Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 2476-3926 3 1 2016 06 01 Max-Plus algebra on tensors and its properties 1 11 EN Hamid Reza Afshin Department of Mathematics, Vali-e-Asr University, Rafsanjan, Islamic Republic of Iran afshin@mail.vru.ac.ir Ali Reza Shojaeifard Department of Mathematics, Faculty of Sciences, Imam Hossein Comprehensive University, Tehran, Islamic Republic of Iran ashojaeifard@ihu.ac.ir 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 http://wala.vru.ac.ir/article_19923.html http://wala.vru.ac.ir/article_19923_88ef62feab4333580c4d29bc8a94d75f.pdf
Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 2476-3926 3 1 2016 06 01 A computational wavelet method for numerical solution of stochastic Volterra-Fredholm integral equations 13 25 EN Fakhrodin Mohammadi 0000-0001-9814-0367 Hormozgan University f.mohammadi62@hotmail.com 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, http://wala.vru.ac.ir/article_19924.html http://wala.vru.ac.ir/article_19924_03eb06bb455bb32b286246d39fdeb99f.pdf
Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 2476-3926 3 1 2016 06 01 *-frames for operators on Hilbert modules 27 43 EN Bahram Dastourian Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran bdastorian@gmail.com Mohammad Janfada Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran janfada@um.ac.ir \$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 http://wala.vru.ac.ir/article_19952.html http://wala.vru.ac.ir/article_19952_c7bf18d637cfcab1233eb3974de29b9a.pdf
Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 2476-3926 3 1 2016 06 01 Inverse Young inequality in quaternion matrices 45 52 EN Seyd Mahmoud Manjegani Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Islamic Republic of Iran manjgani@cc.iut.ac.ir Asghar Norouzi Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Islamic Republic of Iran 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 http://wala.vru.ac.ir/article_19953.html http://wala.vru.ac.ir/article_19953_35469da2a28c83b1b25944b53b87c748.pdf
Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 2476-3926 3 1 2016 06 01 A note on \$lambda\$-Aluthge transforms of operators 53 60 EN Seyed Mohammad Sadegh Nabavi Sales Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran sadegh.nabavi@gmail.com 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 http://wala.vru.ac.ir/article_19955.html http://wala.vru.ac.ir/article_19955_e84b542e36ddd38d3218cc0eb4ef380f.pdf
Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 2476-3926 3 1 2016 06 01 Some results on functionally convex sets in real Banach spaces 61 67 EN Madjid Eshaghi Department of Mathematics&lrm;, &lrm;Semnan University&lrm;, &lrm;P&lrm;. &lrm;O&lrm;. &lrm;Box 35195-363&lrm;, &lrm;Semnan&lrm;, &lrm;Iran, madjid,eshaghi@gmail.com Hamidreza Reisi PhD student of semnan univercity hamidreza.reisi@gmail.com Alireza Moazzen Department of mathematics&lrm;, &lrm;Kosar University of Bojnourd&lrm;, &lrm;Bojnourd&lrm;, &lrm;Iran ar,moazzen@yahoo.com ‎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 http://wala.vru.ac.ir/article_19956.html http://wala.vru.ac.ir/article_19956_c84c54eb7ec49c507aa1fd6074db65fe.pdf