Numerical Computation of Exponential Functions of Nabla Fractional Calculus

In this article, we illustrate the asymptotic behaviour of exponential functions of nabla fractional calculus. For this purpose, we propose a novel matrix technique to compute these functions numerically

Why Delannoy numbers?

This article is not a research paper, but a little note on the history of combinatorics: We present here a tentative short biography of Henri Delannoy, and a survey of his most notable works. This answers to the question raised in the title, as these works are related to lattice paths enumeration, to the so-called Delannoy numbers, and were the first general way to solve Ballot-like problems. These numbers appear in probabilistic game theory, alignments of DNA sequences, tiling problems, temporal representation models, analysis of algorithms and combinatorial structures.Comment: Presented to the conference "Lattice Paths Combinatorics and Discrete Distributions" (Athens, June 5-7, 2002) and to appear in the Journal of Statistical Planning and Inference

An Overview of Variational Integrators

The purpose of this paper is to survey some recent advances in variational integrators for both finite dimensional mechanical systems as well as continuum mechanics. These advances include the general development of discrete mechanics, applications to dissipative systems, collisions, spacetime integration algorithms, AVI’s (Asynchronous Variational Integrators), as well as reduction for discrete mechanical systems. To keep the article within the set limits, we will only treat each topic briefly and will not attempt to develop any particular topic in any depth. We hope, nonetheless, that this paper serves as a useful guide to the literature as well as to future directions and open problems in the subject