The Wave Equation in Non-classic Cases: Non-self Adjoint with Non-local and Non-periodic Boundary Conditions 2 1 چکیده 2 In this paper has been studied the wave equation in some non-classic cases. In the rst 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 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 Fourier method. By compatibility conditions and asymptotic expansions of the Fourier coe cients, the convergence of series solutions are proved. At last series solution are established and the uniqueness of the solution is proved by a special way which has not been used in classic texts. . 1 12 2014/05/1 1393/2/11 2014/05/1 1393/2/11 Mohammad Jahanshahi Mohammad Jahanshahi jahanshahi@azaruniv.edu Asghar Ahmadkhanlu Asghar Ahmadkhanlu s.a.ahmadkhanlu@azaruniv.edu Wave equation Non-local &amp non-periodic Boundary Conditions Asymptotic expansion. ## ##

On Hyper Pseudo BCK-algebras 2 2 In this paper, we introduce the notion of hyper pseudo B C K - algebras, which is a generalization of pseudo BCK -algebras and hyper BCK -algebras and we investigates some related properties. In follow, we de ne some kinds of hyper pseudo BCK -ideals of a hyper pseudo BCK - algebra and we find the relations among them. Finally, we characterize the hyper pseudo BCK -ideals of type 4 generated by a nonempty subset. 13 29 2014/05/12014/05/1 1393/2/11 2014/05/12014/05/1 1393/2/11 R. A. Borzooei R. A. Borzooei borzooei@sbu.ac.ir A. Rezazadeh A. Rezazadeh Rezazade2008@gmail.com R. Ameri R. Ameri rez_ameri@yahoo.com Hyper pseudo BCK-algebras Hyper pseudo BCK-ideals Generated hyper pseudo BCK-ideals . ## ##

Diagonal and Monomial Solutions of the Matrix Equation AXB=C جوابهایی از نوع ماتریسهای قطری و تک جمله ای برای معادله ماتریسی AXB=C 2 2 In this article, we consider the matrix equation $AXB=C$, 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 $min_X |C-AXB |_F$ where $X$ is a diagonal or monomial matrix. The explicit expressions of the optimal solution and the minimum norm solution are both provided. 31 42 2014/05/12014/05/12012/03/23 1391/1/4 2014/05/12014/05/12014/04/8 1393/1/19 مسعود امان Massoud Aman Author mamann@birjand.ac.ir Matrix equation Diagonal matrix Monomial matrix Least squares problem. ## ##

On the Graphs Related to Green Relations of Finite Semigroups 2 2 In this paper we develop an analog of the notion of the con- jugacy graph of nite groups for the nite semigroups by considering the Green relations of a nite semigroup. More precisely, by de ning the new graphs $Gamma_{L}(S)$, $Gamma_{H}(S)$, $Gamma_{J}(S)$ and $Gamma_{D}(S)$ (we name them the Green graphs) related to the Green relations L R J H and D of a nite semigroup S , we first attempt to prove that the graphs $Gamma_{D}(S)$ and $Gamma_{H}(S)$ have exactly one connected component, and this graphs for regu- lar semigroups are complete. And secondly, we give a necessary condition for a nite semigroup to be regular. This study shows an intrinsic di er- ence 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. 43 51 2014/05/12014/05/12012/03/232014/05/1 1393/2/11 2014/05/12014/05/12014/04/82014/05/1 1393/2/11 A. Gharibkhajeh A. Gharibkhajeh a_gharib@iau-tnb.ac.ir H. Doostie H. Doostie doostih@gmail.com Conjugacy graph Regular semigroup Green relations. ## ##

Binary Multiquasigroups with Medial-Like Equations شبه گروه های چند گانه دوتایی دارای اتحادهای شبیه به اتحاد مدیال 2 2 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. 53 62 2014/05/12014/05/12012/03/232014/05/12012/07/30 1391/5/9 2014/05/12014/05/12014/04/82014/05/12014/04/8 1393/1/19 امیر احسانی Amir Ehsani Mahshahr Branch, Islamic Azad University a.ehsani@mahshahriau.ac.ir Yuri Movsisyan Yuri Movsisyan Yerevan State University yurimovsisyan@yahoo.com Medial Paramedial Co-medial Co-paramedial Multiquasigroup Mode. ## ##

Generalized Symmetric Berwald Spaces فضاهای بروالدی متقارن تعمیم یافته 2 2 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. 63 69 2014/05/12014/05/12012/03/232014/05/12012/07/302012/08/20 1391/5/30 2014/05/12014/05/12014/04/82014/05/12014/04/82014/04/8 1393/1/19 پرستو حبیبی Parastoo Habibi Department of Mathematics p.habibi@iau-astara.ac.ir اسدالله رضوی Asadollah Razavi Faculty of Mathematics and Computer Science arazavi@aut.ac.ir Homogeneous Finsler space Symmetric space Generalized symmetric space Berwald space. ## ##

Some Results on TVS-cone Normed Spaces and Algebraic Cone Metric Spaces نتایجی روی فضاهای نرمدار مخروطی 2 2 In this paper we introduce the cone bounded linear mapping and demonstrate a proof to 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 cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we introduce the notion of algebraically cone metric and we will show that every algebraically cone metric space has a topology. 71 80 2014/05/12014/05/12012/03/232014/05/12012/07/302012/08/202012/10/9 1391/7/18 2014/05/12014/05/12014/04/82014/05/12014/04/82014/04/82014/04/8 1393/1/19 Assadollah Niknam Assadollah Niknam professor Saeedeh Shamsi Gamchi Saeedeh Shamsi Gamchi Ph.D student Mohammad Janfada Mohammad Janfada associate professor Cone bounded Equivalent cone norms Algebraically cone metric. ## ##

On Hyperideal Structure of Ternary Semihypergroups 2 1 چکیده 2 In this paper, we introduce and study the concepts of prime left, semiprime left and irreducible left hyperideals in ternary semihyper- groups and investigate some basic properties of them. We introduce the concepts of hyper lter and hypersemilattice congruence of ternary semi- hypergroups. We give some characterizations of hyper lters in ternary semihypergroups. Some relationships between hyper lters, 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. 81 98 2014/05/12014/05/12012/03/232014/05/12012/07/302012/08/202012/10/92014/05/1 1393/2/11 2014/05/12014/05/12014/04/82014/05/12014/04/82014/04/82014/04/82014/05/1 1393/2/11 Kostaq Hila Kostaq Hila kostaq_hila@yahoo.com Bijan Davvaz Bijan Davvaz davvaz@yazd.ac.ir Krisanthi Naka Krisanthi Naka khila@uogj.edu.al Semihypergroup Ternary semihypergroup Hyperideal Prime left hyperideal Semiprime left hyperideal Irreducible left hyperideal Hyper lter Left m-system Left i-system Left p-system. ## ##

ABSTRACTS IN PERSIAN - Vol. 9, No. 1 2 2 Please see the full text contains the Pesian abstracts for this volume. 99 107 2014/05/12014/05/12012/03/232014/05/12012/07/302012/08/202012/10/92014/05/12016/01/27 1394/11/7 2014/05/12014/05/12014/04/82014/05/12014/04/82014/04/82014/04/82014/05/12016/01/27 1394/11/7 Name of Authors in This Volume Name of Authors in This Volume ## ##