eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2016-06-01
3
1
1
11
19923
Max-Plus algebra on tensors and its properties
Hamid Reza Afshin
afshin@mail.vru.ac.ir
1
Ali Reza Shojaeifard
ashojaeifard@ihu.ac.ir
2
Department of Mathematics, Vali-e-Asr University, Rafsanjan, Islamic Republic of Iran
Department of Mathematics, Faculty of Sciences, Imam Hossein Comprehensive University, Tehran, Islamic Republic of Iran
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.
http://wala.vru.ac.ir/article_19923_88ef62feab4333580c4d29bc8a94d75f.pdf
Max plus algebra
Tensor
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2016-06-01
3
1
13
25
19924
A computational wavelet method for numerical solution of stochastic Volterra-Fredholm integral equations
Fakhrodin Mohammadi
f.mohammadi62@hotmail.com
1
Hormozgan University
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.
http://wala.vru.ac.ir/article_19924_03eb06bb455bb32b286246d39fdeb99f.pdf
Legendre wavelets, Brownian motion process, Stochastic Volterra-Fredholm integral equations,
Stochastic operational matrix,
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2016-06-01
3
1
27
43
19952
*-frames for operators on Hilbert modules
Bahram Dastourian
bdastorian@gmail.com
1
Mohammad Janfada
janfada@um.ac.ir
2
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran
$K$-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.pdf
K-framesep *-frame
Hilbert
C^*-module
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2016-06-01
3
1
45
52
19953
Inverse Young inequality in quaternion matrices
Seyd Mahmoud Manjegani
manjgani@cc.iut.ac.ir
1
Asghar Norouzi
2
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Islamic Republic of Iran
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.
http://wala.vru.ac.ir/article_19953_35469da2a28c83b1b25944b53b87c748.pdf
Inverse Young inequality
Quaternion matrix
Right eigenvalue
Complex representation
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2016-06-01
3
1
53
60
19955
A note on $lambda$-Aluthge transforms of operators
Seyed Mohammad Sadegh Nabavi Sales
sadegh.nabavi@gmail.com
1
Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran
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 $$||A|^{2lambda}+|A^ast|^{2-2lambda}|leqmax(|A|^{2lambda},|A|^{2-2lambda})+|tilde{A}_lambda|.$$
http://wala.vru.ac.ir/article_19955_e84b542e36ddd38d3218cc0eb4ef380f.pdf
Aluthge transform, Self-adjoint operators, Unitarily invariant norm
Schatten p-norm
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2016-06-01
3
1
61
67
19956
Some results on functionally convex sets in real Banach spaces
Madjid Eshaghi
madjid,eshaghi@gmail.com
1
Hamidreza Reisi
hamidreza.reisi@gmail.com
2
Alireza Moazzen
ar,moazzen@yahoo.com
3
Department of Mathematics‎, ‎Semnan University‎, ‎P‎. ‎O‎. ‎Box 35195-363‎, ‎Semnan‎, ‎Iran,
PhD student of semnan univercity
Department of mathematics‎, ‎Kosar University of Bojnourd‎, ‎Bojnourd‎, ‎Iran
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.
http://wala.vru.ac.ir/article_19956_c84c54eb7ec49c507aa1fd6074db65fe.pdf
convex set
F--convex set
F--closed set