer Networking: A Top-Down Approach Featuring the Internet 2nd
ed. by Jim Kurose and Keith Ross
Computer Networks 4th Ed. by Andrew.S.Tanenbaum
Computer Networks: A Systems Approach 3rd Ed. by larry L. Peterson and
Bruce S. Davie
Computer Organization And Design - The Hardware Software Interface 3rd
Ed.
Computer Systems Organization and Architecture by John D. Carpinell
Control Systems Engineering 3rd Ed. by Norman S. Nise
Control Systems Engineering by Nise
Design and Analysis of Experiments 6th Ed. by Montgomery
Design Of Analog Cmos Integrated Circuits by Razavi
Design with Operational Amplifiers and Analog Integrated Circuits 3rd
Ed. by Franco, Sergio
Device Electronics for Integrated Circuits 3rd Ed. by Muller and
Kamins
Differential Equations & Linear Algebra by C. Henry
Differential Equations with Boundary-Value Problems 5th Ed. by Zill
and Cullen
Digital communication: Fundamentals and Applications 2nd Ed. by
Bernard Sklar
Digital communications 4th Ed. John Proakis with ebook
Digital Image Processing 2nd Ed. by Gonzalez (Instructor's Manual)
Digital Integrated Circuits by Rabaey 2nd Ed. (selected problems)
Digital signal processing A Computer-Based Approach 1st Ed. by Sanjit
K. Mitra
Digital Signal Processing by Thomas J. Cavicchi
Digital Signal Processing: Principles, Algorithms, and Applications,
3rd Ed. by Proakis & Manolakis
Digital Signals and Filter by S. J. Orfanidis (selected solutions)
Discrete-Time Signal Processing 2nd Ed. by Oppenheim, R.W. Schafer and
J. R. Buck
Distributed Systems Principles and Paradigms by Andrew S. Tanenbaum
and Maarten Van Steen
Econometric Analysis 5th Ed. by William H. Greene
Econometric Analysis of Cross Section and Panel Data by Jeffrey M.
Wooldridge
Electric Circuits 7th Ed. by Nilsson
Electric Machinery 6th Ed. by Fitzgerald, Kingsley, Uman
Electric Machinery and Power System Fundamentals 1st Ed. by Stephen J.
Chapman (Instructor's Manual)
Electric Machinery Fundamentals 4th Ed. by Stephen J Chapma
(Instructor's_Manual)
Electrical Engineering Principles And Applications 4th Edition by
Giorgio Rizzoni
Electrical Engineering Principles And Applications by Hambley
Electronic Circuit Analysis and Design 2nd Ed. by Donald A. Neamen
Electronic Physics by Strabman
Electronics 2nd Ed. by Allan R. Hambley
Element of Electromagnetic by Sadiku
Elementary Differential Equations and Boundary Value problems 7th Ed.
by Boyce, DiPrima (book and solutions)
Elementary Differential Equations and Boundary Value Problems 8th Ed.
Elementary Linear Algebra by K. R. Matthews (book and solution
manuals)
Elementary Mechanics and Thermodynamics by John W. Norbury
Elements of Chemical Reaction Engineering 3rd Ed. by Timothy Hubbard,
Jessica hamman and David Johnson
Elements of Information Theory by Thomas M. Cover
Engineering Biomechanics: Statics by Angela Matos, Eladio Pereira,
Juan Uribe and Elisandra Valentin
Engineering Circuit Analysis 6th Ed. by Hayt
Engineering Electromagnetics 6th Ed. by William H. Hayt, Jr. and Hohn
A. Buck
Engineering Fluid Mechanics 7th Ed. by Crowe
Engineering Mathematics 4th Ed. by John Bird
Engineering Mechanics Dynamics 10th edition by Hibbeler
Engineering Mechanics Dynamics 11th edition by Hibbeler
Engineering Mechanics Dynamics 3rd Ed. by Hibbeler
Engineering Mechanics Dynamics 5th Ed. by Meriam
Engineering Mechanics Dynamics by Bedford and Fowler
Engineering Mechanics statics 10th edition by Hibbeler
Engineering Mechanics statics 11th edition by Hibbeler
Engineering Mechanics Statics 4th Ed. Bedford
Engineering Mechanics Statics by Meriam
Feedback Control of Dynamic Systems 4th Ed. by G. F. Franklin, J. D.
Powell, A. Emami
Fluid mechanics 5th Ed. by White
Fourier and Laplace transforms by Antwoorden (selected solutions)
Fractal Geometry: Mathematical Foundations and Applications by Kenneth
Falconer
Fundamentals of Aerodynamics 2nd Ed. by John D. Anderson
Fundamentals Of Aerodynamics 3rd Ed. by Anderson (Instructor's
Solutions Manual)
Fundamentals of Applied Electromagenetics  5th Ed+
Fundamentals of Differential Equations by Nagle Saff Snider
Fundamentals of Digital Logic with Verilog Design 1st Ed. by S. Brown,
Z. Vranesic
Fundamentals of Digital Logic with VHDL Design 1st Ed. by S. Brown, Z.
Vranesic
Fundamentals of Electric Circuits 2nd Ed. by C.K.Alexander
M.N.O.Sadiku
Fundamentals of Engineering Thermodynamics 5th ed (M. J. Moran & H. N.
Shapiro)
Fundamentals of Financial Management With Infotrac Concise 4th Ed. by
Eugene Brigham
Fundamentals of Fluid Mechanics 3th Ed. by Munson (Student solution
manual)
Fundamentals of Fluid Mechanics 4th Ed. by Munson
Fundamentals of Fluid Mechanics 5th Ed. by Munson
Fundamentals of Heat and Mass Transfer 5th Ed. Incropera
Fundamentals of Logic Design 5th Ed. by  Charles Roth
Fundamentals of Machine Component Design 3rd Ed. by Juvinall and
Marshek
Fundamentals of Machine Component Design 4th Ed. by Juvinall
Fundamentals of Phsics 6th ed. by Halliday, Resnick (instructor's
manual)
Fundamentals of phsics 7th ed. by David Halliday, Robert Resnick, and
Jearl Walker (instructor's manual)
Fundamentals of Thermal-Fluid Sciences by Cengal
Fundamentals of Thermodynamics 6th Ed. Richard E. Sonntag, Claus
Borgnakke, Gordon J. Van Wylen
Guide to Energy Management 5th Ed. by Klaus-Dieter E. Pawlik
Heat Transfer 2nd Ed. by Cengel
Hydraulics in Civil and Environmental Engineering 4th Ed. by Andrew
Chawick
Introduction To Algorithms 2nd Ed. by Philip Bille (selected problems)
Introduction To Algorithms 2nd Ed. by Thomas H. Cormen, Charles
E.Leiserson, Ronald L. Rivest, Clifford Stein
Introduction to Antenna Theory by Palacios
Introduction to electric circuits 6th Ed. by Dorf-Svaboda
Introduction to electrodynamics 3rd Ed. by David Griffiths
Introduction to Fluid Mechanics 5ed. by Fox
Introduction to Fluid Mechanics 6th Ed. by Fox
Introduction to Linear Algebra 3th Ed. by Gilbert Strang
Introduction to Probability by Charles M. Grinstead and J. laurie
Snell
Introduction to Quantum Mechanics 2ed Griffiths, David J.
Introduction to Software Engineering by R. Mall
Introduction to VLSI circuits and Systems by John P. Uyemura
Introduction to Wireless Systems by P. M. Shankar
Investment Analysis and Portfolio Management by Reilly Brown
Linear Algebra and its Applications  3rd Ed.  by Lay
Linear Algebra by Jim Hefferon
Linear circuit analysis by R. A. DeCarlo and P. Lin
Linear Systems and Signals by B P Lathi
Logic Computer Design Fundamentals 2th Ed. by Morris Mano (selected
problems)
Managerial Accounting 11th Ed.
Material Science and Engineering an Introduction 5th Ed. by Callister
Material Science and Engineering an Introduction 6th Ed. by Callister
Materials & Processing in Manufacturing 9th Ed. by Demargo
Mathematical Methods for Physics and Engineering 3rd Ed. by
K.F.RileyandM.P.Hobson
Mathematics for Economics by Simon and Blume
Matrix Analysis And Applied Linear Algebra by Carl D. Meyer
Mechanical Engineering Design 7th Ed. Shigley
Mechanics of Fluids 4th Ed. by I. H. Shames
Mechanics of Fluids 8th Ed. by Bernard Massey
Mechanics of Materials 3rd Ed. Elsevier by S. Nemat-Nasser
Mechanics of Materials 5th 6th Ed. by Gere
Mechanics of materials Hibbeler 6th
Mechanics Of Materials(3rd Ed , By Beer, Johnston, & Dewolf)
Microeconomic Analysis 3rd Ed. by Hal R. Varian
Microeconomic Theory by Andreu Mas-Colell, Jerry R. Green, Michael
Dennis Whinston
Microelectronic Circuits 4th Ed. by Sedra, Smith
Microelectronic circuits 5th Ed. Sedra
Microelectronics Digital and Analog Circuits and Systems by Millman
Microwave and rf design of wireless systems by Pozar
Microwave Engineering 2nd Ed. David M Pozar
Microwave Engineering 3rd Ed. David M Pozar
Microwave Transistor Amplifiers Analysis and Design 2nd Ed. by
Guillermo Gonzalez
Modern Control Engineering 3rd Ed. by K.OGATA
Modern Digital and Analog Communications Systems by B P Lathi
Modern Quantum Mechanics Revised Ed. by J.J. Sakurai (solutions and
book)
Multi Variable Calculus 5th Ed.
Numerical Methods for Engineers by Steven C. Chapra and Raymond P.
Canale
Operating System Concepts 6th Ed. by Abraham Silberschatz
Operating System Concepts 7th Ed. by Abraham Silberschatz
Operating Systems:Internals and Design Principles 4th Ed. by William
Stallings
Options, Futures, & Other Derivatives 4th Ed. by John C. Hull
Organic Chemistry 5th Ed. by Atkins and Carey
Physical Chemistry 7th. Ed. by Peter Atkins & Julio de Paula
Physics for Scientists & Engineers (a strategic approach) by Randall D
Knight
Physics for Scientists & Engineers by Tipler & Mosca 5th Edition
Physics For Scientists And Engineers 3rd Ed. by Douglas C. Giancoli
Physics for Scientists and Engineers 5th Extended Version by Serway
and Faughn
Physics Volume 2 5th Ed. by Halliday, Resnick and Krane
Power System Analysis by John J. Grainger & William D. Stevenson, Jr
Principles of Communication 5th Ed. by R. E. Ziemer, William H.
Tranter
Principles of Physics 4th Ed. Calculus Based by Serway, Raymond A. and
John W. Jewett
Principles with Applications BY Giancoli 6TH Edition
Probability and Statistics for Engineering and the_Sciences 6th Ed.
Probability and Statistics for Engineers and Scientists (selected
problems)
Probability Random Variables and Stochastic Processes 4th Ed. by
Papoulis
Process Systems Analysis and Control by Donald R.coughanowr(selected
problems)
Quantum mechanics by Kyriakos Tamvakis
Quantum Mechanics by P. Saltsidis
Recursive Macroeconomic Theory by Lars Ljungqvist and Thomas J.
Sargent
Recursive Methods in Economic Dynamics by Wright
RF circuit Design Theory and Application by Ludwig bretchko
Sears and Zemansky's University Physics 11th Ed.
Semiconductor Device Fundamentals 1st Ed. by Robert F. Pierret
Semiconductor Devices Physics and Technology 2nd Ed. by S. M. Sze
Semiconductor Physics and Devices 3rd Ed. by Neamen
Serway and Jewett's Physics for Scientists and Engineers 6th ed. by
McGrew and Currie
Signal Processing and Linear Systems by B P Lathi
Signals And Systems 2nd Ed. by Haykin
Signals And Systems 2nd Ed. by Oppenheim
Signals, Systems and Transforms 3rd Ed. by Oppenheim
Soil Mechanics: concepts and applications 2ed William Powrie
Solid State Electronic Device 5th Ed. by Ben Streetman (Instructor's
Manual)
Strengths of Materials by Beer, Johnston, Dewolf
Structural Analysis by R.C. Hibbeler
System Dynamics by Ogata (B problems only)
The C Programming Language 2nd Ed. by Kernighan and Ritchie
The Econometrics of Financial Markets by Petr Adamek
The Science and Engineering of Materials 4th Ed. by Donald R. Askeland
Pradeep P. Phule (Instructor's Manual)
Theory and Applications of OFDM and CDMA Wideband Wireless
Communications (2005)
Thermodynamic 5th ed. Cengal
Thermodynamics of Turbomachinery 5th Ed.
Thermodynamics: An Engineering Approach 5th Ed. by Cengel Boles
(Instructor's Solutions Manual)
Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas
Vol 1
Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas
Vol 2
Transport Phenomena 2nd Ed. by Bird and Stewart(to class 1 and class 2
problems)
Undergraduate Econometrics by Hill, Judge and Griffiths
University Physics with Modern Physics (11th) by  Hugh D. Young and
Roger A. Freedman.
Vector Calculus 3rd Ed. by Susan Jane Colley
Vector Mechanics for engineers dynamics by beer 6th edition
Vector Mechanics for engineers dynamics by beer 7th edition
Vector Mechanics for engineers statics by beer 6th edition
Vector Mechanics for engineers statics by beer 7th edition (nearly the
same with edtion 8)
Wireless Communications principles and practice 2nd Ed. by Theodore
Rappaport 1996
Ebooks:
A First Course in Differential Equations by J. David Logan
Applied Cryptography by A. Menezes. P. van Oorschot and S. Vanstone
Applied mathematics and Modeling for Chemical Engineers by Rice and Do
Applied Mathematics and Modeling for Chemical Engineers by Richard G.
Rice and Duong D. Do
Applied Numerical Methods Using Matlab by Yamg, cao, Chung and Morris
Applied Statistics Probability for Engineers 3rd Ed. by Montogomery
Applied Technology and Instrumentation for Process Control by Douglas
O.J. dsSa
Business Analysis And Valuation Using Financial Statements - Text And
Cases
C++ How to Program 5th Ed. by H. M. Deitel, P. J. Deitel
Calculus Early Transcendentals 5th Ed. by James Stewart
Calculus: Concepts and Contexts 2nd Ed. by Stewart
Computational Fluid Dynamics: Principles and Applications by J. Blazek
Computational Fluid Mechanics and Heat Transfer 2nd Ed. by Tannehill,
Anderson and Pletcher
Computer Organization and Design: The Hardware-Software Interface
Cryptography and Network Security Principles and Practices 2th Ed. by
William Stallings
Cryptography and Network Security Principles and Practices 4th Ed. by
William Stallings
Digital And Analog Communication Systems 5th Ed. by Leon W. Couch
Rabaey.pdf
Digital Signal Processing: A Computer-based Approach 2nd Ed. by Sanjit
K. Mitra
Discrete Mathematics: Elementary and Beyond by Loavz, Pelikan,
Vesztergombi
DWDM Network Designs and Engineering Solutions by Astwin Gumaste and
Tony Antony
Ebook  Wireless Communications principles and practice 1996
Elementary Applied Partial Differential Equations with Fourier Series
and Boundary Value Problems 2nd Ed. by Richard Haberman
Elementary Calculus: An Infinitesimal Approach 2nd Ed. by H. Jerome
keisler
Elements of Electromagnetics 3rd Ed. by Sadiku
Elements of The Theory of Computation 2nd Ed. by Lewis and
Papadimitriou
Financial Accounting McGraw-Hill
Fluid Mechanics 2nd Ed. by Rjucsh K. Kundu and Ira M. Cohen
Fluid Mechanics 4th Ed. by Frank M. White (With Study Guide)
Fundamentals of Aerodynamics by Anderson
Fundamentals of Gas Dynamics 2nd Ed. by Zucker R D , Biblarz
Harper s Biochemistry 26th Ed. by Murray, Granner, Mayes and Rodwell
Heat and Mass Transfer 2nd Ed. by Stephan
Imperfect C++ Practical Solutions for Real-Life Programming by Matthew
Wilson
Introduction to Thermal Systems Engineering: Thermodynamics, fluid
mechanics, and heat tranfer by Moran
Linear Algebra And Its Applications by David C Lay
Microeconomic Theory by Andreu Mas-Colell, Jerry R. Green and Michael
Dennis Whinston
Modern Control Engineeing 3rd Ed. by Katsuhiko Ogata
Modern Operating Systems 2nd Ed. By Tanenbaum
Modern Wireless Communications by Simon Hatkin and Michael Moher
Numerical Analysis by David Kincaid and Ward Cheney
Numerical Methods using MATLAB 3rd Ed. by Mathrews and Fink
Numerical Techniques In Electromagnetics 2nd Ed. by Matthew N. O.
Sadiku
Physics for Scientists and Engineers 6th Ed. by Serway Jewett
Principles and applications of Electrical Engineering by Giorgio
Rizzoni
Principles of Genetics 7th Ed. by Tamarin
Probability, Random Variables, and Random Signal Principles 2nd Ed. by
Peyton Z. Peebles, Jr.
Rules Of Thumb For Chemical Engineers A Manual Of Quick, Accurate
Solutions To Everyday Process Engineering Problems 3rd Ed. by carl
Branan
Schaum's Outline of College Physics by Fredrick J. Bueche and Eugene
Hecht
Scientific Computing An Introductory Survey by Michael T. Heath
Signals And Systems by Oppenheim
Thermal Physics 2nd Ed. by Kittel
Vector Mechanics for engineers statics 7th. Ed. by Ferdinand P. Beer
Wireless Communications by Andrea Goldsmith
===
Subject: Re: 100 solution manual for various textbook in PDF format
All Subjects' solutions manuals in Pdf format
All solutions manuals are in pdf format or Microsoft Word format.
I have tried my best to put up with the collections of my solutions
manual.
Here is the list that only part of my collections:
I will put some time to make up the full list daily.
If you cant find the solution manual listed below, don't give up, feel
free to email me
To get the solutions manual, just email me with a price you want to
get the solutions manual you want.
To see samples, just email me.
My email is edisonee(at)gmail.com
Solutions Manuals
.NET 2.0 Interoperability Recipes by Bruce Bukovics
A Course in Game Theory by Martin J. Osborne and Ariel Rubinstein
A First Course In Probability 7th Ed by Sheldon Ross
Adaptive Control 2nd Ed. by Karl.J.Astrom
Advanced Engineering Marhematics ERWIN KREYSZIG 9E
Advanced Engineering Mathematics 8Ed Erwin Kreyszig
Advanced Engineering Mathematics 8Ed Erwin Kreyszig in korean (all
even and odd no.)
Advanced Macroeconomics by Jeffery Rohaly
Advanced Modern Engineering Mathematics 3rd Ed. by Glyn James
Analog Integrated Circuit Design by David Johns, Ken Martin
Analysis and Design of Analog Intergrated Circuits 4th Ed. by Paul R.
Gray
Analytical Mechanics 7th Ed. by Fowles
Antenna for all application 3rd Ed.by John D. Kraus (Instructor's
Manual)
Antenna Theory 2nd Ed. by balanis
Applied Linear Statistical Models 5th Ed. by MichaelH.Kutner
Applied Numerical Analysis 7th Ed. by Curtis F. Gerald, Patrick O.
Wheatley
Applied Numerical Methods with Matlab for Engineers and Scientists 2nd
Ed. by Chapra
Applied Statistics Probability for Engineers 3rd ed Montogomery
(selected problems)
Applied Strength of Materials 4th Ed. by Robert L. Mott
Automatic Control Systems 8th Ed. Kuo and Golnaraghi
Basic Engineering Circuit Analysis 7th Ed. by Irwin
Basic Principles and Calculations in Chemical Engineering 6th Ed. by
David M. Himmeblau
Biochemistry 2nd Ed. by Philip W. Kuchel, Gregory B. Rakston
Bioprocess Engineering Principles by Pauline M. Doran
Business Statistics A Decision-Making Approach 6th Ed. by Groebner
C++ How to Program 3rd ed. Deitel, Deitel & Nieto (Instructor's
Manual)
Calculus 4th Ed. by James Stewart (Complete Instructors manual)
Calculus 5th Ed. by James Stewart (Complete Instructors Solutions)
Calculus by Jerrold Marsden & Alan Weinstein Vol 1
Calculus Early Transcendentals 5th Ed. by James Stewart
Calculus of Variations by Russak(book and solutions manual)
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===
Subject: Research prime's number
Is (n) the odd numbers.
If the couple it's made up of two numbers 
addition =(n) to no admit common's divisor, 
then(n) is prime number.
example:
 (n) = 23
The couple (2,21), (3,20), (4,19), (5,18),
(6,17), (7,16),(8,15), (9,14), (10,13), (11,12);
no admit common's divisor then (n)=23 is prime number.
(n) = 15
The couple (2,13),(3,12),(4,11),(5,10),(6,9),(7,8);
admit (3,12),(6,9) divisor 3; and (5,10) divisor 5.
Then 15 = 3*5
Who explain it ? 
Good bye
Vincenzo Librandi
vincenzo.librandweoz@alice.it
===
Subject: Re: Research prime's number
As you wish ! I donêt polemize. 
Excuse me for my language. 
I thing: 
m=(a+b) is prime, if and so if, a=prime number, 
example: 
5=3+2; 7=5+2; 13=11+2;  and so on  
7=3+4; 11=7+4; 17=13+4;  and so on 
11=5+6; 13=7+6; 17=11+6; and so on
11=3+8; 13=5+8; 19=11+8; and so on 
Respectful
Vincenzo Librandi
vincenzo.librandweoz@alice.it
===
Subject: Re: Research prime's number
The converse portion of your claim, that
if m can be expressed as a prime number
plus an even number, then m is prime, is
obviously false (as others have pointed
out).  Any square of a positive prime
can be written as that prime plus an
even number:  p^2 = p + p(p-1)
===
Subject: Re: Research prime's number
this is obvious since all (positive)
primes except 2 are odd.
However primes 2,3 cannot be
expressed as a smaller (positive)
prime plus an even number.
===
Subject: Re: Research prime's number
I am sorry for arriving late.
Know it.
When m = a+b is prime ?
to listen again.
Vincenzo Librandi
vincenzo.librandweoz@alice.it
===
Subject: Re: Research prime's number
You asked how to prove:
If A then B.
I showed you:
If not B, then not A
If you don't know how to get from one to the other, then you
are missing some fairly fundamental mathematical tools. 
Google for 'contrapositive' for a start.
Phil
-- 
Home taping is killing big business profits. We left this side blank 
so you can help. -- Dead Kennedys, written upon the B-side of tapes of
/In God We Trust, Inc./.
===
Subject: Re: Research prime's number
When 1 and m are its only divisors.
===
Subject: Re: Research prime's number
 
very well David, 
you understand my problem. 
Therefore ...!!
Saluti
Vincenzo Librandi
vincenzo.librandweoz@alice.it
===
Subject: Re: Research prime's number
No, it isn't, because 9 belong
to the couple(3,6),that has 3 
for divisor.
9 = (2,7),(3,6),(4,5). 
yours sincerely.
Vincenzo Librandi
vincenzo.librandi@alice.it
===
Subject: Re: Research prime's number
Is 4+5 prime?
===
Subject: Re: Research prime's number
You miss understood his badly made claim if I understand it correctly from 
his examples.  I think he is trying to say that n is prime iff when written 

as a sum of 2 positive integers then there is never a pair with a common 
divisor.  He already knew 9 was not prime by his claim as 9=3+6 and they 
have a common divisor of 3.  Of course his claim is easily seen to be true 
and not of any real value.  (n is not prime iff n=jk where jk and integers 
prime, one cannot write it as the sum of two numbers with a common divisor 
===
Subject: Re: Research prime's number
then p|a and p|b. So p|m. So m is not prime.
Phil
-- 
Home taping is killing big business profits. We left this side blank 
so you can help. -- Dead Kennedys, written upon the B-side of tapes of
/In God We Trust, Inc./.
===
===
Subject: sum (for k=1 to +inf) {N*(T^k)*[(1/(1+d))^k;0]
I'm looking for a closed form solution for:
sum (for k=1 to +inf) {N*(T^k)*[(1/(1+d))^k;0]
where N is a 1x2 matrix N=[N1 N2] and T is a 2x2 stochastic matrix
T=[p 1-p; 1-q q].
Let me give you some more details on my problem: Assume a 2-state
Markov chain with transition matrix T as defined above. In t0 there
are N1 individuals in State 1 and N2 individuals in State 2. I would
like to calculate and sum of up the number of individuals in State 1
in Period 1, 2, 3, ... However, since I'm working in a finance
context, I need to discount future periods by a discount factor.
Hence, for every period, the number of individuals in State 1 needs to
be multiplied with (1/(1+d))^k.
I tried to do this with MATLAB
symsum(N*(T^k)*[(1/(1+d))^k;0],k,0,inf)
but got the error message
Exponent must be a numeric integer.
Does anyone know whether a closed-form solution for such an expression
exists at all?
Michael
===
Subject: Re: sum (for k=1 to +inf) {N*(T^k)*[(1/(1+d))^k;0]
I don't know what you mean by the notation [a^k;0] (where a = 1/
(1+d)). Doy you mean that the result is a 1x2 vector with elements
[sum(N1*a^k*T^k(1,1)+N1*a^k*T^k(2,1),
sum(N1*a^k*T^k(1,2)+N1*a^k*T^k(2,2)]? I will assume so. Here is what I
get using Maple 9.5: letting B = T^k, we have
with(LinearAlgebra): <----- lots of packages not shown here
P:=Matrix([[p,1-p],[1-q,q]]);
                             [  p      1 - p]
                        P := [              ]
                             [1 - q      q  ]
               [            k    k          k        k    ]
               [-1 + q + p b  - b        p b  - p - b  + 1]
               [------------------     - -----------------]
               [        c                        c        ]
          B := [                                          ]
               [     k        k            k    k         ]
               [  q b  - q - b  + 1     q b  - b  - 1 + p ]
               [- -----------------     ----------------- ]
               [          c                     c         ]
                              k    k           k        k
              N1 (-1 + q + p b  - b )   N2 (q b  - q - b  + 1)
       v1k := ----------------------- - ----------------------
                         c                        c
                       k        k               k    k
                N1 (p b  - p - b  + 1)   N2 (q b  - b  - 1 + p)
       v2k := - ---------------------- + ----------------------
                          c                        c
In case these don't come out nicely on the screen, here they are
again, simplified:
let b=p+q-1, c=p+q-2, f1 = (N1+N2)(q-1)/c, f2 = (N1+N2)(p-1)/c and g =
[N1(p-1)+N1(q-1)]/c. Then
v1k= f1 + g*b^k and v2k= f2 = g*b^k. These are the two components of
[N1,N2]*T^k.
Now you just have to do sums of the form f*a^k or g*(a*b)^k.
R.G. Vickson
===
Subject: Re: sum (for k=1 to +inf) {N*(T^k)*[(1/(1+d))^k;0]
That shoul be v2k = f2 + g*b^k.
RGV
===
Subject: Re: sum (for k=1 to +inf) {N*(T^k)*[(1/(1+d))^k;0]
Is B what I get when I raise my transition matrix P to the power of k?
I also assume that within B, you made the following two substitutions:
b=p+q-1 and c=p+q-2
Is this right?
I just want to get sure that I got everything right ...
Michael
===
Subject: Re: sum (for k=1 to +inf) {N*(T^k)*[(1/(1+d))^k;0]
Yes, exactly.
Yes. And, of course, a = 1/(1+d).
Note: if all you want are sums from 0 to infinity, or from 1 to
infinity, you really don't need to know exactly what T^k is. It
suffices to know
Q = sum(a^k * T^k, k=1..infinity) = a*T*inverse(I - a*T), which is
computable in MATLAB, or by solving the equation Q = a*T + a*Q*T. The
row vector V = [V1,V2] = [N1,N2]*Q solves the equations V = a*N*T +
a*V*T, so if W = N*T = [W1,W2] = [N1*p + N2*(1-q), N1*(1-p) + N2*q],
then V1 = a*W1 + a*(p*V1 + (1-q)*V2) and V2 = a*W2 + a*((1-p)*V1 +
q*V2), which can be solved symbolically.
R.G. Vickson
===
Subject: Re: sum (for k=1 to +inf) {N*(T^k)*[(1/(1+d))^k;0]
Michael
===
Subject: Re: Code needed for Mathematica re Pythagorean triples
I can see that this is a rare case when a bit of mathematical knowledge may 

hurt your algorithm (am I right?). Mine is ignorant of the known 
parametrization of the P. triples. It's in perl but almost like in C.
%%%%%%%%%  start code   %%%%%%%%%
#!/usr/bin/perl
#
# author: wh
# Pythagorean triples with the given area or perimeter
use integer;
print nnPythagorean triangles with perimeter = $nnn;
$start = times();
$per=0;
# for($a=1; 2*$a*$a < ($n-2*$a)*($n-2*$a); ++$a) perfect but prone to 
overflow
for($a=3; 17*$a < 5*$n; ++$a)
{   for($b=12*($n-$a)/31; ; ++$b)
    {   $c = $n-$a-$b;
        if($ab == $cc)
        {   print $a    $b    $cn;
            ++$per;
            last
}   }   }
$endT = times();
print nThere are $per Pyth. triangles withnperimeter = $nnn;
print     The computation took *** ,$endT-$start, ***nn;
print ********************nn;
print nnPythagorean triangles with area = $n / 2nn;
$start = times();
$ar=0;
{   next if ($a*$b != $n);
    $C = $a*$a + $b*$b;
    for($c=$b+($a*$a)/(2*$b); ; $c=($c+$C/$c)/2)
    {   last if $c*$c < $C;
        if($c*$c==$C)
        {   print $a  $b  $cn;
            ++$ar;
            last
}   }   }
$endT = times();
print nnThere are $ar Pyth. triangles with area = $n / 2nnn;
print         The computation took *** , $endT-$start,  ***nn;
%%%%%%   end code   %%%%%%%
Enjoy,
    Wlod
===
Subject: Re: Code needed for Mathematica re Pythagorean triples
On May 6, 2:36 am, Wlodzimierz Holsztynski (Wlod)
Does the link to mathematica notebook code (top of page) work?
http://mathworld.wolfram.com/PrimitivePythagoreanTriple.html
(primitive triples)
And for triples:
http://mathworld.wolfram.com/PythagoreanTriple.html
===
Subject: how to model linear recurrences using groebner basis?
hi
how to model linear recurrences using groebner basis?
I've tried to solve linear recurrences (solving for the recurrence
equation for a sequence), but always end up solving for the sequence,
instead of finding a equation.
For example, I tried to use as many pairs of relations as possible,
then solve for groebner basis.
(0 1 2 7 20 61)
[(a)+(-1*b)+(1),(a)+(-1*c)+(2),(a)+(-1*d)+(7),(a)+(-1*e)+(20),(a)+
(-1*f)+(61),(b)+(-1*c)+(1),(b)+(-1*d)+(6),(b)+(-1*e)+(19),(b)+(-1*f)
+(60),(d)+(3)+(-1/2*e),(e)+(1/3)+(-1/3*f),(49/6)+(-1/6*f)+(c),(-61)+
(f)]
[(a),(-1)+(b),(-7)+(d),(-20)+(e),(-2)+(c),(-61)+(f)]
This is just the original sequence.
===
Subject: Re: how to model linear recurrences using groebner basis?
I can't tell what you're doing here, but let's suppose 
(0 1 2 7 20 61) is the start of the sequence, and you want to
find a k-term constant-coefficient linear recurrence relation  
x(n) = a_1 x(n-1) + ... + a_k x(n-k) for it.  Every adjacent 
(k+1)-tuple of members of your sequence gives you a linear equation
in a_1, ..., a_k.  You can then try to solve this system of linear
equations.  No need for Groebner, since this is linear.  To uniquely
determine a_1,...,a_k, you need at least k equations, thus 2k members
of your sequence.  In your example, with k=2 the equations
2 = 1 a_1 + 0 a_2
7 = 2 a_1 + 1 a_2
20 = 7 a_1 + 2 a_2
61 = 20 a_1 + 7 a_2
have the unique solution a_1 = 2, a_2 = 3.
-- 
Robert Israel              israel@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            Vancouver, BC, Canada
===
Subject: Re: how to model linear recurrences using groebner basis?
On May 7, 4:21 am, Robert Israel
Ok, I see where I went wrong. The number of variables I used was too
many to begin with.
===
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Mechanical Engineering Design 7th Ed. Shigley
Mechanics of Fluids 8th Ed. by Bernard Massey
Mechanics of materials Hibbeler 6th
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Microeconomic Analysis 3rd Ed. by Hal R. Varian
Microeconomic Theory by Andreu Mas-Colell, Jerry R. Green, Michael Dennis 
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Microelectronic Circuits 4th Ed. by Sedra, Smith
Microelectronic circuits 5th Ed. Sedra
Microelectronics Digital and Analog Circuits and Systems by Millman
Microwave and rf design of wireless systems by Pozar
Microwave Engineering 2nd Ed. David M Pozar
Microwave Engineering 3rd Ed. David M Pozar
Microwave Transistor Amplifiers Analysis and Design 2nd Ed. by Guillermo 
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Modern Control Engineering 3rd Ed. by K.OGATA 
Modern Control Systems 10E by Richard Dorff
Modern Digital and Analog Communications Systems by B P Lathi
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Numerical Methods for Engineers by Steven C. Chapra and Raymond P. Canale
Numerical Methods 3E by Faires
Operating System Concepts 6th Ed. by Abraham Silberschatz
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Operating Systems:Internals and Design Principles 4th Ed. by William 
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Physical Chemistry 7th. Ed. by Peter Atkins & Julio de Paula
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Power System Analysis by John J. Grainger & William D. Stevenson, Jr
Principles of Communication 5th Ed. by R. E. Ziemer, William H. Tranter
Principles of Physics 4th Ed. Calculus Based by Serway, Raymond A. and John 

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Principles with Applications BY Giancoli 6TH Edition
Probability and Statistics for Engineers and Scientists (selected problems)
Probability Random Variables and Stochastic Processes 4th Ed. by Papoulis
Process Systems Analysis and Control by Donald R.coughanowr(selected 
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Quantum mechanics by Kyriakos Tamvakis
Recursive Macroeconomic Theory by Lars Ljungqvist and Thomas J. Sargent
Recursive Methods in Economic Dynamics by Wright
RF circuit Design Theory and Application by Ludwig bretchko
Semiconductor Device Fundamentals 1st Ed. by Robert F. Pierret
Semiconductor Physics and Devices 3rd Ed. by Neamen
Signal Processing and Linear Systems by B P Lathi
Signals And Systems 2nd Ed. by Haykin
Signals And Systems 2nd Ed. by Oppenheim
Signals, Systems and Transforms 3rd Ed. by Oppenheim
Soil Mechanics: concepts and applications 2ed William Powrie
Solid State Electronic Device 5th Ed. by Ben Streetman (Instructor's 
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Solid State Physics solutions
Solved and Unsolved Problems in Number Theory and Geometry by Daniel Shanks
Strengths of Materials by Beer, Johnston, Dewolf
Structural Analysis by R.C. Hibbeler 
System Dynamics by Ogata 3rd
The C Programming Language 2nd Ed. by Kernighan and Ritchie 
The Econometrics of Financial Markets by Petr Adamek
The Science and Engineering of Materials 4th Ed. by Donald R. Askeland 
Pradeep P. Phule (Instructor's Manual)
Theory and Applications of OFDM and CDMA Wideband Wireless Communications 
(2005)
Thermodynamic 5th ed. Cengal
Thermodynamics: An Engineering Approach 5th Ed. by Cengel Boles 
(Instructor's Solutions Manual)
Thermodyanamics of Turbomachinary 5E
Time-Harmonic Electromagnetic Fields by Harrington solutions, 2001
Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas  Vol 1
Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas  Vol 2
Transport Phenomena 2nd Ed. by Bird and Stewart(to class 1 and class 2 
problems)
University Physics with Modern Physics (11th) by  Hugh D. Young and Roger A. 

