Wavelet and Linear AlgebraWavelet and Linear Algebra
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Sun, 18 Feb 2018 03:00:20 +0100FeedCreatorWavelet and Linear Algebra
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Feed provided by Wavelet and Linear Algebra. Click to visit.On the two-wavelet localization operators on homogeneous spaces with relatively invariant ...
http://wala.vru.ac.ir/article_29395_4297.html
In ‎the present ‎paper, ‎we ‎introduce the ‎two-wavelet ‎localization ‎operator ‎for ‎the square ‎integrable ‎representation ‎of a‎ ‎homogeneous space‎ with respect to a relatively invariant measure. ‎We show that it is a bounded linear operator. We investigate ‎some ‎properties ‎of the ‎two-wavelet ‎localization ‎operator ‎and ‎show ‎that ‎it ‎is a‎ ‎compact ‎operator ‎and is ‎contained ‎in‎ a Schatten $p$-class‎.Thu, 30 Nov 2017 20:30:00 +0100Characterizing sub-topical functions
http://wala.vru.ac.ir/article_29393_4297.html
In this paper, we first give a characterization of sub-topical functions with respect to their lower level sets and epigraph. Next, by using two different classes of elementary functions, we present a characterization of sub-topical functions with respect to their polar functions, and investigate the relation between polar functions and support sets of this class of functions. Finally, we obtain more results on the polar of sub-topical functions.Thu, 30 Nov 2017 20:30:00 +0100Linear preservers of Miranda-Thompson majorization on MM;N
http://wala.vru.ac.ir/article_29392_4297.html
Miranda-Thompson majorization is a group-induced cone ordering on Rn induced by the group of generalized permutation with determinants equal to 1. In this paper, we generalize Miranda-Thompson majorization on the matrices. For X, Y 2 Mm;n, X is said to be Miranda- Thompson majorized by Y (denoted by X mt Y ) if there exists some D 2 Conv(G) such that X = DY . Also, we characterize linear preservers of this concept on Mm;n.Thu, 30 Nov 2017 20:30:00 +0100Wilson wavelets for solving nonlinear stochastic integral equations
http://wala.vru.ac.ir/article_29388_4297.html
A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^o-Volterra integral equations. To do this a new stochastic operational matrix of It^o integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operational matrices of integration and stochastic integration, the problem under study is transformed to a system of nonlinear algebraic equations which can be simply solved to obtain an approximate solution for the main problem. Moreover, a new technique for computing nonlinear terms in such problems is presented. Furthermore, convergence of Wilson wavelets expansion is investigated. Several examples are presented to show the eciency and accuracy of the proposed method.Thu, 30 Nov 2017 20:30:00 +0100Some results on Haar wavelets matrix through linear algebra
http://wala.vru.ac.ir/article_29498_4297.html
Can we characterize the wavelets through linear transformation? the answer for this question is certainly YES. In this paper we have characterized the Haar wavelet matrix by their linear transformation and proved some theorems on properties of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.Fri, 05 Jan 2018 20:30:00 +0100On a new G-frame and duality
http://wala.vru.ac.ir/article_26091_0.html
In this note we introduce a new (singleton) g-frame, g-orthonormal and g-Riesz bases and compare them with the corresponding notions in [14] and [1]. Also, we continue our research on frame operator of a g-frame and obtain a relation between Sun [14] and Ali et al. [1] frame operators. Then we study duality in g-frames and establish relations between dual of g-frames and dual of continuous frames. Finally, we illustrate an example which provides a suitable translation from discrete frames to Sun's g-frames.Fri, 23 Jun 2017 19:30:00 +0100Projection Inequalities and Their Linear Preservers
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This paper introduces an inequality on vectors in $mathbb{R}^n$ which compares vectors in $mathbb{R}^n$ based on the $p$-norm of their projections on $mathbb{R}^k$ ($kleq n$). For $p>0$, we say $x$ is $d$-projectionally less than or equal to $y$ with respect to $p$-norm if $sum_{i=1}^kvert x_ivert^p$ is less than or equal to $ sum_{i=1}^kvert y_ivert^p$, for every $dleq kleq n$. For a relation $sim$ on a set $X$, we say a map $f:X rightarrow X$ is a preserver of that relation, if $xsim y$ implies $f(x)sim f(y)$, for every $x,yin X$. All the linear maps that preserve $d$-projectional equality and inequality are characterized in this paper.Thu, 30 Nov 2017 20:30:00 +0100A necessary condition for a Shearlet system to be a frame via admissibility
http://wala.vru.ac.ir/article_26093_0.html
Necessary conditions for shearlet and cone-adapted shearlet systems to be frames are presented with respect to the admissibility condition of genera- tors. Discrete and cone-adapted discrete shearlet systems are studied by Kutyniok and Labate in [11, 13]. They have derived sufficient conditions in [11] for a discrete shearlet system to form a frame for L2(R2) We provide a relation between shearlet frames and admissibility condition of the generators.Fri, 23 Jun 2017 19:30:00 +0100Banach Pair Frames
http://wala.vru.ac.ir/article_26094_0.html
In this article, we consider pair frames in Banach spaces and introduce Banach pair frames. Some various concepts in the frame theory such as frames, Schauder frames, Banach frames and atomic decompositions are considered as special kinds of (Banach) pair frames. Some frame-like inequalities for (Banach) pair frames are presented. The elements that participant in the construction of (Banach) pair frames are characterized. It is shown that a Banach space X has a Banach pair frame with respect to a Banach scalar sequence space l, when it is precisely isomorphic to a complemented subspace of l. It is shown that if we are allowed to choose the scalar sequence space, pair frames and Banach pair frames with respect to the chosen scalar sequence space denote the same concept.Fri, 23 Jun 2017 19:30:00 +0100Some Results on Convex Spectral Functions: I
http://wala.vru.ac.ir/article_29390_0.html
In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-definite programmings and engineering problems.Tue, 02 Jan 2018 20:30:00 +0100padic Shearlets
http://wala.vru.ac.ir/article_29394_0.html
The field $ Q_p $ of p-adic numbers is defined as the completion of the field of the rational numbers Q with respect to the p-adic norm $ |.|_p$. In this paper, we study the continuous and discrete p-adic shearlet systems on $ L^2(Q^2_p)$ . We also suggest discrete padic shearlet frames. Several examples are provided.Tue, 02 Jan 2018 20:30:00 +0100