Volume 25, Issue 1

In this paper we have constructed the goodness-of-fit tests incorporating several components, like expectation and covariance function for identification of a non-centered univariate random sequence or auto-covariances and cross-covariances for identification of a centered multivariate random sequence. For the construction of the corresponding estimators and investigation of their properties we utilized the theory of square Gaussian random variables.

In this paper, we formulate an epidemic model for the spread of an infectious disease in a population of varying size. The total population is divided into three distinct epidemiological subclass of individuals (susceptible, infectious and recovered) and we study a deterministic and stochastic models with saturated incidence rate. The stochastic model is obtained by incorporating a random noise into the deterministic model. In the deterministic case, we briefly discuss the global asymptotic stability of the disease free equilibrium by using a Lyapunov function. For the stochastic version, we study the global existence and positivity of the solution. Under suitable conditions on the intensity of the white noise perturbation, we prove that there are a p -th moment exponential stability and almost sure exponential stability of the disease free equilibrium. Furthermore, sufficient conditions for the extinction of the disease are obtained and the asymptotic behavior around the endemic equilibrium is studied. Finally, we give some numerical simulations to illustrate our theoretical results.

We apply simulated quantum evolution to image processing, and examine its practicality in the context of image denoising. More specifically, in our approach image processing consists of three stages: First, a digitized gray-scale image is represented as a quantum variable – typically, a density matrix. Second, the quantum variable is evolved via the Markovian master equation in Lindblad form. Third, the quantum variable is back-converted into an image. Numerical experiments indicate remarkable denoising results are obtained in this way for a suitable choice of flow parameters. To our knowledge the proposed image processing technique is conceptually new.

In the present article, we study an economic model that was suggested by Anderlini and Canning and which applies to a class of generalized Bayesian abstract fuzzy economy for product measurable spaces together with a related abstract rationality function. We prove that this model is structurally stable which implies that it is robust to ε-equilibria.

In this paper, we deal with a new type of differential equations called generalized anticipated backward doubly stochastic differential equations (GA-BDSDEs). The coefficients of these BDSDEs depend on the future value of the solution (Y,Z)${(Y,Z)}$. We obtain an existence and uniqueness theorem and a comparison theorem for the reflected solutions of these equations.

In this work, under some conditions, we will prove that a scalar stochastic differential equation with periodic coefficients admits almost periodic solutions.