Freedman.
Vector Calculus 3rd Ed. by Susan Jane Colley
Vector Mechanics for engineers dynamics by beer 6th edition
Vector Mechanics for engineers dynamics by beer 7th edition
Vector Mechanics for engineers statics by beer 6th edition
Vector Mechanics for engineers statics by beer 7th edition (nearly the same 

with edtion 8)
Wireless Communications principles and practice 2nd Ed. by Theodore 
Rappaport 1996
===
Subject: extension theoems of lipschitz function.
I've read Mcshine-Whitne & Kirszbraun extension theorems (and them
proof). But now I want to understand their importance and application.
Can you tell me?
===
Subject: Re: extension theoems of lipschitz function.
For example,
http://en.wikipedia.org/wiki/Kirszbraun_theorem
I'm not familiar with a specific application, but it seems
clear that theorems like this are going to be useful, because
there are a lot of results about and characterizations of
globally defined Lipschitz functions - the theorem allows
you to apply these results to functions defined in a subset
of R^n or your Hilbert space or whatever. Seems pretty clear
this is going to be useful in a lot of places.
Ok. Never having been very scholarly, the only specific
example of an application of something analogous that
springs to mind comes from my own work some years ago:
or whatever). We say f is a Zygmund function if there
exists c such that
  |f(x-h) - 2 f(x) - f(x+h)| <= c |h|
whenever x, x+h and x-h all lie in D. (So it's
clear that Lipschitz functions are Zygmund functions,
but the Zygmund class is much larger - it also
often works much better, one reason for which is
that it's a Besov space while Lip_1 is not.)
Now suppose that K is a compact subset of R^n
and let D = R^n  K. Inventing some temporary
terminology, say that K is strongly removable
if every harmonic Zygmund function in D extends
to a harmonic (Zygmund) function in R^n, and
say that K is weakly removable if every Zygmund
function in R^n which happens to be harmonic
in D is actually harmonic in R^n. The problem
is to characterize removable sets K.
Say m_alpha is Hausdorff measure.
Thm 1. K is strongly removable if and only
if m_{n-1}(K) = 0.
The proof used Thm 2 plus an extension
result analogous to the theorems you mention, 
where Thm 2 says that K is weakly
removable if and only if m_{n-1}(K) = 0.
(Carleson proved analogous results for
Lip_alpha, 0 < alpha < 1, but didn't get the
case alpha = 1. Neither did I - the corresponding
question for Lip_1 seems very difficult (it
turns out that removability for Lip_1 is
_not_ equivalent to m_{n-1}(K) = 0). But
I noticed that if 0 < alpha < 1 then Lip_alpha
is equal to a Besov space Lambda_alpha;
on the other hand Lip_1 is not the same as
Lambda_1, in fact Lambda_1 is the Zygmund
class. So it's natural to ask the question
for Lambda_1 = Zyg instead, and _that_
question is easier to answer. When something
works for Lip_alpha, 0 < alpha < 1, but
not for Lip_1, it often turns out that
it does work for the Zygmund class; Krantz
goes almost so far as to claim that the Zygmund
class is what Lip_1 should have been defined
to be...)
************************
David C. Ullrich
===
Subject: What's a bilinear form?
I'm reading a book on general relativity which tells me that the scalar
product is a bilinear form.  What does that mean? 
-- 
http://www.dailymotion.com/video/x1ek5w_wtc7-the-smoking-gun-of-911-updated
http://911research.wtc7.net
http://vehme.blogspot.com
Virtus Tutissima Cassis
===
Subject: Re: What's a bilinear form?
I tried to post basically this same reply some time ago --- but it
never seems to have actually gotten posted. I don't know what
happened, but here it is again and many apologies if it ends up
appearing twice.
Since the time of Banach in the early 20th century, mathematical
concepts are often described in terms of spaces. A space in
mathematics is simply a set with a few additional properties. It is
these additional properties that uniquely define a space (distinguish
it from other spaces). Many of the mathematical concepts from before
the 20th century have been generalized in terms of spaces in the 20th
century.
Examples of spaces include topological spaces (a set together with
some simple set operators like union and intersection) and metric
spaces (a set together with a distance function or metric such as
d(x,y)=|x-y|).
But one of the most general and useful spaces is the vector space. A
vector space is always constructed over some field. The field is
often either the set of real numbers (R) or complex numbers (C). Any
element of the vector space is called a vector; any element of the
field is called a scalar.
A vector space comes equipped with two inherent operators:
  1. vector vector addition operator (+)
  2. scalar vector multiplication operator (x or . or juxtaposition)
With these two operators you can add two vectors and get a new vector.
Or you can multiply a scalar times a vector and get another vector.
(But note that in general you cannot multiply two vectors --- for this
you need an algebra).
The concept of the function in mathematics is a mechanism that maps
elements in one set to elements in the same or another set. In a
vector space, the mechanism that performs this is called an
operator. That is, an operator maps a vector from one vector space
to a vector in another (or the same) vector space. A familiar example
of this is in matrix algebra where we write
  y = Ax
If A is an mxn matrix, then A is an operator that maps x, which is in
the vector space C^n (space of all complex n-tuples), to y, which is
in the vector space C^m.
Another example is a Fredholm operator:
  y(t) = integral k(t,s) x(s) ds
The integral with kernel k(t,s) is the operator that maps the vector
x(t) to another vector y(t).
So an operator maps a vector to a vector, and a function (at least in
terms of high school math) maps from a scalar to a scalar. But what
about mapping from a vector to a scalar? In a vector space, the
mechanism that performs this is called a functional. That is, a
functional maps from a vector space into the field (of scalars) over
which the vector space is constructed. An example of a functional is
any definite integral (say from 0 to 1):
  y = integral_0^1 k(s) x(s) ds
Here the definite integral is a functional that maps the vector x(t)
to the scalar value y.
One of the most common examples of functionals is the norm ||x||.
An example of a norm from matrix algebra is
  ||x||^2 = x^H x
Here, the functional f(x)=||x|| maps the vector x to a scalar.
A vector space equipped with a norm is called a normed linear space.
A functional is called linear if it acts like a straight line
equation through 0. A functional f(x) is linear if is satisfies these
conditions:
  1. f(x+y) = f(x) + f(y)   (additive)
  2. f(ax)   = a f(x)         (homogeneous)
An example of a functional that is linear is any definite integral:
  1. int_0^1 [x(t)+y(t)] dt = int_0^1 x(t) dt + int_0^1 y(t) dt
  2. int_0^1 a x(t) dt = a int_0^1 x(t) dt
An example of a functional that is in general not linear is the norm ||
x|| because, for example,
  ||x+y|| <= ||x|| + ||y||  (subadditive, not additive).
A functional may also accept two vector arguments as in f(x,y) and map
these two vectors together to one scalar value. Such a functional
f(x,y) is linear in the first variable if
  1. f(x1+x2,y) = f(x1,y) + f(x2,y)   (additive in x)
  2. f(ax,y)   = a f(x,y)                  (homogeneous in x)
A functional f(x,y) is a bilinear functional or bilinear form if
it is linear in the first variable and conjugate linear in the second
variable such that
  1. f(x1+x2,y) = f(x1,y) + f(x2,y)
  2. f(ax,y)   = a f(x,y)
  3. f(x,y1+y2) = f(x,y1) + f(x,y2)
  4. f(x,ay)   = a* f(x,y)                (where a* is the conjugate
of a)
One special case (and probably the most common example) of a bilinear
inner product is a bilinear form because
An example of an inner product in matrix algebra is
An example of an inner product using integrals is
A vector space equipped with an inner product is called an inner
product space.
Note that every inner product (or scalar product) is a bilinear form;
but not every bilinear form is an inner product.
An excellent excellent book that introduces many many topics useful to
applied mathematics applications is
  Applied Algebra and Functional Analysis (Dover)
  by Anthony N. Michel and Charles J. Herget
  isbn  0-486-67598-X
  http://www.amazon.com/dp/048667598X
  http://www.worldcat.org/isbn/048667598X
I wish you all the best in learning about general relativity.
Dan Greenhoe
===
Subject: Re: What's a bilinear form?
-- 
Dave Seaman
Oral Arguments in Mumia Abu-Jamal Case to be heard May 17
U.S. Court of Appeals, Third Circuit
===
Subject: Re: What's a bilinear form?
It means you should stop reading that book and first acquire some
serious math. It may take you about an year's time to acquire that
math -- but in the end, it'll be worth it, you'll really understand
relativity.
===
Subject: Re: What's a bilinear form?
That would be an extremely stupid approach to addressing the question.  
I checked Gray's Differential Geometry, Clark's Abstract Algebra, two texts
on vector and tensor analysis as well as a couple texts on mathematical
physics and none  mentions the term in the index.  I found it mentioned in
one math book is such an esoteric form that it would have required days to
figure it out.  I finally checked a book I read a long time ago called
Space Time Matter, by Hermann Weyl and he explains it quite clearly.  That
must have been in the back of my mind any way, since the actual term used
in Misner Thorn and Wheeler is bilinear expression, not bilinear 
form.
-- 
http://www.dailymotion.com/video/x1ek5w_wtc7-the-smoking-gun-of-911-updated
http://911research.wtc7.net
http://vehme.blogspot.com
Virtus Tutissima Cassis
===
Subject: Re: What's a bilinear form?
What is there so problematic about this notion?
two variables in which the map is linear.
the ground field.
So a bilinear form is a map
where V,W are vector spaces over the field K, that
is linear in both variables.
Straight, simple and nothing to agonize about.
H
===
Subject: Re: What's a bilinear form?
Bilinear form is indeed the standard term when dealing with real vector
spaces.  In complex vector spaces, one often speaks of a sesquilinear
form (linear in one argument and conjugate linear in the other).  A
bilinear expression is not necessarily limited to vector spaces and
therefore is less specific.  Since the OP mentioned scalar products, it's
clear that vector spaces are the context for the question.
I note that Google finds:
        560,000 hits for the exact phrase bilinear form,
            819 hits for the exact phrase bilinear expression.
-- 
Dave Seaman
Oral Arguments in Mumia Abu-Jamal Case to be heard May 17
U.S. Court of Appeals, Third Circuit
===
Subject: Re: What's a bilinear form?
I believe I am the one who mentioned the scalar product.  
I'm still not completely sure what is meant by form in the term 
bilinear
(trilinear, multilinear, etc.) form.  Is that 'form' as in 'form of
expression'?  Or 'form' as in 'geometric form'?  IOW, is it referring to
the way the symbols are arranged, or is it referring to something abstract?
Regarding the scalar product, I'm not sure that everybody agrees as to what
is meant by 'inner product'.  One view is that an inner product is
something that satisfies the axioms:
Which means the scalar product of Lorentz spacetime is not an inner product
by that definition.  
Another view is that an inner product is a composite, two argument 
operation
performed on congruent lists.  There is an inner operation (*) and an outer
operation (+).  So basically, it is tensor contraction.  By that
definition, the scalar product of relativity /is/ an inner product.   I
tend to favor the latter definition because it seems to correspond to the
complementary notion of an outer product, which is, IIRC, synonymous with
the Cartesian product for finite sets.
-- 
http://www.dailymotion.com/video/x1ek5w_wtc7-the-smoking-gun-of-911-updated
http://911research.wtc7.net
http://vehme.blogspot.com
Virtus Tutissima Cassis
===
Subject: Re: What's a bilinear form?
You are the OP (original poster).  I failed to notice that when I posted
my previous reply, but my statement that the OP mentioned scalar products
is correct.
A bilinear form, as opposed to a bilinear operator, is defined to take
values in the underlying scalar field.
Correct.  It's an abuse of language.
But that's not how inner product is used in mathematics.
-- 
Dave Seaman
Oral Arguments in Mumia Abu-Jamal Case to be heard May 17
U.S. Court of Appeals, Third Circuit
===
Subject: Re: What's a bilinear form?
http://mitpress.mit.edu/catalog/author/default.asp?aid=1421
Vol I, pg., 269 , ó3.2 The Inner or Scalar Product defines the 
inner product
in exactly that form I am discussing.  That is to say, as the contraction
of two vectors with the metric tensor.
-- 
http://www.dailymotion.com/video/x1ek5w_wtc7-the-smoking-gun-of-911-updated
http://911research.wtc7.net
http://vehme.blogspot.com
Virtus Tutissima Cassis
===
Subject: Re: What's a bilinear form?
Maybe I'm dense, but I don't see how that definition can apply to
infinite-dimensional spaces.
-- 
Dave Seaman
Oral Arguments in Mumia Abu-Jamal Case to be heard May 17
U.S. Court of Appeals, Third Circuit
===
Subject: Re: What's a bilinear form?
A linear mapping of a vector space into the set of _scalars_ is called a 
linear _form_. Likewise a bilinear mapping of a product of two vector spaces 

into the set of scalars is called a bilinear form.
For bilinear mapping:
http://en.wikipedia.org/wiki/Bilinear_operator
With stuff like this in your signature:
http://www.dailymotion.com/video/x1ek5w_wtc7-the-smoking-gun-of-911-updated
http://911research.wtc7.net
http://vehme.blogspot.com
you shouldn't be surprised if some people don't take you seriously. 
===
Subject: positive definite cone
What is the dimension of cone of pos. def. nxn matrices ?
===
Subject: Re: positive definite cone
The dimension of the smallest linear (Euclidean) space that contains
that cone.
===
Subject: Re: positive definite cone
Positive definiteness is an open condition, so (assuming you mean
symmetric matrices) the dimension is n(n+1)/2.
Lee Rudolph
===
Subject: Re: Easy Quadratic Equation Problem
Cancel-Key: sha1:cn57XWpjnLj27DFf8nQZWcbWDsc=
===
Subject: Homeomorphic images of a line in R^2
I have the following question:
What are the possible homeomorphic images of a line in the plane R^2.
(By homeomorphic images i mean images to R^2 itself) ?
===
Subject: Re: Homeomorphic images of a line in R^2
I think that there are very, very many of these.  Obviously, two
equivalent embeddings of R ^ 1 into R ^ 2 must have the property that
the boundaries of their images are homeomorphic.  We have already seen
examples of embeddings whose boundaries are:
Empty
A single point
Two points
A circle
Two disjoint circles
line segments of length 1, having the origin as one endpoint.  You can
find an embedding of the line into the plane which limits on this set,
so we already have a countably-infinite number of embeddings.  There
are a ton of other figures that can be made to be the boundary of an
embedded line, also.
===
Subject: Re: Homeomorphic images of a line in R^2
In my last post, I referred to the boundary of the image of the
embedding several times.  I realized that every point in the image
will be part of the boundary.  What I really meant was, the set of
limit points of the image which are not in the image.
===
Subject: Re: Homeomorphic images of a line in R^2
Yipes -- yes, you're right. A homeomorphic image of R in R^2 is not
necessarily closed in R^2 (as even the simple example of the positive
variations.
For example, you can even get a closed unit disk as the closure of the
image of a homeomorph of R embedded in R^2 (using one of those wierd
space-filling curves).
Clearly, if A and B are homeomorphs of R embedded in R^2 then any
auto-homeomorphism of R^2 which takes A to B must take the closure of
A to the closure of B. Thus, if the closures are topologically
different, then A and B are not equivalent.
Two questions:
(1) Is it sufficient to compare the closures? In other words, if A and
B are homeomorphs of R embedded in R^2, and if the closure of A is
homeomorphic to the closure of B, does that imply the existence of an
auto-homeomorphism of R^2 which takes A to B?
(2) What are all the possible homeomorphism types of closures of a
homeomorph of R embedded in R^2? Certainly, for a set to be such a
closure, it must be path connected. Is that sufficient?
I think it's simpler just to consider the full closures.
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
For question (2), I think the answer must be no.  Consider the figure
Y in the plane.  This figure cannot be the closure of an embedded
line.
The answer to (1) is also negative.  Consider the following two
embeddings of R into R^2:
For the first, the line is embedded into an annulus, so that on end of
the line limits onto the inner boundary circle, and the other end
limits onto the outer boundary circle.
For the second, take two disjoint circles in the plane which are not
contained inside each other (that is, each circle is in the
unbounded component of the complement of the other).  The embedded
line will lie outside the two circles, and one end of the line will
limit onto each circle.
The closures of these embeddings are homeomorphic, but there will be
no self-homeomorphism of R^2 to itself taking one to the other.
===
Subject: Re: Homeomorphic images of a line in R^2
Yes, it's clear that you can't get a Y shape as such a closure.
Yes, nice example.
So within each class of equivalent closures, there can be more than
one equivalence class of homeomorphs of R
Also, back to question (2), am I right that the closures can yield
sets with interior in R^2? I think there can be at most 2 such parts,
one for each end.
The essence of this idea is that only the ends are free to be
creative, and there are only 2 of them. Each end can do its own thing
(within reason). They can be wild if they want to, but an end can't do
2 different things -- it has to choose.
Thus, every homeomorph of R in R^2 has 3 parts. A boring middle part
and 2 independent end parts each of which can have their choice of
certain kinds of closures.
The equivalence class of the embedding then depends on the choice of
those two closures together with their relative placement in R^2. How
the middle part connects appears to be irrelevant.
To formalize one of the above observations, I'll make the following
conjecture:
If A is a subset of R^2 homeomorphic to R, then the interior of the
closure of A has at most 2 components.
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
I'm no longer so sure about the above conjecture, although I don't
have a counterexample. If it is false, I think it fails badly. 
Here's a conjecture at the opposite extreme:
Every open subset of R^2 is the closure of the interior a set which is
homeomorphic to R.
Which of these conjectures, if any, is correct?
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
Correction:
Every open subset of R^2 is the interior of the closure of the
interior of a set which is homeomorphic to R.
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
I have some more observations.
images of R in R^2, these sets needn't be of the first category.
Consider the space-filling curve.
Also, it is still unclear to me that there exists a subset A of R^2
which is homeomorphic to R, such that the closure of A has non-empty
interior.  Can you give an example?
Your corrected conjecture still seems incorrect.  You said:  Every
open subset of R^2 is the interior of the closure of the
interior of a set which is homeomorphic to R.  You would expect a
subset of R^2 which was homeomorphic to R to have empty interior.
Should this be: Every open subset of R^2 is the interior of the
closure of a subset homeomorphic to R?
When you were talking about components of the closure of A, or the
interior of the closure of A, I did not quite understand what you
meant.  We have seen subsets A of R^2, which are homeomorphic to R,
such that the closure of A has 3 path-components.  However, the
closure was still connected, and had empty interior.
===
Subject: Re: Homeomorphic images of a line in R^2
Yep, you're right.
I think such curves should be illegal.
No, once again I fooled myself into thinking a space-filling curve
could do the trick, but those curves are never one-to-one. 
Those damn space filling curves. When I don't want them, they show up
to ruin my conjectures. When I need them to help prove a conjecture,
they refuse.
So now I'm pretty sure that there is no subset A of R^2 which is
homeomorphic to R and such that the closure of A has non-empty
interior. How to prove that, I'm not sure. I'll have to think about
it.
No, based on the apparent lack of interiors for these closures, I
think I'll just withdraw both conjectures.
I don't understand what I meant either.
Perhaps it makes more sense to focus on components of the complement
of the closure. At most 3 components, I think. No?
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
Focussing on the components of the complement of the closure makes
more sense.  However, it is not true that there are at most 3
components.  In the example where we had each end of the line limit
onto a circle, we could just as easily have had each end of the line
limit onto a figure 8.  The end would loop around the outside of the
figure 8, approaching it closer and closer.  In this case, you will
get more than 3 components in the complement of the closure.
===
Subject: Re: Homeomorphic images of a line in R^2
Continuing that idea, it looks like you can get a countably infinite
number of components for the complement of the closure.
Hmmm ...
How about this blind conjecture:
A closed subset S of R^2  is the closure of a set homeomorphic to R
iff S is connected and locally path connected, and the complement of S
is dense in R^2.
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
I believe several of the embeddings we have looked at did not have
locally path connected closure.
===
Subject: Re: Homeomorphic images of a line in R^2
Hmmm. I don't see it instantly. I'll have to retrace the thread. My
intuition with regard to this problem is obviously still somewhat
weak.
Let's consider 3 sets:
   Let A be a subset of R^2 homeomorphic to R.
   
   Let S be the closure of A.
   Let U be the complement of S.
What can we say about A? Well, that's what the original problem. By
hypothesis, A is homeomorphic to R. As a result, A is path connected.
Also, by invariance of domain, A is nowhere dense. A is definitely not
compact. A might or might not be closed. If A is closed, it's easy --
there's only one type (I think).
What can we say about S? By definition, S is closed. Also, S must be
connected. However S is not necessarily path connected, and based on
your comment, S need not even be locally path connected. Of course, if
S is bounded, then S is compact. I think we believe that S is always
nowhere dense but we haven't actually proved this.
What can we say about U? Apparently not much, except that U must be
open. If it's true that S is always nowhere dense, then U must be
dense.
Are we close to characterizing A? No, not that close. 
I know I've certainly made a lot of wrong turns in the attempt so far,
but Jules has kept from going too far off track.
What next on this?
Maybe switch back to one of the other problems.
What are all the homeomorphism types of continuous images of R in R^2?
What are all the homeomorphism types of bijective continuous images of
R in R^2?
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
The question should have been easy.
The fact that we immediately had to fend off all kinds of pathological
creatures (like in the night of the living dead) dramatizes the
weakness of topology.
I mean, topology is beautiful, sure, but if we can't even characterize
homeomorphic images of R in R^2, we need more powerful weapons.
I think it motivates additional structure.
I would expect that in subjects such as
   Combinatorial Topology 
   Differential Topology
   Differential Geometry
   Algebraic Geometry 
questions analogous to the one we struggled with could be more easily
dispatched.
On the other hand, battling those strange beasts was certainly fun.
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
Well, when we say a set is nowhere dense, we mean its closure has
empty interior.  So, if A is nowhere dense, then the closure of A (=
S) must also be nowhere dense.
One note on notation: in topology, if X is a space, and A is a
subspace, we can talk about the pair (X,A).  If (X,A) and (Y,B) are
is contained in B.  You can also talk about a homeomorphism of pairs.
In this language, our original question can be worded: What are the
possible homeomorphism types of (R^2, A), when A is homeomorphic to R?
You claim that, if A is homeomorphic to R and A is closed, then there
is only one possible homeomorphism type for (X,A).  I believe this is
true, but consider the following: Let S^2 be the one-point
compactification of R^2, and S^1 be the one-point compactification of
R.  It is not hard to show that if A is closed, then the inclusion A --
that there is only one possible homeomorphism type for the pair (S^2,
S^1).  The Jordan Curve Theorem would follow as a consequence.
Because the Jordan Curve Theorem is quite tricky to prove, there is
unlikely to be a simple proof of the claim.
===
Subject: Re: Homeomorphic images of a line in R^2
Hmmm. Ok, but now I'm not so sure we know that A is nowhere dense. My
claim that invariance of domain implies that A is nowhere dense may be
overstated. As far as I know, invariance of domain only implies that A
has empty interior which, by itself, says nothing about whether or not
S has empty interior.
Except perhaps by using the Jordna Curve Theorem to prove the claim.
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
Originator: grubb@lola
Some thoughts about homeomorphs of R in R^2:
K=beta(R) into S^2.  It is known that KR has two components. Also, 
h(KR) is disjoint from h(R) (sinceh is a homeomorphism) so the closure 
of h(R) in S^2 has at most two components.
Also, since a locally compact space is open in any compactification,
h(R) is open in h(K), so h(K)h(R) is compact. Translating back to
R^2, we see that h(R) is open in the closure of h(R) and the 'remainder'
is closed. Also, the remainder has at most two bounded components.
This shows that the closure of h(R) does not contain any open set;
if it did, then h(R) would have to. Hence h(R) is nowhere dense.
Now, taking a curve going to a Y and moving the vertex of the Y to 
infinity,
we can get a case where the 'positive infinity remainder' has three
components. This is easily extended.
Next, if the remainder in S^2 has two components, L and M, it is possible
for the complements of L and M to be disconnected. But, if U is the
component of the complement of K which contains M, then K must be
a subset of the closure of U. This means that you cannot have 'nested'
figure 8's (where one figure 8 is inside, say, the upper loop of the other). 

It may be easier to consider homeomorphs of [0,1) in S^2 first and
then look at how they can 'link up' in S^2 to get homeomorphs of
R. Finally, look at how the point at infinity can be excluded.
Just my 2 cents.
--Dan Grubb
===
Subject: Re: Homeomorphic images of a line in R^2
This inspires me to digress (I know, I know, it's unlike me; must
be spring fever).
By definition of the Stone-Cech compactification (as the maximal
compactification), such an extension exists.  We have seen plenty
of examples of h for which no such extension exists for the minimal
(1-point) compactification RP(1) of R, nor for the end-compactification
(2-point) [-infinity,infinity] of R.  Now, there are of course a vast 
array of (more or less horrible) compactifications between beta(R) and 
and RP(1).  Questions: given any non-maximal compactification Q of R,
is there a homeomorphism h of R into R^2 which does not extend to
a continuous map of Q into S^2?  If so, construct it (given a sufficiently
precise description of Q).  If not, how can those compactifications Q
of R, which share the given extension property with K, be otherwise
characterized, and does this set have interesting lattice properties
(for instance, does it include minimal elements, or does its complement
include maximal elements)?
I have no ideas about any of those questions (including whether they're
trivial); it's spring.
Lee Rudolph
===
Subject: Re: Homeomorphic images of a line in R^2
Yes -- actually, I was about to suggest the same thing -- to look at
it as 3 pieces -- namely, the images of (-infinity,-1], [-1,1], and
[1,infinity).
.
Exactly.
Some cool insights, worth a lot more than 2 cents.
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
Originator: grubb@lola
I clearly misspoke here. I meant that the cl[h(R)]h(R) has
at most two components.
--Dan Grubb
===
Subject: Re: Homeomorphic images of a line in R^2
I will try to specify the question, because all _homeomorphic_ images
of a line are homeomorphic...
(Homeomorphism = injective continuous mapping with continuous inverse)
So the question is (I think): Classify up to homeomorphism all images
of continuous mappings: R to R^2.
So for example line, square (with interior), circle, ...
Easy to see, there is at least countable many of them.
===
Subject: Re: Homeomorphic images of a line in R^2
Although this is different than what we were discussing, this is also
an interesting problem.  It seems that the majority of path-connected
subsets of the plane can be the image of R under a continuous map.
One example of a space which cannot is ((R-Q) x R) U (R x {0}).
===
Subject: Re: Homeomorphic images of a line in R^2
We now have 3 questions ...
(1) What are all possible homeomorphism classes of continuous images
of R into R^2?
(2) What are all possible homeomorphism classes of bijective
continuous images of R into R^2?
(3) What are the possible equivalence classes of homeomorphic images
of R in R^2, where 2 such sets are considered equivalent if there is a
homeomorphism of R^2 taking one to the other?
In this thread, I don't think we yet have full answers to any of them.
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
I'll make a conjecture for question (1):
A subset A of R^2 is a continuous image of R iff A is nonempty, path
connected, and first category.
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
Ok, as Jules points out, the above claim is wrong.
Any space-filling curve gives a counterexample.
I seem to often forget to consider space-filling curves.
A subset A of R^2 is a continuous image of R iff A is nonempty, path
connected, and the union of an open set with a set of first category.
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
Let E be the Cantor set, and consider A = (E x [0,1]) union ([0,1] x {0}).
It's certainly path connected and first category, but it's not a 
continuous image of R.  In fact any continuous image of R contained
in A can contain at most countably many of the points (x,1), x in E. 
-- 
Robert Israel              israel@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            Vancouver, BC, Canada
===
Subject: Re: Homeomorphic images of a line in R^2
Hmmm. The Cantor set -- they should make that set illegal also. It's
just as bad as the space-filling curve. In fact, I think they're in
cahoots -- a conspiracy for sure.
nothing is as simple as it seems.
Ok, let A be a continuous image of R in R^2. What can we say about the
topological type of A? Certainly A is path connected.  A may or may
not have interior. Suppose we assume that A has no interior (thus
ruling out space-filling curves). Let's also require that A is closed.
Now we should be able to say something nice about A, no? For example,
can A now be regarded as topologically equivalent to a (potentially
infinite) planar graph, throwing in some points at infinity if needed?
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
No.  At least, it seems clear to me (at the end of a long day) that
the Hawaiian Earring is such an A, and it's not a graph (even an
infinite one) in the usual sense (at the bad point it is not locally
contractible, but any infinite simplicial complex is). 
By the way, the parametrization I think is clearly possible can
even be taken to be a smooth immersion (not, of course, in
general position).  Oy.
Lee Rudolph
===
Subject: Re: Homeomorphic images of a line in R^2
On May 6, 5:42 pm, Robert Israel
I like this example.  It is similar to one that I gave earlier, except
yours is of the first category.  The problem is that this set A is not
second countable in the path topology, as any continuous image of R
must be.
===
Subject: Re: Homeomorphic images of a line in R^2
I neglected to say that this is my latest conjecture:
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
I am sorry. Now I see the corrected question, which is about knot
theory.
===
Subject: Re: Homeomorphic images of a line in R^2
That's easy. They are all homeomorphic to R^1. Of course, that's
surely not the answer you were looking for.
So I think you need to rephrase the question.
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
I'm guessing eugene is asking the Fundamental Question of Knot Theory 
in this context: in the set of subsets X of R^2 with X homeomorphic
to R, what are the equivalence classes if we define X is equivalent
to X' to mean there is an autohomeomorphism f of R^2 such that 
X' = f(X).
I don't know the answer. I can see eight classes.  Are there more (or
fewer)?
For the similar question with X = S^1, the answer is 1 (Shoenflies).
Lee Rudolph
===
Subject: Re: Homeomorphic images of a line in R^2
plane, i.e. those ones of the lines, which can be extended to the
whole plane.
===
Subject: Re: Homeomorphic images of a line in R^2
Ok, that question makes sense.
Hmmm ...
I also see 8 classes.
I'll organize the count by whether or not the ends are bounded.
Classes which are unbounded at both ends:
(1) The x-axis (or any straight line cutting R^2 in half).
(2) The positive x-axis followed by a curve starting at the origin
looping back towards the x-axis, and asymptotic to the positive x axis
as x approaches infinity.
Classes which unbounded at only one end:
(3) The positive x-axis.
(4) The positive x axis followed by a curve starting at the origin and
looping back towards (but not touching) the point (1,0).
Classes which are bounded at both ends:
(5) The open interval (0,1) on the x-axis
(6) An eye-glass curve. Start with the interval (-2,2) on the x-axis
and then loop back on both sides towards the points (-1,0) and (1,0)
respectively.
(7) A curve making the shape of the symbol 6.
(8) A curve making the shape of the symbol 8.
Those are all the ones I see. Are they correct?
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
Here's one more:
(9) A curve with a shape resembling an 8 except that the loops share a
curve as a common border (not just a point as in the figure 8).
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
Those were indeed the 8 ideas I had.  HOWEVER, most of them
AREN'T (as I had imagined, on too little coffee and too much
sleep) subsets of R^2 that are homeomorphic to R.   They *are*
images of homeomorphisms into R^2, however, which would be another
question eugene might have meant to ask.  And there's more
(unless I misread the post by quasi that I was following up to
and managed to delete): a spiral accumulating at one end
or the other, or both, on one or two circles (where the circles
can be mutually exterior or not). 
So now, for the first question, I only see 3.  Any more?
Lee Rudolph
===
Subject: Re: Homeomorphic images of a line in R^2
Hmmm. I thought about ending with a spiral, but then rejected the
idea, thinking it was a duplicate of a non-spiral loop. What makes the
spiral ending topologically different?
Ok, for equivalence classes of subsets of R^2 which are homeomorphic
to R, and where equivalent means there is a homeomorphism of R^2
taking one set to the other, I also see only 3 classes:
(1) The x-axis.
(2) The positive x axis together with a loop from the origin back
towards the positive x-axis, and asymptotic to the positive x-axis as
x approaches infinity.
(3) The open interval (0,1) on the x axis.
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
Clarification: I meant auto-homeomorphism of R^2.
Wait -- I just realized that (2) is the same as (1).
Moreover, I also missed one.
Ok, so now I see these 3:
(1) The x-axis.
(2) The positive x-axis.
(3) The open interval (0,1) on the x-axis.
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
Based on Jules' post, it's clear that I missed more than just 1.
quasi
===
Subject: Re: Homeomorphic images of a line in R^2
I am not so sure that  (2) is really different from (1).  Can you
sketch a proof?
===
Subject: Re: Homeomorphic images of a line in R^2
No, I made a mistake -- they are the same.
quasi
===
Subject: Re: Non-touching hex-triangles
I have improved the bounds to 4/9 <= max density <= 22/49, and I am
tempted to conjecture that the lower bound is optimal. So, has anyone
seen this before?
---
J K Haugland
http://home.no.net/zamunda
===
Subject: Transitive Order of a Relation
Cc:  sperkins@nvcc.edu
Given a relation R, which is a subset of the power set P of the
Cartesian product SxS of a set S with itself, R is either transitive
or it is not. The transitive closure of R is well defined and is
conventionally noted R^t, where t is not an integer, but indicates
transitive.
Matrix multiplication may be used to find the transitive closure of a
graph. The mth power of an ajacency matrix is the number of paths of
length m between the relevant vertices. Each time the adjacency matrix
A of a graph G of a relation R is squared, new paths of length two may
appear. For large graphs this is easier using computer methods than
looking for potential closures in the graph by inspection. When none
appear, we are done; we have found the transitive closure of the
relation.
By defining 0/0 = 0, we may normalize any power of an adjacency matrix
simply to directly represent the transitive closure of a graph. We may
write (piecewise) (R / |R|) to normalize a matrix if 0/0 = 0. Then,
the transitive order of a relation R is
the minimial power n such the normalized adjacency matrices
(piecewise)
( (R^(2^n))  / | R^(2^n)) | )  = ( (R^(2^(n+1)))  / | R^(2^(n+1)))
| ).
The transitive order of a transitive relation is 1.
The transitive closure of a relation with transitive order n is
therefore
( (R^(2^n))  / | R^(2^n)) | ).
Is this known?
Doug Goncz
Replikon Research
Seven Corners, VA 22044-0394
===
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===
Subject: Re: Cantor Confusion
not for the sequence of digts of the diagonal number and any other
entry of the list.
It does only differentiate the reals at a finite index. But at a
finite index it differentiates as well between 0.999... and 1.000....
So, why do you want to exclude these but not those?
===
Subject: Re: Cantor Confusion
Since the diagonal differs from each listed member at some finite 
place value, what happens at later place values is irrelevant to whether 
they are equal or different.
While there may be some subsequence of the original which converges to 
the diagonal, no member of that subsequence EQUALS that diagonal, which 
is all that is required.
The rule by which the diagonal is constructed  makes it differ from both 
representations when those representations have equal values.
In any case, for the set of all binary sequences (not numbers) no two 
are the same, so the issue does not arise.
===
Subject: Re: Cantor Confusion
The number of separated paths is les than the number of nodes at each
finite level. What happen after each finite level is irrelevant.
That is not different in case of 0.999... and 1.000...
Why must it be excluded?
The rule does not make 1.000...   differ from 0.999....
I am interested in the number of real numbers only.
===
Subject: Re: Cantor Confusion
The number of paths, or more properly uncountable sets of paths, 
distinguishable at any level is, like the level itself, finite, but 
there are infinitely many levels, and what happens at any one level is 
not the end. In order to consider the whole tree one must consider all 
infinitely many levels.
For every complete finite tree (all paths of equal length), the number 
of paths equals the number of subsets  of the set of non-leaf levels.
Each path being identified with the set of levels from which it branches 
left.
WM argues elsewhere that what holds in the finite cases must carry over 
to the infinite case.
SO why does WM think that this suddenly becomes false in the limit as 
the number of levels becomes infinite?
WM seems to have one view of limits when he thinks they will support his 
opinions, and the opposite view when they oppose them.
Who says it is? Any decimal expansion which has no 0 or 9 in it must be 
different from any decimal expansion having any of either, and the so 
called Cantor diagonals for decimal expansions have no 0's or 9's.
Why should it? The rule makes the diagonal different from either, and 
from any decimal containing a 0 or 9 digit in any position whatsoever.
There are at least as many binary sequences as reals  in [0,1], as a 
simple surjection from binaries to real shows.
===
Subject: Re: Cantor Confusion
Yes. But if you consider two infinite sequences, namely the sequence
1,2,3... and the sequence 2,4,6,..., and put the tems in bijection,
1-2, 2-4, 3-6, ..., then you can wait and wait and wait: The first
term will never get larger than the second. Even in the infinite this
will not happen.
Nevertheless you wait and wait and, look there is a pink William, the
sum
SUM[n= 0 to oo] (2-1-1) gets uncountable.
It is a pity.
===
Subject: Re: Cantor Confusion
What you are saying has no relevance to paths in my infinite trees.
As paths are determined by whether they branch left or right at a given 
level, one only needs to know the set of levels at which a path branches 
left to know the entire path.
 
