Description:
Mathematical discussions and pursuits.
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Need help with convexity/probability proof
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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.)... more »
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---- ---- ---- congruence
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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... more »
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Source of term "multiplication" in matrix multiplication
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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... more »
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Can you use the word "assigning" to mean "mapping"?
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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... more »
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Is Shannon's Entropy invariant to the mean value!!
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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.
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THE MATHEMATICAL EXACT DEFINITION OF A PRIME NUMBER BY INVERSE19 MATHEMATICS
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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,... more »
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Laurent series question
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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")
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I Think Therefore I Am - rebuttal
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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... more »
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RELATIVITY INCOMPATIBLE WITH QUANTUM MECHANICS OR WITH ITSELF?
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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... more »
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