@article {
author = {Ghaani Farashahi, Arash},
title = {Classical wavelet systems over finite fields},
journal = {Wavelet and Linear Algebra},
volume = {3},
number = {2},
pages = {1-18},
year = {2016},
publisher = {Vali-e-Asr university of Rafsanjan},
issn = {2383-1936},
eissn = {2476-3926},
doi = {10.22072/wala.2016.23236},
abstract = {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},
url = {http://wala.vru.ac.ir/article_23236.html},
eprint = {http://wala.vru.ac.ir/article_23236_5150e489e24248c000bc17f050d8b322.pdf}
}
@article {
author = {Sah, Ashok},
title = {Linear combinations of wave packet frames for L^2(R^d)},
journal = {Wavelet and Linear Algebra},
volume = {3},
number = {2},
pages = {19-32},
year = {2016},
publisher = {Vali-e-Asr university of Rafsanjan},
issn = {2383-1936},
eissn = {2476-3926},
doi = {10.22072/wala.2016.23237},
abstract = {In 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.},
keywords = {Frames,Wave Packet Systems,Linear Combinations},
url = {http://wala.vru.ac.ir/article_23237.html},
eprint = {http://wala.vru.ac.ir/article_23237_9748c2d52d39dc6189458e4f3a485660.pdf}
}
@article {
author = {Sheikhhosseini, Alemeh and Aghamollaei, Golamreza},
title = {Cartesian decomposition of matrices and some norm inequalities},
journal = {Wavelet and Linear Algebra},
volume = {3},
number = {2},
pages = {33-42},
year = {2016},
publisher = {Vali-e-Asr university of Rafsanjan},
issn = {2383-1936},
eissn = {2476-3926},
doi = {10.22072/wala.2016.23238},
abstract = {Let 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.},
keywords = {joint C-numerical radius,C-spectral norm,joint spectral radius},
url = {http://wala.vru.ac.ir/article_23238.html},
eprint = {http://wala.vru.ac.ir/article_23238_64b86b56682082a7a0b0f1d249c90a93.pdf}
}
@article {
author = {Azarmi, Hamide and Kamyabi Gol, Radjabali and Janfada, Mohammad},
title = {Pseudoframe multiresolution structure on abelian locally compact groups},
journal = {Wavelet and Linear Algebra},
volume = {3},
number = {2},
pages = {43-54},
year = {2016},
publisher = {Vali-e-Asr university of Rafsanjan},
issn = {2383-1936},
eissn = {2476-3926},
doi = {10.22072/wala.2016.23239},
abstract = {Let $G$ 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.},
keywords = {Pseudoframe,generalized multiresolution structure,locally compact group, affine pseudoframe},
url = {http://wala.vru.ac.ir/article_23239.html},
eprint = {http://wala.vru.ac.ir/article_23239_9bab4fd5ee9537b7e6c4e65984d3cc78.pdf}
}
@article {
author = {Askari Hemmat, Ataollah and Ismaeelpour, Tahereh and Saeedi, Habibollah},
title = {Quartic and pantic B-spline operational matrix of fractional integration},
journal = {Wavelet and Linear Algebra},
volume = {3},
number = {2},
pages = {55-68},
year = {2016},
publisher = {Vali-e-Asr university of Rafsanjan},
issn = {2383-1936},
eissn = {2476-3926},
doi = {10.22072/wala.2016.23240},
abstract = {In 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.},
keywords = {B-spline,Wavelet,fractional equation,partial differential equation,Operational matrix of integration},
url = {http://wala.vru.ac.ir/article_23240.html},
eprint = {http://wala.vru.ac.ir/article_23240_9ff0784850a6139d46d8de6393191c71.pdf}
}
@article {
author = {Momenaee Kermani, Hossein},
title = {Triangularization over finite-dimensional division rings using the reduced trace},
journal = {Wavelet and Linear Algebra},
volume = {3},
number = {2},
pages = {69-74},
year = {2016},
publisher = {Vali-e-Asr university of Rafsanjan},
issn = {2383-1936},
eissn = {2476-3926},
doi = {10.22072/wala.2016.23241},
abstract = {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},
url = {http://wala.vru.ac.ir/article_23241.html},
eprint = {http://wala.vru.ac.ir/article_23241_1e8aafe10279931fe51e54733c2efcbc.pdf}
}