Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19365220181201*-Operator Frame for End_{\mathcal{A}}^{\ast}(\mathcal{H})1133490410.22072/wala.2018.79871.1153ENRossafiMohamedIbn Tofail University. Kenitra Morocco0000-0002-5662-6921KabbajSamiribn tofail universityJournal Article20180121In this paper, a new notion of frames is introduced: $\ast$-operator frame as generalization of $\ast$-frames in Hilbert $C^{\ast}$-modules introduced by A. Alijani and M. A. Dehghan \cite{Ali} and we establish some results.http://wala.vru.ac.ir/article_34904_640d1329f38755912e93031f21a9b8f6.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19365220181201On the Remarkable Formula for Spectral Distance of Block Southeast Submatrix15203490510.22072/wala.2018.87428.1174ENAlimohammadNazariArak university of Iran0000-0002-3231-0340AtiyehNezamiArak university of Iran0000-0002-3231-0340Journal Article20180602This paper presents a remarkable formula for spectral distance of a given block normal matrix $G_{D_0} = \begin{pmatrix}<br /> A & B \\ <br /> C & D_0<br /> \end{pmatrix} $ to set of block normal matrix $G_{D}$ (as same as $G_{D_0}$ except block $D$ which is replaced by block $D_0$), in which $A \in \mathbb{C}^{n\times n}$ is invertible, $ B \in \mathbb{C}^{n\times m}, C \in \mathbb{C}^{m\times n}$ and $D \in \mathbb{C}^{m\times m}$ with $\rm {Rank\{G_D\}} < n+m-1$<br /> and given eigenvalues of matrix $\mathcal{M} = D - C A^{-1} B $ as $z_1, z_2, \cdots, z_{m}$ where $|z_1|\ge |z_2|\ge \cdots \ge |z_{m-1}|\ge |z_m|$. <br /> Finally, an explicit formula is proven for spectral distance $G_D$ and $G_D_0$ which is expressed by the two last eigenvalues of $\mathcal{M}$.http://wala.vru.ac.ir/article_34905_78e346b85c8a946b0f3cfa66d8b73fb8.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19365220181201C*-Extreme Points and C*-Faces oF the Epigraph iF C*-Affine Maps in *-Rings21283490610.22072/wala.2018.90202.1184ENAliEbrahimi MeymandDepartment of Mathematics, Faculty of mathematical sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Journal Article20180717Abstract. In this paper, we define the notion of C*-affine maps in the<br /> unital *-rings and we investigate the C*-extreme points of the graph<br /> and epigraph of such maps. We show that for a C*-convex map f on a<br /> unital *-ring R satisfying the positive square root axiom with an additional<br /> condition, the graph of f is a C*-face of the epigraph of f. Moreover,<br /> we prove some results about the C*-faces of C*-convex sets in *-rings.<br /> Keywords: C*-affine map, C*-convexity, C*-extreme point, C*-face.<br /> MSC(2010): Primary: 52A01; Secondary: 16W10, 46L89.http://wala.vru.ac.ir/article_34906_0487fcfe738449107469d61b9fb0a584.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19365220181201A Class of Nested Iteration Schemes for Generalized Coupled Sylvester Matrix Equation29453490710.22072/wala.2019.93411.1197ENMaliheSheybaniDepartment of Applied Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranAzitaTajaddiniDepartment of Applied Mathematics, Faculty of Mathematics &amp; Computer Sciences, Shahid Bahonar University of KermanMohammad AliYaghoobiDepartment of Applied Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran.Journal Article20180910Global Krylov subspace methods are the most efficient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose the nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as an inner iteration to approximate each outer iterate, while each outer iteration is induced by a convergence and symmetric positive definite splitting of the coefficient matrices. Convergence properties of this method are investigated. Finally, the effectiveness of the nested splitting conjugate gradient method is explained by some numerical examples.http://wala.vru.ac.ir/article_34907_bfd916a717266b2a7855f332a24eff29.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19365220181201Characterizing Global Minimizers of the Difference of Two Positive Valued Affine Increasing and Co-radiant Functions47583490310.22072/wala.2019.94381.1198ENMohammadAskarizadeh KhanamanMathematics, Mathematics and Computer Science, Shahid Bahonar University of Kerman, Kerman, IranHosseinMohebiShahid Bahonar University of KermanJournal Article20180924Many optimization problems can be reduced to a<br /> problem with an increasing and co-radiant objective function by a suitable transformation of variables. Functions, which are increasing and co-radiant, have found many applications in microeconomic analysis. In this paper, the abstract convexity of positive valued affine increasing and co-radiant (ICR) functions are discussed. Moreover, the basic properties of this class of functions such as support set, subdifferential and maximal elements of support set are characterized. Finally, as an application, necessary and sufficient conditions for the global minimum of the difference of two strictly positive valued affine ICR functions are presented.http://wala.vru.ac.ir/article_34903_c461f903214f87d479115e65193a5909.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19365220181201On Some Special Classes of Sonnenschein Matrices59643299310.22072/wala.2018.92609.1193ENMasodAminizadehVali-e-Asr University of RafsanjanGholamrezaTalebiVali-e-Asr UniversityJournal Article20180827In this paper we consider the special classes of Sonnenschein matrices, namely the Karamata matrices $K[\alpha,\beta]=\left(a_{n,k}\right)$ with the entries <br /> \[{a_{n,k}} = \sum\limits_{v = 0}^k {\left( \begin{array}{l}<br /> n\\<br /> v<br /> \end{array} \right){{\left( {1 - \alpha - \beta } \right)}^v}{\alpha ^{n - v}}\left( \begin{array}{l}<br /> n + k - v - 1\\<br /> \,\,\,\,\,\,\,\,\,\,k - v<br /> \end{array} \right)<br /> {\beta ^{k - v}}},\] and calculate their row and column sums and give some applications of these sums.http://wala.vru.ac.ir/article_32993_0679a9e70167da2fbf8f99f730b4536f.pdf