Max-Plus algebra on tensors and its properties
Hamid Reza
Afshin
Department of Mathematics, Vali-e-Asr University, Rafsanjan, Islamic
Republic of Iran
author
Ali Reza
Shojaeifard
Department of Mathematics, Faculty of Sciences, Imam Hossein
Comprehensive University, Tehran, Islamic Republic of Iran
author
text
article
2016
eng
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.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
3
v.
1
no.
2016
1
11
http://wala.vru.ac.ir/article_19923_88ef62feab4333580c4d29bc8a94d75f.pdf
A computational wavelet method for numerical solution of stochastic Volterra-Fredholm integral equations
Fakhrodin
Mohammadi
Hormozgan University
author
text
article
2016
eng
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.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
3
v.
1
no.
2016
13
25
http://wala.vru.ac.ir/article_19924_03eb06bb455bb32b286246d39fdeb99f.pdf
*-frames for operators on Hilbert modules
Bahram
Dastourian
Department of Pure Mathematics, Ferdowsi University of Mashhad,
Mashhad, Islamic Republic of Iran
author
Mohammad
Janfada
Department of Pure Mathematics, Ferdowsi University of Mashhad,
Mashhad, Islamic Republic of Iran
author
text
article
2016
eng
$K$-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.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
3
v.
1
no.
2016
27
43
http://wala.vru.ac.ir/article_19952_c7bf18d637cfcab1233eb3974de29b9a.pdf
Inverse Young inequality in quaternion matrices
Seyd Mahmoud
Manjegani
Department of Mathematical Sciences, Isfahan University of Technology,
Isfahan, Islamic Republic of Iran
author
Asghar
Norouzi
Department of Mathematical Sciences, Isfahan University of Technology,
Isfahan, Islamic Republic of Iran
author
text
article
2016
eng
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.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
3
v.
1
no.
2016
45
52
http://wala.vru.ac.ir/article_19953_35469da2a28c83b1b25944b53b87c748.pdf
A note on $lambda$-Aluthge transforms of operators
Seyed Mohammad Sadegh
Nabavi Sales
Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran
author
text
article
2016
eng
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 $$||A|^{2lambda}+|A^ast|^{2-2lambda}|leqmax(|A|^{2lambda},|A|^{2-2lambda})+|tilde{A}_lambda|.$$
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
3
v.
1
no.
2016
53
60
http://wala.vru.ac.ir/article_19955_e84b542e36ddd38d3218cc0eb4ef380f.pdf
Some results on functionally convex sets in real Banach spaces
Madjid
Eshaghi
Department of Mathematics‎, ‎Semnan University‎, ‎P‎. ‎O‎. ‎Box 35195-363‎, ‎Semnan‎, ‎Iran,
author
Hamidreza
Reisi
PhD student of semnan univercity
author
Alireza
Moazzen
Department of mathematics‎, ‎Kosar University of Bojnourd‎, ‎Bojnourd‎, ‎Iran
author
text
article
2016
eng
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.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
3
v.
1
no.
2016
61
67
http://wala.vru.ac.ir/article_19956_c84c54eb7ec49c507aa1fd6074db65fe.pdf