sci.math Google Group

Need help with convexity/probability proof

no.em...@please.post (kj) — Sat, 13 Mar 2010 19:56:51 UT

Claim: if the rejection regions for a statistical test are defined
as sets of test values for which the ratio of the rate of growth
of Type I errors to the rate of growth in power is bounded above
by a parameter, then the curve of power vs Type I error is concave.
(A more careful wording of this claim is given below.)

---- ---- ---- congruence

deepk...@yahoo.com (Deep) — Sat, 13 Mar 2010 19:20:55 UT

Consider the following two unrelated equations.
x^k + (1/4)y^k = 0mod(k^2) (1)
x^k + (1/4)y^(2k) = 0 mod(k^2) (2)
Conditions:x, y are relatively prime integers, y is even, k is prime >
3, k is prime to xy.
Assertion: If (1) has solutions then (2) has no solutions.
Any helpful comments about the correctness of the assertion will be

Source of term "multiplication" in matrix multiplication

wpihug...@hotmail.com (William Hughes) — Sat, 13 Mar 2010 17:57:07 UT

Recently, the question was asked in comp.lang.c
why matrix multiplication (a rather complex operation
not obviously related to ordinary mulitplication)
is known as multiplication. Hypotheses have included
the fact that matrix multiplication of nxn matriices
corresponds to the "multiplication" operation in the

Can you use the word "assigning" to mean "mapping"?

cliomse...@kriocoucke.mailexpire.com (Jose Capco) — Sat, 13 Mar 2010 17:36:20 UT

Dear NG,
Recently my supervisor got annoyed when I wrote :
let f:A-->B be a monomorphism assigning each x in A to f(x) in B
blablabla.
He said I should replace the word "assigning" to "mapping".. though I
personally don't think this is something that results into confusion.
I think one can use the word "assigning" every now and then to mean

Is Shannon's Entropy invariant to the mean value!!

mm...@deakin.edu.au (Mohammed Hossny) — Sat, 13 Mar 2010 16:00:08 UT

Hi,
Assuming any pdf p(X; mu, sigma) and an entropy function "entropy";
Does entropy(p(X, mu, sigma))==entropy(p(X, mu+a, sigma))??
if so what are the characteristics of shannon's entropy regarding scaling, and offsetting mu and sigma!?
Regards.

THE MATHEMATICAL EXACT DEFINITION OF A PRIME NUMBER BY INVERSE19 MATHEMATICS

hope9...@verizon.net (Inverse 19 mathematics) — Sat, 13 Mar 2010 15:50:49 UT

Professor Edgar Escultura PHD has beeb pestering us about our
babiblings about Prime numbers, and asked us the definition of a
Prime, Here it is you Respected friend and the greatest mathematician
of the 20th century , you old bull (Phillipino Blonde!), because you
ask questions
REGULAR NUMBERS
These are regular numbers proportioned at exactly 1:3 19 paragon,

Laurent series question

to1m...@yahoo.com (John) — Sat, 13 Mar 2010 14:03:05 UT

Let f be analytic in C\{-1,3}, and -1, 3 are simple poles of f.
can
sum{n = - oo, n = -1} a_n (z-2)^n
be a Laurent series of f in 1<|z-2|<3 ?
(probably the answer should be "no")

I Think Therefore I Am - rebuttal

huangxienc...@yahoo.com (Huang) — Sat, 13 Mar 2010 07:55:18 UT

Descartes said "I Think Therefore I Am", and if you are like me then
you too may have questioned this as a basis for "establishing
existence by means of physical experiment".
That is what Descartes did. He used a physical experiment, the process
of thought itself, and he observes that he thinks, and his conclusion

RELATIVITY INCOMPATIBLE WITH QUANTUM MECHANICS OR WITH ITSELF?

pva...@yahoo.com (Pentcho Valev) — Sat, 13 Mar 2010 07:17:55 UT

From 1907 on Einstein claims that, in a gravitational field, the speed
of light is VARIABLE, not constant (nowadays most Einsteinians claim
the opposite - nobody sees the contradiction and nobody cares). In
1911 Einstein is explicitly using Newton's emission theory of light in
order to show how the speed of light varies with the gravitational

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INVERSE 19 MATHEMATICS -- A CONNECT WITH MATHEMATICIANS, A STATEMENT OF UNDERSTANDING

hope9...@verizon.net (Inverse 19 mathematics) — Sat, 13 Mar 2010 01:52:59 UT

Calling each others names etc serves No Purpose
Two professors have communicated with us telling us that
marthematicians are having difficulty connecting and understanding ,,
Inverse 19 is hard because it is a duiffferent mathematics and
switching gears can cause lack of understanding . Ifb people cannot

Some Subgroups of SL(2,Z) of finite index

mbg-dot-ni...@gmail.com (Marc Bogaerts) — Fri, 12 Mar 2010 23:33:12 UT

I found an interesting exercise (nr. 1) in
[link]
The group G := SL(2, Z) is generated by the matrices
0 1
1 1
and
1 1
0 1
Now consider the subgroup
S := {
a b
c d
What is [G : S]? Determine coset representatives for S in G and a
generating set for S.
I solved this case, but the general case where 3 is replaced by a prime

The name for a filter?

por...@narod.ru (Victor Porton) — Fri, 12 Mar 2010 22:41:42 UT

Let A is a set.
Let F is the set of all sets of the form A\X where X is finite.
Trivially F is a filter on A.
What is the name (term) for the filter F?

COMPLETE WRAP UP OF "PRIME NUMBERS MATHEMATICS" BRIEFLY PUT AT NOW AND GENESIS, AND CIRCALAGE

hope9...@verizon.net (Inverse 19 mathematics) — Fri, 12 Mar 2010 20:53:53 UT

BRIEFLY PUT AT NOW
1. Genesis and Circlage points
The genesis of Prime numbers is in 1/6 , and mainly results from the
mathematical fusion at 3:4 numbers because of -1. The Introduction of
of 0.166666666666(11), and 0.8333333333(11) into proportions starts
the prime numbers as. Circilager points are where Prime numbers are

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