It is certainly a pity that WM doesn't understand this stuff.
===
Subject: Re: Cantor Confusion
Nntp-Posting-Host: apps.cwi.nl
...
Dutch, indeed.  But I have read thousands (yes, indeed) English books since
I was 13.  My writing may reflect my native tongue, my reading is pretty
well (I think).  And what Wolfgang states is just his usual balderdash.
Harping on many different meanings in colloquial English while trying to
conduct a mathematical discussion.  When he had looked up a dictionary he
would have found the several meanings of single in English.  And most
of them would not translate to a single term in either Dutch or German.
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland, 
+31205924131
home: bovenover 215, 1025 jn  amsterdam, nederland; http://www.cwi.nl/~dik/
===
Subject: Re: Cantor Confusion
Nntp-Posting-Host: apps.cwi.nl
...
What meaning of single are you using here?
1.  Not married
2.  Unaccompanied by others
3.  Consisting of or having only one part...
4.  Consisting of a separate unique whole: individual <every single
5.  (not relevant)
6.  (not relevant)
7.  having no equal or like
8.  (not relevant)
So my answer is yes if you are using meanings (4) or (7).
And those are (in your opinion) only finitely many.  Or can I ask for
infinitely many paths?
Opinion again.
There is a subtle difference.  With the diagonal proof we always remain in
the finite.  With the paths we can also always remain in the finite because
any two different paths have a node where they differ *in the finite*. So
for each node there is a path p' that has it in common with p.  But also
for each p' != p there is a node in p that is not in p'.
But infinite paths do not have a final node, so what do you mean?
Yes.  Pray note that theorems imply previous definitions and possibly
axioms.  So what is a set of theorems in the context of some axioms may
not be a theorem in the context of another set of axioms.  So the theorem
that 'i' forms the algebraic closure of the 'numbers' is only true within
the context of particular definitions and axioms.  It is *not* true in the
context of the p-adics numbers.
Perhaps.  But as completed as such is not a mathematical term, I wonder
what you mathematically *do* mean with it.
You can do countably many tests?  I thought you could only do finitely
many tests.  But again, in mathematics it is *not* necessary to test
each and every individual.  Otherwise you could not even prove that
   sum{i = 1..n} i = (n + 1) * n / 2
for all n, but only for finitely many n.
But we can mention and test only finitely many paths.  So you now say that
there are only finitely many paths?  And that
   sum{i = 1..n} i = (n + 1) * n / 2
holds only for those n for which it has been tested?
Yes.  But to mathematicians that is not a problem.  Stronger, try to
factorise largish numbers without the use of numbers that are not
representable by a finite number of digits.  All those numbers that are
used in methods like the Number Field Sieve are unique paths within your
trees, although you are not able to find a distinguishing feature at some
finite point in your trees.
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland, 
+31205924131
home: bovenover 215, 1025 jn  amsterdam, nederland; http://www.cwi.nl/~dik/
===
Subject: Re: Cantor Confusion
No. You ma yask for a set of infinitely many paths, but not for
infinitely many paths.
It is proven by Cantor that there are uncountably many real numbers.
It is also clear that there are only countably many questions, no?
That's why it fails for numbers with infinitely many digits.
No. Only for those p' you can ask for. There must be others, because
there is no node which belongs only to p alone.
I mean that the speech of all or complete or finished is in clear
contradiction with infinite.
Sure.
Please read carefully. We cannot do more than countably many. And in
finite time, we cannot do more than finitely many.
Of course this is only true for finitely many n. For infinitely many
natural numbers, we get aleph_0.
It holds for finitely many natural numbers. The natural numbers are a
countable set.
Have you ever tried to handle a natural number with 10^100 digits
which are not given by an abbreviation which can be defined by less
than 10^100 bits? Or do you doubt the existence of those natural
numbers?
===
Subject: Re: Cantor Confusion
So one can ask for, and get,  a set with infinitely many elements but it 
will not have infinitely many elements?
That does not happen is a well regulated logical system.
Define question!
If it does not fail for infinite binary strings, and it doesn't, then it 
does not fail for numbers either.
It must be true for every pair of paths whatsoever or else one does not 
actually have a complete infinite binary tree at all.
Not in ZF or NBG. What axiom system are you proposing in which things 
are otherwise?
In ZF and NBG there are infinite sets which are completed in the sense 
that nothing remains other than that which is already in them.
So in ZF and NBG, your completed is irrelevant.
If you want a system that behaves as you want it to, you will have to 
build it yourself, as our systems just don't work your way.
As ZF and NBG are not time-bound, that is irrelevant in them.
WM is quite free to include time in his axiom system, whenever he gets 
to finishing it, but it does not appear in ZF or NBG.
When we get if for ALL, that means for every member of the set of all 
naturals, but not for the set itself, any more that a set of horses has 
to be a horse.
Then WM is saying that it does NOT hold for some members of N.
In ZF and NBG, when one gets around to defining the set of natural 
numbers N, one of N's properties is induction:
   (1) the first (0 or 1, depending on one's taste) is a member
   (2) for each member , x there is another called succ(x) such that
      (a) succ(x) is not the first, or is it x
      (b) for x and y in N, Succ(x) = Succ(y) iff x = y
   (3) If K is a subset of n such that 
       (a) the first member of N is a member of K and
       (b) whenever x is a member of K so is succ(x)
       then K = N
Thus in ZF and NBG, the kind of anomaly  where 
sum{i = 1..n} i = (n + 1) * n / 2 is only true for finitely many n in N
cannot happen, because one can show it true for n = 1 and also show that 
if true for n = x it is also true for n = succ(c), thus it must be true 
for all n in N.
===
Subject: Re: Cantor Confusion
You cannot ask for infinitely many elements.
And yes, you never will have infinitely many elements, that is correct
too, but does not matter here.
You cannot ask for infinitely many elements.
A question is an element of a countable set of words over a finite
alpabet. That is enough to see that my statement is correct.
That may well be possible.
It holds for all members of N, and it holds for every finite series 1
+ 2 + 3  ... + n. That means every series out of N is finite.
Correct. Obviously this is a finite set.
The inductive proof is valid for all series of natural numbers
1+2+3+...+n. It is not valid for an infinite series. That means all
series of natual numbers do *not* include an infinite series.
===
Subject: Re: Cantor Confusion
ZF not only asks for  what turns out to be infinitely many elements, it 
demands it. So does NBG. So do all standard set theories.
ZF not only asks for  what turns out to be infinitely many elements, it 
demands it. So does NBG. So do all standard set theories.
ZF not only asks for  what turns out to be infinitely many elements, it 
demands it. So does NBG. So do all standard set theories.
According to WM's definition, it appears as if a question must be a word.
Not in ZFor NBG , at least not in the Dedekind sense, as one can prove 
that it injects to a proper subset of itself.
And not in ZF or NBG if one uses the von Neumann definition of N as one 
can prove that N is not a member of itself, but that every finite 
ordinal is a member of N.
No one said otherwise, but N is infinite and for each n in N, the sum of 
all naturals up to and including n is n*(n+1)/2, as provable by 
induction.
===
Subject: Re: Cantor Confusion
Nntp-Posting-Host: apps.cwi.nl
What does this statement mean?
Why not?  For every node of p there is a p' such that K(p, n) = K(p', n)
and for every path p' different from p there is an n such that
K(p, n) != K(p', n).  There is no contradiction.
Which proof?
Now a semi-finitistic view.  The path that goes only to the left at every
node is different from all other paths, because there is no other path that
goes only to the left at every node.
This is nonsense.  Bunches *all* start at the root by your definition.
If a bunch splits in two bunches at a node that would mean that those
two new bunches start at the node, and they do not.
You mean edges, not bunches.
So you retract your statement that a bunch of paths is a set of nodes
which have a node in common?  To what does the which refer?  You
*did* mean a bunch of paths is a set of paths which have a node in
common.
What are separated bunches?
What are separated path bunches?
What are separated bunches?
Before you say something like this you should first define your terms.
When are two bunches separated?  When I analise carefully, I find the
following:
(1) A path bunch is the maximal set of paths that have some set of nodes
    in common.
(2) Two path bunches are separated if they have no path in common.
    that start at the root and where nodes are connected by edges.  So a
    path bunch is either a finite path or an infinite path.
(4) Two bunches are separated if there is a node in one of them (after the
    bijection) that is not in the other and the other way around.
(5) A bunch comes in at a node when that node is (after the bijection) in
    the set of nodes, and it is the last node.
(6) A bunch comes out at a node when that node is (after the bijection) in
    the set of nodes, and it is *not* the last node.
When I use this I find that I can biject the bunches that are finite paths
with the edges in the tree (and they are countable), because for all such
bunches there is a terminating edge.  I am still at a loss with those
bunches that are an infinite path (actually a single path).
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland, 
+31205924131
home: bovenover 215, 1025 jn  amsterdam, nederland; http://www.cwi.nl/~dik/
===
Subject: Re: Cantor Confusion
Even in the *infinite* tree a path cannot be distinguished from all
other paths. That means, a real number which cannot be described by a
finite formula (and most of them cannot) does not exist.
Cantor's diagonal proof fails, because the diagonal number is never
distinguished from all other real numbers (if uncountably many real
numbers exist).
All start at the root node, but they terminate by splitting.
No. Look at the discussion about that:
Let us continue this discussion there.
yes.
yes.
yes.
yes.
Do they occupy more nodes than all the nodes occupied by finite
bunches. Look at a formalizaton by Franziska Neugebauer which I
replied to in:
===
Subject: Re: Cantor Confusion
What axiom requires that a number must be defined by a finite formula in 
order to exist?
Cantor's diagonal proof only involves binary strings, not numbers, and 
a very simple rule distinguishes the diagonal form every member of the 
list. 
Does WM claim that none of the paths in a bunch extend beyond the 
termination of a bunch?
And, as yet, WM has given no mathematically satisfactory definition of 
bunch nor of termination of a bunch, nor any of his other attempts 
to confuse by non-definition.
===
Subject: Re: Cantor Confusion
What kind of existence has an undefinable number?
Only finite strings have been tested so far.
===
Subject: Re: Cantor Confusion
What kind of existence does a defineable number have?
Certainly not physical. So all numbers are equally mental, existing only 
in the imagination, and to those who can imagine undefineable numbers 
they exist on the same basis as any others.
Physical testing of what transpires in the worlds of imagination is 
neither necessary nor possible.
===
Subject: Re: Cantor Confusion
There are an infinite number of members to check.  However, each of
them
only requires checking a finite string.
Whoops
Over there! A pink elephant!
There are an infinite number of members to check.  So to check
them all you have to check an infinite string.
                                       - William Hughes
===
Subject: Re: Cantor Confusion
Axiomatic?
===
Subject: Re: Cantor Confusion
Ah, it is about that.  That is also in his book, and I have mentioned it
in the review.  I think it is what I call number 8 in his chapter 9.  In
his book he does *not* prove that it is an equivalence relation
(transitivity is not proven, only shown by a single example), moreover,
it only works for ordered sets.  So if not all sets can be ordered it is
not an equivalence relation on sets.
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland, 
+31205924131
home: bovenover 215, 1025 jn  amsterdam, nederland; http://www.cwi.nl/~dik/
===
Subject: Re: Cantor Confusion
for real numbers and their subsets it is simple, but would not fit to
the frame. For other sets, much has to be investigated.
Just these points are to be discussed.
===
Subject: Re: Cantor Confusion
Nntp-Posting-Host: apps.cwi.nl
removed...
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland, 
+31205924131
home: bovenover 215, 1025 jn  amsterdam, nederland; http://www.cwi.nl/~dik/
===
Subject: Re: Cantor Confusion
Excuse me, here are the valid URLs:
Binay Tree:
Intercession
Sometimes it is preferable  to have a calm atmosphere.
===
Subject: Re: Cantor Confusion
Definition: A set M is countable, if there is a one-to-one
correspondence with the set N of natural numbers.
There is a one-to-one correspondence of M and N if and only if all
elements m_n of M can be enumerated, i.e., if and only if a list can
be defined:
1) m_1
2) m_2
3) m_3
...
n) m_n
...
Theorem 1: The set of finitely definable numbers is countable and can
be put into a list.
Proof: All finite definitions are finite words over a finite alphabet.
All finite words can be ordered lexicographically. This is the finite
definition of a list.
Theorem 2: The set of finitely defined numbers cannot be put into a
list.
Proof: Assume such a list exists. This means, such a list has been
finitely defined. Construct the diagonal number. It is a finitely
defined number. Find the set of finitely definable numbers is
uncountable.
So there are countable sets which are not in one-to-one correspondence
with the set of natural numbers?
===
Subject: Re: Cantor Confusion
Nntp-Posting-Host: apps.cwi.nl
...
Wrong.  Existence does *not* mean finitely definable.  Have a look at
Turings work.  There *does* exist a (finitely deinable) list of Turing
machines that purport to generate numbers.  So the list is certainly
countable.  However, the subset of that list that actually *does*
generate numbers is not finitely definable.
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland, 
+31205924131
home: bovenover 215, 1025 jn  amsterdam, nederland; http://www.cwi.nl/~dik/
===
Subject: Re: Cantor Confusion
Marthematical existence does mean definable. What else should it mean?
Definitions can only be finite.
Fine. That means, the set is countable but there is no bijection with
N definable. Why then do you require a definable bijection between
paths and nodes in the tree?
===
Subject: Re: Cantor Confusion
But not necesssarily finitely so.
That may be one of WM's axioms, but does not appear in ZF or NBD.
We don't! In fact, we reject any such thing in any tree with more than 
one node.
There is, however, a bijection between the power set of the set of  
non-leaf levels (in any tree in which all paths are of the same finite 
length or are all endless) and the set of paths in that tree.
===
Subject: Re: Cantor Confusion
Who can give or understand an infinite definition?
That is the basis of logic which ZF or NBG have to obey (if they are
logical systems).
===
Subject: Re: Cantor Confusion
Some definitions of pi are infinite but quite well understood.
What logical rule in any predicate logic says that a thing must have a 
finite definition in order to exist?
In ZF and NBG those things exist which are required to exist by the 
axioms themselves or by theorems derived from those axioms, and that 
requires that there exist a power set of the set of naturals, which all 
its members, in both ZF and NBG.
===
Subject: Re: Cantor Confusion
Really? What definitions would these be?
-- 
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
Wovon man nicht sprechen kann, daruber muss man schweigen
 - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
===
Subject: Re: Cantor Confusion
The ones that define it as the limit of an infinite sequence, as such  
processes are, in theory, infinite, but usually in practice soon close 
enough for all practical purposes.
While the process can, in some senses, be finitely defined, the exact 
value cannot be finitely determined.
===
Subject: Re: Cantor Confusion
No it means that while a bijection exists it is not finitely
definable.
Outside of Wolkenmuekenheim this is a result.  Inside of
Wolkenmuekenheim
it is not a resut because Muekenheim goes
WAAH WAAH WAAH, I can't hear you if anyone tries
to explain it to him.
                                    - William Hughes
 Why then do you require a definable bijection between
===
Subject: Re: Cantor Confusion
The bijection with this countable set is not finitely definable.
Why then do you require a finitely definable bijection between paths
and nodes in the tree?
===
Subject: Re: Cantor Confusion
You are the one pushing finitely definable, whatever that means.
But as the construction of the Cantor diagonal is finitely defineable, 
and finitely defined, there should be no objection to it.
===
Subject: Re: Cantor Confusion
That means: You cannot determine or define or construct or write down
or tell me a bijection between the set of numbers which are definied
by a definition identifying them uniquely and the set of natural
numbers.
That is not the point here. The point is that there are subsets of
countable sets which do not allow for a bijection with N. Translate
this fact to the binary tree.
===
Subject: Re: Cantor Confusion
In Zf, every set, including N, has a power set, and there is provably no 
surjection from any set in ZF to its power set, but trivially an 
injection, so that the cardinality of any set is less that that of its 
power set.
The paths in a complete infinite binary tree  in ZF are easily seen to 
biject with the power set of N, so that set of paths has cardinality 
greater than N. 
And nothing that WM can say can change that.
Finite subsets of countable sets are the only subsets of those countable 
sets which do not allow for a bijection with N, at least in ZF.
I terms of a binary tree each of the uncountably a many subsets of N 
determines a unique path wish branches left from each level indexed in 
that set of naturals and right at each level no in that set.
That achieves precisely the requested translation.
===
Subject: Re: Cantor Confusion
No.  there are subsets of a finitely definable set which are not
finitely definitable.
The difference is...
   M:  WAHH! WAHH! WAHH! I'm not listening.
                            - William Hughes
===
Subject: Re: Cantor Confusion
I dont.  I require that p' and p have a node not in common.
I do not require that this node be finitely definable.
A: simple true statement.
Crank: <Stupid arguement that simple true statement
      Why do you make this dumb statement?
                       - William Hughes
===
Subject: Re: Cantor Confusion
WM has not defined finitely, nor finitely defineable nor set nor 
list.
If he is trying to use definitions from ZF or NBG then he must use all 
of ZF or all of NBG, both of which require the power set of N to exist 
and can prove it to be of greater cardinality than N.
Such a list of infinitely many assignments can be finitely defined by 
giving a rule of assignment which applies equally well to infinitely 
many cases.
The function which tales a natural and returns its square is finitely 
defined and provides a list of squared naturals.
So that WM's argument that such list cannot exist is demonstrably false.
Besides which, there is nothing in ZF or NBG which requires anything to 
be finitely defined, whatever than may mean.
===
Subject: Re: Cantor Confusion
It has been explained a lot of times to M.9fckenheim that this is not a
valid conclusion.  He is just a liar.
-- 
Carsten Schultz (2:38, 33:47)
http://carsten.codimi.de/
PGP/GPG key on the pgp.net key servers,
fingerprint on my home page.
===
Subject: Re: Cantor Confusion
They prove
2-1-1+2-1-1+2-1-1+-... =< 2
wrong, i.e., they prove 2-1-1 =/= 0.
===
Subject: Re: Cantor Confusion
They prove WM's claims irrelevant to the validity of ZF and NBG.
In ZF and NBG all assumptions over and above the validity of formal 
logic are explicit. None of WM's implicit assumptions are, or can be, 
required to hold in such systems.
In particular, there exists in ZF the set N of all naturals, and, P(N), 
the power set of all naturals which is of larger cardinality than the 
set of all naturals, and a CIBT whose set of paths bijects with P(N).
These prove beyond mathematical doubt that, in ZF and NBG, CIBTs exist 
and have uncountably many paths.
ZF specifically allows all of this, and no explicit assumptions in ZF 
prohibit any of this, and no implicit assumptions are allowed in ZF.
Similarly for NBG.
That WM wants to have a system in which things go his way is obvious.
It equally obvious that he is not competent to construct such a system 
in which every assumption has been made explicit, as mathematical axiom 
systems require.
===
Subject: Re: Cantor Confusion
What you say proves that you never have thought about that topic deep
enough. One implicit assumption is that, in Hessenberg's proof of
Cantor's theorem, the set of all natural numbers which are not mapped
on subsets of P(N) which do contain them, does exist together with the
mapping pescription (you know that a function consists of formula,
domain and range, I hope. Such a set need exists as little as the set
which the largest natural number is mapped upon.
You are wrong to assume that I did not study set theory. But the
formalism veils the problem it is built upon.
Even if this was clear, then the result
 2-1-1+2-1-1+2-1-1+-... <= 2
would show that set theory is self contradictive.
===
Subject: Re: Cantor Confusion
What you say is inane.
(1) If a presentation of a proof uses any principles or premises
whatsoever other than first order logic applied to the Z axioms, then
that presentation is not that of a Z set theory proof. So, to
reiterate, since you are so very obtuse, if you find that some
presentation or another uses some premises or principles other than
first order logic applied to the Z axioms, then that presentation is
not of a Z set theory proof.
(2) Usual textbook presentations of the theorem that no set maps onto
its power set use nothing but first order logic applied to the axioms
of Z set theory.
(3) In ordinary set theory, a function is a certain kind of set of
ordered pairs and, in ordinary set theory, a function is NOT a triple
of a formula, domain, and range. That you even think a set theoretic
function must have a FORMULA (!) as a component shows, again, your
lack of understanding even the basics of set theory.
(4) I don't know about Hessenberg's presentations, but in ordinary
presentations, even though we don't need to prove by contradiction, it
is sometimes easy to set the proof up that way. Then from the reductio
assumption of a function mapping N onto PN, as to the set of elements
of N that are not mapped to a member of PN, we PROVE that set exists
by a simple use of the axiom schema of separation. That you even
question that shows that you do not understand even such basic things
about set theory as the axiom schema of separation.
(5) As to the function from N onto PN, again its existence is either a
reductio assumption, or, by modus tollens or some other principle that
is included in first order logic, we prove such a function does not
exist.
I infer it by the ignorance you display.
Whatever you think that means, my point stands: Proofs of theorems of
formal Z set theory make no use of anything other than first order
logic applied to the axioms. Your claim about 'implicit assumptions'
is pure bull.
It's clear if you'd read a good textbook such as Enderton's or
Suppes's.
You've not given any set theoretic definition of
2-1-1+2-1-1+2-1-1+-... 
If you want to talk about an infinite sumation, then you need to be
able to eliminate the '...' and put it in the form: Sum(from n to oo)
F(n).
You'll see that once you force yourself to move on from UNDEFINED
expressions (such as 2-1-1+2-1-1+2-1-1+-... ) to actually defined
notation of set theory in which an infinite summation is the limit of
a sequence of sums each of which is based on a function F, then the
contradictions you claim to have found are in fact not any
contradiction in set theory itself. That is, you ought not conflate
your undefined expressions with any rendering of a term or formula of
set theory. Set theory does not have to answer to your  fingerpainting
with symbols.
MoeBlee
===
Subject: Re: Cantor Confusion
What you say is insane.
Function, as understood in mathematics, is a procedure, a rule,
assigning to any object a from the domain of the function a unique
object b, the value of the function at a. A function, therefore,
represents a special type of relation, a relation where every object a
from the domain is related to precisely one object in the range,
namely, to the value of the function at a.
Please do not believe that I will repeat for another 1000 postings
your controversy with other great mathematicians about the properties
of a function.
Best by avoiding any formula and any clear idea what you do.
Obviously you are not very good in concluding from given facts on
hidden facts.
Then use your axioms to understand the binary tree.
Everybody who has studied a bit of set theory should know
2-1-1+2-1-1+2-1-1+-...  < 2+1+1+2+1+1+2+1+1+... = alep_0
So whatever misunderstanding you may want to apply,
2-1-1+2-1-1+2-1-1+-...  < 3 < aleph_0.
Sum [n in N] (2-1-1) < 3.
That is but another way of writing 2-1-1+2-1-1+2-1-1+-...  < 3.
If you have problems with infinite sums or products then you should
look up set theory, for instance Koenigs theorem.
===
Subject: Re: Cantor Confusion
It's not insane just to point out that a proof in formal Z set theory
is one that uses only first order logic applied to the axioms of
formal Z set theory.
(1) If a presentation of a proof uses any principles or premises
whatsoever other than first order logic applied to the Z axioms, then
that presentation is not that of a Z set theory proof. So, to
reiterate, since you are so very obtuse, if you find that some
presentation or another uses some premises or principles other than
first order logic applied to the Z axioms, then that presentation is
not of a Z set theory proof.
(2) Usual textbook presentations of the theorem that no set maps onto
its power set use nothing but first order logic applied to the axioms
of Z set theory.
There's nothing that is insane about any of that. Indeed, what I
mentioned  are simple matters that you need to understand.
That is a very common NON-formal definition and notion of function
found in a great amount of mathematics. However, it is NOT the set
theoretic defintion that is being used in formal Z set theory and is
NOT the definition that is used in formal Z set theory to prove
Cantor's theorem that there is no function from a set onto its power
set.
If you INSIST on using 'function' in a sense that is NOT the sense in
formal Z set theory, then you are not talking about formal Z set
theory.
All you need to do is pick up a textbook on set theory to see that in
ordinary set theory 'function' is defined to be a certain kind of set
of ordered pairs and not as you define.
No, a function is not ITSELF a triple of a formula, domain, and range,
but a formula may DEFINE a certain set of ordered pairs that is a
function. You need to understand such basics of set theory.
I have no idea what hidden facts you're thinking of.
I offered to consider your tree argument if you would only tell me
from the outset certain things about your intended context and terms
of discussion. You refused. I am not at all inclined to enter into a
quagmire of argument in which you will not even agree as to defintions
that we can trace back to primitives and axioms. But if you ever get
around to stating your logisitc system, axioms, primitives and
SYSTEMATICALLY given defintions, then please do let me know.
I said you didn't define 2-1-1+2-1-1+2-1-1+-...  And you still
haven't.
That is not a DEFINITION of 2-1-1+2-1-1+2-1-1+-... 
I have no problem with infinte sums and products. I am just pointing
out that your notation is NOT justified as infinite summation until
you specify what F is in Sum(from n to oo) Fn.
As I said, set theory is not answerable to your fingerpainting with
symbols. Nor am I.
MoeBlee
===
Subject: Re: Cantor Confusion
I only corrected your misprint which you deleted here.
It is a definition from a book on set theory, called Introduction to
Set Theory. So it gives basic set theory. It shows that your
statement
is as wrong as most of your statements.
I never wanted to talk about astrology, why should I talk about formal
set theory?
Did I oppose to a function being a set? I don't know why I should have
done that. Perhaps your understanding is not as sharp as you think?
Do I need that, in fact? Best taught by you? Amusing.
I see.
Why do you dislike it?
There are definitions like Sum [n in N] (1) = aleph_0 in several books
on set theory.
Do you miss the sentence: let n be a finite ordinal, and let N be the
set of all finite ordinals, then ...?
Fn = (2-1-1)
It is the number of separated path coming out of the n-th element of
the tree minus the number of ingoing separated paths minus the number
of nodes of this element.
It seems to be a rather sad theory.
===
Subject: Re: Cantor Confusion
Actually, in your reply, YOU deleted the SUBSTANTIVE comments I made
in that part of my post, thus you did not respond to that part of my
post, but instead rested with the joke of writing  'insane' in reply
to inane', which is quite inane.
address:
(1) If a presentation of a proof uses any principles or premises
whatsoever other than first order logic applied to the Z axioms, then
that presentation is not that of a Z set theory proof. So, to
reiterate, since you are so very obtuse, if you find that some
presentation or another uses some premises or principles other than
first order logic applied to the Z axioms, then that presentation is
not of a Z set theory proof.
(2) Usual textbook presentations of the theorem that no set maps onto
its power set use nothing but first order logic applied to the axioms
of Z set theory.
(1) Who is the author of that book? I'd like to look it up to see just
what is written there.
(2) You can look at the most commonly used and respected textbooks in
set theory to see that they don't define a function as a formula,
domain, and range. Enderton; Suppes; Levy; Quine; Bernays; Kunen;
Stoll; Halmos; Moschovakis; Jech; Takeuti & Zaring; Shoenfield (in the
set theory chapter); Chang & Keisler (in the set theory chapter);
Mendelson (in the set/class theory chapter), Godel (in his small book)
do not define a function as a formula, domain, and range.
(3) In such textbook proofs of Cantor's theorem (the theorem that no
set maps onto its power set), the definition of 'function; used is the
one I've mentioned and is not that of a formula, domain, and range.
(4) No matter what ANY author says, the formal Z set theory proof that
I point to (which agrees with those authors anyway) is using the
definition of 'function' that I mentioned and not that of a formula,
domain, and range.
(5) Taking a function to be formula, domain, and range in a formal
proof of Cantor's theorem would be NONSENSE. We don't do that. We take
a function to be just what I've said it is and we prove that, for all
x, there is no function on x and onto Px. And if you think that that
proof uses the definition of a function as being a formula, domain and
range, then you have NO IDEA what the proof is.
I said that the proof in formal Z set theory of Cantor's theorem uses
nothing but first order logic applied to the axioms of set theory. You
have not refuted that, and you could see for yourself that it is true
if you only knew basic predicate calculus and even less than what one
learns by the end of a first semester course in set theory.
You WERE talking about when you tried to dispute me as to proving
Cantor's theorem in formal set theory. And when you're talking about
set theory in general, if you're not talking about with an
understanding that it has a formal version, then your remarks pertain
only to informal versions of set theory that have LONG AGO been
supplanted by the rigorous formalization as a formal first order
theory. And that is what is at stake in such issues as to whether
there are hidden assumptions (or whatever phrase you used).
By saying that a function is a formula, domain, and range you
contradict the set theoretic definition of a function being a certain
kind of set of ordered pairs. And, as to understanding, notice that I
did NOT say that you contradicted that a function is a set, but rather
I am informing you that in SET THEORY (such as ordinary textbook set
theory and as formalized as formal first order theory) a function is a
certain kind of set of ORDERED PAIRS, and you contradict that as you
take a function to be a formula, domain, and range, since whatever
that is, either formalized as a triple or not formalized at all, it is
not a set of ordered pairs and, a fortiori, not the kind of set of
ordered pairs that a function is in set theory.
Apparently you do! You claim that in set theory a function is a
formula, domain, and range. So you DO need to be told that in set
theory that is NOT what a function is.
You see; who else does? You see hidden facts but only respond with
I see when I mention that I have no idea what hidden facts you're
thinking of. Indeed, you really are a crank. Hidden facts.
Positively risible.
It's not a matter of dislike. It's just that it's not a definition!
You can mention anything in particular so that I can evaluate the
context of the notation.
That doesn't lend a definition to:
2-1-1+2-1-1+2-1-1+-... 
My notational slip actually. I meant to write:
Sum(n=0 to oo) Fn
or whatever range you wish instead of starting at 0.
Anyway, your Fn = 2-1-1 is just a constant function! What infinite
summation do you think you get from a constant function?!  Sheesh!
And you just said that for n it is 2-1-1. So it's a constant function.
So, for an infinite summation, just do the correct math given F is a
constant function!
What do you think Sum(n=0 to oo) 2-1-1 = Sum(n=0 to oo) 0 is?
Since you don't even know its basics, your comments on it are rather
pointless.
MoeBlee
===
Subject: Re: Cantor Confusion
It may very well be a very naive set theory for non-mathematicians.
introduction?
It shows that your
In ZF, since everything is a set, functions, if they are to exist at all 
in ZF , MUST be sets. Thus, in ZF, the ONLY relevant definition of a 
function is as a set. 
Because you set yourself up as a critic of formal set theory, and you DO 
talk about it all the time, and in  unwarrantedly disparaging terms.
Yes!
Neither do we.
And perhaps our collective understanding is a good deal sharper than you 
think. 
 
