Journal of Hyperstructures
Volume:8 Issue: 2, Summer and Autumn 2019

In this paper we prove two pseudo-generalizations of Shannon inequality for the case of norm Inaccuracy Measure and norm entropy. Further, we establish a result on noiseless coding theorem for the proposed mean code length interms of generalized inaccuracy measure

Over the last few decades, several authors have investigated the relationship between the commutativity of ring R and the existence of certain specified derivations of R. In this paper, we introduce the concept of right derivation on semigroups and we study some of the properties of right derivation of semigroups. We prove that if d be a non-zero right derivation of a cancellative ordered semigroup M, then M is a commutative ordered semigroup.

In this paper, the concept of hyper UP-algebras is introduced and some related properties are investigated. Also, the concepts of hyper UP-ideals have been introduced and analyzed. In addition, the concept of homomorphisms between hyper UPalgebras is also considered.

The concept of quasi-ideals, minimal quasi-ideals for Γsemihyperrings are introduced. Characterization of quasi-ideals and of minimal quasi-ideals of Γ-semihyperring with the help of ideals of Γ-semihyperrings have been taken into account. It is proved that for a Γ-semihyperring R with zero, one can find a quasi-ideal of R generated by X, where X is any non empty subset of R. Also the notion of quasi-simple Γ-semihyperring is introduced and proved some properties in this respect.

In this paper c-system , n-system and complete prime Γ-radical in a Γ-semihypergroup are introduced and studied while definition of m-system has been revised. Maximal Γ-hyperideals are studied and the conditions under which maximal Γ-hyperideals are prime and vice versa are investigated. It is proved that intersection of distinct maximal Γ-hyperideals in Γ-semihypergroup is non-empty. Relations between completely prime Γ-hyperideals, c-system and complete prime Γ-radicals are examined.

In this paper, we investigate asymptotic stability of several integral and differential equations.

In this paper, we present quadratic rule for approximate solution of integrals using spline quasi-interpolant. The method is applied for solving the linear Volterra integral equations. Also the convergence analysis of the method is given. The method is applied to a few examples to illustrate the accuracy and implementation of the method.