2019-09-15T18:23:53Z
http://wala.vru.ac.ir/?_action=export&rf=summon&issue=3344
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2016
3
1
Max-Plus algebra on tensors and its properties
Hamid Reza
Afshin
Ali Reza
Shojaeifard
In this paper we generalize the max plus algebra system of real matrices to the class of real tensors and derive its fundamental properties. Also we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverses of tensors is characterized.
Max plus algebra
Tensor
2016
06
01
1
11
http://wala.vru.ac.ir/article_19923_88ef62feab4333580c4d29bc8a94d75f.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2016
3
1
A computational wavelet method for numerical solution of stochastic Volterra-Fredholm integral equations
Fakhrodin
Mohammadi
A Legendre wavelet method is presented for numerical solutions of stochastic Volterra-Fredholm integral equations. The main characteristic of the proposed method is that it reduces stochastic Volterra-Fredholm integral equations into a linear system of equations. Convergence and error analysis of the Legendre wavelets basis are investigated. The efficiency and accuracy of the proposed method was demonstrated by some non-trivial examples and comparison with the block pulse functions method.
Legendre wavelets, Brownian motion process, Stochastic Volterra-Fredholm integral equations,
Stochastic operational matrix,
2016
06
01
13
25
http://wala.vru.ac.ir/article_19924_03eb06bb455bb32b286246d39fdeb99f.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2016
3
1
*-frames for operators on Hilbert modules
Bahram
Dastourian
Mohammad
Janfada
$K$-frames which are generalization of frames on Hilbert spaces, were introduced to study atomic systems with respect to a bounded linear operator. In this paper, $*$-$K$-frames on Hilbert $C^*$-modules, as a generalization of $K$-frames, are introduced and some of their properties are obtained. Then some relations between $*$-$K$-frames and $*$-atomic systems with respect to an adjointable operator are considered and some characterizations of $*$-$K$-frames are given. Finally perturbations of $*$-$K$-frames are discussed.
K-framesep *-frame
Hilbert
C^*-module
2016
06
01
27
43
http://wala.vru.ac.ir/article_19952_c7bf18d637cfcab1233eb3974de29b9a.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2016
3
1
Inverse Young inequality in quaternion matrices
Seyd Mahmoud
Manjegani
Asghar
Norouzi
Inverse Young inequality asserts that if $nu >1$, then $|zw|ge nu|z|^{frac{1}{nu}}+(1-nu)|w|^{frac{1}{1-nu}}$, for all complex numbers $z$ and $w$, and equality holds if and only if $|z|^{frac{1}{nu}}=|w|^{frac{1}{1-nu}}$. In this paper the complex representation of quaternion matrices is applied to establish the inverse Young inequality for matrices of quaternions. Moreover, a necessary and sufficient condition for equality is given.
Inverse Young inequality
Quaternion matrix
Right eigenvalue
Complex representation
2016
06
01
45
52
http://wala.vru.ac.ir/article_19953_35469da2a28c83b1b25944b53b87c748.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2016
3
1
A note on $lambda$-Aluthge transforms of operators
Seyed Mohammad Sadegh
Nabavi Sales
Let $A=U|A|$ be the polar decomposition of an operator $A$ on a Hilbert space $mathscr{H}$ and $lambdain(0,1)$. The $lambda$-Aluthge transform of $A$ is defined by $tilde{A}_lambda:=|A|^lambda U|A|^{1-lambda}$. In this paper we show that emph{i}) when $mathscr{N}(|A|)=0$, $A$ is self-adjoint if and only if so is $tilde{A}_lambda$ for some $lambdaneq{1over2}$. Also $A$ is self adjoint if and only if $A=tilde{A}_lambda^ast$, emph{ii}) if $A$ is normaloid and either $sigma(A)$ has only finitely many distinct nonzero value or $U$ is unitary, then from $A=ctilde{A}_lambda$ for some complex number $c$, we can conclude that $A$ is quasinormal, emph{iii}) if $A^2$ is self-adjoint and any one of the $Re(A)$ or $-Re(A)$ is positive definite then $A$ is self-adjoint, emph{iv}) and finally we show that $$opnorm{|A|^{2lambda}+|A^ast|^{2-2lambda}oplus0}leqopnorm{|A|^{2-2lambda}oplus|A|^{2lambda}}+ opnorm{tilde{A}_lambdaoplus(tilde{A}_lambda)^ast}$$ where $opnorm{cdot}$ stand for some unitarily invariant norm. From that we conclude that $$||A|^{2lambda}+|A^ast|^{2-2lambda}|leqmax(|A|^{2lambda},|A|^{2-2lambda})+|tilde{A}_lambda|.$$
Aluthge transform, Self-adjoint operators, Unitarily invariant norm
Schatten p-norm
2016
06
01
53
60
http://wala.vru.ac.ir/article_19955_e84b542e36ddd38d3218cc0eb4ef380f.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2016
3
1
Some results on functionally convex sets in real Banach spaces
Madjid
Eshaghi
Hamidreza
Reisi
Alireza
Moazzen
We use of two notions functionally convex (briefly, F--convex) and functionally closed (briefly, F--closed) in functional analysis and obtain more results. We show that if $lbrace A_{alpha} rbrace _{alpha in I}$ is a family $F$--convex subsets with non empty intersection of a Banach space $X$, then $bigcup_{alphain I}A_{alpha}$ is F--convex. Moreover, we introduce new definition of notion F--convexiy.
convex set
F--convex set
F--closed set
2016
06
01
61
67
http://wala.vru.ac.ir/article_19956_c84c54eb7ec49c507aa1fd6074db65fe.pdf