eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2019-01-12
5
2
1
13
10.22072/wala.2018.79871.1153
34904
*-Operator Frame for End_{mathcal{A}}^{ast}(mathcal{H})
Rossafi Mohamed
rossafimohamed@gmail.com
1
Kabbaj Samir
samkabbaj@yahoo.fr
2
Ibn Tofail University. Kenitra Morocco
ibn tofail university
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.
http://wala.vru.ac.ir/article_34904_640d1329f38755912e93031f21a9b8f6.pdf
$ast$-frame
operator frame
$ast$-operator frame
$C^{ast}$-algebra
Hilbert $mathcal{A}$-modules
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2019-01-12
5
2
15
20
10.22072/wala.2018.87428.1174
34905
On the Remarkable Formula for Spectral Distance of Block Southeast Submatrix
Alimohammad Nazari
a-nazari@araku.ac.ir
1
Atiyeh Nezami
a-nezami@arshad.araku.ac.ir
2
Arak university of Iran
Arak university of Iran
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 $mathcal{M}$.
http://wala.vru.ac.ir/article_34905_78e346b85c8a946b0f3cfa66d8b73fb8.pdf
Eigenvalues
Normal matrix
Distance norm
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2019-01-12
5
2
21
28
10.22072/wala.2018.90202.1184
34906
C*-Extreme Points and C*-Faces oF the Epigraph iF C*-Affine Maps in *-Rings
Ali Ebrahimi Meymand
a.ebrahimi@vru.ac.ir
1
Department of Mathematics, Faculty of mathematical sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
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.
http://wala.vru.ac.ir/article_34906_0487fcfe738449107469d61b9fb0a584.pdf
C*-affine map
C*-convexity
C*-extreme point
C*-face
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2019-01-12
5
2
29
45
10.22072/wala.2019.93411.1197
34907
A Class of Nested Iteration Schemes for Generalized Coupled Sylvester Matrix Equation
Malihe Sheybani
malihe@gmail.com
1
Azita Tajaddini
atajadini@uk.ac.ir
2
Mohammad Ali Yaghoobi
yaghoobi@uk.ac.ir
3
Department of Applied Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Applied Mathematics, Faculty of Mathematics &amp; Computer Sciences, Shahid Bahonar University of Kerman
Department of Applied Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran.
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.
http://wala.vru.ac.ir/article_34907_bfd916a717266b2a7855f332a24eff29.pdf
Generalized coupled Sylvester equation
NSCG method
inner and outer iteration
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2019-01-12
5
2
47
58
10.22072/wala.2019.94381.1198
34903
Characterizing Global Minimizers of the Difference of Two Positive Valued Affine Increasing and Co-radiant Functions
Mohammad Askarizadeh Khanaman
m.askarizadeh2018@gmail.com
1
Hossein Mohebi
hmohebi@uk.ac.ir
2
Mathematics, Mathematics and Computer Science, Shahid Bahonar University of Kerman, Kerman, Iran
Shahid Bahonar University of Kerman
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.
http://wala.vru.ac.ir/article_34903_c461f903214f87d479115e65193a5909.pdf
Abstract convexity
co-radiant function
increasing function
affine increasing and co-radiant function
global minimum
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2019-01-12
5
2
59
64
10.22072/wala.2018.92609.1193
32993
On Some Special Classes of Sonnenschein Matrices
Masod Aminizadeh
m.aminizadeh@vru.ac.ir
1
Gholamreza Talebi
gh.talebi@vru.ac.ir
2
Vali-e-Asr University of Rafsanjan
Vali-e-Asr University
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.
http://wala.vru.ac.ir/article_32993_0679a9e70167da2fbf8f99f730b4536f.pdf
Sonnenschein matrix
Binomial coefficients identity
Sequence space