In this paper, we show that a linear unbounded operator associated with an Euler–Bernoulli beam equation under shear boundary feedback generates a C0-semigroup in the underlying state Hilbert space. This provides an answer to a long time unsolved problem due to the lack of dissipativity for the operator. The main steps are a careful estimation of the Green’s function and the verification of the...

A least-squares linear fixed-interval smoothing algorithm is derived to estimate signals from uncertain observations perturbed by additive white noise. It is assumed that the Bernoulli variables describing the uncertainty are only correlated at consecutive time instants. The marginal distribution of each of these variables, specified by the probability that the signal exists at each observation...

The classical Helmholtz problem is applied for modelling and numerical investigation of inviscid cusp-ended separated flow around circular cylinder. Two coordinate systems are used: polar for initial calculations and parabolic as topologically most suited for infinite stagnation zone. Scaling by the shape of the unknown free line renders the problem to computational domain with fixed boundaries...

In this work we study the relativistic mechanics of continuous media on a fundamental level using a manifestly covariant proper time procedure. We formulate equations of motion and continuity (and constitutive equations) that are the starting point for any calculations regarding continuous media. In the force free limit, the standard relativistic equations are regained, so that these equations ...

We establish various bounds on the solutions to a Stein equation for Poisson approximation in Wasserstein distance with nonlinear transportation costs. The proofs are refinement of those Barbour and Xia (Bernoulli 12:943–954, 2006) using results Liu Ma (Ann Inst H Poincaré Probab Stat 45:58–69, 2009). As corollary, we obtain an estimate error measured $$L^2$$ -Wasserstein distance.

The concepts of Bernoulli numbers B n , Bernoulli polynomials B n (x), and the generalized Bernoulli numbers B n (a, b) are generalized to the one B n (x; a, b, c) which is called the generalized Bernoulli polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships between B n , B n (x), B n (a, b), and B n (x; a, b, c) are established.

Arithmetic properties of integer sequences counting periodic points are studied, and applied to the case of linear recurrence sequences, Bernoulli numerators, and Bernoulli denominators.

The Adomian Decomposition Method (ADM) is employed in this paper to investigate the free vibrations of the uniform cracked Euler-Bernoulli beams. The proposed ADM method can be used to analyze the vibration of beams consisting of an arbitrary number of cracks through a recursive way. Based on the ADM and employing some simple mathematical operations, the natural frequencies and the correspondin...

Two types of open-loop systems of an Euler–Bernoulli equation with variable coefficient and Dirichlet boundary control and collocated observation are considered. The uncontrolled boundary is either hinged or clamped. It is shown, with the help of multiplier method on Riemannian manifold, that in both cases, systems are well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. ...

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...