Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
4
2
2017
12
01
On the two-wavelet localization operators on homogeneous spaces with relatively invariant measures
1
12
EN
Fatemeh
Esmaeelzadeh
Department of Mathematics‎, ‎Bojnourd Branch‎, ‎Islamic Azad University‎, ‎Bojnourd‎, ‎Iran
faride.esmaeelzadeh@yahoo.com
Rajab Ali
Kamyabi-Gol
Department of Mathematics‎, ‎Center of Excellency in Analysis on Algebraic Structures(CEAAS)‎, ‎Ferdowsi University Of Mashhad‎, Iran
kamyabi@ferdowsi.um.ac.ir
Reihaneh
Raisi Tousi
‎Ferdowsi University Of Mashhad
raisi@ferdowsi.um.ac.ir
10.22072/wala.2017.61228.1109
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.
homogenous space,square integrable representation,wavelet transform, localization operator,Schatten $p$-class operator
http://wala.vru.ac.ir/article_29395.html
http://wala.vru.ac.ir/article_29395_ef5554cee1c1583c3bc9f17d5bb7d85c.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
4
2
2017
12
01
Characterizing sub-topical functions
13
23
EN
Hassan
Bakhtiari
Shahid Bahonar University of Kerman
hbakhtiari@math.uk.ac.ir
Hossein
Mohebi
Shahid Bahonar University of Kerman
hmohebi@uk.ac.ir
10.22072/wala.2017.61257.1110
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.
sub-topical function,elementary function,polar function,plus-co-radiant set,abstract convexity
http://wala.vru.ac.ir/article_29393.html
http://wala.vru.ac.ir/article_29393_0ee808b7959b2874e9dabf0d4972296f.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
4
2
2017
12
01
Linear preservers of Miranda-Thompson majorization on MM;N
25
32
EN
Ahmad
Mohammadhasani
Department of Mathematics, Sirjan University of technology, Sirjan, Iran
a.mohammadhasani53@gmail.com
Asma
Ilkhanizadeh Manesh
Vali-e-Asr University of Rafsanjan
a.ilkhani@vru.ac.ir
10.22072/wala.2017.61736.1113
Miranda-Thompson majorization is a group-induced cone ordering on $mathbb{R}^{n}$ induced by the group of generalized permutation with determinants equal to 1. In this paper, we generalize Miranda-Thompson majorization on the matrices. For $X$, $Yin <strong>M</strong>_{m,n}$, $X$ is said to be Miranda-Thompson majorized by $Y$ (denoted by $Xprec_{mt}Y$) if there exists some $Din rm{Conv(G)}$ such that $X=DY$. Also, we characterize linear preservers of this concept on $<strong>M</strong>_{m,n}$.
Group-induced cone ordering,Linear preserver,Miranda-Thompson majorization
http://wala.vru.ac.ir/article_29392.html
http://wala.vru.ac.ir/article_29392_451002d1ba46987bb96f23d9a78e8e6a.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
4
2
2017
12
01
Wilson wavelets for solving nonlinear stochastic integral equations
33
48
EN
Bibi Khadijeh
Mousavi
Department of Pure Mathematica, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
khmosavi@gmail.com
Ataollah
Askari Hemmat
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
askarihemmat@gmail.com
Mohammad Hossien
Heydari
Shiraz University of Technology, Shiraz,
heydari@stu.yazd.ac.ir
10.22072/wala.2017.59458.1106
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 efficiency and accuracy of the proposed method.
Wilson wavelets,Nonlinear stochastic It^o-Volterra integral equation,Stochastic operational matrix
http://wala.vru.ac.ir/article_29388.html
http://wala.vru.ac.ir/article_29388_cab6f5111dc82287318b83ae253c9278.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
4
2
2017
12
01
Some results on Haar wavelets matrix through linear algebra
49
59
EN
Siddu
Shiralasetti
Pavate nagar
shiralashettisc@gmail.com
Kumbinarasaiah
S
Pavate nagar
kumbinarasaiah@gmail.com
10.22072/wala.2018.53432.1093
Can we characterize the wavelets through linear transformation? the answer<br /> for this question is certainly YES. In this paper we have characterized the Haar<br /> wavelet matrix by their linear transformation and proved some theorems on properties<br /> of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.
Linear transformation,Haar wavelets matrix,Eigenvalues and vectors
http://wala.vru.ac.ir/article_29498.html
http://wala.vru.ac.ir/article_29498_344e26e2a5021349b589b01c71d47239.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
4
2
2017
12
01
Projection Inequalities and Their Linear Preservers
61
67
EN
Mina
Jamshidi
Graduate University of Advanced Technology, Kerman, Iran.
m.jamshidi@kgut.ac.ir
Farzad
Fatehi
University of Sussex, Brighton, United Kingdom.
f.fatehi@sussex.ac.uk
10.22072/wala.2017.63024.1115
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<br /> projections on $mathbb{R}^k$ ($kleq n$).<br /> 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.
projectional inequality,Linear preserver,inequality of vectors
http://wala.vru.ac.ir/article_29391.html
http://wala.vru.ac.ir/article_29391_0c3c85a7a89bc6f8ac60bfcc89b198b0.pdf