If you set yourself up as a critic of set theory, it helps to be aware 
of what goes on in what you are criticizing. Since you choose not to be 
aware, you are bound to make a fool of yourself occasionally. 
If fact you do s frequently.
Best taught by you? Amusing.
Since you seem to be incapable of learning it without help, any help is 
better that you are doing on your own.
I doubt it.
There are all sorts of things in naive set theory texts that formal set 
theories do not allow.
In that case, it is irrelevant.
Much more relevant wold be a count of the number of paths in a finite 
binary tree in which each path has n branchings (edges).
I.e., the number of non-leaf levels is n, and the number of non-leaf 
nodes in any path is n,
Then the number of paths equals the number of subsets of the set of 
levels.
In the limit, the number of levels becomes N so the number of paths 
becomes the cardinal of P(N).
Not anywhere near as sad as WM's futile attempts to build a theory.
===
Subject: Re: Cantor Confusion
Karel Hrbacek and Thomas Jech: Introduction to Set Theory
Marcel Dekker Inc., New York, 1984, 2nd edition. 250 pages.
For students of set theory.
===
Subject: Re: Cantor Confusion
I can see online the pages in that book defining 'ordered pair',
'binary relation', and other terms in the the completely usual set
theoretic manner. But the online view cuts off before the section on
functions. So I would like to know the exact quote in this book for
the definition of 'function'.
Moreover, no matter what definition this particular book gives, what I
said, as quoted above and stated here again, stands:
['A formula, domain and range'] is a very common NON-formal definition
and notion of function found in a great amount of mathematics.
However, it is NOT the set theoretic defintion that is being used in
formal Z set theory and is NOT the definition that is used in formal Z
set theory to prove Cantor's theorem that there is no function from a
set onto its power set.
MoeBlee
===
Subject: Re: Cantor Confusion
Now please, before we rush to look it up:  I guess that everyone here
agrees that a function is a special kind of relation, where a relation
is a subset of a cartesian product of two sets.  What is debated is that
there is an additional requirement that a function has to assign values
according to a rule in a sense which implies computation, definability
or something similar.  So what exactly is it that the book you mention
says?  And when you answer, please distinguish between a technical
definition and illustrative prose.
Carsten
-- 
Carsten Schultz (2:38, 33:47)
http://carsten.codimi.de/
PGP/GPG key on the pgp.net key servers,
fingerprint on my home page.
===
Subject: Re: Cantor Confusion
Too late. I'm afraid I've already rushed to look it up.
I only found the 1999 edition of Hrbacek and Jech, but perhaps
that will be a close approximation of the wording in the
1984 edition. I searched Google Books with
      Hrbacek  Jech set theory function
and got the definition of function in the 1999 edition.
(Unfortunately, I can't copy and paste from there. Pardon
the typos, please.)
Oddly enough, the definition of function there looks essentially
identical to every other (mathematical) definition of function I
have ever seen.
Jim Burns
/Introduction to Set Theory/, by Karel Hrbacek, Thomas J. Jech
(1999) [pages 23-4]
:
: * 3. Functions *
:
: Function, as understood in mathematics, is a procedure, a
: rule, assigning to any object /a/ from the domain of the
: function a unique object /b/, the value of the function
: at /a/. A function, therefore, represents a special type
: of relation, a relation where every object /a/ from the
: domain is related to precisely one object in the range,
: namely, to the value of the function at /a/.
:
: * 3.1 Definition * A binary relation /F/ is called a
: /function/ (or /mapping/, /correspondence/) if /aFb_1/
: and /aFb_2/ imply /b_1 = b_2/ for any /a/, /b_1/, and
: /b_2/. In other words, a binary relation /F/ is a function
: if and only if for every /a/ from dom /F/ there is exactly
: one /b/ such that /aFb/. This unique /b/ is called
: /the value of F at a/ and is denoted /F(a)/ or /F_a/.
: [F(a) is not defined if /a [not in] dom F/.] If /F/ is
: a function with /dom F = A/ and /ran /F/ [subset] B/,
: The range of the function /F/ can then be denoted
: /{F(a)| a [in] A}/ or /{F_a}_a[in]A/.
:
===
Subject: Re: Cantor Confusion
My remarks in this post are upon the supposition that, between the
older and more recent editions, there is not a material difference on
this matter of functions..
Even in that informal description, the authors do not mention a
formula as did WM.
Right, a function is a relation. A function is not itself, as WM
claimed the authors to represent, a formula, domain, and range.
And, moving past the informal descriptions and motivation, here is the
explicit definition:
And there it is, exactly the EXPLICIT DEFINITION that is the very set
theoretic definition I've told WM about, and the one that is of
concern in formal Z set theory statements and proofs of Cantor's
theorem.
WM rested upon giving the authors' initial account of an informal
notion in general mathematics as he failed to recognize the exact
formal definition that I has already referred to.
The 'not defined' part can be handled differently though, if one
adopts certain formulations. But that is not at issue here anyway.
Yep, entirely usual all the way.
In set theory, a function is a relation such that every member of the
domain maps to exactly one thing.
And, WM is completely, and as usual, incorrect as to even such basic
matters of set theory when he claims that these authors represent that
the set theoretic definition of 'function' is that of a formula,
domain, and range.
MoeBlee
===
Subject: Re: Cantor Confusion
As usual, WM includes only the irrelevant bits and excludes the part 
that gives the formal definition, and, incidentally, proves him wrong.
===
Subject: Re: Cantor Confusion
So, is he dishonest or just clueless?
-- 
Carsten Schultz (2:38, 33:47)
http://carsten.codimi.de/
PGP/GPG key on the pgp.net key servers,
fingerprint on my home page.
===
Subject: Re: Cantor Confusion
WM has all the earmarks of one of Eric Hofer's true believers, whom 
are, I suppose, closer to clueless than dishonest.
===
Subject: Re: Cantor Confusion
He strikes me as dishonestly clueless and cluelessly dishonest.
MoeBlee
===
Subject: Re: Cantor Confusion
I am not interested in formal set theory but only in the question: Are
there uncountably many real numbers?
Why?
===
Subject: Re: Cantor Confusion
There are uncountably many binary strings, and only countably many of 
them map to duplicates of other strings when interpreted as reals in 
[0,1], so, in ZF or NBG, yes!
Because you never are counting anything but bunches each of which 
represents a set of uncountably many paths, so the number of bunches is 
not relevant to the number of paths.
===
Subject: Re: Cantor Confusion
What Wm says is insane, at least in ZF and NBG.
And he has yet to produce any system in which it is not insane.
A function may be a instantiated as a procedure, but in ZF, it must be a 
set, as everything in ZF is a set.
It is perfectly clear to mathematicians. If it is not to WM, that is not 
the fault of mathematics.
AS WM's assertions about set theory are quite often false in ZF and NBG, 
and he does not provide us with any system in which we can find them 
true, we are driven to conclude that WM's knowledge of set theory is 
considerably less than what he claims it is.
We have, and it gives us in ZF an infinite tree in which the paths 
biject with the power set of N.
This tree is so different from any tree WM visualizes, that WM cannot be 
using any recognizable set theory.
===
Subject: Re: Cantor Confusion
Not at all. it is just that all assumptions are explicit, so no implicit 
ones are needed, or used.
 
The existence of that set follows directly from the axiom schema of 
specification in ZF.
The formalism is all there is.
 
Only to such True Believers as choose not to see that they are assuming 
things not true in ZZF or NBG.
===
Subject: Re: Cantor Confusion
That is obviously nonsense for linear sets which, after having been
separated, never meet again. I wonder how one can post such a mess.
Pink elephants are more realistic.
No, p is never separated from those uncountably many paths which you
cannot ask for (because you can only ask for countably many paths, in
fact you can only ask for a separation at a finite index n, i.e., you
can only ask for finitely many separated paths p').
===
Subject: Re: Cantor Confusion
If K(p,n) refers to the nth node of path p, then in every CIBT, there 
are uncountably many paths which have been with p for all nodes
K(p, m) with m < n, for any n.
The only way to separate one path of  CIBT from all others is to take 
an infinite subset of its nodes, through which there will be only one 
path, Through every node in any finite set of nodes, either no path 
passes or uncountably many pass.
One does not have to ask for what is already there.
===
Subject: Re: Cantor Confusion
Thats right, after the last path p' has separated p has to be single.
Whoops, how does one show there is a last path.
Look! Over there! A pink elephant!
                                          - William Hughes
===
Subject: Re: Cantor Confusion
That has nothing to do with a last path.
If in the infinite binary tree a path does not get single, then it
will never exist as a single.
===
Subject: Re: Cantor Confusion
The fact that:
      p' is never single is true even though
            p can be separated from every p' and
            if p' separates from p it never rejoins p.
has nothing to do with a last path
Whoops! this is wrong.
Look! Over there! A pink elephant!
The fact that
p' is never single is true
has nothing to do with a last path
                 - William Hughes
===
Subject: Re: Cantor Confusion
That seems necessary to make us believe  that a paths that shares
every node with another path does not share every node with another
path. But it is not sufficient.
===
Subject: Re: Cantor Confusion
If WM believes that one path in any tree can share every node with 
another and different path, he has passed beyond reason into some sort 
of fugue state.
===
Subject: Re: Cantor Confusion
Can you explain, how every node of p is shared by other paths, but not
every node is shared by at least one path p'? Do the companion paths
alternate? E.g., p' for every even node and p'' for every odd node?
===
Subject: Re: Cantor Confusion
If p represents a path and p' a different path in a CIBT, then the set 
of shared nodes is finite but not empty, and will have a last, or 
highest level, node in it. 
However, the set of ALL paths which pass through that last common node 
will biject with the set of all paths in the entire tree (just cut them 
off below that node so that node becomes the new root node).
, but not
===
Subject: Re: Cantor Confusion
Yep.
An uncountable number of paths share only the first node of p
An uncountable number of paths share only the first two nodes of p
An uncountable number of paths share only the first three nodes of p
....
Since there is no last path which branches off, this list never ends.
So every node of p is shared by other paths.
However,  every path branches of somewhere, so there
is no path p' which shares every node of p.
                                    - William Hughes
===
Subject: Re: Cantor Confusion
Crank rule #1:  When losing an argument, change the subject.
Every node, n, of path p is shared with another path
p'(n).  Note that p'(n) can be different for every n.
Look! Over there! A pink elephant!
Every node, n, of path p is shared with another path
p'.  p' never changes.
                        - William Hughes
===
Subject: Re: Cantor Confusion
You are very good at that topic.
Note that p'(n) need not diffrent for every n.
For every n there is a p' which has not changed from 1 to n.
===
Subject: Re: Cantor Confusion
He has certainly managed to point out one of WM's foibles.
===
Subject: Re: Cantor Confusion
However, it cannot be the same for all n.
Call it p'(n)
Look! Over there! A pink elephant!
p'(n) never has to change.
                            - William Hughes
===
Subject: Re: Cantor Confusion
For every subset of the set of levels in a CIBT there is a SINGLE path 
branching left from just those levels and right from all others.
How much more single does a path have to get?
===
Subject: Re: Incorrectness of Gauss-Kummer Formula
After some error analysis work,
I discovered that the Gauss-Kummer Formula
for the perimeter of an ellipse is incorrect.
The last (almost) term must be;
h^^5 * 143/65536
instead of;
h^^5 * 49 / 65536.
The corrected formula gives much improved 
Also a Cantrell like formula 
for the perimeter is;
4 (a+b ) + (Pi-4) a b / (a+b).
This formula is accurate for both 
===
Subject: 
=?windows-1256?B?zdXR7ccg4d7Yx8og4+Qg3e3h4yDa49Hm0+Hj7CDj2sfkxyDmyNMg3e3P7eY

g
LSDV5tE=?=
===
Subject: Problem Definition/Development  Limits?
Hello Math Forum:
I was wondering if anybody knew of work on the Limits to problem defintion 
and development. As this would indicate to me a limit to possible Math 
answers and knowledge.
Zim Olson
http://www.zimmathematics.com
===
Subject: Re: Problem Definition/Development Limits?
You know, folks, you really should visit that site. It is a working
example of feel good, everyone is equal, idiocracy in action
ideas. That's the future of math.
===
Subject: Re: Problem Definition/Development Limits?
http://www.zimmathematics.com
Porky:
I admit part of my style of Mathematics writing is to address as many 
educated people as possible. Including K-16+. In my own situation I feel 
this 
is the best approach to disseminating this material.  It is so different I 
don't feel it will be published any time soon.
If you read my Applications section you will see I have an Axiom where no 
existential Item(s)/Event(s) are equal in terms of their Quantitative and/or 

Qualitative properties. Including people. This has serious implications to 
myself anyway.
As per your own response, I am sorry you don't feel good about my 
Mathematics site. It is not required however.
And as for my original question:  I am not sure I am adding anything to the 

InCompleteness Thereom of Godel, by saying Definitions are a limiting 
construct in themselves. Feel free to correct me if I am wrong on this 
subject!
Zim Olson
http://www.zimmathematics.com
===
Subject: Re: Questions about Algebraic Functions
Just to make it clear, the example I stated in my first post is not the real 

f(z) that I have to deal with. It was just an example I made up. My real 
f(z) 
is too complicated to type out here, though it does have some radicals in 
it.
The radicals in my actual f(z) cannot be given a plus or minus sign. The 
physics of the problem imposes constraints that limit it to the all +'s 
version only. So there is really only one branch.
I think there is come confusion here, due to the fact that I have been using 

the term branch sloppily. My f(z) does not have multiple branches (or, at 
least, the other branches of the radicals are of no physical interest). 
However, my f is a function of some parameters p: f = f(z,p). When I speak 
of 
branches, I've been talking about root branches. In other words, for each 
p, there are one or more values of z that satisfy f(z, p) = 0. Graphing 
these 
values of z as a function of p yields a diagram of root branches. For some 
ranges of p, there appear to be two values of z which satisfy f(z,p) = 0. 
For 
other ranges of p, just one. Therefore, there are special values of p at 
which such a root branch stops abruptly.
That is what I've been asking about.
Due to Robert Israel's reply below, I think I now understand how and why 
this is possible.
===
Subject: Re: Dial 999 for the real number line
        There aren't uncountably many anything. One of the important
consequences of this way of understanding infinity is that the distinction
between countable and uncountable is undermined. There is only one
infinity.
        Your criticism here is curiously inept. Of course pi exists, is a
real number. What I am asking is whether the infinte decimal expansion
(.14159.............) exists; or rather what is the meaning or status of
such an infinite expansion.
        I should have been more explicit. The proposal is that some
numbers, irrational numbers in particular, do not exist as individual
members in this list, but as embedded sequences. (Incidentally, since what
is at issue is infinite decimal expansions, infinite 0s included, the table
should more accurately have simply omitted the trailing 0s). So, reverting
to decimal (binary was chosen for compression rather than perspicuity), pi
-3 would be:
.1
.14
.141
.1415
etc.
        The important thing, I am suggesting, is that there should be
something driving this infinite sequence, some formula or rule or pattern.
Arbitrary infinite decimal expansions are a mirage.
        For rational numbers, which in the unit interval will be proper
fractions, we can always choose some number base in which the expansion
terminates -- trivially and at least the base which is the whole number the
denumerator. However we can also regard for example 1/3 in the binary table
as being represented not by a single member, but by an embedded sequence,
namely:
.01
.0101
.010101
etc,
        Because I didn't start out with any such finitistic assumptions. In
a sense, as a summary of my point of view, yes, I don't believe infinite
decimal expansions exist. But the point is to get at the meaning of such
decimal expansions, rather than to rule them out by fiat.
        That would be the conventional point of view. You introduced the
notion of computable reals, though. I'm talking about the reals per se. It
would be a consequence of my point of view, I think, that there are no
unspecifiable reals. I'm not sure whether computablility adds anything new.
Six Letters
===
Subject: Re: Dial 999 for the real number line
Do you claim that there is a bijection between the naturals and the
reals?
You will never understand real numbers until you get over your hangup on
decimal representations.  A real number is an equivalence class of Cauchy
sequences of rationals.  Or, a real number is Dedekind cut.  Either
definition will do, and neither makes any reference to decimal digits.
You are only confusing yourself by dragging in irrelevant considerations.
What does it mean for a mathematical object to literally exist?  Does
the empty set literally exist?  Where can I find it?  Keep in mind that
there can only be one empty set, by the axiom of extensionality.  Does it
reside in our galaxy, the Milky Way?  Wouldn't that be an amazing
coincidence?  Does that mean that civilizations in other galaxies cannot
do mathematics?
Every real number has an infinite decimal expansion.  It exists, whether
we can write down all the digits or not.
What you are trying to say here is that the numbers in your table are
dense in the reals.  That's true, but it does not change the fact that
the set of numbers in your table is not identical to the set of real
numbers.  An accumulation point of a set need not be a member of the set.
I repeat my question.  On which line of your table does the number 1/3
appear?
Yes, you should have said that.  It would have been even better if you
had simply said that your table of numbers is dense in [0,1].  That would
be much clearer.
Do you accept the axiom of the power set?
Yawn.  Another long-winded way of pointing out that your table of numbers
is dense in [0,1].
There is no axiom that says we can count to infinity.  There is, however,
an axiom that implies the existence of an infinite set.  There is a
difference.
Then I will ask again:  do you accept the axiom of the power set?
What do you mean by a specification?  If a number can be specified by a
formula or an algorithm, then it is a computable real.  Is it possible to
specify a real without providing a formula or an algorithm?
-- 
Dave Seaman
Oral Arguments in Mumia Abu-Jamal Case to be heard May 17
U.S. Court of Appeals, Third Circuit
===
Subject: Re: Dial 999 for the real number line
...
...
...
...
...
...
Hi Dave,
You can represent each Cauchy sequence or Dedekind cut, of a number
between zero and one, as a string of digits, no, ie a sequence no
different in value?  Their definitions are equivalent (and some don't
find Dedekind/Cauchy sufficient to represent all the real numbers,
only some of them).
Yeah, 1 = 1.0000..., and 0 = (0,0,0,0,0,...).
I don't accept the axioms of regularity or infinity.
Do you accept that there are everywhere and only real numbers between
zero and one?  There are.  (Well-order the reals, divide by zero.)
If an algorithm describes constructing an infinite sequence, then have
it do each of them.  Then, where as above you claim no algorithm can
ever construct all of them, constructing Cauchy sequences or Dedekind
cuts won't, and there are thus some that aren't so built.  Perhaps
then above you meant computable.
Ross
--
Finlayson Consulting
C/C++/Java
===
Subject: Re: Dial 999 for the real number line
Dave Seaman a .8ecrit :
Look for Chaitin number
===
Subject: Re: Dial 999 for the real number line
Yes, I take your point, but I wanted him to explain exactly what he meant.
-- 
Dave Seaman
Oral Arguments in Mumia Abu-Jamal Case to be heard May 17
U.S. Court of Appeals, Third Circuit
===
Subject: Re: Dial 999 for the real number line
Six Letters
===
Subject: Re: Dial 999 for the real number line
        Since what is at issue is the status of infinite strings of
integers considered as decimal (or other base) expansions, it would have
been more accurate to simply omit the 0s. So the table should really be:
.0
.1
.01
.11
etc..
        The proposal is that some numbers, irrational numbers in
particular, do not exist as individual members of such a list, but as
embedded sequences.  Reverting to decimal, pi, for example would be the
infinite sequence (omitting the whole number part 3):
.1
.14
.141
.1415
etc.
Six Letters
===
Subject: a few Bezier curve usage questions
First, given a grid of 10k x 10k points with a marked path through
that grid (determined by an A* search), what is the best/right way to
chop / interpolate that path into quadratic Bezier curves? I was
planning to use a method like found here:
http://www.antigrain.com/research/bezier_interpolation/index.html
which would require me to find all the lines (some kind of linear
interpolation) first. Does that sound like a good plan? Or am I better
off trying to do an A* search through a map with obstacles using
Bezier curves directly rather than chopping the map into a grid?
Second, I was planning to use weighted quadratic Bezier curves as
discussed in the JAUS RA Part 1 document page 29. (You can find that
at jauswg.org). However, I have curvature constraints. What is the
easiest way to calculate the minimum turn radius (tightest curvature)
in any given quadratic Bezier curve? As I understand it, a quadratic
Bezier curve is the same as a conic section. Therefore, if I use six
points of my curve I can solve the six equations to determine the
equation, I could get curvature quite easily. Six simultaneous
equations, though, is a bit complex for my 56MHz on-board processor.
There must be some easier way.
Third, I need to calculate the nearest point on the path to some other
given point. Is there an equation for this or do I need to do the same
thing above where I find the equation for the conic section, then use
a system of equations for the tangent through the given point?
Forth, I need the length of the quadratic Bezier curve. I see lots of
formula or have a good link for length of a quadratic Bezier curve?
Wow. I feel like I should be better at math than this -- I shouldn't
Brannon
===
Subject: Re: a few Bezier curve usage questions
For any computer, even 56MHz, 6 simultaneous equations are nothing. My FEM 
methods solve 30.000 simultaneous equations in a second or so (albeit on a 
2.5 GHz machine with SSE2). Of course you need a well-implemented sparse 
matrix type and the right type of solver :)
Nevertheless, 6 equations require inversion of a 6x6 matrix, which in worst 

