The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities...

In the present manuscript, the second strain gradient (SSG) is utilized to investigate the primary resonance of a nonlinear Euler-Bernoulli nanobeam is analyzed in this paper...

We first obtain by analogy with the continuous (differential) case the general solution of the discrete Riccati equation. Moreover, we establish the full equivalence between our discrete Riccati equation and a corresponding homogeneous second order discrete linear equation. Our results can be considered the discrete analog of Mielnik's construction in supersymmetric quantum mechanics [J. Math. ...

In this manuscript, by using the semigroup theory, well-posedness and exponential stability for a Rao-Nakra sandwich beam equation with internal damping time delay is proved. The system consists of two wave equations longitudinal displacements top bottom layers, one Euler-Bernoulli transversal displacement. To best our knowledge from literature , time, no attention was given to asymptotic model...

Abstract. The study of the identities of symmetry for the Bernoulli polynomials arises from the study of Gauss’s multiplication formula for the gamma function. There are many works in this direction. In the sense of p-adic analysis, the q-Bernoulli polynomials are natural extensions of the Bernoulli and Apostol-Bernoulli polynomials (see the introduction of this paper). By using the N-fold iter...

2 Inaugurated by D. Bernoulli (1700-1782), the analysis of epidemics and their dissemination have been studied by various mathematicians. The benets from epidemic modelling are threefold: understanding mechanisms of spread of epidemics, predicting their future course and developing strategies to control them. Recently, epidemic algorithms (also known as gossip algorithms) have been proposed as ...

Localized oscillating fields are beam splitters that can entangle internal and longitudinal momentum states in an atomic beam. Differentially detuned separated oscillatory fields and an am modulator constitute a “white fringe” longitudinal interferometer which rephases velocity averaging by a process analogous to half a spin echo. Differentially detuned separated oscillatory fields are used to ...

For a sum of the form ∑ k F (n, k)G(n, k), we set up two systems of equations involving shifts of F (n, k) and G(n, k). Then we solve the systems by utilizing the recursion of F (n, k) and the method of undetermined coefficients. From the solutions, we derive linear recurrence relations for the sum. With this method, we prove many identities involving Bernoulli numbers and Stirling numbers.