*-Operator Frame for End_{\mathcal{A}}^{\ast}(\mathcal{H}) Rossafi Mohamed Ibn Tofail University. Kenitra Morocco author Kabbaj Samir ibn tofail university author text article 2019 eng In 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. Wavelet and Linear Algebra Vali-e-Asr university of Rafsanjan 2383-1936 5 v. 2 no. 2019 1 13 http://wala.vru.ac.ir/article_34904_640d1329f38755912e93031f21a9b8f6.pdf dx.doi.org/10.22072/wala.2018.79871.1153 On the Remarkable Formula for Spectral Distance of Block Southeast Submatrix Alimohammad Nazari Arak university of Iran author Atiyeh Nezami Arak university of Iran author text article 2019 eng ‎‎‎This paper presents a remarkable formula for spectral distance of a given block normal matrix $G_{D_0} = \begin{pmatrix}‎ ‎A & B \\‎ ‎C & D_0‎ ‎\end{pmatrix}$ 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 $\rm {Rank\{G_D\}} < n+m-1$‎ ‎and given eigenvalues of matrix $\mathcal{M} = D‎ - ‎C A^{-1} B$ as $z_1‎, ‎z_2‎, ‎\cdots‎, ‎z_{m}$ where $|z_1|\ge |z_2|\ge \cdots \ge |z_{m-1}|\ge |z_m|$‎. Finally, an explicit formula is proven for spectral distance $G_D$ and $G_D_0$ which is expressed by the two last eigenvalues of $\mathcal{M}$. Wavelet and Linear Algebra Vali-e-Asr university of Rafsanjan 2383-1936 5 v. 2 no. 2019 15 20 http://wala.vru.ac.ir/article_34905_78e346b85c8a946b0f3cfa66d8b73fb8.pdf dx.doi.org/10.22072/wala.2018.87428.1174 C*-Extreme Points and C*-Faces oF the Epigraph iF C*-Affine Maps in *-Rings Ali Ebrahimi Meymand Department of Mathematics, Faculty of mathematical sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. author text article 2019 eng Abstract. In this paper, we define the notion of C*-affine maps in the unital *-rings and we investigate the C*-extreme points of the graph and epigraph of such maps. We show that for a C*-convex map f on a unital *-ring R satisfying the positive square root axiom with an additional condition, the graph of f is a C*-face of the epigraph of f. Moreover, we prove some results about the C*-faces of C*-convex sets in *-rings. Keywords: C*-affine map, C*-convexity, C*-extreme point, C*-face. MSC(2010): Primary: 52A01; Secondary: 16W10, 46L89. Wavelet and Linear Algebra Vali-e-Asr university of Rafsanjan 2383-1936 5 v. 2 no. 2019 21 28 http://wala.vru.ac.ir/article_34906_0487fcfe738449107469d61b9fb0a584.pdf dx.doi.org/10.22072/wala.2018.90202.1184 A Class of Nested Iteration Schemes for Generalized Coupled Sylvester Matrix Equation Malihe Sheybani Department of Applied Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran author Azita Tajaddini Department of Applied Mathematics, Faculty of Mathematics &amp;amp; Computer Sciences, Shahid Bahonar University of Kerman author Mohammad Ali Yaghoobi Department of Applied Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran. author text article 2019 eng Global 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. Wavelet and Linear Algebra Vali-e-Asr university of Rafsanjan 2383-1936 5 v. 2 no. 2019 29 45 http://wala.vru.ac.ir/article_34907_bfd916a717266b2a7855f332a24eff29.pdf dx.doi.org/10.22072/wala.2019.93411.1197 Characterizing Global Minimizers of the Difference of Two Positive Valued Affine Increasing and Co-radiant Functions Mohammad Askarizadeh Khanaman Mathematics, Mathematics and Computer Science, Shahid Bahonar University of Kerman, Kerman, Iran author Hossein Mohebi Shahid Bahonar University of Kerman author text article 2019 eng ‎Many optimization problems can be reduced to a 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. Wavelet and Linear Algebra Vali-e-Asr university of Rafsanjan 2383-1936 5 v. 2 no. 2019 47 58 http://wala.vru.ac.ir/article_34903_c461f903214f87d479115e65193a5909.pdf dx.doi.org/10.22072/wala.2019.94381.1198 On Some Special Classes of Sonnenschein Matrices Masod Aminizadeh Vali-e-Asr University of Rafsanjan author Gholamreza Talebi Vali-e-Asr University author text article 2019 eng ‎In 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 ‎${a_{n,k}} = \sum\limits_{v = 0}^k {\left( \begin{array}{l}‎ ‎n\\‎ ‎v‎ ‎\end{array} \right){{\left( {1‎ - ‎\alpha‎ - ‎\beta } \right)}^v}{\alpha ^{n‎ - ‎v}}\left( \begin{array}{l}‎ ‎n‎ + ‎k‎ - ‎v‎ - ‎1\\‎ ‎\,\,\,\,\,\,\,\,\,\,k‎ - ‎v‎ ‎\end{array} \right)‎ ‎{\beta ^{k‎ - ‎v}}},$ and calculate their row and column sums and give some applications of these sums‎. Wavelet and Linear Algebra Vali-e-Asr university of Rafsanjan 2383-1936 5 v. 2 no. 2019 59 64 http://wala.vru.ac.ir/article_32993_0679a9e70167da2fbf8f99f730b4536f.pdf dx.doi.org/10.22072/wala.2018.92609.1193