case is still only *so little* operations, even a 56MHz machine can do them 

in a flash. Is there some other limitation? (like not being able to do 
decent floating point operations?)
Nils 
===
Subject: Towards a Formula for Primes
My pages on the Pythagorean Perimeters Theorem, which I discovered,
are here:
http://www.wehner.org/pythag/
For the starting concept
http://www.wehner.org/pythag/ratios.htm
For further examples
The whole thing is based on DIOPHANTINE arithmetic.
In each case, there is a rectangle with a Diophantine ratio.
Using the procedure, one gets a Pythagorean triple.
When the rectangle is constructed on the smallest side of the
triangle, its perimeter matches that of the triangle.
Here is an example:
The ratio 3:2 delivers the 8:15:17 Pythagorean BASE triple.
I say that it is a BASE triple, which could be called BASIC triple,
because the 6:8:10 triangle is not unique - it is the 3:4:5 scaled by
2. However, 3:4:5 is a BASE triple.
For reasons that take too many words, the numbers 3:4:5, or whatever,
of a BASE triple will always be COPRIME.
So we take the coprime pair 3:2 and get the coprime triple 8:15:17
Unfortunately, the pair and the triple are not coprime to each other.
There are not - nor can there be - five coprime numbers. This is
because the 3:2 rectangle is constructed (in this version) upon the
smallest side of the triple, and will therefore be a scaled edition.
The 8:15:17 perimeter is 40.
A 3:2 rectangle constructed on side 8 is a 12:8 rectangle. Perimeter
40.
However, there is more to be found.
Because we have a coprime triple 8:15:17, we can now create six ratios
from it.
8:15
8:17
15:17
15:8
17:8
17:15
ALL are coprime.
Each of these will expand out into a BASE triple.
So prime numbers are being brought into the results in a manner that
they, due to the coprimality, are ISOLATED from one another.
Recursing around the algorithm should bring the extensio ad infinitum.
Perhaps within this concept lurks the narrow gateway - the key - to
entering into the solving of the problem of finding a test of, or
formula for, primes.
Charles Douglas Wehner
===
Subject: Re: Towards a Formula for Primes
The problem of finding a test for primes was solved by Euclid. 
The problem of finding an *efficient* test for primes, well, 
that one is still open - but I'd be more confident of your chances 
if I thought you knew anything about the progress that has been 
made on that problem over the last two thousand years, and 
especially over the last 25 years or so. Are you familiar with, 
say, the Adleman-Pomerance-Rumely-Cohen-Lenstra method? 
Do you know how good it is? Do you have any reason to believe 
that your concept will lead to anything better?
-- 
===
Subject: Re: Towards a Formula for Primes
to
.
. The problem of finding a test for primes was solved by Euclid.
You do not appear to be very rigorous in your contemplation of what I
have said. Of course there are such things as the Sieve of
Eratosthenes, which laboriously go along a number-line in jumps of
two, three and so on until all non-primes have been struck out.
The thread I opened here is titled TOWARDS a Formula for Primes. It
is based on what is very likely to be a new discovery, but I have not
explored it in enormous depth because I have other things to do.
. The problem of finding an *efficient* test for primes, well,
. that one is still open
THAT is what it is all about. It is about the possibility of creating
a formula that can be applied to GENERATE primes, or a formula that
will test a number to see if it is prime. It is not a suggestion for
another Sieve procedure.
.
- but I'd be more confident of your chances
. if I thought you knew anything about the progress that has been
. made on that problem over the last two thousand years, and
. especially over the last 25 years or so. Are you familiar with,
. say, the Adleman-Pomerance-Rumely-Cohen-Lenstra method?
That is a very glib loaded question. What I know for sure is that YOU
YOURSELF do not know all the research that has been done in the last
two thousand years. Until you have made YOURSELF familiar with ALL the
research of the entire PLANET over the last 2000 YEARS you cannot
condemn others who have not made that effort.
. Do you know how good it is? Do you have any reason to believe
. that your concept will lead to anything better?
Lenstra comes through in my memory in connection with something I was
doing which overlapped. This name rings a bell, and I am sure the work
WORLD. This is not a prize fight.
I am familiar with the nonsense work of somebody whom I will call
a book in which he gave his Formula for Primes. It was very simple
and delivered the first seven.
At the same time I was reading The Art of Computer Programming by
Professor Donald E. Knuth. In one volume, he gave a formula for primes
which worked only for the first seven. He warned that you have to try
such formulae for the eighth and more, because they may not work.
Herbert Herbert was hailed in the Guardian newspaper as the
discoverer of the long-sought efficient formula for Primes. The
Japanese beat a path to his door, and he was invited to Japan. He was
feted in the universities, and introduced to Japan's chief economist.
Meanwhile, the eminent crystallographer Alan Coutanceau-Clark, the
world authority on the geometry of nested spheres, and a very dear
friend, examined the book and found that the formula did not deliver
the eighth.
I had written machine-code to illustrate one of Alan's theorems. I
used the obvious formula 6n plus-or-minus 1. It was quick enough, but
does not deliver the 2 or 3. In addition, it delivers false primes. 25
is 6*4 plus 1. It is non-prime. Similarly, 35 is 6*6 minus 1. It is
non-prime. Similarly, 49 is 6*8 plus 1. It is also non-prime. I simply
used a Sieve to test only the output of 6n plus-or-minus 1, and the
Sieve decided the outcome. When the algorithm delivers all the
primes (except 2 and 3) it is good, but spoilt by the false primes,
leading to the need for further testing.
Herbert Herbert returned from Japan, showing off his photos of
himself with professors and economists in japan. We were chuckling.
Then, he was summoned back to Japan. It seems the Japanese, having now
overcome the language barrier, had tested his formula for the eighth.
He was required to explain himself. Why, after all that fuss, did his
formula not work?
What is so special about the Pythagorean Perimeters Theorem is that it
can convert a coprime DUPLE to a coprime TRIPLE. Therefore, built into
it is the concept NEW PRIME. It requires some careful and rigorous
analysis to find out the exact rules as to what kind of NEW PRIME is
created.
the 3:2 rectangle delivers 8:15:17
The 2 is delivered three times in the eight.
The 3 is delivered once in the 15.
The 15 also delivers NEW PRIME 5.
The 17 is also a NEW PRIME.
So we get two new primes, but I only guarantee one. That is because
when a duple becomes a triple, only one is added. The other new prime
is spurious, and cannot be guaranteed.
The 3:1 rectangle delivers 7:24:25
The 7 is a NEW PRIME.
The 3 is contained in the 24.
The 24 also delivers NEW PRIME 2 (three times)
The 25 delivers NEW PRIME 5 (twice).
Duples can be picked out from the triple, and so yet more NEW PRIMES
will appear. There will also be some redundancy. Accordingly, there is
room here for research - to maintain the concept of NEW PRIME until
the essence of the primality of numbers can be found. That leads to a
new formula.
When Pythagoras produced his theorem, he did not prove that 3*3 plus
4*4 is 5*5. If you have not studied what Pythagoras actually found -
the Locked to the Rightangle Grid concept - I suggest you
investigate it. Even a child can multiply three by three, add it to
four by four and compare with five by five. The question was deeper,
but takes too many words to describe.
Similarly, here, I do not make this suggestion lightly. The axioms of
arithmetic are obviously too incomplete for a solution to the problem
of a formula for efficient prime-generation, or for efficient prime-
testing, to come from arithmetic alone.
The Pythagorean Perimeters Theorem is a very, very simple GEOMETRICAL
theorem. There is something in the GEOMETRY of a single Diophantine
rectangle, translating into a single Diophantine right triangle of the
same perimeter that throws up a guaranteed NEW PRIME.
So there will be no false primes. However, whether any resulting
formula delivers an array of primes with some primes missing, or
whether it delivers them all, depends on whether the approach can lead
to a formula. Only after investigation of the suggestion can it be
decided whether the approach has its merits.
When the axioms of a system are incomplete, as probably here in
arithmetic, one reaches into another system, as in geometry here. That
is how problems are solved.
Mine is not an ANSWER. Mine is a discovery that can be taken further.
I have found a source of NEW PRIMES. You work with two primes and
find you have got three.
Charles Douglas Wehner
===
Subject: Re: Towards a Formula for Primes
On 7 May 2007 12:19:24 -0700, charleswehner@hotmail.com
I agree that your method converts a coprime duple into a coprime
triple. But that's not such a rare phenomenon.
For example, start with a coprime duple a,b.
Then a,b,a+b is a coprime triple.
This could then be iterated by taking one of the pairs a,a+b or b,a+b
as the new duple.
quasi
===
Subject: Re: Towards a Formula for Primes
I haven't condemned anybody. 
You say your concept may be the key to finding a test for primes. 
Don't you owe it to yourself to find out what tests for primes are 
already out there? If your concept leads to a test which will tell 
in 10 seconds whether a given 100-digit number is prime, but 
there's already a test out there which will do the same thing in 
a millisecond, has your concept really made a contribution? 
You know the Newton quote about seeing farther by standing on 
the shoulders of giants? That's how mathematics generally works. 
We make progress by building on what's been done by others who 
came before us, not by ignoring what they've done and charging 
ahead on our own. 
There is no trick to producing new primes. Take all the primes you know 
and multiply them together and add 1; that number is guaranteed to 
deliver a new prime (in that either that number will be a new prime, 
or it will be a product of two or more new primes). 
Or consider the sequence 
    2^1 + 1, 2^2 + 1, 2^4 + 1, 2^8 + 1, 2^16 + 1, 2^32 + 1, ....
where the exponents 1, 2, 4, 8, 16, 32, ... are the powers of 2. 
Every number in this sequence delivers a new prime. 
Well, why don't you do your investigation and get back to us.
-- 
===
Subject: Re: Towards a Formula for Primes
Only if you factor the number.
===
Subject: Re: Towards a Formula for Primes
To be sure. But I imagine the same applies to what OP proposes.
-- 
===
Subject: Re: Towards a Formula for Primes
likely?   Justify this statement.
This is the hallmark of a crank.  Make an absurd claim, then state
that you
don't have time to do the work.  If you want to be taken seriously, I
suggest
that you refrain from this kind of behavior.
Actually, it is not open. We have an efficient test.  The AKS test
runs in polynomial
time.
Such formulae already exist.  Read, for example  Paulo Ribenboim's
Book of Prime Number Records
We already have such a formula. It is called Wilson's theorem.
We also have efficient algorithms.
Actually, it is a pretty good bet that Gerry knows most of what has
been published.
He is a professional number theorist.
Noone can know work that has not been published.  But Gerry knows most
of what
has been published.
and Hendrik's
the work of
either of them. You, OTOH, appear to be dropping names.  Can you
state
even one theorem or algorithm that they have produced???
You are writing mathematical gibberish, because you have not even
defined
the term NEW PRIME
It is not a discovery of any kind and can not be taken further.
Pythagorean triples have very little to do with primes, except that
one side of a
primitive triple sometimes has a  prime value.  It is very simple to
prove that
a primitive triple can never contain more than one prime.  It is also
very simple
to prove that if a side is prime, then it must be 1 mod 4;  it can
never be 3 mod 4.
If you want to be taken seriously, you will demonstrate to this group
that you have
at least some mathematical ability by proving what I have just stated.
===
Subject: Re: Towards a Formula for Primes
Which makes it efficient in a technical sense, but not in a real world 
sense. When you're testing a 500-digit number for primality, do you 
use the efficient AKS test? or do you use a test that is not known to 
run in polynomial time? 
Even in the real world sense, efficient is a relative term. I'd like 
to see a primality test that runs as fast as a coprimality test - now 
*that's* what I call efficient.
-- 
===
Subject: Re: Towards a Formula for Primes
...
3,4,5 ?
11, 60, 61 ?
-- 
David Hartley
===
Subject: Re: Towards a Formula for Primes
one side of a
It is true that only one SIDE can be prime. One also must be 0 mod 4.
The *hypotenuse* can also be prime, but it is distinguished from
a side  I should have been more careful in delineating side
from hyptotenuse.
Further clarification.  Every prime that is 1 mod 4 is the hypotenuse
of only one prim. pyth. triangle.  Every prime is the *side* of at
least
one such.
===
Subject: Re: Towards a Formula for Primes
I see. But perhaps you should also have explained that in the next 
sentence - it is also very simple to prove that if a side is prime, 
then it must be 1 mod 4; it can never be 3 mod 4 - you had changed the 
meaning again and side now meant hypotenuse.:}
-- 
David Hartley
===
Subject: Re: Towards a Formula for Primes
You seem to be forgetting that Bob had just ploughed through 
vast tracts of utter gibber-jabber. His brain was probably in 
tears by that stage asking for the nonsense to just go away.
Best to respond to gibber-jabber with vast quantities of snipping, 
and a simple no you're a loon, to protect the innocent, and 
ensure that Usenet-post traumatic stress disorder does not kick in.
Phil
-- 
Home taping is killing big business profits. We left this side blank 
so you can help. -- Dead Kennedys, written upon the B-side of tapes of
/In God We Trust, Inc./.
===
Subject: Re: Towards a Formula for Primes
did the OP prove that this algorithm always makes primes?
the famous result by what-is-his-**** also generates negative values,
which are either composite, or not necessarily prime
(I forgot .-)
I think, it was a formula in 26 variables and 25 degrees i.e.,
usually given as multinomial factors, as part of a result,
proving that there is no formula to solve any Diophantine eq.
... correct?
thus:
wow; what that report says about the rate
of increase of our militaryis use is astounding, although
it certainly comports to Big Peak Oil's statistics --
it's leading them, along with the sudden cut-off
of Iraqi oil when Cheeny hacked the veephood ... although
H-Dubya and Al-Junior were the biggest hackers
of that office, of all.
I mean, Halliburden could've done that
withut the war.
yeah, all you world patriots & matriots;
just sit on your hands, while Dick goes ape
in Sudan, Iran and possibly all other once and
future British quagmires.
Belize, Canada, Trinidad AND Tobago;
the list goeth on.
tudy_says_oil_reliance_strains_military?mode=PF
thus:
I really don't see that, either, because the 'Gon is a massively
reinforced concrete thing (apparently,
a plane hit the Empire State, and it didn't come down);
it's like a bug hitting your windshield,
with extra volatiles.
the report quoted below, as the sole reference
for the original posting, herein, says soem thing
of significance about the magnitudes of energy,
directly at the top of page 5.
look, up in the sky -- it's Googoltude (TM) ?!?
http://www.ldeo.columbia.edu/LCSN/Eq/20010911_WTC/WTC_LDEO_KIM.pdf
--nnerfmann!
===
Subject: Re: Towards a Formula for Primes
Bullcrap. Gerry's a razor-sharp mathemetician, and he shredded your
almost-meaningless babble with one swipe.
Phil
-- 
Home taping is killing big business profits. We left this side blank 
so you can help. -- Dead Kennedys, written upon the B-side of tapes of
/In God We Trust, Inc./.
===
Subject: Re: An exact simplification challenge - 12
Hi.  Mathematica 6 does not reduce the equation to zero since it assumes 
z 
could be Complex:
equ = Exp[Cosh[z]]^Sinh[z] - Exp[Sinh[z]]^Cosh[z];
Both:
 Simplify[equ]
and
 Assuming[Element[z, Complexes], Simplify[equ]]
However:
Assuming[Element[z, Reals], Simplify[equ]]
 0
-- 
Dana
===
Subject: Re: Abelian/Tauberian theorems - history.
Content-Length: 1057
Originator: rusin@vesuvius
.................
Thm 4. Godfrey Harold HARDY (1877-1947)
in Proc.London Math.Soc. (2) 8(1910)301-320.
Thm 5.  Alfred TAUBER (1866-1942)
in Monatshefte fuer Math.,8(1897)273-277.
Thm 6. John Edensor LITTLEWOOD (1975-1977)
in Proc.London Math.Soc. (2) 9(1910)434-448.
===
Subject: Re: Abelian/Tauberian theorems - history.
On 6 May 2007 08:41:18 -0700, alex.lupas@gmail.com
************************
David C. Ullrich
===
Subject: Re: Abelian/Tauberian theorems - history.
Content-Length: 937
Originator: rusin@vesuvius
***********************  David C. Ullrich
Thm 1. Augustin Louis CAUCHY (1789-1857)
in Analyse algebrique,Paris,1821.
Thm 2. Niels Henrik ABEL (1802-1829)
see Oeuvres,Christiania, Grondal &Son,1881,Band 1,page 223.
Thm 3. Ferdinand Georg FROBENIUS (1849-1917) ?
in J.fuer Math. Band 89(1880)262-264.
  Note: Ernesto CESARO (1859-1906)
===
Subject: Re: The N-Body Problem
This is what is called a 'hidden variables' theory -- and there is an
excellent argument, provided by John Bell, against hidden variables.
    http://en.wikipedia.org/wiki/Bell%27s_theorem
Although this does not rule out *all* hidden variables theories, it
does
rule out *local* hidden variables theories -- which is to say, all
such
theories that respect the speed of light as a limit on causality.
===
Subject: Re: The N-Body Problem
A dubious claim. To what degree of accuracy? What about solar eruption
and decay, comets, asteroids, etc.
Sure, you can make a deterministic mathematical model if you postulate
an extremely simple model with no interference and no degradation due
to aging. But then, that would just be a paper model, not a model of
the real solar system. With such a highly simplified model, there's
little chance of accurately predicting the real motions over long
periods of time.
quasi
===
Subject: Re: The definition of ordinal.
Though I don't know the answer to this question of mine, but yet I
think there can be a better definition.
I think this definition is equivalent to the standard definition of x
is ordinal with or without regularity.
Here is Dave Seaman's proof of equivalence between
transitive))
and the standard definition of x is ordinal. It demands regularity.
-----------------------------------
Call a set A a _pseudoordinal_ if A is transitive and each member of A
is
transitive.
It is clear that evey ordinal is also a pseudoordinal.  The converse
may
fail in the absence of regularity:  if a = {a}, then { 0, a } is a
counterexample.  We therefore assume regularity in what follows.
Lemma.  Suppose A is a pseudoordinal and L is an ordinal that is a
subset
of A.  If AL is nonempty, then L is a member of A.
Proof.  Let E = AL.  By regularity, we may choose x in E such that x
is
disjoint from E, implying by transitivity that x must be a subset of
L.
But the only subset of L that can be a member of E is L itself,
Q.E.D.
Proposition.  Let A be a pseudoordinal and let L be the least ordinal
that is not a member of A.  Then A = L.
Proof.  We are given that L is a subset of A.  However, L is not a
member
of A, implying that AL is empty.
Corollary.  Every pseudoordinal is an ordinal.
----------------------------------------
So I think this new definition that I have stated , can be prooved in
the same manner, since it is clear that every ordinal according to
this new definition is well founded.
This definition is actually simpler than the standard one.
Zuhair
===
Subject: Re: The definition of ordinal.
To prove that, it would be sufficient to prove that the right side of
the biconditional in your definition entails:
Let me know what you find...
MoeBlee
===
Subject: Re: The definition of ordinal.
I thoght it would be sufficient to prove that x is well founded.
Since that is all what Dave Seaman's proof requires( see above ).
It is easy to proove that no member b of x is in itself.
since if we have beb and bex , then {b} would be a subset of x that
doesn't have a member which is disjoint from it.
Similarly we cannot have and infinite membership in x without reaching
{ } , i.e we cannot have this condition x={k, m, n,.......} were mek,
and nem, .... and not ultimately reaching { }.
Even more extensivelly : if we order sets in x such that for any two
sets m and k in x :m preceeds k if and only if mek then we cannot have
an infinite subset M of x that have k and its predecessors as members
and that doesn't have { } in it.
becuase by then we will vioate the condition of having a member in M
that is disjoint from M.
Since the old definition require regularity, then it is obvious that
this definition doesn't. Because x is well founded.
Since we know that x is well founded then this definition is
equivalent to the standard one, and we can use the same Proof of Dave
Seaman that I have quoted above.
I don't think there is a need to go steps back to prove what you've
mentioned.
Zuhair
===
Subject: Re: The definition of ordinal.
No, you have to prove that x is an ordinal. We do have that every
nonempty subset of x has an epsilon-least member and we have that x is
a epsilon-transitive, but that is not sufficient to show x is an
ordinal. You're probably thinking that 'x is well ordered by
membership' just means 'every nonempty subset of x has an epsilon-
least member'. But that is not all there is to x being well ordered by
membership. Look up the definition of 'well ordering' (in the strict
sense, the one that doesn't include the identity relation).
I didn't read all that, since I surmise (if I'm wrong, tell me) it is
just to show that every nonempty subset of x has an epsilon-least
member. I already know that fact. But it's not enough to establish
that x is well ordered by membership.
Please just display the definition of 'x is well ordered by R' (strict
well ordering, not the one that includes the identity relation, by the
way). Then complete the proof that x is well ordered by membership.
MoeBlee
===
Subject: Re: The definition of ordinal.
Yes, that is true.
 Appearently you didn't understand my argument , because you didn't
 What I meant is that all of what we need for Dave Seaman's proof to
work is regularity. ( see this proof of Dave's, I already quoted it in
this thread ).
But here with this new definition we don't need regularity, since
according to the new definition the right side of the biconditional
implies that regularity applies to x, i.e x is well founded.
So since x is well founded , then we can use Dave Seaman's proof to
prove the equivalence of this definition with the standard definition.
You got what I mean now?
Just see if Seaman's proof is applicable to this new definition or
not.
Zuhair
===
Subject: Re: The definition of ordinal.
I always got what you meant about that. And it seems to me to be a
good intuition, but it's not in itself enough for a proof. I'll even
restate the situation so that you can see that I very well know what
your argument is:
(1) With the axiom of regularity we have this theorem:
transitive).
(2) Your definition of 'zuordinal' includes that x is epsilon
sets that can be of matter are subsets of x, it should be sufficient
that all those subsets obey the axiom of regularity, and they do in
the sense that you put the minimality clause into your definition
also.
(3) But the only problem now is that it should work that way is not
an inference rule. So you have some options: (a) You can just plow
ahead to prove that x is well ordered without using your it should
work that way argument, (b) ADAPT Dave Seaman's proof so that you
basically go through the steps he did but with respect to the
particular x we're talking about, or (c) find some lemma that comes
out of his proof to connect with your proof about x as such a lemma
would make your it should work that way argument actually snap right
into place in logical (as opposed to handwaving it should work that
way) form.
So, please stop posting to me things like you didn't read all of what
each step of the way here. It seems to me (I don't know) that your
intuition is correct that Dave Seaman's result should carry over to x
itself, and it might even be trivial to show that it does, but you
just haven't done it. Just saying
since x is well founded, then we can use Dave Seaman's proof to
prove the equivalence is NOT itself proof. So, again, as I said, you
can either try to adapt to x the step by step argument Seaman gave, or
maybe you can extract a neat little bridging lemma to SHOW that since
only subsets of x could possibly be involved, it must follow that x is
an ordinal, or start from scratch to simply show that x is well
ordered, just as I set up for you as all you need to show is that
And by the way, just out of mathematical curiosity, you might be
interested in showing 'men v nem' irrespective of the Seaman result,
since if x is indeed an ordinal, then indeed men or nem.
MoeBlee
===
Subject: Re: The definition of ordinal.
forgive my doubts , I only wanted to be sure. It seem's that you
understood what I meant even more that I myself do?
Ok, then, I'll work on that next week.
Zuhair
===
Subject: Re: The definition of ordinal.
hmmm..............., Ok.
===
Subject: Re: The definition of ordinal.
Ok, I will try to think about it next week, if I have time.
Zuhair
===
Subject: Re: The definition of ordinal.
Yes, that is true, {{A}} is the answer.
Zuhair
===
Subject: Opinions?!
Hi all,
What would be contradictive, undesirable or inconvenient with the
following rather simple first order logic with identity set theory
having axioms:
2) Empty: ExAy(~yex)
theorem: E!xAy( ~yex)
proof: Extensionality.
4) Comprehension schema: if F is a formula in which x is not free then
all closures of
are axioms.
Do anybody think that this theory gives rise to Russell's paradox, or
any other known paradox?
Is this theory clearly inconsistent?
Is it vague?
IF it is not clearly inconsistent, is it worth contemplating, or
it is so undesirable that it is unworthy even to consider?
Any opinion?
Zuhair
===
Subject: Amazing Wallpapers!
A great site!!
it has 1000's of pictures of all categories including New Zealand,
wildlife landscape.. absolutely everything!!!
www.amazingwallpapers.co.nr
hope you'll like it!
===
Subject: Re: An exact simplification challenge - 10
Something like the following? 
 {seq(solve(y=i,{pi}),i=eval(S,Pi=pi))}:
 eval({seq(solve(i[],y),i=%)},pi=Pi);
                            2              2
                   {- -------------, -------------}
                                1/2            1/2
                      (4 + 2 Pi)     (4 + 2 Pi)
Problem is, I cannot garantee that no solutions may have been lost, 
or additionally generated  in this calculation. 
Given the first, the latter option can be excluded, because of:
 S_list := [S[]];
         [true, true, false, false, true, false, true, false]
However, according to Maple 8, 
 map(is,S_list,positive);
          [true, true, false, FAIL, FAIL, FAIL, FAIL, false]
???
===
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Hydraulics in Civil and Environmental Engineering 4th Ed. by Andrew
Chawick
Introduction To Algorithms 2nd Ed. by Philip Bille (selected problems)
Introduction To Algorithms 2nd Ed. by Thomas H. Cormen, Charles
E.Leiserson, Ronald L. Rivest, Clifford Stein
Introduction to Antenna Theory by Palacios
Introduction to electric circuits 6th Ed. by Dorf-Svaboda
Introduction to electrodynamics 3rd Ed. by David Griffiths
Introduction to Fluid Mechanics 5ed. by Fox
Introduction to Fluid Mechanics 6th Ed. by Fox
Introduction to Linear Algebra 3th Ed. by Gilbert Strang
Introduction to Quantum Mechanics 2ed Griffiths, David J.
Linear Algebra and its Applications  3rd Ed.  by Lay
Linear Algebra by Jim Hefferon
Linear circuit analysis by R. A. DeCarlo and P. Lin
Linear Systems and Signals by B P Lathi
Logic Computer Design Fundamentals 2th Ed. by Morris Mano (selected
problems)
Managerial Accounting 11th Ed.
Material Science and Engineering an Introduction 6th Ed. by Callister
Material Science and Engineering an Introduction 7th Ed. by Callister
Materials & Processing in Manufacturing 9th Ed. by Demargo
Mathematical Methods for Physics and Engineering 3rd Ed. by
K.F.RileyandM.P.Hobson
Mathematics for Economics by Simon and Blume
Mathematical Physics by Arfken
Matrix Analysis And Applied Linear Algebra by Carl D. Meyer
Mechanical Engineering Design 7th Ed. Shigley
Mechanics of Fluids 8th Ed. by Bernard Massey
Mechanics of materials Hibbeler 6th
Mechanics Of Materials(3rd Ed , By Beer, Johnston, & Dewolf)
Microeconomic Analysis 3rd Ed. by Hal R. Varian
Microeconomic Theory by Andreu Mas-Colell, Jerry R. Green, Michael
Dennis Whinston
Microelectronic Circuits 4th Ed. by Sedra, Smith
Microelectronic circuits 5th Ed. Sedra
Microelectronics Digital and Analog Circuits and Systems by Millman
Microwave and rf design of wireless systems by Pozar
Microwave Engineering 2nd Ed. David M Pozar
Microwave Engineering 3rd Ed. David M Pozar
Microwave Transistor Amplifiers Analysis and Design 2nd Ed. by
Guillermo Gonzalez
Modern Control Engineering 3rd Ed. by K.OGATA
Modern Control Systems 10E by Richard Dorff
Modern Digital and Analog Communications Systems by B P Lathi
Multi Variable Calculus 5th Ed.
Numerical Methods for Engineers by Steven C. Chapra and Raymond P.
Canale
Numerical Methods 3E by Faires
Operating System Concepts 6th Ed. by Abraham Silberschatz
Operating System Concepts 7th Ed. by Abraham Silberschatz
Operating Systems:Internals and Design Principles 4th Ed. by William
Stallings
Orbital Mechanics for Engineering Students by Curtis, 1st
Orbital Mechanics for Engineering Students Curtis
Organic Chemistry 5th Ed. by Atkins and Carey
Physical Chemistry 7th. Ed. by Peter Atkins & Julio de Paula
Physics for Scientists & Engineers by Tipler & Mosca 5th Edition
Physics For Scientists And Engineers 3rd Ed. by Douglas C. Giancoli
Physics for Scientists and Engineers: A Strategic Approach by Knight
Physics for Scientists and Engineers by KNIGHT
Physics for Scientists and Engineers 5th Extended Version by Serway
and Faughn
Physics for Scientists and Engineers 6th ed. Serway Jewett
Physics Volume 2 5th Ed. by Halliday, Resnick and Krane
Power System Analysis by John J. Grainger & William D. Stevenson, Jr
Principles of Communication 5th Ed. by R. E. Ziemer, William H.
Tranter
Principles of Physics 4th Ed. Calculus Based by Serway, Raymond A. and
John W. Jewett
Principles with Applications BY Giancoli 6TH Edition
Probability and Statistics for Engineers and Scientists (selected
problems)
Probability Random Variables and Stochastic Processes 4th Ed. by
Papoulis
Process Systems Analysis and Control by Donald R.coughanowr(selected
problems)
Quantum mechanics by Kyriakos Tamvakis
Recursive Macroeconomic Theory by Lars Ljungqvist and Thomas J.
Sargent
Recursive Methods in Economic Dynamics by Wright
RF circuit Design Theory and Application by Ludwig bretchko
Semiconductor Device Fundamentals 1st Ed. by Robert F. Pierret
Semiconductor Physics and Devices 3rd Ed. by Neamen
Signal Processing and Linear Systems by B P Lathi
Signals And Systems 2nd Ed. by Haykin
Signals And Systems 2nd Ed. by Oppenheim
Signals, Systems and Transforms 3rd Ed. by Oppenheim
Soil Mechanics: concepts and applications 2ed William Powrie
Solid State Electronic Device 5th Ed. by Ben Streetman (Instructor's
Manual)
Solid State Physics solutions
Solved and Unsolved Problems in Number Theory and Geometry by Daniel
Shanks
Strengths of Materials by Beer, Johnston, Dewolf
Structural Analysis by R.C. Hibbeler
System Dynamics by Ogata 3rd
The C Programming Language 2nd Ed. by Kernighan and Ritchie
The Econometrics of Financial Markets by Petr Adamek
The Science and Engineering of Materials 4th Ed. by Donald R. Askeland
Pradeep P. Phule (Instructor's Manual)
Theory and Applications of OFDM and CDMA Wideband Wireless
Communications (2005)
Thermodynamic 5th ed. Cengal
Thermodynamics: An Engineering Approach 5th Ed. by Cengel Boles
(Instructor's Solutions Manual)
Thermodyanamics of Turbomachinary 5E
Time-Harmonic Electromagnetic Fields by Harrington solutions, 2001
Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas
Vol 1
Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas
Vol 2
Transport Phenomena 2nd Ed. by Bird and Stewart(to class 1 and class 2
problems)
University Physics with Modern Physics (11th) by  Hugh D. Young and
Roger A. Freedman.
Vector Calculus 3rd Ed. by Susan Jane Colley
Vector Mechanics for engineers dynamics by beer 6th edition
Vector Mechanics for engineers dynamics by beer 7th edition
Vector Mechanics for engineers statics by beer 6th edition
Vector Mechanics for engineers statics by beer 7th edition (nearly the
same with edtion 8)
Wireless Communications principles and practice 2nd Ed. by Theodore
Rappaport 1996
===
Subject: Re: What Is a Mathematician?
practical
Named your dog Cauchy
AND
Like to compute strange things just for the fun of it
AND
Don't care a red jammed cent if any theoretical
mathematics will ever find any practical application.
===
Subject: Re: What Is a Mathematician?
11 is already used.
-- 
Michael Press
===
Subject: Re: A Different Kind of Boolean Logic
Actually 'xor' was the only operation I'd managed to figure out, but
===
Subject: Re: A Different Kind of Boolean Logic
In sci.math, John Schutkeker
Standard Boolean truth tables (A on left, B on top):
0     0 0      0   0 1      0     0 1    0   1 1      0    1 0
1     0 1      1   1 1      1     1 0    1   0 1      1    0 1
and of course
not  0 1
     1 0
Arithmetic formulations can be done as follows,
if one uses 0 and 1.
not(x) = 1-x
x and y = x * y
x or y = x+y - x*y
x xor y = x+y - 2*x*y
-- 
#191, ewill3@earthlink.net
Windows Vista.  Because it's time to refresh your hardware.  Trust us.
-- 
===
Subject: Re: Maple and Finite Fields
I figured out how to get Maple to compute in finite fields.  It is indeed a 

wonderful feature, and it saved me a huge amount of time when I had analyzed 

my examples.  By the way, the examples I did look at helped me figure out my 

problem.
===
Subject: Two questions on algebra and real analysis.
Hi!
I want to ask some questions relating algebra and real anaylsis.
Algebra
-If R is commutative ring with inity and M_1 , M_2 is maximal ideals,
then M_1 intersection M_2 = M_1*M_2.
Analysis
-To show L^infinite (T) space is not separable.
here T is a unit circle and the norm of L^infinite (T) space is
essential supremum.
Any help would be very appreciated.
===
Subject: Re: Two questions on algebra and real analysis.
We assume M_1 and M_2 distinct, of course. Then M_1 + M_2 is an
ideal bigger than either, so it is R, and there is some expression
m_1 + m_2 = 1 (with m_i in M_i). Thus every r can be written as
rm_1 + rm_2. If r is in M_1 and in M_2, both terms are in M_1 *M_2.
This is actually a fairly standard argument in a more general 
setting where you assume directly that  M_1 + M_2 = R (a strong
sense of relatively prime).  You can then go on to prove that 
the quotient ring R/(M_1*M_2) is isomorphic to the direct product 
of R/M_1 and R/M_2 (the Chinese Remainder Theorem). 
William C. Waterhouse
Penn State
===
Subject: Re: Two questions on algebra and real analysis.
Hmmm...  it's not true in the case M_1 = M_2.  
Hint... consider indicator functions of intervals.
-- 
Robert Israel              israel@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            Vancouver, BC, Canada
===
Subject: Re: Two questions on algebra and real analysis.
On 5Ë.9d7è.93, 
Ëè.8eÄ12.bd[Ca
pitalATilde]22.bc[CapitalEth], Robert Israel
I got missed the condition M 1, M 2 should be distinct.
Your hint for analysis problem is turned out to be crucial. You may
mean that use the binary expansion of real number and its carndinality
===
Subject: An interesting quadratic-like optimization problem
underline{Setup:}
begin{itemize}
item $V$ is a real matrix of size $m times k$, where $k<m$;
furthermore $V$ is orthonormal, i.e., $V^T V = I_k$, where $I_k$ is
the $k times k$ identity matrix.
item We define $P_v eqdef V V^T$ as the $m times m$, rank $k$,
symmetric positive semi-definite projection matrix.
item $Sigma_n$ is a $m times m$ is a {em positive definite}
diagonal matrix.
item We define $B eqdef  left( Sigma_n + sigma_x^2 I_m right)
item $x in {mathbb R}^m$ is some arbitrary vector of size $m
times 1$.
end{itemize}
underline{Problem:}
[
min_V frac{ | Sigma_n^{1/2} B^{-1} P_v x |^2 }{ | B^{-1/2} P_v
x |^2 } eqdef Cost
]
underline{Remark:}
[
Cost ; geq ; lambda_{min} left( B^{-1/2} Sigma_n B^{-1/2}
right) ,
]
where $lambda_{min} left( B^{-1/2} Sigma_n B^{-1/2} right)$ is
the minimum eigenvalue of $B^{-1/2} Sigma_n B^{-1/2}$.
underline{Conjecture:} 
The optimal $V$ that solves the problem is diagonal.
Note that at the moment just showing that optimal $V$ is diagonal
(instead of finding optimal $V$ itself) is sufficient for us.
===
Subject: Re: An interesting quadratic-like optimization problem
If you can't be arsed to write your question as text, then 
people won't be arsed even reading it. 
Phil
-- 
Home taping is killing big business profits. We left this side blank 
so you can help. -- Dead Kennedys, written upon the B-side of tapes of
/In God We Trust, Inc./.
===
Subject: Re: An interesting quadratic-like optimization problem
Note that this is a plain text newsgroup. Perhaps some may bother to
fire up their TeX compiler to be able to read this, but most won't.
Compile it yourself, make a pdf file out of it and post a link to it
here if you can't bring yourself to post it in the usual newsgroup
notation.
--Lynn
===
Subject: Deriving Statistical Distribution (Mathematical Expression) of 
Sample Data
Need some input from fellow experts, lets say I have a bunch of data,
say the price of gold at 10 mins interval for year 2006. There are
52560 data.
I would like to construct a statistical distribution for the 52560
data in a mathematical form. Is there any way of deriving it? I would
prefer not to fit it in existing distributions through the use of
statistical software such as JMP or Minitab. I would like to derive
it
systematically.
I have difficulty finding literature/books on such technique.
BTW, if the sample of gold price is collected at 5 min interval
rather
than 10 mins, the sample statistical distribution will change, how to
capture it into the mathematical expression when deriving the
distribution?
===
Subject: Re: Deriving Statistical Distribution (Mathematical Expression) of 

Sample Data
Modeling Data involves a lot of work and involves gaining insight into
your data set. First, if you want to forget that this is a time series
(which has information about how a value is changing over time) you
can calculate the empirical cumulative distribution of the data. You
might also compute some stastics like the mean and variance of the
data.
Rank your observations 1 to 52560 by how large the price of gold is.
Let k be the rank of a price.
Now consider the set of pairs: (price, k/52560) This set of pairs is
the cumulative distribution for the data. You can graph this data and
Now take the derivative of this curve, and get the density function
for this data. That is basically the liklihood of a particular price
occuring. Look at the shape of this distribution. Does it look like a
normal distribution, or a lognormal distribution? Is there any
pattern? If you want you can try to fit the density or the cumulative
to a standard function. How good it the fit? Does the distribution
chosen make sense?
Now try to understand how the values are changing with time. Is their
a trend? Is the value 1 time unit later correlated with the previous
value? n time units later? Also look at the differences (change in
price from time n to time n+1). How are these differences distributed?
Are they correlated? Is the relationship between one value and next
next pretty much the smae throughout the life of this time series, or
are things changing?
Anyway, these steps are just the first steps in trying to understand
the data....
Josh
===
Subject: Re: Deriving Statistical Distribution (Mathematical Expression) of 

Sample Data
Cannot help you on the distribution, but I hardly see how fitting it
to your own distribution could do you anygood.
I normally would use som statistic package and have it to fit the data
to one of the many knowed distributions. For this my favorit is SAS
Institute, but thats mainly because that is what is thaught at my
university.
The part about the distribution should change when the intervals are
changed to every 5 mins, you shouldn't worry. You would have double as
many observation and the distribution first fitted, probably will
change to a more accurate one.
===
Subject: Re: John Baez Is Stupid as ! ahahahaha... Re: This Week's
 Irrelevant Crap...
still lickin ezekiels ass loooisss?
how many computers have you saved today loooisss?
still believe your gonna save the world loooisss?
Whatsamatta? U a giver not taker?
And where oh where is yo big stick loooisss?
===
Subject: Re: I Need Help
An algorithm is a method for achieving a result with a proof that 
it terminates and produces the result advertised. You provide a 
computer program that could fail for any number of reasons: bug in 
the program, bug in the database program, computer failure, memory 
allocation failure ...
This is not a program? 
If not, why not use Cartesian product in a familiar mathematical 
notation. 
Hey, everybody, I am on a crusade!
-- 
Michael Press
===
Subject: The special connection of some primes to some composites!
101010101 = a composate and one of its'
largest prime factors is--
 9091.
-----------------------------------------------------------
1010101010101 = a composite and one of its'
largest prime factors is --
909091.
-----------------------------------------------------------
101010101010101010101010101010
1010101
= a composite and one of its' largest prime
factors is --
909090909090909091
-----------------------------------------------------------
101010101010101010101010101010
1010101010101010101010101010101
= a composite and one of its' largest prime
factors is --
909090909090909090909090909091
-----------------------------------------------------------
101010101010101010101010101010
101010101010101010101010101010
101010101010101010101010101010
101010101010101
= a composite and one of its' largest prime
factors is --
909090909090909090909090909090
9090909090909090909091
----------------------------------------------------------
101010101010101010101010101010
101010101010101010101010101010
101010101010101010101010101010
101010101010101010101010101010
1010101010101
= a composite and one of its' largest prime
factor is --
909090909090909090909090909090
909090909090909090909090909090
909091
---------------------------------------------------------
The next is--
10101..01 This composite has 585 digits
and its largest prime factor 90909..91 has 292
digits.
--------------------------------------------------------
The digit length of the composite is always
odd and the largest factors' digit length is
always even.
Where d = the composite digit length and
the largest prime factor digit length = pd.
Then --  pd = (d -1)/2
Are there many more of  these composites
(1010101..) with the same characteristics
that have (90909..91) as its largest prime
factor?
Also can 1010101..01 ever be prime after 101?
Dan
===
Subject: Re: The special connection of some primes to some composites!
Your pattern is easily explained with a little high school agebra.
Please note that  10^(ab) + 1   is divisible by 10^b + 1  when a is
odd.
Indeed,   x^ab+1  is divisible by   x^b+1  when a is odd, for any b.
And this is all there is to it.
===
Subject: Re: The special connection of some primes to some composites!
The next one is --
Composite = 10101..01 has 1281 digits and
prime factor = 90909..91 has 640 digits.
What is also interesting about any of these is,
divide the composite by the prime factor and
the quotient =
11111.. also a composite.
So finding the next set only the prime factor
(90909..091) has to be found.
Dan
===
Subject: why do these two methods yield differet answers?
find the average of  (3x + 1)^2 on the iterval -1 to 1
method 1.
1/2  Integral [ (3 x + 1)^2  dx] =  1/2  Integral [ 9 x^2 + 6 x + 1
dx ]
                           | 1
3 x^3 + 3 x^2 + x  |        =  8
                           | -1
method 2
1/2  Integral [ (3 x + 1)^2  dx]
u = 3x + 1
du = 3 dx
1/3 du = dx
 
| 4
(1/2 ) ( 1/3 ) Integral [ u^2 du ] = ( 1/6 ) ( 1/3 ) u^3 |
 
| -2
= 4
How did the limits of the integrals change in the second example?
===
Subject: Re: why do these two methods yield differet answers?
It looks to me like both methods yield the same results.  You just
forgot the part where you multiply by 1/2 in the first method.
Incidentally, you caould just make the last answer be (1/6)(1/3)
(3x-1)^3 and evaluate that between -1 and 1.  You get the same answer
yet again.
Achava
===
Subject: Re: why do these two methods yield differet answers?
You've forgotten to carry the 1/2 in the first method, and only
calculated the integral itself.
Remember to divide by 2 and you get the same answer with both methods.
And the limits in the second integral changed by your transformation
from x to u.
Since the original integral is from x = -1 to x = 1, the integral in u
must be
from u = 3 (-1) +1 = -2   to   u = 3*1 + 1 = 4.
As u = 3x +1.
Hope that clears it up. =)
===
Subject: Archimedes problem
Let G_f and G_g dnote the graphs of the functions f(x) and g(x)
respectively
and suppose f(x) g(x) satisfy the following conditions
(1)f(a)=g(a),f(b)=g(b)
(2)f''(x)<0  and g''(x)<0  for all x in (a,b)
(3)g(x)<f(x)  for all x in (a,b)
then Archimedes says that the length of G_f is larger than the length
of G_g
Why ???
===
Subject: Re: Archimedes problem
since adding (the same) linear function to f and g does not change any
of the conditions (you need to check this!), we can assume, wlog, that
f(a)=f(b)=g(a)=g(b)=0. By scaling, we can assume a=0 and b=1.
by (2), the functions are always concave downward.
Draw two concave-down curves from the origin to (0,1). Be certain that
they do not cross, except at the endpoints (to satisfy (3)). the lower
one is g. Graphically it should now be obvious that g is the shorter
curve.
If you want a mathematical proof, then post what you have done so far,
and what level of methematics you are at.
http://www.youtube.com/watch?v=cBcvL1VGVis
==
Subject: limits
I  have problem understanding this.
lim      2 sin x cos x       lim       sin x
          --------------------  =           -----------   =  1
Coudl some show me why that is the case?
it undefined?
===
Subject: Re: limits
First:  2 sin x cos x = sin ( 2 x )
Second:Draw the graph of sin ( 2 x) and the graph of 2 x. Look at the
vicinity of x= 0.
Third: Look at the definition of lim.
Fourth: 0/0 does not make sense with constant numbers.
x/ x or (sin x )/ x is the value of the proportion of two varying
elements. Here the proportion does make sense, even when x = 0.
With friendly greetings
Hero
===
Subject: Re: limits
equal to sin(2x), not to sin(x),
Why? The limit of the numerator is also 0. Have you ever been exposed
Jose Carlos Santos
===
Subject: New mathematics/physical sciences positions at 
http://jobs.phds.org, May 07, 2007
New job listings at http://jobs.phds.org - Jobs for PhDs
List your job at no cost! http://jobs.phds.org/jobs/post
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===
Subject: Website
hi
jokes, sms jokes, entertainment and many things...
Wanna see the website..
www.dailychennai.com
And in that website, there is one topic named Pets corner. It will be
more interesting...
http://www.dailychennai.com/pets.php
===
Subject: question
how to find answer to this question ?
which of the following numbers is diffrence between two squares of
natural numbers bigger than zero ( a^2 - b^2 ) ?
1000, 1001, 1002, 1003
===
Subject: Re: question
(a^2-b^2) = (a+b)*(a-b)
Phil
-- 
Home taping is killing big business profits. We left this side blank 
so you can help. -- Dead Kennedys, written upon the B-side of tapes of
/In God We Trust, Inc./.
===
Subject: Re: question
So I get (a+b)*(a-b) = 1000 and what now check all combinations of two
numbers which multiplied gives 1000 ?
a+b=10,
a-b=100.
a+b=2,
a-b=500.
===
Subject: Re: question
Yep. Note that if (a+b) is even, then so is (a-b). So factorisations
which split into odd*even will never have solutions in the integers.
(Odd*odd, and even*even are both OK.)
Phil
-- 
Home taping is killing big business profits. We left this side blank 
so you can help. -- Dead Kennedys, written upon the B-side of tapes of
/In God We Trust, Inc./.
===
Subject: Re: question
Another note: using the above, since 1 is odd, if a - b = 1, you can
get any odd number in the product (and thus the difference of
squares). If you have ever looked at successive differences of
squares, this should not be a surprising result!
===
Subject: Cauchy-Swartz Inequality Proof
This appears in Edwards's _Advanced_ _Calculus_ _of_ _Several_ _Variables_
as a theorem for which he provides the proof: given two vectors a and b,
First he says the case of a=0 or b=0 is trivial.  Then he assumes neither 
is
zero and creates two new vectors u = a/||a|| and v = b/||b||, both of which
clearly have a magnitude of 1.  Then
The next thing he does seems unnecessary.  He then says we should replace a
of the set used in the previous step.  I don't see how his last step adds
any new information.  Am I missing something?
  
