فهرست مطالب

موجکها و جبر خطی - سال سوم شماره 2 (2016)
  • سال سوم شماره 2 (2016)
  • تاریخ انتشار: 1395/10/15
  • تعداد عناوین: 6
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  • Arash Ghaani Farashahi * Pages 1-18
    This 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.
    Keywords: Finite field, classical wavelet group, quasi, regular representation, classical wavelet systems, classical dilation operators
  • Ashok Kumar Sah* Pages 19-32
    In this paper we study necessary and sufficient conditions for some types of linear combinations of wave packet frames to be a frame for L^2(R^d). Further, we illustrate our results with some examples and applications.
    Keywords: Frames, Wave Packet Systems, Linear Combinations
  • Alemeh Sheikhhosseini, Golamreza Aghamollaei * Pages 33-42
    Let ýX be an ýýn-ýýýýýýsquare complex matrix with the ýCartesian decomposition ýýX = A i ýBýýýýý, ýwhere ýýA ýand ýýB ýare ýýýn ýýtimes ný ýHermitian ýmatrices. ýIt ýis ýknown ýthat ýý$Vert X Vert_p^2 ýleq 2(Vert A Vert_p^2 Vert B Vert_p^2)ýýý$, ýwhere ýý$ýp ýýgeq 2ý$ý ýand ýý$ýýVert . Vert_p$ ýis ýthe ýSchatten ýýýýp-norm.ý ýý ýýIn this paperý, this inequality and some of its improvements are studied and investigated ýfor the joint C-numerical radius, joint spectral radius, and for the ýC-spectral norm of matrices.
    Keywords: ?joint C, numerical radius?, ?C, spectral norm?, ?joint spectral radius
  • Hamide Azarmi, Radjabali Kamyabi Gol, Mohammad Janfada * Pages 43-54
    ýLet $G$ be a locally compact abelian groupý. ýThe concept of a generalized multiresolution structure (GMS) in $L^2(G)$ is discussed which is a generalization of GMS in $L^2(mathbb{R})$ý. ýBasically 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 levelý. ýAlsoý, ýthe construction of affine frames for $L^2(G)$ based on a GMS is presentedý.
    Keywords: ?Pseudoframe, generalized multiresolution structure, locally compact group?, ?affine pseudoframe?
  • Ataollah Askari Hemmat *, Tahereh Ismaeelpour, Habibollah Saeedi Pages 55-68
    In this work, we proposed an ef ective method based on cubic and pantic B-spline scaling functions to solve partial di fferential equations of frac- tional order. Our method is based on dual functions of B-spline scaling func- tions. 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 e fectivity of the technique.
    Keywords: B, spline, Wavelet, fractional equation, partial differential equation, Operational matrix of integration
  • Hossein Momenaee Kermani * Pages 69-74
    In 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.
    Keywords: Triangularizable, Semigroup, Irreducible, Division ring, Reduced trace