Optimality conditions for the calculus of variations with higher-order delta derivatives

We prove the Euler-Lagrange delta-differential equations for problems of the calculus of variations on arbitrary time scales with delta-integral functionals depending on higher-order delta derivatives.Comment: Submitted 26/Jul/2009; Revised 04/Aug/2010; Accepted 09/Aug/2010; for publication in "Applied Mathematics Letters

On a Linear Chaotic Quantum Harmonic Oscillator

We show that a linear quantum harmonic oscillator is chaotic in the sense of Li-Yorke. We also prove that the weighted backward shift map, used as an infinite dimensional linear chaos model, in a separable Hilbert space is chaotic in the sense of Li-Yorke, in addition to being chaotic in the sense of Devaney.Comment: LaTex file. Applied Mathematics Letters, to appea

Symmetric Differentiation on Time Scales

We define a symmetric derivative on an arbitrary nonempty closed subset of the real numbers and derive some of its properties. It is shown that real-valued functions defined on time scales that are neither delta nor nabla differentiable can be symmetric differentiable.Comment: This is a preprint of a paper whose final and definite form will be published in Applied Mathematics Letters. Submitted 30-Jul-2012; revised 07-Sept-2012; accepted 10-Sept-201

A stochastic SICA epidemic model for HIV transmission

We propose a stochastic SICA epidemic model for HIV transmission, described by stochastic ordinary differential equations, and discuss its perturbation by environmental white noise. Existence and uniqueness of the global positive solution to the stochastic HIV system is proven, and conditions under which extinction and persistence in mean hold, are given. The theoretical results are illustrated via numerical simulations.Comment: This is a preprint of a paper whose final and definite form is with 'Applied Mathematics Letters', ISSN 0893-9659. Submitted 22/Jan/2018; Revised 03/May/2018; Accepted for publication 03/May/201

Homomorphisms between fuzzy information systems revisited

Recently, Wang et al. discussed the properties of fuzzy information systems under homomorphisms in the paper [C. Wang, D. Chen, L. Zhu, Homomorphisms between fuzzy information systems, Applied Mathematics Letters 22 (2009) 1045-1050], where homomorphisms are based upon the concepts of consistent functions and fuzzy relation mappings. In this paper, we classify consistent functions as predecessor-consistent and successor-consistent, and then proceed to present more properties of consistent functions. In addition, we improve some characterizations of fuzzy relation mappings provided by Wang et al.Comment: 10 page