We study the asymptotic behavior of the Euler-Bernoulli beam which is clamped at one end and free at the other end. We apply a boundary control with memory at the free end of the beam and prove that the “exponential decay” of the memory kernel is a necessary and sufficient condition for the exponential decay of the energy.

This paper deals with the measure-theoretical entropy of a linear cellular automaton (LCA) Tf @-l,rD :m Ø m , generated by a bipermutative local rule f Ix-l, ... , xrM  ⁄i-l r ai xi Hmod mL (m ¥ 2 and l, r œ +), with respect to the Bernoulli measure mp on m  defined by a probability vector p  Ip0, p1, ... , pm-1M. We prove that the measure entropy of the one-dimensional LCA Tf @-l,rD wi...

In this paper, we give a short new proof of a recent result due to Schumacher concerning an extension of Faulhaber’s identity for the Bernoulli numbers. Our approach follows from basic manipulations involving the ordinary generating function for the Bernoulli polynomials in the context of the Zeon algebra.

It has equilibrium (and in fact reversible) measure μ the product Bernoulli measure of density p on {0, 1}Z. It can also be constructed by attaching a Poisson process clock to every site in Z. Every time a clock rings, the site is refreshed to a Bernoulli variable of parameter p, but only if its right neighbour is empty. This constraint creates the ”bubbles” one can see on the picture. A natura...

We consider explicit expansions of some elementary and q-functions in basic Fourier series introduced recently by Bustoz and Suslov. Natural q-extensions of the Bernoulli and Euler polynomials, numbers, and the Riemann zeta function are discussed as a by-product. © 2002 Elsevier Science (USA)

In this study, we construct the two-variable Dirichlet q-L-function and the two-variable multiple Dirichlet-type Changhee q-L-function. These functions interpolate the q-Bernoulli polynomials and generalized Changhee q-Bernoulli polynomials. By using the Mellin transformation, we give an integral representation for the two-variable multiple Dirichlet-type Changhee q-L-function. We also obtain r...

We study the problem of entropy increase of the Bernoulli-shift map without recourse to the concept of trajectory and we discuss whether, and under which conditions if it does, the distribution density entropy coincides with the Kolmogorov-Sinai entropy, namely, with the trajectory entropy. 05.45.+b,03.65.Sq,05.20.-y Typeset using REVTEX 1

For d ≥ 2, we use results of Hochman and Meyerovitch to construct examples of Zd shifts of finite type of entropy logN , N ∈ N, which cannot factor topologically onto the Zd Bernoulli shift on N symbols.

1 Department of Mathematics and Computer Science, KonKuk University, Chungju 138-70, Republic of Korea 2 Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea 3 Department of Mathematics, Yuvaraja’s College, University of Mysore, Mysore 570# 005, India 4 Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea 5 Department of ...