-- 
http://www.dailymotion.com/video/x1ek5w_wtc7-the-smoking-gun-of-911-updated
http://911research.wtc7.net
http://vehme.blogspot.com
Virtus Tutissima Cassis
===
Subject: Re: Cauchy-Swartz Inequality Proof
************************
David C. Ullrich
===
Subject: Re: Cauchy-Swartz Inequality Proof
. Inequality
 |x|   =< A means that
 X=<A   and   -X=<A .
Please not forget that a scalar product
is a bilinear form , e.g.
the norm is positive omogen, that is
||-a||= ||a||. Perhaps help !
===
Subject: [Maple] Working with Units (bits, bytes)
Hi
I'm having trouble converting bits and bytes in Maple 7
with(Units);
a := 5*Unit(bit);
b := 6*Unit(byte);
convert(b,units,bit);
        48 [bit]
convert(a+b,units,bit);
Error, (in convert/units) unable to convert `1` to `bit`
Any help?
===
Subject: Re: [Maple] Working with Units (bits, bytes)
I think it's best to convert before adding.  Avoid adding quantities
that are in different units.  But you could try
  map(convert, a+b, units, bit);
-- 
Robert Israel              israel@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            Vancouver, BC, Canada
===
Subject: geometric progressions
Wondered if some one could help with the solution to this problem ASAP
please.
investment gains interest at 12% per annum compounded annually. How
much will be in the account when it is closed on 31st of Dec 19999.
having problems, using the formula Sn = a(1-r^n)/(1-r)
can you explain fully your answer please.
===
Subject: Re: geometric progressions
Nntp-Posting-Host: apps.cwi.nl
      What banking institutions are open January 1?
Will mankind still be here in 19999?
-- 
44 months after Japan attacked Pearl Harbor, Japan surrendered.
49 months after US attacked Iraq, it's time for the US to surrender.
pmontgom@cwi.nl    Microsoft Research and CWI      Home: Bellevue, WA
===
Subject: Re: geometric progressions
Hi martin,
there are two ways to solve this problem and one can be used to verify
the other.
First method: Iterative
This can easly be done by using a SpreadSheet Software like OpenOffice
or M$Excel.
Start in the first Cell with the start capital (1000$). Every cell
(the next 9) below it can be filled with the formula CELLABOVE * (1 +
0.12) + 1000
The first part is simply the capital plus interest and the last
+1000 is the additional deposit for that year.
When you copy that formula to the next cell it will be applied to the
result of the previous cell thus forming an iterative solution (btw $
16,548.74).
Now the second method: Creating a formula
Once you understood the first method it is easy to derive a formula
from it. Think of it this way:
In the first year (1990) 1000$ become deposited for 9 years. This
amounts to 1000*(1 + 0.12)^9 at the end of year 9.
In the second year (1991) again 1000$ are deposited but only for a
time of 8 years. Hence 1000*(1+0.12)^8.
And so on for the next years.
Finally the last deposit in 1999 will amount to 1000*(1+0.12) (I
assume that the interest for a full year gets payed).
The total sum of the deposits plus interests can be calculated as sum
of the deposits-with-interest. This leads us to the Formula:
SUM_N_from_1_to_9 : 1000(1+0.12)^N
Which (luckily) amounts to $ 16,548.74
Hope this has helped.
Sebastian
===
Subject: Re: geometric progressions
I worked out the answer pretty much like you said, the problem being
it doesn't equate to the answer in the book, think  either the book
has a print error somewhere along the line or I am totally missing
pretty useful. Will have the answer clarified tomorrow.
PS. I am a parent frantically trying to help my daughter, but it seems
my maths is failing me, been too long out of it!!!
Martin
===
Subject: Re: geometric progressions
You should give both your answer and that of the book. That way, we
can judge whether: (a) your are wrong; (b) the book is wrong; (c) you
are both right (or both wrong), but your answers just differ in some
trailing decimal places.
R.G. Vickson
===
Subject: partition of 1
Hi all,
I know that every
paracompact C^infty manifold
modeled on a separable Hilbert space H
admits partitions of unity of class C^infty,
as shown for example by Lang
in his Fundamentals of Differential Geometry.
My ask is:
Is it possible to remove the hypotesis
on the Hilbert space H to be separable,
in other words, is it true that
every paracompact C^infty manifold
modeled on a Hilbert space H with
H not necessarly separable
admits partition of unity of class C^infty ?
===
Subject: How to decompose ideals with primary ideals?
Hi!
In Z, how to decompoe the ideal (6^3)?
Is it possible, to write it with (2^3) intersection (3^3)?
I think it is possible beween maximal ideals.
===
Subject: Re: How to decompose ideals with primary ideals?
[...]
Yes. If 2^3*r = 3^3*t then 3^3 divides r in Z so 2^3*r is in 6^3Z.
Cleary 6^3*r is in both 2^3Z and 3^3Z.
-- 
Paul Sperry
Columbia, SC (USA)
===
Subject: EC-funded Research Visits: Application Deadline 15/05/2007
REMINDER!
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-----------------------------------------------------------------
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for visits starting from July 2007
-----------------------------------------------------------------
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 - Technical support and consultancy
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   who work in the EU and Associated States
See http://www.hpc-europa.org/ta.html 
for more information, eligibility conditions and online application form.  
Current success rate for applications: around 65%
++++++++++++++++++++++++++++++++++++++++++++++++++++++
+  Next deadline for applications                    +
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++++++++++++++++++++++++++++++++++++++++++++++++++++++
Apply to one of the Transnational Access centres:
CINECA (Italy), BSC (Spain), EPCC (UK), HLRS (Germany), 
IDRIS (France), SARA (The Netherlands)
===
Subject: =?iso-8859-1?q?=A3100,000=2E00_Project=2E=2E=2E?=
How often do you hand out you small change?
How much do you hand out?
Well I'm wanna test my luck and see how long it will take to collect
£100,000.00 Hope you have the time to join my project.
This is no scam!!!
All money collected will be used by me in the best possible way.
Donations welcome to this email:[tazz8u@gmail.com] at this secure
site
[https://www.moneybookers.com/app/?rid=3203802]
===
Subject: Re: ZFC is Consistent - No Axiom Infers the Negation of Any Axiom
True, they think they're inconsistent and ignore that belief.  But
they can ignore that belief because the proof that naive set theory is
inconsistent is wrong.  The whole argument is based on assumptions
concerning set and property that are arbitrary.  This same
arbitrariness leads to inconsistency or other conclusions.  Why the
asymmetry between set and property?  Why is not being a member of
oneself a property and not applying to oneself not a set?  (It is?
Then you reach the same contradiction.)
The assumption is that ~(x e x) is a wff and so not being a member of
oneself is expressible.  The distiction between expressible and a
property is then clouded and they suddenly call it a property.
If you assume that set = property then the proof that naive set theory
is inconsistent fails because we are assuming that not applying to
oneself is a property i.e. not being an element of oneself defines a
set, which is not the case.
The problem arises with the introduction of asymmetry between set and
property with no formal justification.
===
Subject: Re: ZFC is Consistent - No Axiom Infers the Negation of Any Axiom
No, usually they have a clear universe of discourse which is already a
set, so they are not inconsistent and they don't believe they are,
either.
May be. But then the problematic Axiom of (Unrestricted) Comprehension
is of course hopelessly circular. So your purported solution turns out
to be no solution at all.
groente
-- Sander
===
Subject: Re: ZFC is Consistent - No Axiom Infers the Negation of Any Axiom
It is a meaningless exercise to debate the difference or properties of
sets versus properties.  We formalize intuitive notions such as a
set and define certain syntax to have certain meaning (semantics.)  We
don't debate the properties of the syntax without it having been given
any semantics.
ZFC et. al. give meaning to sets.  When someone then says What
about 'properties'? and starts debating what their properties are,
they are totally misapplying the concept of formalizing.
set is intuitive.  We formalize it.
property is synonymous with set.  No reason to formalize it as an
intuitive notion as it is just another word for set.
If you want to make up some rules and define property as having
these rules apply, then we are considering an alternate formalization
of set.  Then you can compare the two formalizations, but that says
nothing about the intuitive notion of a set.  You are then just
saying:
Formalization 1 will be called a set.
Formalization 2 will be called a property.
Note the difference between set and property.
But the assignment of meanings, rules, semantics to set and
property was arbitrary - especially as to the choice of which term
(syntax) the rules etc. (semantics) apply, set or property.
If you are completely formal, you can see that there is no difference
between set and property as in both cases you are using the two terms
to declare arbitrary rules.
The real problem is that naitve set theory is not inconsistent and
that it is silly to say that the aleph-1 or more sets do not encompass
the aleph-0 wffs.
===
Subject: Re: ZFC is Consistent - No Axiom Infers the Negation of Any Axiom
What are classes?  Answer: kludges that were introduced in an attempt
to fix set theory rather than having any counterpart in Mathematics/
Logic.  There's no inherent reason to include classes because, what
is the intuitive notion of a class?  There is none.
C-B
===
Subject: Re: ZFC is Consistent - No Axiom Infers the Negation of Any Axiom
What is in play is the expressive power of various systems.  If we let
SE(x,y) mean y is an element of x, and TW(x,y) mean wff x with one
free variable replaced by y is a true sentence, we are talking about
the relative expressive powers of SE and TW.
(sets) has negation: the complement of a set is a set.  If P is
expressible as a set then ~P is expressible as a set.  Does SE include
all TW?  No.  Why?  Because TW includes all SE.  That is the
assumption that is utilized when we refer to the expression ~(x e x)
being a wff.
It is all a matter of definitions.  If we don't define TW as including
all of SE then SE can contain all of TW.  And since SW is 2nd order
and TW is only 1st order (there are aleph-0 wffs and at least aleph-1
sets) it makes more sense to say that SE contains TW and TW does not
contain SE.  Then there is no expression ~(x e x) and naive set theory
is NOT  inconsistent.
ZFC is just a stupid little system where:
1. There's lots of things you cannot decide.
2. You can decide only simple statements about which sets exist.
Anything outside of that requires additional axoms (e.g. Peano
Arithmetic.)
3. You can map the natural numbers to unique sets that can also be
expressed using set theory syntax - but that is true of all formal
systems: the set of expressions is recursively enumerable.  You can
represent or express the natural numbers in ANY formal system.
Math more general than the natural numbers requires additional axioms.
How can anyone justify the selection of ZFC axioms?  And then consider
a dozen alternatives and explain that.  The true explanation: the
mistake was saying that naive set theory is inconsistent without
actually formalizing what was being said.
C-B
===
Subject: Models of the theory of Categories
  I was going over basic category theory again the other day and was
enjoying the elementary bits.  When I got to the definition of the
functor, I stopped dead in my tracks.  Naturally, the presented theory
of categories was a model of said theory within the theory of SETS.
For the very elementary stuff it was all very intuitive but for the
notion of functor, I felt quite let down.  That the functor is the
basic representation of metaphor, within mathematics anyway, embodies
to me its most beautiful uses.  In fact, I would put the theory of
categories down AS a theory of metaphors.  The fact that those
metaphors are given as being between mathematical structures, is just
that much more exciting.
  Perhaps, I would propose that the theory of categories itself be
presented, first off, as a theory of metaphors without reference to
SETS.  Now, the problem, as I see it, is that any colloquial topos
(that is what I would call it anyway, or perhaps a natural language is
better, or perhaps even better would be an interpretation structure)
which includes concepts like metaphor (as basic, semantic objects)
should be roughly equivalent to the topos of SET (like.....what do I
mean by that? except isomorphic, I guess).  I mean simply, it would
form a topos.  So, whatever language you are best in would be THE
place for you to reason about the theory of categories. To perform
more complicated feats of reasoning, for example in cases where you
may want to actually calculate some quality of the reasoning structure
itself, then a structure like set would be most useful.
  For purposes of the application of the theory of categories, or its
preliminary use in in the constructing of theories about the world
out there, I would just as soon avoid its models all together.
===
Subject: Re: Models of the theory of Categories
personally
  i feel  metaphor  is unformalisable consistently
  because of its unescapable self-referentiality
all language is metaphor
the symbol is not the referent
the polish logicians struggled with this
  almost as the fundamental point of their restructuring of
phenomenalism
however
  there is a very strong case for semantics and syntax in category
theory
which revolutionised computer science in the latter part of last
century
in this view
  syntax and semantics are galois adjoint
if one takes the category of logical theories L
  ( ie. mathematical syntactic axiomatisation )
and the category of collections of mathematical structures CS
  ( ie. the power category of structures )
then galois adjunction relates the natural maps between them
in terms of interpretations
this in turn relates intimately with operationalist programmes of
science
  and the interpretation of language in phenomena
you have already shown familiarity with lawvere
  who is definitely the father of this program
but if you are interested in following through with some of the modern
approaches
i would suggest works also by dana scott, tierney, moerdijk
  and those in working in categorial computer science
  and so-called  algebraic set theory 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
===
Subject: Re: Models of the theory of Categories
  So far, I haver been of the opinion that to understand metaphor, one
needs to look at cognitive science.  To that end I look at the work of
hardcore scientist, i.e. someone who makes theories about the world
out there and by that I mean George Lakoff.  There is a precedent of
mathematicians being quick to cross the line and declare the rules of
thought, as Boole did.  Nowadays, people are more comfortable with a
notion of models of how we think, and the far more conservative
Philosophy of mind.  Were one to be as bold as Boole, and I suppose
Lawvere's Conceptual Mathematics was like that, I would wager on a
title like Categories: Models of Metaphor. There is such a delicate
boundary which scientists need to tread when they create models of
things like mind and language.
   This is the way we think!
   NO!  This is a model of how we think!
===
Subject: Re: Models of the theory of Categories
if you are familiar with lakoff's work
  then i suspect you are also familiar with langacker
but if not
he is a great resource on metaphor as well
also
  i would strongly suggest review
of the fodor - churchland debates of the 90's
which played out the structural-grammatical approach (fodor)
and the connectionist (churchland) counterapproach
  in the linguistic foundations of science
although more basic in content
  they definitely help map out the issues involved
before reading them
  i was strongly anti-chomsky
and even had strong leanings towards the poetic logic school
and the idea that understanding nonverbal reasoning and epiphany
  were crucial to any real philosophy of math and science
several prominent feminists had influenced me here
after spending some time with the various schools
  as a part of a research programme
in the linguistic foundations of science
i grew to respect the computational completeness
  of the two major approaches
eventually i have come to suspect that the nonverbalisable realm
  is value-free
that valuations are equivalent to verbalisation
and there is only aesthetic influence which remains unspeakable
i don't mean to push these conclusions on you
as they are certainly not as well formulated as i would desire
  or even very conclusive
but i hope these give you some more references for research
also
  if you are interested in pursuing some of the more biological
models of neuroarchitectonics
i would suggest
  arbib
  szentogathai
and others working on neural modeling in a compositional programme
strangely
  that field has barely recognised category theory
despite its natural abstraction capabilities
as an declarative language of intensional description
  and easy interpretation in neural nets
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
===
Subject: Re: Models of the theory of Categories
===
Subject: Re: Models of the theory of Categories
You might be interested in the book _Conceptual Mathematics_ by
Lawvere and Schanuel which develops elementary mathematical topics
from the basis of category theory notions.  Imagine, category theory
for middle school students!
===
Subject: Re: Models of the theory of Categories
I have been reading it and I agree with your sentiments.
===
Subject: Re: Models of the theory of Categories
            days. My association with the Department is that of an alumnus. 

I don't much care for the use of metaphor, but otherwise, see:
F. William Lawvere, The category of categories as a foundation for
mathematics, pp. 1-20 in _Proc. Conf. Categorical Algebra (La Jolla,
Calif., 1965), ed. S. Eilenberg et al. Springer-Verlag, 1966. MR
34#7332. 
The first paragraph of the Mathematical Reviews text on the paper reads:
    The author's purpose is to found a theory of categories, not in
    axiomatic set theory, but in first-order predicate calculus. As
    the title suggests, the aim is not only at autonomy but at empire;
    all mathematics should be formulable within this
    theory. Technically, it would seem sufficient to annex set theory
    itself. But this would mean no more than equal standing for the
    new system, if category theory can also be adequately formulated
    in set theory. The claim is advanced that a categorical foundation
    can be more natural because it gives more prominence to the notion
    of isomorphism. 
-- 
It's not denial. I'm just very selective about
 what I accept as reality.
    --- Calvin (Calvin and Hobbes by Bill Watterson)
Arturo Magidin
magidin-at-member-ams-org
===
Subject: Re: Models of the theory of Categories
particular sentence?
===
Subject: Re: Models of the theory of Categories
            days. My association with the Department is that of an alumnus.
The title in question is the title of Lawvere's paper. 
The point the reviewer seems to me to be making is that Lawvere was
categories, and thus that Category Theory was a theory that did not
require Set Theory as a foundational notion (autonomy of Category
Theory from Set Theory), but rather that his aim was to base all of
Category Theory into the empire). 
-- 
It's not denial. I'm just very selective about
 what I accept as reality.
    --- Calvin (Calvin and Hobbes by Bill Watterson)
Arturo Magidin
magidin-at-member-ams-org
===
Subject: Re: Models of the theory of Categories
A related question whose answer you may know: a while back I was
thinking about metaphors and how one might describe them
mathematically, and one way that seemed feasible at the time (I was
wasted) was considering a category whose objects were algebras of
arbitrary variety, and whose arrows were pairs of functions, one an
arity-preserving map from the operators of one algebra to those of
another, and the other an operator-preserving map from the elements of
one algebra to the other. My question is, has anyone fruitfully
investigated such a category? My guess is that it would be too general
to yield an interesting theory, but I would love to be wrong about
this.
-Rotwang
===
Subject: Re: Models of the theory of Categories
[...]
|a category whose objects were algebras of
|arbitrary variety, and whose arrows were pairs of functions, one an
|arity-preserving map from the operators of one algebra to those of
|another, and the other an operator-preserving map from the elements
of
|one algebra to the other.
Have a look at http://math.ucr.edu/home/baez/universal/.
I didn't see your construction explicitly, but I think it's
implicit.
Keith Ramsay
===
Subject: Re: Models of the theory of Categories
-Rotwang
===
Subject: Re: Models of the theory of Categories
|A related question whose answer you may know: a while back I was
|thinking about metaphors and how one might describe them
|mathematically, and one way that seemed feasible at the time (I was
|wasted) was considering a category whose objects were algebras of
|arbitrary variety, and whose arrows were pairs of functions, one an
|arity-preserving map from the operators of one algebra to those of
|another, and the other an operator-preserving map from the elements
of
|one algebra to the other. My question is, has anyone fruitfully
|investigated such a category? My guess is that it would be too
general
|to yield an interesting theory, but I would love to be wrong about
|this.
I'm pretty sure I've seen something very much like this, although I
can't give a reference offhand. There are people using category theory
methods to work on universal algebra, and they do things like
this, I'm pretty sure.
Instead of considering an n-ary function on the underlying set of an
algebra S, you can be more general and consider an arrow from Sx...xS,
the n-th fold product of an object S in a category, to S. :-)
Keith Ramsay
===
Subject: Re: Models of the theory of Categories
            days. My association with the Department is that of an alumnus.
If I understand you correctly, what you have is a category of algebras
of type Omega, and a second category of algebras of type Omega',
possibly different from Omega. Then you have an identification of the
operations Omega to (some) of the operations in Omega', in such a way
that arity is preserved.
For example, you can consider Groups as (.,^{-1},e)-algebras
(multiplication, inverses, neutral element); Rings with unity as
(+,*,-,0,1)-algebras (addition, multiplication, additive inverses, 0
element, multiplicative unity). Then you want have a pair of maps, say
f and g, where f sends the underlying set of a group into the
underlying set of a ring, and g maps the operation . to one of
+ or * (same arity), maps ^{-1} to -, and maps e to either 0 or 1, in
such a way that
f(a.b) = f(a)g(.)f(b)
f(a^{-1}) = g(^{-1})(f(a))
f(e) = g(e)
but your map allows for g to be non-injective, etc...
If this is accurate, it seems to me that you are simply talking about
the left adjoint of a (generalized) forgetful functor. In the above
example (which is perhaps a bit special since g will necessarily send
. to +) you would be talking of a kind of adjoint to the forgetful
functor that goes from Rings to Groups, mapping each ring to its
additive group.
Not necessarily so. For example, the question of what groups can occur
as additive groups of rings (with and without unity) is an interesting
one, explored in Fuchs's books on abelian groups. 
-- 
It's not denial. I'm just very selective about
 what I accept as reality.
    --- Calvin (Calvin and Hobbes by Bill Watterson)
Arturo Magidin
magidin-at-member-ams-org
===
Subject: Re: Models of the theory of Categories
Indeed, and the category I defined would have as its class of objects
the union of the classes of objects in the categories you mentioned
above, for *all* possible Omega.
I'll have to have a think about this (adjunctions are pretty new to me
and I am not yet at the stage of being able to recognise them without
sitting down with pen and paper for a while).
I will check it out, thank you.
-Rotwang
===
Subject: Minimum area
An ellipse is of the form x^2/a^2 + y^2/b^2 = 1, and the circle
(x-1)^2 + y^2 = 1 lies inside it. Find the values of a and b so that
the area of the ellipse is minimum?? Please help.......!!
===
Subject: Re: Minimum area
You might start by finding the minimum of (x-1)^2 + y^2 on the
ellipse.  Caution: there are two cases to consider.
-- 
Robert Israel              israel@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            Vancouver, BC, Canada
===
Subject: website
wonderful website
www.dailychennai.com
===
Subject: Leech Lattice
I am learning M24, Steniner S(5,8,24) and the Golay Code.
I am interested in how this relates to the Leech Lattice,
Conway groups and ultimately the Monster.
But first, could someone expound on
a1 + a2 + ... + a24 = 4a1 = 4a2 .. =4a24 (mod 8) where
= is really cong=, what this means, why it is multiplied
by 2^-3/2 and how this relates to binary Golay code
words, etc. Also the significance of 1^2 + 2^2 ... 24^2=70^2 as the norm 
vector 0, and the LL is w(ortho)/w
And finally where R^24=C^12 in various subgroups of
Co1 and what in the world the Leech Lattice has
to do with Z(e^2pi/3)^12?
Let's start with this before going onto the involution
centralizer of the Monster...
PGH
===
Subject: Re: Leech Lattice
I don't know if it will answer your specific questions, but you may
be interested in
 http://motls.blogspot.com/2007/05/monstrous-symmetry-of-black-holes.html
which discusses the Monster and Leech lattices from a stringy
perspective.
John R Ramsden
===
Subject: Re: Leech Lattice-
J.H. Conway and N.J.A. Sloane: Sphere packings, lattices and groups - 2nd 
edition. 
Springer Verlag, 1993, ISBN 0-387-97912-3
This more than excellent book treats in great detail all what one can 
possibly know about 
the Mathieu groups, the Leech lattice, Conway's sporadic groups, the 
associated theta 
functions etc. Of course the densest sphere packings in 8D and 24D receive 
particularly 
close attention.
Happy studies and enjoy the experience!
Johan E. Mebius
===
Subject: Re: Leech Lattice-
I will second this recommendation, but add a word of warning.
To some extent C&S is a reference book rather than the best textbook.
IOW if your background is not quite up to the task, it will quickly
become painful reading. I use it for quickly finding stuff about the
densest lattices etc, but my students often get a headache, as well
as the engineers I have referred to this book.
My Jugendtraum was to learn everything about the monster by reading 
this, but I hardly ever have the time to really look at the group 
theoretic chapters. Presumably they are excellent, but do assume
the reader to have a relatively strong background.
Jyrki
===
Subject: Re: Leech Lattice-
Yes, it's true, it's a very rich, difficult book. My goal
at this point isn't even to get to the Monster, just
the Leech Lattice. I have read the chapter dealing with
M24 and the Golay Code which I was introduced to by
Steven Culliane's webpages on the Geometry of the 4 X 4 Square, the MOG and 

such. I also reading Robin Chapman's
paper on the Binary and Ternary Golay Codes. Right now
I am merely trying to get solid with M24 especially.
An examination of the construction of the character table
of M24 would be helpful at this point.
The codeword puzzles at the bottom of the pages in C&S
are kind of entertaining. 
I found another page on picturing the smallest projective
page which leads to the MOG. Dumb question: What exactly
does it mean when SC says: Sums of the 4-subsets of
A pictured in A Obviously picturing is some form of
imaging but I can't seem to find the algorithm for this.
He also compares the 35 lines as 15 + 10 + 10 with
2-sets and 3-sets of 6 which is interesting.
This all started as a way of looking at 12-tone and
24-tone (quartertone) musical systems and their properties.
I see these numbers are important clear up to the Monster
and related topics.
PGH
===
Subject: Re: Leech Lattice-
I own it. I have read a few chapters (it can take days
just to get through one, at my level). What are the 
theta functions?
PGH
===
Subject: Re: Leech Lattice
my questions on the Leech Lattice.
Since I am still learning M24, Conway etc. I'd rather
start there before attacking E8 or even the Monster.
===
Subject: Optimization
With one of my projects I end up with a data matrix L[i,j]:
L:=array(1..n,1..4);
Row i=1..n is the product. Columns j=1..4 are product properties.
I have the following constraints that must be satisfied in an ideal 
product:
|L[i,1]-C| should be minimal, where C is a constant
|L[i,2]| should be maximal
L[i,3] should be minimal
L[i,4] should me maximal
Is there any way I can use Maple to sort the rows according to which 
product
satisfies all constraints optimally simultaneously?
Sorry if this is a trivial question. I have no idea how data optimization
works. Is this some sort of linear-programming problem? Does it have to do
anything with Simplex?
-- 
I.N. Galidakis --- http://ioannis.virtualcomposer2000.com/
----------------------------------------------------------
There's ALWAYS a mistake somewhere
===
Subject: Re: Optimization
Data, where is the data ??
Chris
===
Subject: Re: Optimization
These objectives may be in conflict. For example, the i (say i1)
giving the smallest |L(i,1)-C| might not give the largest |L(i,2)|,
etc. However, there may be another i (say i2) whose |L(i2,1)-C| value
is only slightly larger than that of i1 but whose |L(i2,2)| is much
better (even if not maximal, yet). To determine whether there is a
solution at all, let I1 be the set of i that mimize |L(i,1)-C|, I2 be
the set that maximzes |L(i,2)|, etc. (These sets are singletons if the
choices of i are unique.) If the intersection of I1, I2, I3 and I4 .is
nonempty, you have a solution; otherwise, there is no i that works,
and you need to go with some form of compromise. For more details:
look at multiple objective optimization methods; in particlular,
consider the concept of Pareto Optimality.
R.G. Vickson
===
Subject: Re: Optimization
product:
Google but I didn't find anything really useful. Just loads of technical
papers. Regardless, here are the ranges of my objectives:
1700<=L[i,1]<oo
C=5785
0<=L[i,2]<=100
0<=L[i,3]<oo
0<=L[i,4]<683
My non-specialist intuition tells me to do the following: Assign a weight
W(j), j=1..4 (user's preferences?) to the corresponding objectives 1,2,3,4 
and
then maximize the function:
F(i):=W(1)/|(L[i,1]-C| + W(2)*|L[i,2]| + W(3)/L[i,3] + W(4)*L[i,4]
Is there any reason this won't work? In particular, how does it come to
conflict with your observation that if the intersection of I_i is empty 
there
is no solution?
-- 
I.N. Galidakis --- http://ioannis.virtualcomposer2000.com/
----------------------------------------------------------
There's ALWAYS a mistake somewhere
===
Subject: Re: Optimization
You will have a problem if there are places where one or more
denominator vanishes. Writing W(1)/(a+|L(i,1)-C|), etc., would be
example, choosing a =1 might be appropriate. Another problem is that
changes in 1/denom are not directly comparable to changes in denom.
For small denom, a slight change makes a big difference to i/denom,
but for large denom, even a significant change might not produce much
of a difference in 1/denom. As an alternative, you could just maximize
F(i) = -W(1)*|L(i,1)-C| + W(2)*|L(i,2)| - W(3)*L(i,3) + W(4)*L(i,4).
Typically, you can choose a fixed normalization such as sum W(j) = 1.
You will then face the problem of estimating appropriate weights W(j).
Here is where personal preferences come into play. Your preferred
choice of W(j) might be different from that of your friend, and it
cannot be said that one of you is right and the other is wrong.
Methods have been developed to help people make these choices and
estimates. Textbooks on multiple objective decision making will have
chapters or sections on this topic.
I don't understand this question. If there is no ideal solution
because the I_j intersection is empty, then finding a weighted
solution using F(i) is one way of making the needed compromises. It is
not the only way, however, and some writers even consider it to be
flawed, especially in combinatorial problems that can have duality
gaps and non-convex pareto-optimal frontiers.
R.G. Vickson
===
Subject: Re: Optimization
Yes, obviously. I was just busting my head with the obvious on how to avoid
vanishing denominators, since the data includes that.
Understood.
Agreed. In my case I think it will be easy. They are essentially different
lamp data. In particular:
L[i,1]=Correlated Color Temperature
L[i,2]=Emulation of Black Body color of T=CCT (0..100%)
L[i,3]=Distance from Daylight on the CIE 1931 chromaticity diagram
L[i,4]=Lamp Efficiency
So, the weights can be chosen depending on the desired application. 
Obviously
if a user requires the best lamp efficiency, w(4) should be large, if he
desires a very good CCT w(1) should be large, etc.
-- 
I.N. Galidakis --- http://ioannis.virtualcomposer2000.com/
----------------------------------------------------------
There's ALWAYS a mistake somewhere
===
Subject: Re: Optimization
It depends on what you mean by work.  You're optimizing a weighted
average of the individual objectives.  OK, if that's what you want.
It's what Vickson referred to as a compromise.  There's no conflict:
he's just pointing out that this may or may not optimize the individual
objectives, which is what you said you wanted to do.
-- 
Robert Israel              israel@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            Vancouver, BC, Canada
===
Subject: Re: Optimization
I may have misstated what I wanted. I basically am looking for a 
compromise.
-- 
I.N. Galidakis --- http://ioannis.virtualcomposer2000.com/
----------------------------------------------------------
There's ALWAYS a mistake somewhere
===
Subject: Re: Optimization
Those are not constraints, they are objectives.
In general you can't optimize several different things at once, although
people try to do that all the time.  Look up multi-objective 
programming.
If you can come up with a way to compare two rows and decide which is
better, Maple can sort the rows.  Actually, Maple sorts lists rather
than matrices, so you can do something like this:
where F is a function that takes two rows A and B and returns true
if A should come before B, false otherwise.
  
Not if you're just rearranging the rows.
-- 
Robert Israel              israel@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            Vancouver, BC, Canada
===
Subject: The fundamental theorem of algebra and operator theory
Hi all:
http://www.arxiv.org/abs/math/0509113
It pretends to be a proof of the Fundamental Theorem of Algebra using
Fredholm operators. It looks totally worthless to me, but perhaps that I
am missing something here. For instance, at first sight it looks as if
the proof also works over the real field!
Jose Carlos Santos
===
Subject: Re: The fundamental theorem of algebra and operator theory
Actually I think there is something there, though the presentation leaves 
a lot to be desired.  The point is this.  Suppose p is a polynomial of 
q_k(z) = k^(-n) p(kz).  
Now consider the bounded linear operators q_k(U) where U is the
q_k(U) is non-surjective for sufficiently large n.  Fix such a k.
Now 1/q_k(z) is analytic in a neighbourhood of D, so it has
a Maclaurin series sum_{j=0}^infty c_j z^j with radius of convergence 
where you're using the complex field!].  Since ||U|| = 1, 
(1/q_k)(U) = sum_j c_j U^j converges, and  (1/q_k)(U) q_k(U) = I, so 
it is surjective after all, contradiction.  
Well, there may be some slight problems here.  For one thing, the fact
that if a function is analytic in a neighbourhood of D its Maclaurin 
I think, is to use Cauchy's estimates, and these in turn come from the 
Cauchy integral formula.  But if you have the Cauchy integral formula, 
you don't need to mess about with Fredholm operators.  You can simply 
say, if C is the unit circle, 
contradiction.   
-- 
Robert Israel              israel@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            Vancouver, BC, Canada
===
Subject: Re: The fundamental theorem of algebra and operator theory
It's certainly illiterate. The first problem I can see
is his assertion that P having no root implies that Q
has no root. Why?
Victor Meldrew
I don't believe it!
===
Subject: Re: The fundamental theorem of algebra and operator theory
Well, as those of us who know him from sci.math.research can
attest, his English is sometimes Farsical.  But my Farsi is non-
existent, so I will refrain from criticizing his literacy.
Because (up to interpreting the division symbol as plus or minus)
Q(z) = P(z plus or minus epsilon).  It's perfectly standard and quite
correct.
However I don't intend to read further.
Lee Rudolph
===
Subject: Tensor Visualization
am in a quandary as to how one can visualize (in Cartesian space) a rank-2
tensor of nine components.  A tensor of rank 1 (vector) has both magnitude
and direction and consists of 3 components.  The vector can be drawn as a
directed line segment.  A tensor of rank 2 (dyadic) has nine components,
John Wood (Code 5550)        e-mail: wood@itd.nrl.navy.mil                   

  
Naval Research Laboratory
4555 Overlook Avenue, SW
Washington, DC 20375-5337
===
Subject: Re: Tensor Visualization
If it is a symmetric tensor, the most common visualization is through
the
3-circle diagrams of Mohr (1882).   Applets at
http://engapplets.vt.edu/Mohr/java/nsfapplets/MohrCircles2-3D/mohrcircles2-3

d.htm
For asymmetric rank-2 there are the Cauchy dual ellipsoids.
===
Subject: Re: Tensor Visualization
Corrected web site:
http://www.engapplets.vt.edu/Mohr/java/nsfapplets/MohrCircles2-3D/Applets/ap

plet.htm
===
Subject: partial differentiation- pretty simple
Im trying to do the partial derivative w.r.t. x  of a function f=1/r,
where r^2=x^2+y^2+z^2
I have used the chain rule (d/dx(u^n)=n.(u(n-1)).(du/dx)
where u=x^2+y^2+z^2 and n= -1
This gives me the result fx=-x/(r^3)
However, this is not a partial derivative, it's the standard typwe of
derivative.
can anybody help me find the partial derivative of 1/r w.r.t. x?
I know its probably very simple but i cant seem to get my head around
it today
Adam
===
Subject: Re: partial differentiation- pretty simple
            days. My association with the Department is that of an alumnus.
This is incorrect. You should be using n=-1/2, since your function is
1/sqrt(x^2+y^2+z^2),
not
1/(x^2+y^2+z^2).
However, you seem to have done it correctly. Since f =
(x^2+y^2+z^2)^{-1/2}, the partial derivative with respect to x is:
(-1/2)(x^2+y^2+z^2)^{-3/2}*(2x) = -x/(x^2+y^2+z^2)^{3/2} = -x/r^3,
where r=(x^2+y^2+z^2)^{1/2}, which is what you say below:
I do not understand what you mean with this However comment.
The partial derivative with respect to x is the result of taking the
standard type derivative of the function, treating all variables
other than x as constants. So in this case, you have a function of x
of the form   (x^2+c)^{-1/2},  where c is a constant, namely
y^2+z^2. This is what you did. So what is the problem?
-- 
It's not denial. I'm just very selective about
 what I accept as reality.
    --- Calvin (Calvin and Hobbes by Bill Watterson)
Arturo Magidin
magidin-at-member-ams-org
===
Subject: Re: partial differentiation- pretty simple
You make sense.
Silly me, I forgot to check the true meaning of partial
differentiation!
d'oh!
===
Subject: Re: partial differentiation- pretty simple
            days. My association with the Department is that of an alumnus.
I think you mean me, but it is hard to tell since you failed to
provide context for your response.
newsgroup! Please remember to quote and trim the message you are
replying to in order to provide context.
-- 
It's not denial. I'm just very selective about
 what I accept as reality.
    --- Calvin (Calvin and Hobbes by Bill Watterson)
Arturo Magidin
magidin-at-member-ams-org
===
Subject: Help on solving a differential equation
Could somebody help me on the I.V.P.
y' + ay = int_0^b y dx, y(0) = c
I am reading in a book that this particular equation can be solved
using the method of parameters changing. What I understand from what
I read in the book, is that, if we substitute m = int_0^b y dx, then
we can find a solution which will contain m.
But how do we find m then?
PS: Can somebody confirm that method of parameters changing is a
proper term?
===
Subject: Re: Help on solving a differential equation
By integrating the solution from x=0 to b, setting the result equal to m,
and solving the resulting equation for m.  That may or may not be possible,
depending on the values of a, b and c.
 
