Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
5
2
2019
01
12
*-Operator Frame for End_{mathcal{A}}^{ast}(mathcal{H})
1
13
EN
Rossafi
Mohamed
0000-0002-5662-6921
Ibn Tofail University. Kenitra Morocco
rossafimohamed@gmail.com
Kabbaj
Samir
ibn tofail university
samkabbaj@yahoo.fr
10.22072/wala.2018.79871.1153
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.
$ast$-frame,operator frame,$ast$-operator frame,$C^{ast}$-algebra,Hilbert $mathcal{A}$-modules
http://wala.vru.ac.ir/article_34904.html
http://wala.vru.ac.ir/article_34904_640d1329f38755912e93031f21a9b8f6.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
5
2
2019
01
12
On the Remarkable Formula for Spectral Distance of Block Southeast Submatrix
15
20
EN
Alimohammad
Nazari
0000-0002-3231-0340
Arak university of Iran
a-nazari@araku.ac.ir
Atiyeh
Nezami
0000-0002-3231-0340
Arak university of Iran
a-nezami@arshad.araku.ac.ir
10.22072/wala.2018.87428.1174
This 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 $A in mathbb{C}^{ntimes n}$ is invertible, $ B in mathbb{C}^{ntimes m}, C in mathbb{C}^{mtimes n}$ and $D in mathbb{C}^{mtimes m}$ 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 $mathcal{M}$.
Eigenvalues,Normal matrix,Distance norm
http://wala.vru.ac.ir/article_34905.html
http://wala.vru.ac.ir/article_34905_78e346b85c8a946b0f3cfa66d8b73fb8.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
5
2
2019
01
12
C*-Extreme Points and C*-Faces oF the Epigraph iF C*-Affine Maps in *-Rings
21
28
EN
Ali
Ebrahimi Meymand
Department of Mathematics, Faculty of mathematical sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
a.ebrahimi@vru.ac.ir
10.22072/wala.2018.90202.1184
Abstract. 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.
C*-affine map,C*-convexity,C*-extreme point,C*-face
http://wala.vru.ac.ir/article_34906.html
http://wala.vru.ac.ir/article_34906_0487fcfe738449107469d61b9fb0a584.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
5
2
2019
01
12
A Class of Nested Iteration Schemes for Generalized Coupled Sylvester Matrix Equation
29
45
EN
Malihe
Sheybani
Department of Applied Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
malihe@gmail.com
Azita
Tajaddini
Department of Applied Mathematics, Faculty of Mathematics &amp; Computer Sciences, Shahid Bahonar University of Kerman
atajadini@uk.ac.ir
Mohammad Ali
Yaghoobi
Department of Applied Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran.
yaghoobi@uk.ac.ir
10.22072/wala.2019.93411.1197
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.
Generalized coupled Sylvester equation,NSCG method,inner and outer iteration
http://wala.vru.ac.ir/article_34907.html
http://wala.vru.ac.ir/article_34907_bfd916a717266b2a7855f332a24eff29.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
5
2
2019
01
12
Characterizing Global Minimizers of the Difference of Two Positive Valued Affine Increasing and Co-radiant Functions
47
58
EN
Mohammad
Askarizadeh Khanaman
Mathematics, Mathematics and Computer Science, Shahid Bahonar University of Kerman, Kerman, Iran
m.askarizadeh2018@gmail.com
Hossein
Mohebi
Shahid Bahonar University of Kerman
hmohebi@uk.ac.ir
10.22072/wala.2019.94381.1198
Many 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.
Abstract convexity,co-radiant function,increasing function,affine increasing and co-radiant function,global minimum
http://wala.vru.ac.ir/article_34903.html
http://wala.vru.ac.ir/article_34903_c461f903214f87d479115e65193a5909.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
5
2
2019
01
12
On Some Special Classes of Sonnenschein Matrices
59
64
EN
Masod
Aminizadeh
Vali-e-Asr University of Rafsanjan
m.aminizadeh@vru.ac.ir
Gholamreza
Talebi
Vali-e-Asr University
gh.talebi@vru.ac.ir
10.22072/wala.2018.92609.1193
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 <br /> [{a_{n,k}} = sumlimits_{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.
Sonnenschein matrix,Binomial coefficients identity,Sequence space
http://wala.vru.ac.ir/article_32993.html
http://wala.vru.ac.ir/article_32993_0679a9e70167da2fbf8f99f730b4536f.pdf