*-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; 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