Journal of Mathematical Extension
Volume:12 Issue: 3, Summer 2018

In this paper, we introduce a new kind of the logical entropy through a local relative approach. The notions of local relative logical entropy and local relative conditional logical entropy from an observer’s viewpoint on local relative probability measure space are introduced and some of their ergodic properties are studied. Some properties of the local relative logical entropy of independent partitions are investigated and the concavity property for the local relative logical entropy has been proved. We show that, the basic properties of Shannon entropy of partitions on probability measure spaces, are established for the case of the local relative logical entropy. So the suggested measures can be used besides of the Shannon entropy of partitions. Using the concept of the local relative logical entropy of partitions, we define the local relative logical entropy of a dynamical system and present some of its properties. Finally, it is shown that the local relative logical entropy of dynamical systems is invariant under isomorphism. So the notion of local relative logical entropy of dynamical systems can be a new tool for distinction of non-isomorphic relative dynamical systems

The main purpose of this paper is to investigate weak amenability of semigroup algebras. We relate this to a new notion of weak amenability modulo an ideal of Banach algebras. As an important result, we show that l 1 (S) is weakly amenable modulo Iσ, where Iσ is the corresponding ideal of the group congruence σ

In the literature, the Euler-Maruyama (EM) method for approximation purposes of stochastic differential Equations (SDE) driven by α-stable Lévy motions is reported. Convergence in probability of that method was proven but it is surrounded by some ambiguities. To accomplish the but without ambiguities, this article has derived convergence in probability of numerical EM method based on diffusion given by semimartingales for SDEs driven by α-stable processes. Some examples are provided, their numerical solution are obtained and theoretical results are reconfirmed. The adopted method could be applied to other subclasses of semimartingales.

This paper suggests a novel and efficient method for solving systems of Fredholm-Volterra integro-differential equations (FVIDEs). A Chebyshev matrix approach is implemented for solving linear and nonlinear FVIDEs under initial boundary conditions. The aim of this work is to construct a quick and precise numerical approximation by a simple, tasteful and powerful algorithm based on the Chebyshev series representation for solving such systems. The properties of shifted Chebyshev polynomials are used to transform the system of FVIDEs into a system of algebraic equations. Then, the corresponding matrix equation will be solved by using the Galerkin-like procedure to find the unknown coefficients which are related to the approximate solution. Also, the polynomial convergence rate of our method is discussed by preparing some theorems and lemmas. Finally, some numerical examples are given to illuminate the reliability and high accuracy of this algorithm in comparison with some other well-known methods.

We propose a new class of continuous distributions with two extra shape parameters named the Odd Log-Logistic Poisson-G family. Some of its mathematical properties including moments, quantile, generating functions and order statistics are obtained. We estimate the model parameters by the maximum likelihood method and present a Monte Carlo simulation study. The importance of the proposed family is demonstrated by means of three real data applications. Empirical results indicate that proposed family provides better fits than other well-known classes of distributions in real applications.

In this paper we construct the Stancu type q-KantrovichSz´asz-Mirakjan operators generated by Dunkl generalization of the exponential function. We obtain some approximation results using the Korovkin approximation theorem and the weighted Korovkin-type theorem for these operators. We also study convergence properties by using the modulus of continuity and the rate of convergence for functions belonging to the Lipschitz class. Furthermore, we obtain the rate of convergence in terms of the classical, the second order, and the weighted modulus of continuity

A larger class of algebraic hyperstructures satisfying the group-like axioms is the class of Hv-groups. In this paper, without any condition and in general, we define the Hv-normal subgroup and the Hv-quotient group of an Hv-group. We introduce the fundamental equivalence relation of an Hv-quotient group and prove the first and third isomorphism theorems for Hv-groups.

Following the concept of L-limited sets in dual Banach spaces introduced by Salimi and Moshtaghioun, we introduce the concept of almost L-limited sets in dual Banach lattices and then by a class of disjoint limited completely continuous operators on Banach lattices, we characterize Banach lattices in which almost L-limited subsets of their dual, coincide with L–limited sets.