I think you're talking about the method of variation of parameters.
That says, once you have the solution of the homogeneous equation
(in this case the solution of y' + a y = 0 is y(x) = A exp(-ax)), 
you change the arbitrary constant A to A(x), plug the result
(y(x) = A(x) exp(-ax)) into your differential equation, and get a simpler
differential equation for A(x).  
-- 
Robert Israel              israel@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            Vancouver, BC, Canada
===
Subject: Re: Help on solving a differential equation
What is the name/author of this book?
You have y = f(x,m), so you get an equation of the form m = int_0^b
f(x,m) dx.
R.G. Vickson
===
Subject: RMS and Average power for phase dimmed ac waveform
I am trying to calculate the average power in an ac signal which has been 
dimmed using forward phase control, for example;
(Best viewed using a fixed font)
                  ...             ...
                 .   .           .   .
                .     .         .     .
              ------------------------------------ 0V
                        .     .         .     .
                         .   .           .   .
                          ...             ...
is dimmed to
                  ...             ...
                  |  .            |  .
                  |   .           |   .
              ------------------------------------ 0V
                  |    |  |   .           |   .
                  | p  |  |  .            |  .
I have attempted to calculate the RMS voltage using the formula for a 
continuous function at http://en.wikipedia.org/wiki/Root_mean_square.
phase  RMS
0      0
20     0.046926234
40     0.127950381
60     0.221077537
80     0.312254002
100    0.390509203
120    0.448469311
140    0.483351528
160    0.497793058
180    0.5
As it is a symmetrical signal, these values are doubled and a relative RMS 
is obtained.
squaring the RMS.
The RMS values seem correct, but the average power ones do not seem quite 
right. I am comparing results to that in figure 16.4 in 
Are my results / is my method correct??
Any help is highly appreciated,
  Nick
===
Subject: Re: RMS and Average power for phase dimmed ac waveform
?? At 180 degrees must be 1/sqrt(2)
For full wave use:
  Vrms = sqrt( (p-.5*sin(2*p))/(2*pi) )
  (p: phase angle in radians)
That formula gives (phase angle in degrees)
phase   Vrms
0               0.00000
20              0.06636
40              0.18095
60              0.31265
80              0.44159
100             0.55226
120             0.63423
140             0.68356
160             0.70399
180             0.70711
Eduardo.
===
Subject: Re: RMS and Average power for phase dimmed ac waveform
How do I go from this to working out the average power of the signal, 
relative to the power at p = 180, can I simply square it and scale it??
  Nick
===
Subject: Re: RMS and Average power for phase dimmed ac waveform
  P(phase) = Pfull * ( phase - .5*sin(2*phase))/pi
Eduardo.
===
Subject: Re: RMS and Average power for phase dimmed ac waveform
If I had inductive loads, would the value depend on the inductance, i.e. 
would I have to work out Irms also and then multiply, or is there a simpler 

way??
  Nick
===
Subject: After the Deletion of Google Answers U Got Questions Fills the Gap 

Answering and Asking the Tough Questions
My friend asked some tough questions 
http://ugotquestions.blogspot.com/2007_05_01_archive.html
unlike yahoo answers ( Which Generates Content with Answers ) U got
questions picks only the best, Real Person Questions.,yeah so there is
this second book called E.T. and the BOOK OF THE GREEN PLANET... yeah,
what happens in it... i heard he dies, and what happend to elliot....
this has been bugging me for years...so someone please tell
mehttp://ugotquestions.blogspot.com/2007_04_01_archive.html - i start
my car and shut it off 4 to 5 times it starts fine but when i continue
repeat this procedure for another 2 to 3 times then it dies. it doesnt
start at all. the headlights and all other lights dont go dim so might
not be the battery. then i have to wait for 3 to 5 minutes for it to
start again. it does crank slowly sometime then start. the alternator
was replaced 2 years ago so was the battery. the car has 129000miles
its 01 maxima. automatic. as far as i think it could be the
starter...http://ugotquestions.blogspot.com/2007/05/y-alert-yahoo-
answers_7473.html 1- if you ask anyone in the town that: Are you a
wise human? and he says yes, what you can say about him? 2- tree
mathematicians are talking about their trip to this town: 1st man
says: in my trip to the town, I ask John (a people of the town) are
you a wise human? and with his reply, I could not rcognize what is he.
2nd man says: I also ask John are you a loony human? and with his
reply, I could not recognize what is he too. 3rd man says: I also ask
John are you a wise devil? and with his...http://
ugotquestions.blogspot.com/2007/05/y-alert-yahoo-answers_7075.html
Which major should I choose before law school if I want to practice
criminal and civil law and I also want in the future be a judge.The
majors that I like are criminal justice,politcal science and
finance.But I don't know which should I choose.I already know the
speech that law schools don't care about your mayor but I want to know
which one of those three could help me more in my goals fo practice
ugotquestions.blogspot.com/2007/05/y-alert-yahoo-answers_6058.html
Everyday I wake up to my mom yelling about something I did. All she
does is come home from work sit on the couch and watch a movie she
gets from blockbuster everyday while we are suppose to be doing
chores. She dosnt let us watch her movies becuase she pays for them,.
we dont have cable and we havnt gone grocery shopping in two months
becuase she says we dont hav the money.( while she gets take out
everyday at work and a blockbuster movie everyday to. )She told me i
cant wash my clothes for...
===
the Gap Answering and Asking the Tough Questions
Excessive crossposting.
===
Subject: normal extensions - splitting fields 
The Galois theory guy was talking about the fact that if an extension 
(finite) E is the splitting field of a non separable polynomial than it 
isn't a galois extension and it ain't a separable extension. Still, it is 
normal. Indeed he claimed that:
1. The fact that E is a splitting field for a polynomial f over F implies 
that every element a of E has a minimum polynomial that splits in linear 
factors in E[x]
2. If E is an extension of finite degree of F, then every a of E has a 
minimum polynomial in F that splits in linear factors in E[x]  which means 
that E is a splitting field for a polynomial that belongs to F[x].
He proved this fact (2) by posing E=F(a_1,a_2,a_3,...a_n), each a_i 
algebraic over F with minimum polynomial f_i. He than claimed that E is the 

splitting field of the product of all the f_i. I don't quite get this. How 
can he say that the product of all the f_i splits in linear factors in E[x]? 

Why can't any of the f_i have a root that isn't in E?
????
===
Subject: Re: normal extensions - splitting fields
|The Galois theory guy was talking about the fact that if an extension
|(finite) E is the splitting field of a non separable polynomial than
it
|isn't a galois extension and it ain't a separable extension. Still,
it is
|normal. Indeed he claimed that:
|1. The fact that E is a splitting field for a polynomial f over F
implies
|that every element a of E has a minimum polynomial that splits in
linear
|factors in E[x]
|2. If E is an extension of finite degree of F, then every a of E has
a
|minimum polynomial in F that splits in linear factors in E[x]  which
means
|that E is a splitting field for a polynomial that belongs to F[x].
Your (1.) and (2.) look like sketches of proofs that if E is normal,
then these conditions are equivalent: (a) E is the splitting field of
a polynomial with coefficients in F, and (b) E is an extension of
finite degree of F. In (2.), I don't think E is being assumed to be a
splitting field of a polynomial; it appears that that's what's to be
proven. I also don't see the non-separability of the polynomial
playing
a role. So I suspect in (1.) and (2.) he wasn't still assuming that
E was a splitting field of a non-separable polynomial.
|He proved this fact (2) by posing E=F(a_1,a_2,a_3,...a_n), each a_i
|algebraic over F with minimum polynomial f_i. He than claimed that E
is the
|splitting field of the product of all the f_i. I don't quite get
this. How
|can he say that the product of all the f_i splits in linear factors
in E[x]?
|Why can't any of the f_i have a root that isn't in E?
My guess would be that it had already been proven that if a polynomial
P with coefficients in F has a root r in a normal extension E, then
it splits in E. (Sometimes instructors leave results out by accident,
so that's possible too.) In one way of presenting these results, this
is done by considering an automorphism of an algebraic closure
of E that fixes F and takes the root r to a given other root r'. Since
E is normal, this automorphism takes E to E, hence r' is in E.
Keith Ramsay
===
Subject: Geomview 1.9 released
Full-Name: Lloyd Wood
http://www.geomview.org/
Geomview is an interactive program for creating, viewing, and
manipulating 3D and higher-dimensional geometric objects. Geomview can
be used as a standalone viewer for static objects or as a display
engine for other programs which produce dynamically-changing geometry.
Geomview 1.9 is the first packaged release of Geomview in six years.
Geomview builds with current compilers on current platforms, including
gcc 4.0 on Mac OS X. The 1.9 releases include improvements to
rendering, to use of higher dimensions, new commands, and an
integrated hypertext manual. Download Geomview 1.9.1 now!
http://www.geomview.org/
===
Subject: Math (Mathematics)
Math (Mathematics)
http://www.academic-genealogy.com/math.htm
Math for everyone: learning basic number systems,
K-12 educational resources for students and teachers,
advanced concepts and connections.
===
Subject: homomorphisms
Are there any other group homomorphisms from Z_6 to Z_45 besides f(x)
= 0?
===
Subject: Re: homomorphisms
How about f( x mod 6 ) = x mod 45?
===
Subject: Re: homomorphisms
Nntp-Posting-Host: apps.cwi.nl
    That is not well-defined.  For ezample, the equivalence
classes (2 mod 6) and (26 mod 6) are the same, but
those of (2 mod 45) and (26 mod 45) are different.
-- 
44 months after Japan attacked Pearl Harbor, Japan surrendered.
49 months after US attacked Iraq, it's time for the US to surrender.
pmontgom@cwi.nl    Microsoft Research and CWI      Home: Bellevue, WA
===
Subject: Re: homomorphisms
===
Subject: Re: homomorphisms
Consider the possible orders of elements of Z_n, for arbitrary n.
Now of M is a homomorphism from Z_6 to Z_45, and x is an element of
Z_6, ask yourself what the order of Mx can possibly be.
-- 
Chris Henrich
http://www.mathinteract.com
God just doesn't fit inside a single religion.
===
Subject: Re: homomorphisms
 i'm not sure i understand...
===
Subject: Re: homomorphisms
Do you know what the order of an element is? 
If so, can you find the order of each element of Z_6? 
of Z_45? 
If M is a group homomorphism, and you know something 
about the order of a group element x, can you say anything 
useful about the order of M(x)?
-- 
===
Subject: Re: homomorphisms
does it matter if these are to be additive groups?
===
Subject: coset - subgroups
if two different subgroups with two different right cosets are equal
as sets, do the subgroups have to be equal?
===
Subject: Re: coset - subgroups
Yes.  What happens if you multiply a coset by the inverse of any
element of that coset?
===
Subject: Re: coset - subgroups
 ..you get the coset?
===
Subject: Re: coset - subgroups
No (well, not always). Did you try it? Pick a group, 
any group, pick a coset, pick an element in that coset, 
multiply every element of the coset by the inverse of 
the element you chose - do it, see what you get.
-- 
===
Subject: Solutions Manual
how long does it take to get a copy of the solutions manual...i would
need it ASAP!
===
Subject: Complete electronic solution manual in PDF! Get it in hours!
I have the complete electronic SOLUTION MANUAL in PDF format
containing ALL (odd and even - except where noted) solutions for the
books listed below. These are not paper books, they are ebooks.
The price is $8 each. I accept payment through paypal only. If
interested, just send me an email to deltabooks@gmail.com mentioning
which solution manual you want. I will promptly reply you with details
of where you can send the paypal payment. As soon as the payment is
received, a download link for the solution manual will be sent to your
email address within a few hours. Fast service!
NB: Don't post replies here. If interested, send me an email to
deltabooks@gmail.com
Books for which I have electronic solution manual:
1. Calculus: Early Transcendentals (5th Ed) by James Stewart [ISBN:
0534393217]
2. Digital Communications (4th Ed) by Proakis, John [ISBN:
0072321113]
3. Engineering Mechanics - Dynamics (10th Ed) by Russell C. Hibbeler
[ISBN: 0131416782]
4. Engineering Mechanics - Statics (10th Ed) by Russell C. Hibbeler
[ISBN: 0131411675]
5. Engineering Mechanics , Dynamics (5th Ed) by J. L. Meriam, L. G.
Kraige [ISBN: 0471406457]
6. Electric Machinery Fundamentals (4th Ed) by Stephen J. Chapman
[ISBN: 0072465239]
7. First Course in Probability, A (7th Ed) by Ross, Sheldon [ISBN:
0131856626]
8. Vector Mechanics for Engineers, Statics (7th Ed) by Beer, Ferdinand
P.; Johnston Jr., E [ISBN: 0072930780]
9. Microwave and Rf Design of Wireless Systems (1st Ediiton) by Pozar,
David M. [ISBN: 0471322822]
10. Communication Systems Engineering (2nd Ed) by Proakis, John G
[ISBN: 0130617938]
11. Introduction to Solid State Physics (8th Ed) by Charles Kittel
[ISBN: 047141526X]
12. Semiconductor Physics And Devices (3rd Ed) by Donald Neamen [ISBN:
0072321075]
13. Advanced Modern Engineering Mathematics (3rd Ed) by Glyn James
[ISBN: 0130454257]
14. Physical Chemistry (7th Ed) by Julio Paula, Peter Atkins [ISBN:
0716735393]
15. Introduction to Quantum Mechanics (2nd Edition) by David J.
Griffiths [ISBN: 0131118927]
16. Digital Signal Processing by Thomas J. Cavicchi [ISBN:
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17. Electric Circuits (7th Ed) by Nilsson, James W.; Riedel, Susan
[ISBN:0131465929]
18. Computer Networks (4th Ed) by Tanenbaum, Andrew S. [ISBN:
0130661023]
19. Adaptive Filter Theory (4th Ed) by Haykin, Simon [ISBN:
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20. Wireless Communications: Principles and Practice (2nd Ed) by
Theodore Rappaport [ISBN: 0130422320]
21. Principles of Communication: Systems, Modulation and Noise (5th
Ed) by R. E. Ziemer, W. H. Tranter [ISBN: 0471392537]
22. Automatic Control Systems (8th Ed) by Kuo, Benjamin C.;
Golnaraghi, Farid [ISBN: 0471134767]
23. Microwave Engineering (3rd Ed) by Pozar, David M. [ISBN:
0471448788]
24. Discrete-Time Signal Processing (2nd Ed) by Oppenheim, Alan V
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25. Introduction to Electrodynamics (3rd Ed) by Griffiths, David
[ISBN: 013805326X]
26. Communications Systems (4th Ed) by Haykin, Simon [ISBN:
0471178691]
27. Control Systems Engineering (4th Ed) by Nise, Norman S. [ISBN:
0471445770]
28. Design of Analog CMOS Integrated Circuits (1st Ed) by Behzad
Razavi [ISBN: 0072380322]
29. Signals and Systems (2nd Ed) by Alan V. Oppenheim, Alan S. Willsky
[ISBN: 0138147574]
30. Signal Processing and Linear Systems by B. P. LAthi [ISBN:
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31. Engineering Circuit Analysis (6th Ed) by William H. Hayt, Jack
Kemmerly, Steven M. Durbin [ISBN: 0072853204]
32. RF Circuit Design: Theory and Applications by Reinhold Ludwig,
Pavel Bretchko [ISBN: 0130953237]
33. Engineering Electromagnetics (6th Ed) by William H. Hayt, John A.
Buck [ISBN: 0072551666]
34. Physics for Scientists and Engineers (6th Ed) by Raymond A.
Serway, John W. Jewett [ISBN: 0534408427]
35. Antennas for All Applications (3rd Ed) by John D. Kraus, Ronald J.
Marhefka [ISBN: 0072321032]
36. Digital Communications: Fundamentals and Applications (2nd Ed) by
Bernard Sklar [ISBN: 0130847887]
37. Digital Image Processing (2nd Ed) by Rafael Gonzalez, Richard
Woods [ISBN: 0201180758]
38. Fundamentals of Digital Logic with Verilog Design (1st Ed) by
Stephen Brown, Zvonko Vranesic [ISBN: 0072838787]
39. Electronic Circuit Analysis (2nd Ed) by Donald Neamen [ISBN:
0072451947]
40. Fundamentals of Electric Circuits (2nd Ed ) by Charles Alexander,
Matthew Sadiku [ISBN: 0073048356]
41. Device Electronics for Integrated Circuits (3rd Ed) by Richard
Muller, Theodore Kamins, Mansun Chan [ISBN: 0471593982]
42. Linear Circuit Analysis: Time Domain, Phasor, and Laplace
Transform Approaches (2nd Ed) by Raymond DeCarlo, Pen-Min Lin [ISBN:
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43. Computer Networks: A Systems Approach (3rd Ed) by Larry L.
Peterson, Bruce S. Davie [ISBN: 155860832X]
44. Fundamentals of Electromagnetics with Engineering Applications by
Stuart M. Wentworth [ISBN: 0471263559]
45. Feedback Control of Dynamic Systems (4th Ed) by Gene Franklin,
David Powell, Abbas Naeini [ISBN: 0130323934]
46. Fundamentals of Physics (7th Ed) by David Halliday, Robert
Resnick, Jearl Walker [ISBN: 0471216437]
47. Introduction to Electric Circuits (6th Ed) by Richard C. Dorf,
James A. Svoboda [ISBN: 0471447951]
48. Fundamentals of Thermodynamics (5th Ed) by Richard E. Sonntag,
Claus Borgnakke, Gordon J. Van Wylen [ISBN: 047118361X]
49. Semiconductor Device Fundamentals (1st Ed) by Robert F. Pierret,
[ISBN: 0201543931]
50. Applied Numerical Analysis (6th Ed) by Curtis F. Gerald, Patrick
O. Wheatley [ISBN: 0321133048]
51. Digital Signal Processing (4th Ed) by John G. Proakis, Dimitris K
Manolakis [ISBN: 0131873741]
52. Physics for Scientists and Engineers (1st Ed) by Randall D. Knight
[ISBN: 0805386858]
53. Physics for Scientists and Engineers, Volume 1 (1st Ed) by Randall
D. Knight [ISBN: 0805389644]
54. Physics for Scientists and Engineers, Volume 4 (1st Ed) by Randall
D. Knight [ISBN: 0805389733]
55. Vector Mechanics for Engineers: Dynamics (7th Ed) by Beer,
Ferdinand P.; Johnston Jr., E [ISBN: 0073209260]
56. Physics: Principles with Applications (6th Ed) by Douglas C.
Giancoli [ISBN: 0130606200]
57. Physics for Scientists and Engineers (5th Ed) by Paul A. Tipler,
Gene Mosca [ISBN: 0716783398]
58.Materials Science and Engineering: An Introduction (6th Ed) by
William D. Jr. Callister [ISBN: 0471135763]
59. Engineering Mechanics - Statics (11th Ed) by Russell C. Hibbeler
[ISBN: 0132215004]
60. Elementary Differential Equations and Boundary Value Problems (8th
Ed) by William E. Boyce, Richard C. DiPrima [ISBN: 0471433381] (Mostly
all solutions, only a few missing)
61. Partial Differential Equations and Boundary Value Problems with
Fourier Series (2nd Ed) by Nakhle H. Asmar [ISBN: 0131480960] (Student
solution manual)
Thornton , Jerry B. Marion [ISBN: 0534408966]
63. Power System Analysis by(1st Ed) John Grainger, Jr., William
Stevenson [ISBN: 0070612935]
64. Fundamentals of Applied Electromagnetics (1st Ed) Fawwaz Ulaby
[ISBN: 013185089X]
65. Microelectronics (2nd Ed) by Jacob Millman, Arvin Grabel [ISBN:
007100596X]
66. Microeconomic Theory by Andreu Mas-Colell, Michael D. Whinston,
Jerry R. Green [ISBN: 0195073401]
67. Econometric Analysis (5th Ed) by William H. Greene [ISBN:
0130661899]
68. Fluid Mechanics (5th Ed) by Frank M. White [ISBN: 0072831804]
69. Mechanical Engineering Design (7th Ed) by Charles Mischke, Joseph
Shigley, Richard Budynas [ISBN: 0072921935]
70. Linear Algebra And It's Applications (3rd Ed) by David C. Lay
[ISBN: 0321287134]
71. Single Variable Calculus (5th Ed) by James Stewart [ISBN:
0534393306]
72. Modern Physics (4th Ed) by Paul Tipler, Ralph Llewellyn [ISBN:
0716743450]
73. Thermodynamics (5th Ed) by Michael Boles, Yunus Cengel [ISBN:
0073107689]
74. University Physics with Modern Physics (11th Ed) by Hugh Young,
Roger Freedman [ISBN: 0805387773]
75. Fundamentals of Thermal-Fluid Sciences (2nd Ed) by Yunus Cengel,
Robert Turner [ISBN: 0072976756]
76. Fundamentals of Engineering Thermodynamics (5th Ed) by Michael
Moran, Howard Shapiro [ISBN: 0471274712]
77. Principles and Applications of Electrical Engineering (5th Ed) by
Giorgio Rizzoni [ISBN: 0073220337]
78. Modern Digital and Analog Communication Systems (3rd Ed) by B. P.
Lathi [ISBN: 0195110099]
79. Mechanics of Materials (6th Ed) by Russell C. Hibbeler [ISBN:
013191345X]
80. Introduction to Fluid Mechanics (6th Ed) by Robert Fox, Alan
McDonald, Philip Pritchard [ISBN: 0471202312]
81. Fundamentals of Heat and Mass Transfer (5th Ed) by Frank
Incropera, David DeWitt [ISBN: 0471386502]
82. Engineering Mechanics - Statics (5th Ed) by J. L. Meriam (Author),
L. G. Kraige [ISBN: 0471406465]
83. Materials Science and Engineering: An Introduction (7th Ed) by
William D. Jr. Callister [ISBN: 0471736961]
===
Subject: Re: I don't like the Axiom of Choice
The Hartogs function of the power set of the integers
has cofinality greater than omega with or without choice.
There are oodles of models not satisfying choice, even
if they satisfy restricted versions.  I suggest you
read _Consequences of the Axiom of Choice_ by Paul
Howard and Jean E. Rubin.  
At least most of the models start with one satisfying
choice and upon which a group operates; the group 
preserves the element relation.  One keeps the elements
of the model which, with their elements, and their
elements, etc., are invariant under large subgroups.
For the Cohen models, this can be done because one
cannot compare sets of sets of integers under forcing.
-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558
===
Subject: Re: I don't like the Axiom of Choice
|Given a proof in which choice is used of a statement P we can
transform it
|into a proof of P is true in the constructible hierarchy in which
choice
|is not used. For arithmetical statements P is true in the
constructible
|hierarchy is equivalent to P itself. Combining these results yields
the
|observation that choice is never necessary to prove an arithmetical
|statement, which is indeed not obvious.
We can go even further. In Eliminating the Continuum Hypothesis,
Richard A. Platek, Journal of Symbolic Logic, Vol. 34, No. 2 (1969),
219-225, it shows that a Pi-1-4 sentence provable from ZF+AC+GCH is
provable from ZF. A Pi-1-4 sentence is one of the form (for all S1)
(there exists S2)(for all S3)(there exists S4) P(S1, S2, S3, S4) where
S1, S2, S3, and S4 are sets of integers, and P is formula with only
quantifiers over integers. Here GCH is the generalized continuum
hypothesis, that for each infinite cardinal X, the next cardinality
after X is 2^X. If I remember correctly the result is sharp in the
sense that there's a Sigma-1-4 sentence (like a Pi-1-4 but with the
quantifier alternation starting with a there exists S1) provable
from
ZFC but not ZF. The original poster may take comfort from this: the
Pi-1-4 theorems of mathematics cover a lot of what we actually
care about. Even in cases where you're dealing with sets of reals,
they can often be encoded as single reals.
The axiom of choice was used in the proof of Fermat's Last Theorem, if
you count the results Wiles built on top of as part of the proof.
There's an extension of the field Q_p of p-adic numbers known as C_p,
and from AC it's possible to prove that C_p is isomorphic as a field
(in a horribly discontinuous way) with the complex numbers C. Once you
assume the axiom of choice, then each of them as a field is just an
algebraically closed field of characteristic 0, and transcendence
degree
the cardinality of the continuum. This isomorphism is used in the
proof
of some result that Wiles used.
I was told, however, that someone had mentioned around that time how
it was possible to avoid using this isomorphism, simply in number
theory
terms, with no reference to mathematical logic. My impression is that
the
isomorphism was used just as a kind of convenience.
Keith Ramsay
===
Subject: Re: I don't like the Axiom of Choice
but always had trouble remembering where I saw the proof. 
There's one aspect here that might be puzzling to some readers -- though
since it's puzzling only when you know enough of the technical details 
about
constructibility those puzzled are probably capable of thinking it through
themselves. The proof that the axiom of choice is never necessary in 
proving
an arithmetical statement outlined by me, i.e. noting that P is true in 
the
constructible hierarchy implies P for arithmetical statements and thus we
can remove choice by relativizing the proof to the constructible hierarchy,
generalizes, by the Shoenfield absoluteness theorem, to Sigma-1-3 
statements.
However, this is the best we can do, that is V=L is not conservative for
Pi-1-3 statements or statements of greater logical complexity. Platek's
proof is by a different technique, and shows that ZFC+GCH+AC, instead of 
ZFC + V=L, is conservative for Pi-1-4 statements.
-- 
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
Wovon man nicht sprechen kann, daruber muss man schweigen
 - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
===
Subject: Re: I don't like the Axiom of Choice
I don't like it either, but not for the stupid logic you say later.
That's true, but what you say next is garbage:
There's nothing wrong with the math that yields Hilbert's Hotel.
It comes directly out of the most basic study of automatons.
Consider a program that prints out the number of seconds since midnight.
Consider another program that prints out the number of seconds
since one second after midnight.
The output of the two programs are relatively offset by one (second).
By one logic, they produce corresponding output, parallel streams
of numbers that are numerically offset by one.
But by another logic, looking just at the *set* of numbers
eventually produced by each program, one program produces a number
not produced by the other.
Hence the sequences of numbers are order-isomorphic,
but the sets of numbers have one set larger than the other.
That's really the principle of Hilbert's Hotel.
So what makes you think Hilbert's Hotel is just making up claims
without any evidence they are true? It's pretty obvious to me that
if both programs are allowed to run forever, they produce exactly
the same amount of output, yet produce sets that have a proper
subset relation. Why do you have so much trouble accepting such facts?
Why don't pyramid scams or chainletters really work? Because the
total size of available members is finite. If there were an
unlimited (infinite) number of available members, the scam really
could work. Everyone who joins could achieve an eventual profit.
Think of Ponzi's Hotel! Grok it in fullness!!
Live from New York^H^H^H^H^H^H^H^HLos Angeles, it's the Paris Hilton Hotel!
===
Subject: Re: I don't like the Axiom of Choice
Is this possible within ZF?   There is always a set, *the* set, of
countable ordinals.  If this had to be of cofinality only omega,
then it would be a countable union of countable sets.
That wouldn't necessarily require for it to be a countable set itself,
for any old sets, but maybe for a well-ordered set of ordinals it
would?
Would it?  I can't tell, either way.
Maybe.  It's hard to know what consequences of non-AC are
pathological,
when (a) we're so used to considering it true and applying it almost
automatically, and (b) there are plenty of pathologies in ZFC anyway.
Including a fair few that come specifically *because of* AC!  It is
hard
to know what is more pathological than what else, sometimes.
Well yes, for the latter, I think so.  One can imagine a world of sets
that
include only those that are definable in some sense.  If any sense
can
be made of this, (and I suspect it can), then all of ZF would apply to
it,
but not AC.
----------------------------------------------------------------------
       Bill Taylor             W.Taylor@math.canterbury.ac.nz
----------------------------------------------------------------------
Set theory is a shotgun marriage - between well-ordering and power-
set.
The two parties get along OK; but they hardly seem made for each
other.
----------------------------------------------------------------------
===
Subject: Re: I don't like the Axiom of Choice
|Well yes, for the latter, I think so.  One can imagine a world of
sets
|that
|include only those that are definable in some sense.  If any sense
|can
|be made of this, (and I suspect it can), then all of ZF would apply
to
|it,
|but not AC.
I'm not sure what the best way to make your idea rigorous is, but
it's not clear that it will fail AC. The minimal transitive model of
ZF, for example, satisfies V=L, and consequently AC. In general,
inside of each model of ZF, there is an internal L which is a model
of ZF+V=L, although it does not typically contain all sets definable
in the containing model.
Suppose we take the countable set of elements of a model of ZF
that are first-order definable in it. I don't actually know offhand
whether that's always a countable model of ZF, or if so under
what conditions it satisfies AC. Perhaps if the containing model
satisfies some of the usual assumptions contrary to V=L, the
subset will be a model of ZF violating AC. But I don't find it
at all obvious.
Keith Ramsay
===
Subject: Re: I don't like the Axiom of Choice
It is consistent with ZF that omega_1 has cofinality omega.
Why would the axioms of ZF apply? In particular, why would the axiom of
powersets and the axiom of replacement apply? The most straightforward
interpretation of 'definable' would give us something like L_omega_1^CK in
which not all axioms of set theory hold. Also, while it is clear that the
conception of sets as definable -- in whatever sense -- collections does 
not
justify choice, it's not clear how it justifies the failure of choice.
-- 
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
Wovon man nicht sprechen kann, daruber muss man schweigen
 - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
===
Subject: Re: Comprehensive Solution Manual for Textbooks
i d like to buy the correct answer for the book Microeconomics - Jeffrey 
Perloff (4th edition) (ISBN: 0321414527) please reply me as soon as possible 

