We consider the von Kármán nonlinearity and the Casimir force to develop reduced-order models for prestressed clamped rectangular and circular electrostatically actuated microplates. Reduced-order models are derived by taking flexural vibration mode shapes as basis functions for the transverse displacement. The in-plane displacement vector is decomposed as the sum of displacements for irrotatio...

in this paper, we consider the construction of a new class ofnumerical methods based on the backward differentiation formulas(bdfs) that be equipped by including two off--step points. werepresent these methods from general linear methods (glms) pointof view which provides an easy process to improve their stabilityproperties and implementation in a variable stepsize mode. thesesuperiorities are ...

With the exception of q-hypergeometric summation, the use of computer algebra packages implementing Zeilberger’s “holonomic systems approach” in a broader mathematical sense is less common in the field of q-series and basic hypergeometric functions. A major objective of this article is to popularize the usage of such tools also in these domains. Concrete case studies showing software in action ...

In this article we introduce some definitions concerning measurable functions and prove related properties. In this paper k is a natural number, r is a real number, i is an integer, and q is a rational number. The subset Z − of R is defined by: (Def. 1) r ∈ Z − iff there exists k such that r = −k. Let us note that Z − is non empty. The following three propositions are true: (1) N ≈ Z −. Z is a ...