K e y w o r d s B e r n o u l l i polynomials, Euler polynomials, Generating functions, Bernoulli numbers, Euler numbers, Addition theorem, Multiplication theorem~ Generalized Bernoulli polynomials and numbers, Generalized Euler polynomials and numbers. 1. I N T R O D U C T I O N T h e classical Bernoulli polynomials Bn(x) and the classical Euler polynomials En(x) are usual ly def ined by m e a...

Although the mathematics that define the operation of an impeller can be complex (it is the stuff of Bernoulli and Euler), its purpose is straight forward. An impeller is designed to impart energy to a fluid so that it will flow or, if it is already flowing, undergo some increase in its elevation or pressure. It accomplishes this by increasing the fluid’s velocity as it travels through its vane...

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)

The aim of this paper is to provide a general framework allowing to use exact observability of infinite dimensional systems to solve a class of inverse source problems. More precisely, we show that if a system is exactly observable, then we can identify a source term in this system by knowing the corresponding intensity and appropriate observations which often correspond to the measure of some ...

We show that the Akiyama-Tanigawa algorithm and Chen’s variant for computing Bernoulli numbers can be generalized to Carlitz’s q-Bernoulli numbers. We also put these algorithms in the larger context of generalized Euler-Seidel matrices.

Abstract: This work describes the modeling and control of an experimental platform associated to a single link flexible robot, whose motion is restricted to an horizontal plane, thus neglecting the gravity effects. The modeling problem is addressed using the so-called Euler-Bernoulli beam equation. The design, construction and integration of an experimental set-up developed for this work is als...

1. Paevsky, V.V. Euler’s work in demography. In collected papers Leonard Euler. Moscow – Leningrad, 1935, pp. 103 – 110 ... 2. Bernoulli, D. On the mean duration of marriages, etc. (1768). Translated from Russian translation in Ptukha, M.V. (History of Statistics), vol. 1. Moscow, 1955, pp. 453 – 464... 3. Ondar, Kh.O. On the works of Davidov in probability theory and on his methodological view...

Résumé. Cet article présente une méthode basée sur les cartes auto-organisatrices probabilistes dédiées à la classification non supervisée et la visualisation de données catégorielles et des données mixtes contenant des composantes quantitatives et binaires. Pour chacun de ces types de données, nous proposons un formalisme probabiliste dans lequel les unités de la carte topologique sont représe...

It is well known that beam is one of the basic structures in architecture. It is greatly used in the designing of bridge and construction. Recently, scientists bring forward the theory of combined beams. That is to say, we can bind up some stratified structure copings into one global combined beam with rock bolts. The deformations of an elastic beam in equilibrium state, whose two ends are simp...