— We consider a network of vibrating elastic strings and Euler-Bernoulli beams. Using a generalized Poisson formula and some Tauberian theorem, we give a Weyl formula with optimal remainder estimate. As a consequence we prove some observability and stabilization results. Résumé (Formule de Weyl avec reste optimal de quelques réseaux élastiques et applications) Nous considérons un réseau de cord...

This paper employs the numerical assembly method NAM to determine the exact frequencyresponse amplitudes of an offshore structure such as piles or towers having the form of a hollow column filled with multiple fluids, immersed in water, carrying an eccentric tip mass supported by a translational spring and/or a rotational spring, and subjected to a harmonic force. The hollow column is modeled a...

Recently, a large amount of studies have been related to nonlinear systems with multi-degrees of freedom as well as continuous systems. The purpose of this paper is to optimize passive vibration absorbers in linear and nonlinear states for an Euler-Bernoulli beam with a nonlinear vibratory behavior under concentrated moving load. The goal parameter in the optimization is maximum deflection of t...

We give a characterization of the family of all probability measures on the extended line (−∞,+∞], which may be obtained as the distribution of the maximum of some linear Bernoulli process. On a probability space (Ω,P) consider a linear process

Consider a given pattern H and a random text T of length n. We assume that symbols in the text occur independently, and various symbols have diierent probabilities of occurrence (i.e., the so called asymmetric Bernoulli model). We are concerned with the probability of exactly r occurrences of H in the text T. We derive the generating function of this probability, and show that asymptotically it...

Let L (u, a), oo < u < + oo denote the Fourier-Stieltjes transform, 00 f eluoda(x), of a distribution function u(x), oo < x < + co . Thus if 00 /3(x) is the distribution function which is 0, J, 1 according as x -1 < x ,< 1, 1 < x, then L (u,,8) = cos u ; and so, if b is a positive constant, cos (u/b) is the transform of the distribution function /3(bx) . Hence, if a is a positive constant, the ...

A The chaos hierarchy 12 A.1 Ergodicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 A.2 Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 A.3 K Systems (Kolmogorov) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 A.4 B-Systems (Bernoulli) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...