Iranian Journal of Mathematical Sciences and Informatics
Year:2014 | Volume:9 | Issue:1|Papers Count:8

In this paper the wave equation in some non-classic cases has been studied. In the first case boundary conditions are non-local and non- periodic. At that case the associated spectral problem is a self-adjoint problem and consequently the eigenvalues are real. But in the second case the associated spectral problem is non-self-adjoint and consequently the eigenvalues are complex numbers, in which two cases, the solutions of the problem are constructed by the Fourier method. By compatibility conditions and asymptotic expansions of the Fourier coefficients, the convergence of series solutions are proved.Finally, series solutions are established and the uniqueness of the solution is proved by a special way which has not been used in classic texts.

In this paper, we introduce the notion of hyper pseudo BC K - algebras, which is a generalization of pseudo BC K -algebras and hyper BC K -algebras and we investigates some related properties. In follow, we define some kinds of hyper pseudo BC K -ideals of a hyper pseudo BC K - algebra and we find the relations among them. Finally, we characterize the hyper pseudo BC K -ideals of type 4 generated by a nonempty subset.  

In this article, we consider the matrix equation AX B=C, where A, B, C are given matrices and give new necessary and sufficient conditions for the existence of the diagonal solutions and monomial solutions to this equation. We also present a general form of such solutions. Moreover, we consider the least squares problem min X C -AX B F where X is a diagonal or monomial matrix. The explicit expressions of the optimal solution and the minimum norm solution are both provided.

In this paper we develop an analog of the notion of the conjugacy graph of finite groups for the finite semigroups by considering the Green relations of a finite semigroup. More precisely, by defining the new graphs ΓL (S), ΓR (S), ΓH (S), ΓJ (S) and ΓD (S) (we name them the Green graphs) related to the Green relations L, R, J, H and D of a finite semigroup S, we first attempt to prove that the graphs ΓL (S) and ΓH (S) have exactly one connected component, and this graphs for regular semigroups are complete. Next, we give a necessary condition for a finite semigroup to be regular. This study shows an intrinsic difference between the conjugacy graphs (of groups) and the Green graphs (of semigroups) as well. Finally, our calculations include two kinds of semi- groups, mostly involving the well known Lucas numbers, and examining the proved assertions.

In this paper paramedial, co-medial and co-paramedial binary multiquasigroups are considered and a characterization of the corresponding component operations of these multiquasigroups is given.

In this paper we study generalized symmetric Berwald spaces. We show that if a Berwald space (M, F) admits a parallel s-structure then it is locally symmetric. For a complete Berwald space which admits a parallel s-structure we show that if the flag curvature of (M, F) is everywhere nonzero, then F is Riemannian.

In this paper we introduce the cone bounded linear mapping and show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two TVS-cone norms are equivalent if and only if they induce equivalent topologies. In the sequel, the notion of algebraic cone metric is introduced and it is shown that every algebraic cone metric space has a topology and the Banach fixed point theorem for contraction mappings on algebraic cone metric spaces is proved.

In this paper, we introduce and study the concepts of prime left, semiprime left and irreducible left hyperideals in ternary semihypergroups and investigate some basic properties of them. We introduce the concepts of hyperfilter and hypersemilattice congruence of ternary semi- hypergroups. We give some characterizations of hyperfilters in ternary semihypergroups. Some relationships between hyperfilters, prime hyper- ideals and hypersemilattice congruences in ternary semihypergroups are considered. We also introduce the notion of hyperideals extensions in ternary semihypergroups and some properties of them are investigated.