Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19363220161201Classical wavelet systems over finite fields1182323610.22072/wala.2016.23236ENArash Ghaani FarashahiUniversity of ViennaJournal Article20151123This article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. It is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full wavelet frames as well, and hence each vector defined over a finite field can be represented as a finite coherent sum of classical wavelet coefficients as well.Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19363220161201Linear combinations of wave packet frames for L^2(R^d)19322323710.22072/wala.2016.23237ENAshok KumarSahUniversity of DelhiJournal Article20151004In this paper we study necessary and sufficient conditions for some types of linear combinations of wave packet frames to be a frame for L2(Rd). Further, we illustrate our results with some examples and applications.Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19363220161201Cartesian decomposition of matrices and some norm inequalities33422323810.22072/wala.2016.23238ENAlemeh SheikhhosseiniDepartment of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, IranGolamreza AghamollaeiDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranJournal Article20160226Let X be an n-square complex matrix with the Cartesian decomposition X = A + i B, where A and B are n times n Hermitian matrices. It is known that $Vert X Vert_p^2 leq 2(Vert A Vert_p^2 + Vert B Vert_p^2)$, where $p geq 2$ and $Vert . Vert_p$ is the Schatten p-norm. In this paper, this inequality and some of its improvements are studied and investigated for the joint C-numerical radius, joint spectral radius, and for the C-spectral norm of matrices.Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19363220161201Pseudoframe multiresolution structure on abelian locally compact groups43542323910.22072/wala.2016.23239ENHamide AzarmiPh. D. student in Ferdowsi University of MashhadRadjabali Kamyabi GolDepartment of pure Mathematics; Ferdowsi University of Mashhad;Mohammad JanfadaDepartment of pure Mathematics;Ferdowsi University of Mashhad;Journal Article20151231Let $G$ be a locally compact abelian group. The concept of a generalized multiresolution structure (GMS) in $L^2(G)$ is discussed which is a generalization of GMS in $L^2(mathbb{R})$. Basically a GMS in $L^2(G)$ consists of an increasing sequence of closed subspaces of $L^2(G)$ and a pseudoframe of translation type at each level. Also, the construction of affine frames for $L^2(G)$ based on a GMS is presented.Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19363220161201Quartic and pantic B-spline operational matrix of fractional integration55682324010.22072/wala.2016.23240ENAtaollah Askari HemmatDepatrment of Mathematics Graduate University of Advanced TechnologyTahereh IsmaeelpourShahid Bahonar University of KermanHabibollah SaeediShahid Bahonar University of Kerman, Kerman, IranJournal Article20160531In this work, we proposed an effective method based on cubic and pantic B-spline scaling functions to solve partial differential equations of fractional order. Our method is based on dual functions of B-spline scaling functions. We derived the operational matrix of fractional integration of cubic and pantic B-spline scaling functions and used them to transform the mentioned equations to a system of algebraic equations. Some examples are presented to show the applicability and effectivity of the technique.Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19363220161201Triangularization over finite-dimensional division rings using the reduced trace69742324110.22072/wala.2016.23241ENHossein Momenaee KermaniDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of KermanJournal Article20160727In this paper we study triangularization of collections of matrices whose entries come from a finite-dimensional division ring. First, we give a generalization of Guralnick's theorem to the case of finite-dimensional division rings and then we show that in this case the reduced trace function is a suitable alternative for trace function by presenting two triangularization results. The first one is a generalization of a result due to Kaplansky and in the second one a triangularizability condition which is dependent on a single element is presented.