===
Subject: Re: Comprehensive Solution Manual for Textbooks
hey,
who did you order the solution manual for  Elementary Number Theory
from?
I really really need it, and by teusday. I'll buy it from you if your
selling.
dave
===
Subject: Re: Comprehensive Solution Manual for Textbooks
===
Subject: Re: Comprehensive Solution Manual for Textbooks
Updated List per May 8, 2007
I have the current edition of these comprehensive solutions manual for
the following textbooks in electronic format (PDF/Word). The solutions
manual are comprehensive with answers to both even & odd problems in
the text. The price is US$35 for each.
There are two methods of payments. One is through PAYPAL (if you have
a Paypal account) and another through PROPAY (if you don't have a
Paypal and you only have a credit/debit card).
Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If
you could not find the book you are looking for, please let me know, I
********************************
Fundamentals of Organic Chemistry - John McMurry - Test Bank (5th
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Fundamentals of Probability, with Stochastic Processes - Saeed
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Fundamentals of Signals and Systems - Edward Kamen (3rd edition)
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Fundamentals of Statistics -  Michael Sullivan (2nd edition) (ISBN:
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Further Mathematics for Economic Analysis - Knut Sydsaeter et al (1st
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Geometry: Theorems and Constructions - Allan Berele (1st edition)
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High-Speed Networks and Internets: Performance and Quality of Service
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Income Tax Fundamentals 2006 - Gerald E. Whittenburg (24th edition)
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Interactive Statistics - Martha Aliaga, Brenda Gunderson (3rd edition)
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Intermediate Accounting - James D. Stice (16th edition) (ISBN:
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International Accounting - Frederick Choi (5th edition) (ISBN:
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International Economics - Charles Sawyer, Richard Sprinkle (2nd
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International Economics - James Gerber (3rd edition) (ISBN:
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International Economics: Theory And Policy - Paul Krugman, Maurice
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International Money and Finance - Michael Melvin (7th edition) (ISBN:
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Introduction to Abstract Algebra - Olympia Nicodemi (1st edition)
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Probabilistic Systems and Random Signals - Abraham Haddad (1st
edition) (ISBN: 0130094552)
Probability and Statistical Inference - Robert Hogg, Eliot Tanis (7th
edition) (ISBN: 0131464132)
Probability and Statistics - Morris DeGroot, Mark Schervish (3rd
edition) (ISBN: 0201524880)
Probability and Statistics for Engineers - Richard Johnson, Irwin
Miller, John Freund (7th edition) (ISBN: 0131437453)
Probability Random Variables, and Stochastic Processes - Papoulis et
al (4th edition) (ISBN: 0073660116)
Process Control Instrumentation Technology - Curtis Johnson (8th
edition) (ISBN: 0131194577)
Quantum Chemistry and Spectroscopy - Thomas Engel (1st edition) (ISBN:
0805339795)
Solid State Electronic Devices - Ben Streetman (6th edition) (ISBN:
013149726X)
Spectral Analysis of Signals - Peter Stoica, Randolph Moses (1st
edition) (ISBN: 0131139568)
Statics and Strengths of Materials -  Harold I. Morrow (6th edition)
(ISBN: 0131719777)
Statistics for Business and Economics -  Paul Newbold,  William L.
Carlson (6th edition) (ISBN: 0132203847)
Statistics for Business and Economics - David R. Anderson (Test Bank)
(10th edition) (ISBN: 0324360681)
Statistics for Management and Economics - Gerald Keller (7th edition)
(ISBN: 0534491243)
Statistics for Science and Engineering - John Kinney (1st edition)
(ISBN: 0201437201)
Statistics for the Life Sciences - Myra Samuels (3rd edition) (ISBN:
013041316X)
Strategic Management and Business Policy - Tom Wheelen (10th edition)
(ISBN: 0131494597)
Structure and Interpretation of Signals and Systems - Edward Lee,
Pravin Varaiya (1st edition) (ISBN: 0201745518)
Technical Calculus with Analytic Geometry -  Allyn J. Washington (4th
edition) (ISBN: 0201711125)
Theory of Asset Pricing -  George Pennacchi (1st edition) (ISBN:
032112720X)
Thermodynamics: An Engineering Approach - Yunus Cengel (5th edition)
(ISBN: 0073107689)
Thomas' Calculus -  George B. Thomas, Jr. (11th edition) (ISBN:
0321185587)
Understanding Modern Economics - Roger Miller (1st edition) (ISBN:
0321245822)
Vector Calculus - Susan Colley (3rd edition) (ISBN: 0131858742)
West Federal Taxation 2007 Comprehensive - Eugene Willis (30th
edition) (ISBN: 0324313497)
West Federal Taxation 2007 Corporations - William Hoffman (30th
edition) (ISBN: 0324313616)
West Federal Taxation 2007 Individual - Eugene Willis, William Hoffman
(30th edition) (ISBN: 0324399618)
West's Business Law - Kenneth W. Clarkson (10th edition) (ISBN:
0324303904)
Wireless Communications & Networks - William Stallings (2nd edition)
(ISBN: 0131918354)
===
Subject: Re: Comprehensive Solution Manual for Textbooks
Updated List per May 8, 2007
I have the current edition of these comprehensive solutions manual for
the following textbooks in electronic format (PDF/Word). The solutions
manual are comprehensive with answers to both even & odd problems in
the text. The price is US$35 for each.
There are two methods of payments. One is through PAYPAL (if you have
a Paypal account) and another through PROPAY (if you don't have a
Paypal and you only have a credit/debit card).
If you are interested, please email me at
sbooks4sale[at]hotmail[dot]com
******************************************
Accounting Chapters 1-13 - Charles T. Horngren et al (7th edition)
(ISBN: 0132249952)
Accounting Chapters 12-25 - Charles T. Horngren et al (7th edition)
(ISBN: 0132249960)
Accounting Chapters 1-25 - Charles T. Horngren et al (7th edition)
(ISBN: 0132439603)
Accounting Chapters 1-26 - Charles T. Horngren et al (6th edition)
(ISBN: 0131088513)
Accounting Concepts and Applications - Steve Albrecht (9th edition)
(ISBN: 0324187564)
Accounting Information Systems - James Hall (5th edition) (ISBN:
0324312954)
Accounting Information Systems - Marshall Romney, Paul Steinbart (10th
edition) (ISBN: 0131475916)
Accounting Information Systems - Ulric J. Gelinas (7th edition) (ISBN:
0324378823)
Advanced Accounting - Floyd Beams (9th edition) (ISBN: 0131851225)
Advanced Calculus - G. B. Folland (1st edition) (ISBN: 0130652652)
Dunlap (1st edition) (ISBN: 0534392946)
Analytical Mechanics - Grant Fowles, George Cassiday (7th edition)
(ISBN: 0534494927)
Applied Algebra - Darel Hardy (1st edition) (ISBN: 0130674648)
Applied Linear Algebra - Chehrzad Shakiban, Peter J. Olver (1st
edition) (ISBN: 0131473824)
Applied Partial Differential Equations - Richard Haberman (4th
edition) (ISBN: 0130652431)
Auditing and Assurance Services - Alvin A. Arens et al (11th edition)
(ISBN: 0131867121)
Auditing Assurance and Risk - W. Robert Knechel, Steve Salterio, Brian
Ballou (3rd edition) (ISBN: 0324313187)
Auditing Cases - Mark Beasley (3rd edition) (ISBN: 0131494910)
Automation, Production Systems, and Computer-Integrated Manufacturing
- Mikell P. Groover (2nd edition) (ISBN: 0130889784)
Biochemistry - Mary Campbell (4th edition) (ISBN: 0534405215)
Biochemistry (with Lecture Notebook) - Mary Campbell (4th edition)
(ISBN: 0534391818)
Business Law and the Legal Environment - Jeffrey F. Beatty (4th
edition) (ISBN: 0324303971)
Business Law: Text and Exercises - Roger LeRoy Miller (5th edition)
(ISBN: 032464096X)
Calculus - Dale Varberg (9th edition) (ISBN: 0131429248)
Calculus and Its Applications - Larry Goldstein (11th edition) (ISBN:
0131919636)
Calculus for the Life Sciences -  Marvin L. Bittinger (1st edition)
(ISBN: 0321279352)
Calculus With Applications - Margaret L. Lial et al (8th edition)
(ISBN: 0321228146)
Cases in Management Accounting and Control Systems - Brandt Allen (4th
edition) (ISBN: 0135704251)
Chemistry : An Introduction to General, Organic, Biological Chemistry
- Karen Timberlake (9th edition) (ISBN: 0805330151)
Chemistry : The Molecular Science - John Moore (2nd edition) (ISBN:
0534422012)
edition) (ISBN: 0534408966)
CMOS Circuit Design, Layout, and Simulation - David E. Boyce et al
(1st edition) (ISBN: 0780334167)
College Accounting 1-12 - Jeffrey Slater (9th edition) (ISBN:
0131071696)
College Accounting 1-25 - Jeffrey Slater (10th edition) (ISBN:
0132286386)
College Accounting Chapters 1-15 - James Heintz (19th edition) (ISBN:
0324382499)
College Accounting Chapters 1-27 - James Heintz (19th edition) (ISBN:
0324376162)
College Accounting Chapters 1-9 - James Heintz (19th edition) (ISBN:
0324382480)
College Geometry - David C. Kay (2nd edition) (ISBN: 0321046242)
Comparative International Accounting -  Christopher Nobes (9th
edition) (ISBN: 0273703579)
Complex Variables With Applications - A. David Wunsch (3rd edition)
(ISBN: 0201756099)
Computer Algorithms - Allen Van Gelder, Sara Baase (3rd edition)
(ISBN: 0201612445)
Computer Networking with Internet Protocols - William Stallings (1st
edition) (ISBN: 0131410989)
Computer Organization and Architecture - William Stallings (7th
edition) (ISBN: 0130351199)
Computer Organization and Architecture: Designing for Performance -
William Stallings (7th edition) (ISBN: 0131856448)
Computer Systems Organization & Architecture - John D. Carpinelli (1st
edition) (ISBN: 0201612534)
Concepts in Federal Taxation 2007 - Kevin Murphy (14th edition) (ISBN:
0324313527)
Concepts In Systems and Signals -  John D. Sherrick (2nd edition)
(ISBN: 0131782711)
Concrete Structures -  Mehdi Setareh (1st edition) (ISBN: 0131988271)
Corporate Finance -  Jonathan Berk (1st edition) (ISBN: 0321415116)
Cost Accounting - Charles T. Horngren, George Foster, Srikant M. Datar
(12th edition) (ISBN: 0131495380)
Cost Accounting - Edward J. Vanderbeck (14th edition) (ISBN:
0324374178)
Cost Accounting: Traditions & Innovations - Jesse Barfield (5th
edition) (ISBN: 032418090X)
Course in Probability - Neil Weiss (1st edition) (ISBN: 0201774712)
Cryptography and Network Security - William Stallings (4th edition)
(ISBN: 0131873164)
Data and Computer Communications -  William Stallings (8th edition)
(ISBN: 0132433109)
Derivatives Markets -  Robert L. McDonald (2nd edition) (ISBN:
032128030X)
Differential Equations - John Polking (2nd edition) (ISBN: 0131437380)
Differential Equations and Linear Algebra -   Jerry Farlow (2nd
edition) (ISBN: 0131860615)
Differential Equations With Boundary Value Problems - John C. Polking
(2nd edition) (ISBN: 0130911062)
Digital & Analog Communication Systems - Leon Couch (7th edition)
(ISBN: 0131424920)
Digital Communications - John Proakis (4th edition) (ISBN: 0072321113)
Digital Design - Morris Mano (4th edition) (ISBN: 0131989243)
Digital Signal Processing - John Proakis (4th edition) (ISBN:
0131873741)
Digital Systems: Principles and Applications - Ronald Tocci et al
(10th edition) (ISBN: 0131725793)
Discrete and Combinatorial Mathematics - Ralph P. Grimaldi (5th
edition) (ISBN: 0201726343)
Discrete Mathematics - Edgar G. Goodaire, Michael M Parmenter (3rd
edition) (ISBN: 0131679953)
Discrete Mathematics - Otto, Eynden, Dossey, Spence (4th edition)
(ISBN: 0321079124)
Discrete Mathematics - Richard Johnsonbaugh (6th edition) (ISBN:
0131176862)
Economic Development - Michael Todaro, Stephen Smith (9th edition)
(ISBN: 0321278887)
Economic Growth - David Weil (1st edition) (ISBN: 0201680262)
Economics of Money, Banking, and Financial Markets, Update - Frederic
Mishkin (7th edition) (ISBN: 0321331850)
Economics Today: The Macro View - Roger Miller (13th edition) (ISBN:
0321278992)
Economics Today: The Micro View - Roger Miller (13th edition) (ISBN:
0321278984)
Electrical Machines, Drives and Power Systems - Theodore Wildi (6th
edition) (ISBN: 0131776916)
Electronics and Computer Math - Bill Deem (8th edition) (ISBN:
0131711377)
Electronics Fundamentals: Circuits, Devices and Applications - Thomas
Floyd (7th edition) (ISBN: 013219709X)
Elementary Differential Equations - Werner E. Kohler, Lee W.Johnson
(1st edition) (ISBN: 0201709260)
Elementary Differential Equations With Boundary Value Problems - Lee
Johnson et al (1st edition) (ISBN: 0321121643)
Elementary Number Theory - Kenneth H. Rosen (5th edition) (ISBN:
0321237072)
Elementary Statistics - Mario F. Triola (9th edition) (ISBN:
0201775700)
Elementary Statistics - Mario F. Triola (10th edition) (ISBN:
0321331834)
Engineering Materials: Properties and Selection - Ken Budinski (8th
edition) (ISBN: 0131837796)
Environmental and Natural Resource Economics - Tom Tietenberg (7th
edition) (ISBN: 0321305043)
Error Control Coding - Daniel J. Costello Jr., Shu Lin (2nd edition)
(ISBN: 0130426725)
Financial & Managerial Accounting - Carl S. Warren (9th edition)
(ISBN: 0324401884)
Financial Accounting - Jane Reimers (1st edition) (ISBN: 0131492012)
Financial Accounting - Walter Harrison, Charles Horngren (6th edition)
(ISBN: 0131499459)
Financial Accounting: An Integrated Statements Approach - Jonathan
Duchac (2nd edition) (ISBN: 0324312113)
Financial Management For Public, Health, and Not-for-Profit
Organizations - Steven Finkler (2nd edition) (ISBN: 0131471988)
Financial Reporting and Analysis - Charles Gibson (10th edition)
(ISBN: 0324304455)
Financial Reporting and Analysis - Lawrence Revsine (3rd edition)
(ISBN: 0131430211)
Financial Reporting and Analysis Using Financial Accounting
Information - Charles Gibson (10th edition) (ISBN: 0324304455)
Financial Reporting, Financial Statement Analysis, and Valuation -
Clyde P. Stickney (6th edition) (ISBN: 0324302959)
Finite Math and Its Application - Larry Goldstein (9th edition) (ISBN:
0131873644)
Finite Mathematics - Margaret L. Lial et al (8th edition) (ISBN:
032122826X)
Finite Mathematics with Applications -  Margaret L. Lial (9th edition)
(ISBN: 0321386728)
First Course in Abstract Algebra - John Fraleigh (7th edition) (ISBN:
0201763907)
First Course in Abstract Algebra - Joseph Rotman (3rd edition) (ISBN:
0131862677)
First Course In Probability - Sheldon M. Ross (7th edition) (ISBN:
0131856626)
Foundations of Finance - Arthur Keown, William Petty, John Martin,
David Scott (5th edition) (ISBN: 0131856057)
Foundations of Geometry - Gerard Venema (5th edition) (ISBN:
0131437003)
Foundations of MEMS - Chang Liu (1st edition) (ISBN: 0131472860)
Fraud Examination - Steve Albrecht (2nd edition) (ISBN: 0324651155)
Friendly Introduction to Analysis -  Witold A.J. Kosmala (2nd edition)
(ISBN: 0130457965)
Fundamentals of Applied Electromagnetics -  Fawwaz T. Ulaby (5th
edition) (ISBN: 0132413264)
Fundamentals of Complex Analysis - Edward Saff (3rd edition) (ISBN:
0139078746)
Fundamentals of Differential Equations - Kent Nagle, Edward Saff (6th
edition) (ISBN: 0321145720)
Fundamentals of Financial Management - Eugene Brigham (11th edition)
(ISBN: 0324319800)
Fundamentals of Investing -  Lawrence J. Gitman (10th edition) (ISBN:
0321489381)
===
Subject: Re: Comprehensive Solution Manual for Textbooks
sir i want asolution of a book  Computer Organization and Architecture
- William Stallings (7th
edition) (ISBN: 0130351199)
in electronic formate so please send me this book
i m not capaable to purchase this book so please send me this book
===
Subject: Re: Comprehensive Solution Manual for Textbooks
===
Subject: Re: Comprehensive Solution Manual for Textbooks
I am in desperate need of your help! But I don't need the solution
manual in a few days (I have a few more weeks before the class
begins).
The text book name is Physical Chemistry...4th Ed, by Tinoco, Sauer,
Wang, Publisi.
But, the solution manual for this text that I need is named: Solution
manual for Principles and Applications in Biological Sciences, 4th ed.
Tinoco, Sauer, Wang and Puglisi, 2002
Will the solution manual be in PDF formatting? Please email me if you
need additional information etc. I could not find the isbn number
unfortunately.
===
Subject: Re: Comprehensive Solution Manual for Textbooks
All Subjects' solutions manuals in Pdf format
All solutions manuals are in pdf format or Microsoft Word format.
I have tried my best to put up with the collections of my solutions
manual.
Here is the list that only part of my collections:
I will put some time to make up the full list daily.
If you cant find the solution manual listed below, don't give up, feel
free to email me
To get the solutions manual, just email me with a price you want to
get the solutions manual you want.
To see samples, just email me.
My email is edisonee(at)gmail.com
Solutions Manuals
.NET 2.0 Interoperability Recipes by Bruce Bukovics
A Course in Game Theory by Martin J. Osborne and Ariel Rubinstein
A First Course In Probability 7th Ed by Sheldon Ross
Adaptive Control 2nd Ed. by Karl.J.Astrom
Advanced Engineering Marhematics ERWIN KREYSZIG 9E
Advanced Engineering Mathematics 8Ed Erwin Kreyszig
Advanced Engineering Mathematics 8Ed Erwin Kreyszig in korean (all
even and odd no.)
Advanced Macroeconomics by Jeffery Rohaly
Advanced Modern Engineering Mathematics 3rd Ed. by Glyn James
Analog Integrated Circuit Design by David Johns, Ken Martin
Analysis and Design of Analog Intergrated Circuits 4th Ed. by Paul R.
Gray
Analytical Mechanics 7th Ed. by Fowles
Antenna for all application 3rd Ed.by John D. Kraus (Instructor's
Manual)
Antenna Theory 2nd Ed. by balanis
Applied Linear Statistical Models 5th Ed. by MichaelH.Kutner
Applied Numerical Analysis 7th Ed. by Curtis F. Gerald, Patrick O.
Wheatley
Applied Numerical Methods with Matlab for Engineers and Scientists 2nd
Ed. by Chapra
Applied Statistics Probability for Engineers 3rd ed Montogomery
(selected problems)
Applied Strength of Materials 4th Ed. by Robert L. Mott
Automatic Control Systems 8th Ed. Kuo and Golnaraghi
Basic Engineering Circuit Analysis 7th Ed. by Irwin
Basic Principles and Calculations in Chemical Engineering 6th Ed. by
David M. Himmeblau
Biochemistry 2nd Ed. by Philip W. Kuchel, Gregory B. Rakston
Bioprocess Engineering Principles by Pauline M. Doran
Business Statistics A Decision-Making Approach 6th Ed. by Groebner
C++ How to Program 3rd ed. Deitel, Deitel & Nieto (Instructor's
Manual)
Calculus 4th Ed. by James Stewart (Complete Instructors manual)
Calculus 5th Ed. by James Stewart (Complete Instructors Solutions)
Calculus by Jerrold Marsden & Alan Weinstein Vol 1
Calculus Early Transcendentals 5th Ed. by James Stewart
Calculus of Variations by Russak(book and solutions manual)
Calculus: One and Several Variables 8th Ed. by Salas, Hille and Etgen
Chemical And Engineering Thermodynamics 3Ed by Wiley
Chemical Engineering Solutions to the Problems in Volume 1 by J R
Backhurst
Classical Dynamics 5th Ed. by Thornton
Classical Electrodynamics 3rd Ed. by J.D. Jackon
CMOS Analog Circuit Design 2nd Ed. by P.E. Allen
Communication Systems 4th Ed. by Simon Haykin
Communication Systems Engineering 2nd Ed. by Proakis J.
Communication Systems: An Introduction to Signals and Noise in
Electrical Communication 4th. Ed. by Bruce Carlson
Computational Techniques for Fluid Dynamics by K. Srinivas and
C.A.J.Fletcher
Computer Architecture Design and Performance 2nd Ed. by Barry
Wilkinson
Computer Networking A top-down approach 3rd Ed. by James F. Jurose
Computer Networking: A Top-Down Approach Featuring the Internet 2nd
ed. by Jim Kurose and Keith Ross
Computer Networks 4th Ed. by Andrew.S.Tanenbaum
Computer Networks: A Systems Approach 3rd Ed. by larry L. Peterson and
Bruce S. Davie
Computer Organization And Design - The Hardware Software Interface 3rd
Ed.
Computer Systems Organization and Architecture by John D. Carpinell
Control Systems Engineering 3rd Ed. by Norman S. Nise
Control Systems Engineering by Nise
Design and Analysis of Experiments 6th Ed. by Montgomery
Design Of Analog Cmos Integrated Circuits by Razavi
Design with Operational Amplifiers and Analog Integrated Circuits 3rd
Ed. by Franco, Sergio
Device Electronics for Integrated Circuits 3rd Ed. by Muller and
Kamins
Differential Equations & Linear Algebra by C. Henry
Differential Equations with Boundary-Value Problems 5th Ed. by Zill
and Cullen
Digital communication: Fundamentals and Applications 2nd Ed. by
Bernard Sklar
Digital communications 4th Ed. John Proakis with ebook
Digital Image Processing 2nd Ed. by Gonzalez (Instructor's Manual)
Digital Integrated Circuits by Rabaey 2nd Ed. (selected problems)
Digital signal processing A Computer-Based Approach 1st Ed. by Sanjit
K. Mitra
Digital Signal Processing by Thomas J. Cavicchi
Digital Signal Processing: Principles, Algorithms, and Applications,
3rd Ed. by Proakis & Manolakis
Digital Signals and Filter by S. J. Orfanidis (selected solutions)
Discrete-Time Signal Processing 2nd Ed. by Oppenheim, R.W. Schafer and
J. R. Buck
Distributed Systems Principles and Paradigms by Andrew S. Tanenbaum
and Maarten Van Steen
Econometric Analysis 5th Ed. by William H. Greene
Econometric Analysis of Cross Section and Panel Data by Jeffrey M.
Wooldridge
Electric Circuits 7th Ed. by Nilsson
Electric Machinery 6th Ed. by Fitzgerald, Kingsley, Uman
Electric Machinery and Power System Fundamentals 1st Ed. by Stephen J.
Chapman (Instructor's Manual)
Electric Machinery Fundamentals 4th Ed. by Stephen J Chapma
(Instructor's_Manual)
Electrical Engineering Principles And Applications 4th Edition by
Giorgio Rizzoni
Electrical Engineering Principles And Applications by Hambley
Electronic Circuit Analysis and Design 2nd Ed. by Donald A. Neamen
Electronic Physics by Strabman
Electronics 2nd Ed. by Allan R. Hambley
Element of Electromagnetic by Sadiku
Elementary Differential Equations and Boundary Value problems 7th Ed.
by Boyce, DiPrima (book and solutions)
Elementary Differential Equations and Boundary Value Problems 8th Ed.
Elementary Linear Algebra by K. R. Matthews (book and solution
manuals)
Elementary Mechanics and Thermodynamics by John W. Norbury
Elements of Chemical Reaction Engineering 3rd Ed. by Timothy Hubbard,
Jessica hamman and David Johnson
Elements of Information Theory by Thomas M. Cover
Engineering Biomechanics: Statics by Angela Matos, Eladio Pereira,
Juan Uribe and Elisandra Valentin
Engineering Circuit Analysis 6th Ed. by Hayt
Engineering Electromagnetics 6th Ed. by William H. Hayt, Jr. and Hohn
A. Buck
Engineering Fluid Mechanics 7th Ed. by Crowe
Engineering Mathematics 4th Ed. by John Bird
Engineering Mechanics Dynamics 10th edition by Hibbeler
Engineering Mechanics Dynamics 11th edition by Hibbeler
Engineering Mechanics Dynamics 3rd Ed. by Hibbeler
Engineering Mechanics Dynamics 5th Ed. by Meriam
Engineering Mechanics Dynamics by Bedford and Fowler
Engineering Mechanics statics 10th edition by Hibbeler
Engineering Mechanics statics 11th edition by Hibbeler
Engineering Mechanics Statics 4th Ed. Bedford
Engineering Mechanics Statics by Meriam
Feedback Control of Dynamic Systems 4th Ed. by G. F. Franklin, J. D.
Powell, A. Emami
Fluid mechanics 5th Ed. by White
Fourier and Laplace transforms by Antwoorden (selected solutions)
Fractal Geometry: Mathematical Foundations and Applications by Kenneth
Falconer
Fundamentals of Aerodynamics 2nd Ed. by John D. Anderson
Fundamentals Of Aerodynamics 3rd Ed. by Anderson (Instructor's
Solutions Manual)
Fundamentals of Applied Electromagenetics  5th Ed+
Fundamentals of Differential Equations by Nagle Saff Snider
Fundamentals of Digital Logic with Verilog Design 1st Ed. by S. Brown,
Z. Vranesic
Fundamentals of Digital Logic with VHDL Design 1st Ed. by S. Brown, Z.
Vranesic
Fundamentals of Electric Circuits 2nd Ed. by C.K.Alexander
M.N.O.Sadiku
Fundamentals of Engineering Thermodynamics 5th ed (M. J. Moran & H. N.
Shapiro)
Fundamentals of Financial Management With Infotrac Concise 4th Ed. by
Eugene Brigham
Fundamentals of Fluid Mechanics 3th Ed. by Munson (Student solution
manual)
Fundamentals of Fluid Mechanics 4th Ed. by Munson
Fundamentals of Fluid Mechanics 5th Ed. by Munson
Fundamentals of Heat and Mass Transfer 5th Ed. Incropera
Fundamentals of Logic Design 5th Ed. by  Charles Roth
Fundamentals of Machine Component Design 3rd Ed. by Juvinall and
Marshek
Fundamentals of Machine Component Design 4th Ed. by Juvinall
Fundamentals of Phsics 6th ed. by Halliday, Resnick (instructor's
manual)
Fundamentals of phsics 7th ed. by David Halliday, Robert Resnick, and
Jearl Walker (instructor's manual)
Fundamentals of Thermal-Fluid Sciences by Cengal
Fundamentals of Thermodynamics 6th Ed. Richard E. Sonntag, Claus
Borgnakke, Gordon J. Van Wylen
Guide to Energy Management 5th Ed. by Klaus-Dieter E. Pawlik
Heat Transfer 2nd Ed. by Cengel
Hydraulics in Civil and Environmental Engineering 4th Ed. by Andrew
Chawick
Introduction To Algorithms 2nd Ed. by Philip Bille (selected problems)
Introduction To Algorithms 2nd Ed. by Thomas H. Cormen, Charles
E.Leiserson, Ronald L. Rivest, Clifford Stein
Introduction to Antenna Theory by Palacios
Introduction to electric circuits 6th Ed. by Dorf-Svaboda
Introduction to electrodynamics 3rd Ed. by David Griffiths
Introduction to Fluid Mechanics 5ed. by Fox
Introduction to Fluid Mechanics 6th Ed. by Fox
Introduction to Linear Algebra 3th Ed. by Gilbert Strang
Introduction to Probability by Charles M. Grinstead and J. laurie
Snell
Introduction to Quantum Mechanics 2ed Griffiths, David J.
Introduction to Software Engineering by R. Mall
Introduction to VLSI circuits and Systems by John P. Uyemura
Introduction to Wireless Systems by P. M. Shankar
Investment Analysis and Portfolio Management by Reilly Brown
Linear Algebra and its Applications  3rd Ed.  by Lay
Linear Algebra by Jim Hefferon
Linear circuit analysis by R. A. DeCarlo and P. Lin
Linear Systems and Signals by B P Lathi
Logic Computer Design Fundamentals 2th Ed. by Morris Mano (selected
problems)
Managerial Accounting 11th Ed.
Material Science and Engineering an Introduction 5th Ed. by Callister
Material Science and Engineering an Introduction 6th Ed. by Callister
Materials & Processing in Manufacturing 9th Ed. by Demargo
Mathematical Methods for Physics and Engineering 3rd Ed. by
K.F.RileyandM.P.Hobson
Mathematics for Economics by Simon and Blume
Matrix Analysis And Applied Linear Algebra by Carl D. Meyer
Mechanical Engineering Design 7th Ed. Shigley
Mechanics of Fluids 4th Ed. by I. H. Shames
Mechanics of Fluids 8th Ed. by Bernard Massey
Mechanics of Materials 3rd Ed. Elsevier by S. Nemat-Nasser
Mechanics of Materials 5th 6th Ed. by Gere
Mechanics of materials Hibbeler 6th
Mechanics Of Materials(3rd Ed , By Beer, Johnston, & Dewolf)
Microeconomic Analysis 3rd Ed. by Hal R. Varian
Microeconomic Theory by Andreu Mas-Colell, Jerry R. Green, Michael
Dennis Whinston
Microelectronic Circuits 4th Ed. by Sedra, Smith
Microelectronic circuits 5th Ed. Sedra
Microelectronics Digital and Analog Circuits and Systems by Millman
Microwave and rf design of wireless systems by Pozar
Microwave Engineering 2nd Ed. David M Pozar
Microwave Engineering 3rd Ed. David M Pozar
Microwave Transistor Amplifiers Analysis and Design 2nd Ed. by
Guillermo Gonzalez
Modern Control Engineering 3rd Ed. by K.OGATA
Modern Digital and Analog Communications Systems by B P Lathi
Modern Quantum Mechanics Revised Ed. by J.J. Sakurai (solutions and
book)
Multi Variable Calculus 5th Ed.
Numerical Methods for Engineers by Steven C. Chapra and Raymond P.
Canale
Operating System Concepts 6th Ed. by Abraham Silberschatz
Operating System Concepts 7th Ed. by Abraham Silberschatz
Operating Systems:Internals and Design Principles 4th Ed. by William
Stallings
Options, Futures, & Other Derivatives 4th Ed. by John C. Hull
Organic Chemistry 5th Ed. by Atkins and Carey
Physical Chemistry 7th. Ed. by Peter Atkins & Julio de Paula
Physics for Scientists & Engineers (a strategic approach) by Randall D
Knight
Physics for Scientists & Engineers by Tipler & Mosca 5th Edition
Physics For Scientists And Engineers 3rd Ed. by Douglas C. Giancoli
Physics for Scientists and Engineers 5th Extended Version by Serway
and Faughn
Physics Volume 2 5th Ed. by Halliday, Resnick and Krane
Power System Analysis by John J. Grainger & William D. Stevenson, Jr
Principles of Communication 5th Ed. by R. E. Ziemer, William H.
Tranter
Principles of Physics 4th Ed. Calculus Based by Serway, Raymond A. and
John W. Jewett
Principles with Applications BY Giancoli 6TH Edition
Probability and Statistics for Engineering and the_Sciences 6th Ed.
Probability and Statistics for Engineers and Scientists (selected
problems)
Probability Random Variables and Stochastic Processes 4th Ed. by
Papoulis
Process Systems Analysis and Control by Donald R.coughanowr(selected
problems)
Quantum mechanics by Kyriakos Tamvakis
Quantum Mechanics by P. Saltsidis
Recursive Macroeconomic Theory by Lars Ljungqvist and Thomas J.
Sargent
Recursive Methods in Economic Dynamics by Wright
RF circuit Design Theory and Application by Ludwig bretchko
Sears and Zemansky's University Physics 11th Ed.
Semiconductor Device Fundamentals 1st Ed. by Robert F. Pierret
Semiconductor Devices Physics and Technology 2nd Ed. by S. M. Sze
Semiconductor Physics and Devices 3rd Ed. by Neamen
Serway and Jewett's Physics for Scientists and Engineers 6th ed. by
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Signal Processing and Linear Systems by B P Lathi
Signals And Systems 2nd Ed. by Haykin
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Soil Mechanics: concepts and applications 2ed William Powrie
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Manual)
Strengths of Materials by Beer, Johnston, Dewolf
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The C Programming Language 2nd Ed. by Kernighan and Ritchie
The Econometrics of Financial Markets by Petr Adamek
The Science and Engineering of Materials 4th Ed. by Donald R. Askeland
Pradeep P. Phule (Instructor's Manual)
Theory and Applications of OFDM and CDMA Wideband Wireless
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Thermodynamic 5th ed. Cengal
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Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas
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Undergraduate Econometrics by Hill, Judge and Griffiths
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Vector Calculus 3rd Ed. by Susan Jane Colley
Vector Mechanics for engineers dynamics by beer 6th edition
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Ebooks:
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===
Subject: Re: Comprehensive Solution Manual for Textbooks
I am interested in the solutin manual for West's Dederal Taxation 2007
Individual (ISBN: 0324399618).  How do i go about purchasing these
from you?
===
Subject: Re: Comprehensive Solution Manual for Textbooks
I would like to buy the solution manual for the following book.
Discrete Mathematics - Richard Johnsonbaugh (6th edition) (ISBN:
0131176862)
Please let me know how should I pay and download the same.
===
Subject: Re: English is a mess.
                        .................
Logic is a property of English?  Self-reference allows 
paradoxes, and mathematics had to distinguish between
truth, which is metamathematical, and provability,
which is mathematical.
For neither is the x anything but a placeholder.  It
can be replaced by any other variable, and often expressions.
For more complicated statements, there is the rule that no
occurrence of a variable can be accidentally quantified or
dequantified by a substitution, so one cannot replace the
second x in (forall x)[x = x] by y, or the (forall x) by
(forall y) without also replacing the x's in the statement
by y's, using the rules of substitution.
-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558
===
Subject: Re: English is a mess.
Are you so insensitive to language that you can't recognize an
analogy?
Brian suggested that formal logic is X, formal logic is mathematics,
therefore mathematics is X (i.e., Socrates is a man, Socrates is
mortal, therefore all men are mortal).
If that is valid, then If English is X, and English is a language,
then all language is X.
Logic explains that that is not a valid inference.
And no, logic is not a property of human language.
Yet another way it's not like pronouns.
===
Subject: Re: English is a mess.
On 7 May 2007 20:08:17 -0700, Peter T. Daniels
in sci.math,sci.lang:
[...]
I did not.  You made a general claim about variables in
mathematics, and I produced a counterexample from a
particular branch of mathematics.
[...]
Brian
===
Subject: Re: English is a mess.
Mathematics uses all of the restricted predicate calculus.
The restriction is that predicates are not quantifiable.
Steps in mathematical proofs allow quantification under
certain circumstances, and proofs using existential
statements.
For example, if lines of a proof are
        A       (exist x) (phi(x))
        {m}     phi(u)
                ..................
        B       psi
        C       psi
where C = A u (B  {m}) provided certain conditions
are met.  There are other rules for allowing the
addition and removal of quantifiers.
The entire set of logical rules can fit on one 
page.
-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558
===
Subject: Re: English is a mess.
Including the extensions of logic that have been developed to try to
deal with language, such as fuzzy logic and modal logic?
Have you ever heard of Montague Grammar?
===
Subject: Re: English is a mess.
That pronouns do not have unique referents as used is the
cause of the confusion which requires variables to unravel.
Is there any real need of pronouns in natural languages?
One could get by without any, but it would be clumsy.  The
situation is the same for variables, which need not be 
restricted to temporary names for objects, but can be used
for adjectives, adverbs, verbs, etc.  
-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558
===
Subject: Re: English is a mess.
Finally you admit that variables are not like pronouns.
Oh, puh-leez. _Any_ baby introduction to language will give you an
example of a paragraph written without pronouns.
Define the parts of speech of mathematics.
===
Subject: Re: English is a mess.
Am 7 May 2007 16:56:24 -0400 schrieb Herman Rubin:
And it still is _with_ pronouns.
Joachim
===
Subject: Re: English is a mess.
what about my suggestion
  that variables are queries or interrogatives?
  wh-movements?
those have referrents specific only to a given context
  just like variables
and respect the scoping that is being debated...
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
===
Subject: Re: English is a mess.
On 4 May 2007 13:56:42 -0700, Peter T. Daniels
in sci.math,sci.lang:
I'm not.  I'm refuting a general assertion about
mathematical variables by supplying a counterexample.  It's
immaterial whether the counterexample comes from topology,
logic, combinatorics, geometry, set theory, analysis,
algebra or what have you.
So 'rose' is a name (*not* noun) in 'for each rose, that
rose is a rose'?  And 'each' defines it specifically?
Same problem.  Is 'elephant' a name in 'there is an elephant
such that that elephant stands more than two hands high'?
It's beside the point: it's an argument against Herman's
favorite analogy but not an argument for the notion that
variables are analogous to names.
I suppose that you might consider a variable to be a kind of
placeholder name, like 'dingus', 'thingummy', 'wossname',
'whatchamacallit', etc.
Brian
===
Subject: Re: English is a mess.
if you go for whatchamacalit
  why not my suggestion that variables are interrogatives?
  queries or wh-movements?
that usage is context dependent
  ( the referents to what vary in the context of the question )
and respect the scoping debate going on here
x + 3 = 5
   |
   |
   V
 what plus 3 equals five? 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
===
Subject: Re: English is a mess.
talking to me. Some other times they may use the name Paul
meaning somebody else. The name Paul can refer to any one
of a quite large subset of humanity.
It seems to me, Joachim,  that the name Paul (in fact, a name
in general) is closer analogy to a variable than anything else.
I'd say, only some names are unique enough to be constants,
such as Henry VIII, Ghengis Khan, etc.  :-)
pjk
===
Subject: Re: English is a mess.
But even such specific names can have variable referents from context 
to context.  If you just got finished watching a production of 
Shakespeare's _Henry VIII_, you might very well use Henry VIII to 
talk about the main character of the play instead of the actual 
historical figure.
And in when using the name in this context, the referent could vary 
even further, depending on whether you are talking about the 
character, the particular performance of the character, or even 
by-passing the character and talking about the actor who played the 
role.
Unlike the referents of mathematical constants, the referent of a 
completely unambiguous name could be the actual person or any one of 
an unlimited number of related, but distinct, entities.
Nathan
-- 
Nathan Sanders
Linguistics Program
Williams College
http://wso.williams.edu/~nsanders/
-- 
===
Subject: Re: English is a mess.
Hm, that is all very true.
It's still not such a bad analogy though.
A similar comments could be made about mathematical
constants. For example, Joachim's capital PI can be
a constant and couple paragraphs later it can be a math
operator, a symbol for a set, etc. So even the precise
meaning of the names of constants rely on context.
pjk
===
Subject: Re: English is a mess.
Hm. The difference I see is that this usage of Paul is not ad hoc;
it's using part of a constant because it's identifying enough in the
context.
A variable is meant to give ad-hoc identifications to objects that
don't have a name (or at least I don't know it), so one might call it
a temporal name. I don't think natural language has the concept of a
temporal name - the only means it has for temporal identification are
fall into this group), and that's a bit limited. Typically language
becomes cumbersome if you have to describe situations in which with a
number of more than two persons or objects occur. 
Joachim