There are many cryptographic constructions in which one uses a random power or multiple of an element in a group or a ring. We describe a fast method to compute random powers and multiples in certain important situations including powers in the Galois field F2n , multiples on Koblitz elliptic curves, and multiples in NTRU convolution polynomial rings. The underlying idea is to form a random exp...

The linear and nonlinear Rossby wave solutions are examined in homogeneous square basins on the /-plane both with and without a thin meridional barrier. In the presence of the meridional barrier the basin is almost partitioned into two; only two small gaps of equal width, d, to the north and south of the barrier allow communication between the eastern and western sub-basins. Solutions are force...

Les références principales pour l’interprétation du produit de mélange de deux séries en termes d’automates et les applications aux identités syntaxiques sont [Lo 2002] 1.3 et [J 1980]. Dans le cours du 14 mars les exemples suivant sont traités: 1. Mélange de deux éléments de K < X > 2. L’identité x∗0x(x1 · · ·xn) = x∗0x1x∗0x2 · · ·x∗0xnx∗0 3. L’identité (x0 + x1)∗ = x∗0xx∗1 4. L’identité (1 + ...

Le molluscum contagiosum est une tumeur cutanée bénigne d'origine virale. L'agent responsable est un Poxvirus à ADN fréquemment retrouvé chez les enfants de 3 à 16 ans, les immunodéprimés et plus rarement chez les adultes immunocompétents. Le syndrome d'hyper immunoglobulinémie E ou de Job-Buckley fait partie des déficits immunitaires primitifs complexes, caractérisé par l'association constante...

Internal multiples have long been recognized as a problem in seismic imaging. Some theoretical developments have been made to attenuate them, but there is no 3D theory as yet that is valid for a wide range of velocity models. The goal of this paper is to present such a theory. Through the development of this theory we show that, unless certain simplifying assumptions are made about the velocity...

where [a, b, . . .] denotes the least common multiple of a, b, . . . . For the first term above represents the density of the multiples of a1 , the second represents the density of those multiples of a 2 that are not multiples of a 1 , and so on . Now suppose we start from an infinite sequence a,, a2 , . . . (arranged in increasing order) instead of from a finite set . It is plain that A(ai, a2...