eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2017-12-01
4
2
1
12
10.22072/wala.2017.61228.1109
29395
On the two-wavelet localization operators on homogeneous spaces with relatively invariant measures
Fatemeh Esmaeelzadeh
faride.esmaeelzadeh@yahoo.com
1
Rajab Ali Kamyabi-Gol
kamyabi@ferdowsi.um.ac.ir
2
Reihaneh Raisi Tousi
raisi@ferdowsi.um.ac.ir
3
Department of Mathematics‎, ‎Bojnourd Branch‎, ‎Islamic Azad University‎, ‎Bojnourd‎, ‎Iran
Department of Mathematics‎, ‎Center of Excellency in Analysis on Algebraic Structures(CEAAS)‎, ‎Ferdowsi University Of Mashhad‎, Iran
‎Ferdowsi University Of Mashhad
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.
http://wala.vru.ac.ir/article_29395_ef5554cee1c1583c3bc9f17d5bb7d85c.pdf
homogenous space
square integrable representation
wavelet transform
localization operator
Schatten $p$-class operator
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2017-12-01
4
2
13
23
10.22072/wala.2017.61257.1110
29393
Characterizing sub-topical functions
Hassan Bakhtiari
hbakhtiari@math.uk.ac.ir
1
Hossein Mohebi
hmohebi@uk.ac.ir
2
Shahid Bahonar University of Kerman
Shahid Bahonar University of Kerman
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.
http://wala.vru.ac.ir/article_29393_0ee808b7959b2874e9dabf0d4972296f.pdf
sub-topical function
elementary function
polar function
plus-co-radiant set
abstract convexity
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2017-12-01
4
2
25
32
10.22072/wala.2017.61736.1113
29392
Linear preservers of Miranda-Thompson majorization on MM;N
Ahmad Mohammadhasani
a.mohammadhasani53@gmail.com
1
Asma Ilkhanizadeh Manesh
a.ilkhani@vru.ac.ir
2
Department of Mathematics, Sirjan University of technology, Sirjan, Iran
Vali-e-Asr University of Rafsanjan
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 $<strong>M</strong>_{m,n}$.
http://wala.vru.ac.ir/article_29392_451002d1ba46987bb96f23d9a78e8e6a.pdf
Group-induced cone ordering
Linear preserver
Miranda-Thompson majorization
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2017-12-01
4
2
33
48
10.22072/wala.2017.59458.1106
29388
Wilson wavelets for solving nonlinear stochastic integral equations
Bibi Khadijeh Mousavi
khmosavi@gmail.com
1
Ataollah Askari Hemmat
askarihemmat@gmail.com
2
Mohammad Hossien Heydari
heydari@stu.yazd.ac.ir
3
Department of Pure Mathematica, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
Shiraz University of Technology, Shiraz,
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.
http://wala.vru.ac.ir/article_29388_cab6f5111dc82287318b83ae253c9278.pdf
Wilson wavelets
Nonlinear stochastic It^o-Volterra integral equation
Stochastic operational matrix
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2017-12-01
4
2
49
59
10.22072/wala.2018.53432.1093
29498
Some results on Haar wavelets matrix through linear algebra
Siddu Shiralasetti
shiralashettisc@gmail.com
1
Kumbinarasaiah S
kumbinarasaiah@gmail.com
2
Pavate nagar
Pavate nagar
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.
http://wala.vru.ac.ir/article_29498_344e26e2a5021349b589b01c71d47239.pdf
Linear transformation
Haar wavelets matrix
Eigenvalues and vectors
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2017-12-01
4
2
61
67
10.22072/wala.2017.63024.1115
29391
Projection Inequalities and Their Linear Preservers
Mina Jamshidi
m.jamshidi@kgut.ac.ir
1
Farzad Fatehi
f.fatehi@sussex.ac.uk
2
Graduate University of Advanced Technology, Kerman, Iran.
University of Sussex, Brighton, United Kingdom.
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.
http://wala.vru.ac.ir/article_29391_0c3c85a7a89bc6f8ac60bfcc89b198b0.pdf
projectional inequality
Linear preserver
inequality of vectors