For each m 3 1, let A(m) = {N E Z x Z : Q(N) = m>. Note that CNEacrn) P(N) = 0 for each m > 1 if and only if e(,; P, Q) = 0. Let G denote the group of integral automorphs (of determinant &l) of Q(X). The first result in [I] states that if P(X) is a spherical polynomial with respect to Q(X) and if O(T; P, Q) E 0, then CUEG P(UX) = 0. The following theorem shows that this result holds for any hom...

K e y w o r d s P a r a m e t r i c measure, Nonparametric measure, Csiszg~r's f-divergence, Information measure. 1. I N T R O D U C T I O N There are several types of information divergence measures s tudied in l i te ra ture which compare two probabi l i ty d is t r ibut ions and have appl icat ions in informat ion theory, s tat is t ics and engineering. A convenient classification to differe...

We give three consequences of Schanuel’s Conjecture. The first is that P(e)Q(e) and P(π)Q(π) are transcendental, for any non-constant polynomials P(x),Q(x)∈Q¯[x]. second π≠αβ, algebraic numbers α β. third the case Gelfond’s conjecture (about transcendence a finite power tower) in which all elements equal.

ions apply to concretions more or less exactly as in the π-calculus. Definition 6.3. The application G@C of a φ-abstraction and concretion is defined as follows: ((~ w)P )@ν~z〈 ~y 〉.Q =def ν~z( {~y/~ w}P ‖ Q ) where ~ y and ~ w have the same length, and where names in N must be substituted for names in N , and names in X for names in X . Applications can of course be carried out in the context ...

A new improved ”Simple complete proofs of the Serre spectral sequence theorems”. In ([B]) I set forth a proof of the Serre calculation of E and claimed among other things that unlike my previous attempts to prove this in graduate course lectures, this proof was routine. On presenting this material in class, I discovered it was not as routine as I had imagined. With the help of Pallavi Jayawart ...

This article fits in many studies of multifractal analysis of measure [1, 2, 3, 4, 6, 7, 8, 9]. We took as a starting point the work of F. Ben Nasr in [2] to give a new inequality involving Dim(X α ) which would be, in certain cases, finer than the inequality Dim(X α ) ≤ inf q≥0 (αq +Bμ(q)), established by L. Olsen in [6]. Besides we elaborated an application of our result which gives a better ...

The Prolog program "prove(M,I) :append(Q,[C|R],M), \+member(-_,C), append(Q,R,S), prove([!],[[-!|C]|S],[],I). prove([],_,_,_). prove([L|C],M,P,I) :(-N=L; -L=N) -> (member(N,P); append(Q,[D|R],M), copy_term(D,E), append(A,[N|B],E), append(A,B,F), (D==E -> append(R,Q,S); length(P,K), K<I, append(R,[D|Q],S)), prove(F,S,[L|P],I)), prove(C,M,P,I)." implements a theorem prover for classical first-ord...