We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves discontinuous, and even distributional, coefficients and right-hand side. The general problem is solved by application of functional analytic techniques to obt...

This paper presents a simple approach to invert the matrix P n + I n by applying the Euler polynomials and Bernoulli numbers, where P n is the Pascal matrix.

A generalisation of the odd Bernoulli polynomials related to the quantum Euler top is introduced and investigated. This is applied to compute the coefficients of the spectral polynomials for the classical Lamé operator.

In this paper we establish some symmetric identities on a sequence of polynomials in an elementary way, and some known identities involving Bernoulli and Euler numbers and polynomials are obtained as particular cases.

Keywords: Genocchi numbers and polynomials q-Genocchi numbers von Staudt–Clausen's theorem Kummer congruence a b s t r a c t Recently, the von Staudt–Clausen's theorem for q-Euler numbers was introduced by Kim (2013) and q-Genocchi numbers were constructed by Araci et al. (2013). In this paper, we give the corresponding von Staudt–Clausen's theorem for q-Genocchi numbers and also get the Kummer...

In this paper, we use the Stein-Chen method to determine a non-uniform bound for approximating the distribution of sums of dependent Bernoulli random variables by Poisson distribution. We give two formulas of non-uniform bounds and their applications.

Finite mixture models can be used in estimating complex, unknown probability distributions and also in clustering data. The parameters of the models form a complex representation and are not suitable for interpretation purposes as such. In this paper, we present a methodology to describe the finite mixture of multivariate Bernoulli distributions with a compact and understandable description. Fi...

In some distributions, such as the binomial distribution, the variance is determined by the mean. However, in practice, overdispersion is often observed where the variance is larger than that predicated by the mean, and underdispersion is sometimes observed where the variance is smaller. It is well known that overdispersion or underdispersion cannot be modeled for dichotomous responses having a...

We prove that two independent continuous-time simple random walks on the infinite open cluster of a Bernoulli bond percolation in the lattice Z meet each other infinitely many times. An application to the voter model is also discussed. 2000 MR subject classification: 60K

When an unsmooth flexible tube rotates, rich tones are produced. We propose a physical model that simulates this behavior. The tube is modeled as an open-ended organ pipe blown by an air stream pumped by a rotationally induced pressure which follows Bernoulli’s principle.