In this paper, transverse and longitudinal vibration of nonlinear plate under exciting of orbiting mass is considered based on first-order shear deformation theory. The nonlinear governing equation of motion are discretized by the finite element method in combination with Newmark’s time integration scheme under von Karman strain-displacement assumptions. For validation of method and formulation...

A complete investigation on the free vibration of bilayer graphene nanoribbons (BLGNRs) mod-eled as sandwich beams taking into account tensile-compressive and shear effects of van der Waals (vdWs) interactions between adjacent graphene nanoribbons (GNRs) as well as between GNRs and polymer matrix is performed in this research. In this modeling, nanoribbon layers play role of sandwich beam layer...

Pseudo-Newtonian gravitational potential describing the gravitational field of static and spherically symmetric black holes in the universe with a repulsive cosmological constant is introduced. In order to demonstrate the accuracy of the pseudo-Newtonian approach, the related effective potential for test-particle motion is constructed and compared with its general relativistic counterpart given...

Using the integral expression of Mathieu's series and some integral and analytic inequalities involving periodic functions and the generating function of Bernoulli numbers, we present several new inequalities and estimates for Mathieu's series and generalize Math-ieu's series. Two open problems are proposed.

Scan statistics have been widely applied to test for unusual cluster of events in many scientific areas. It has been of practical interest on how to select the window size of a scan statistic. An adaptive procedure for multiple window scan statistics is proposed and the distributions are studied for independent identically distributed Bernoulli trials and uniform observations on (0, 1) in one-d...

Using Szenes formula for multiple Bernoulli series, we explain how to compute Witten series associated to classical Lie algebras. Particular instances of these series compute volumes of moduli spaces of flat bundles over surfaces, and also multiple zeta values.

We discuss the asymptotic expansions of certain products of Bernoulli numbers and factorials, e.g., n ∏

In [7] we further proved that H1(p−1) ≡ 0 (mod p ) if and only if p divides the numerator of Bp−3, which never happens for primes less than 12 million [2]. There is another important equivalent statement of Wolstenholme’s Theorem by using combinatorics. D.F. Bailey [1] generalizes it to the following form. Theorem 1.1. ([1, Theorem 4]) Let n and r be non-negative integers and p ≥ 5 be a prime. ...

Using Szenes formula for multiple Bernoulli series, we explain how to compute Witten series associated to classical Lie algebras. Particular instances of these series compute volumes of moduli spaces of flat bundles over surfaces, and also certain multiple zeta values.