Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19363120160601Max-Plus algebra on tensors and its properties11119923ENHamid RezaAfshinDepartment of Mathematics, Vali-e-Asr University, Rafsanjan, Islamic
Republic of IranAli RezaShojaeifardDepartment of Mathematics, Faculty of Sciences, Imam Hossein
Comprehensive University, Tehran, Islamic Republic of IranJournal Article20160530In 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.http://wala.vru.ac.ir/article_19923_88ef62feab4333580c4d29bc8a94d75f.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19363120160601A computational wavelet method for numerical solution of stochastic Volterra-Fredholm integral equations132519924ENFakhrodinMohammadiHormozgan University0000-0001-9814-0367Journal Article20160530A 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.http://wala.vru.ac.ir/article_19924_03eb06bb455bb32b286246d39fdeb99f.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19363120160601*-frames for operators on Hilbert modules274319952ENBahramDastourianDepartment of Pure Mathematics, Ferdowsi University of Mashhad,
Mashhad, Islamic Republic of IranMohammadJanfadaDepartment of Pure Mathematics, Ferdowsi University of Mashhad,
Mashhad, Islamic Republic of IranJournal Article20150403$K$-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.http://wala.vru.ac.ir/article_19952_c7bf18d637cfcab1233eb3974de29b9a.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19363120160601Inverse Young inequality in quaternion matrices455219953ENSeyd MahmoudManjeganiDepartment of Mathematical Sciences, Isfahan University of Technology,
Isfahan, Islamic Republic of IranAsgharNorouziDepartment of Mathematical Sciences, Isfahan University of Technology,
Isfahan, Islamic Republic of IranJournal Article20151103Inverse 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.http://wala.vru.ac.ir/article_19953_35469da2a28c83b1b25944b53b87c748.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19363120160601A note on $lambda$-Aluthge transforms of operators536019955ENSeyed Mohammad SadeghNabavi SalesDepartment of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, IranJournal Article20151211Let $A=U|A|$ 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 $$||A|^{2lambda}+|A^ast|^{2-2lambda}|leqmax(|A|^{2lambda},|A|^{2-2lambda})+|tilde{A}_lambda|.$$http://wala.vru.ac.ir/article_19955_e84b542e36ddd38d3218cc0eb4ef380f.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19363120160601Some results on functionally convex sets in real Banach spaces616719956ENMadjidEshaghiDepartment of Mathematics‎, ‎Semnan University‎, ‎P‎. ‎O‎. ‎Box 35195-363‎, ‎Semnan‎, ‎Iran,HamidrezaReisiPhD student of semnan univercityAlirezaMoazzenDepartment of mathematics‎, ‎Kosar University of Bojnourd‎, ‎Bojnourd‎, ‎IranJournal Article20160201We 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.http://wala.vru.ac.ir/article_19956_c84c54eb7ec49c507aa1fd6074db65fe.pdf