Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
1
1
2014
08
01
A recursive construction of a class of finite normalized tight frames
1
7
EN
A.
Abdollahi
Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Islamic
Republic of Iran
M.
Monfaredpour
Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Islamic
Republic of Iran
Finite normalized tight frames are interesting because they provide decompositions in applications and some physical interpretations. In this article, we give a recursive method for constructing them.
Frames,Tight frames
http://wala.vru.ac.ir/article_6346.html
http://wala.vru.ac.ir/article_6346_895b0ba8664f383e834b9250eddf7e7b.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
1
1
2014
08
01
Dilation of a family of g-frames
9
18
EN
M.
Abdollahpour
Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh
Ardabili, Ardabil, Islamic Republic of Iran
In this paper, we first discuss about canonical dual of g-frame ΛP = {ΛiP ∈ B(H, Hi) : i ∈ I}, where Λ = {Λi ∈ B(H, Hi) : i ∈ I} is a g-frame for a Hilbert space H and P is the orthogonal projection from H onto a closed subspace M. Next, we prove that, if Λ = {Λi ∈ B(H, Hi) : i ∈ I} and Θ = {Θi ∈ B(K, Hi) : i ∈ I} be respective g-frames for non zero Hilbert spaces H and K, and Λ and Θ are unitarily equivalent (similar), then Λ and Θ can not be weakly disjoint. On the other hand, we study dilation property for g-frames and we show that two g-frames for a Hilbert space have dilation property, if they are disjoint, or they are similar, or one of them is similar to a dual g-frame of another one. We also prove that a family of g-frames for a Hilbert space has dilation property, if all the members in that family have the same deficiency.
g-Riesz basis,G-Frame,disjointnes
http://wala.vru.ac.ir/article_6347.html
http://wala.vru.ac.ir/article_6347_0ea5a42f7e87f2c43f8086abf7878646.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
1
1
2014
08
01
Legendre wavelets method for numerical solution of time-fractional heat equation
19
31
EN
M. H.
Heydari
Department of Mathematics, Faculty of Mathematics, Yazd University, Yazd, Islamic
Republic of Iran
F. M.
Maalek Ghaini
Department of Mathematics, Faculty of Mathematics, Yazd University, Yazd, Islamic
Republic of Iran
M. R.
Hooshmandasl
Department of Mathematics, Faculty of Mathematics, Yazd University, Yazd, Islamic
Republic of Iran
In this paper, we develop an efficient Legendre wavelets collocation method for well known time-fractional heat equation. In the proposed method, we apply operational matrix of fractional integration to obtain numerical solution of the inhomogeneous time-fractional heat equation with lateral heat loss and Dirichlet boundary conditions. The power of this manageable method is confirmed. Moreover, the use of Legendre wavelets is found to be accurate, simple and fast.
Legendre wavelets,Operational matrix of fractional integration,Time-fractional heat equation
http://wala.vru.ac.ir/article_6348.html
http://wala.vru.ac.ir/article_6348_52d83c0167386adc6df2799b9a2ea736.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
1
1
2014
08
01
Application of Shannon wavelet for solving boundary value problems of fractional differential equations I
33
42
EN
K.
Nouri
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box:
19395-5746, Tehran, Islamic Republic of Iran
N.
Bahrami Siavashani
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences,
Semnan University, P. O. Box: 35195-363, Semnan, Islamic Republic of Iran.
Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. Therefore, a reliable and efficient technique as a solution is regarded. This paper develops approximate solutions for boundary value problems of differential equations with non-integer order by using the Shannon wavelet bases. Wavelet bases have different resolution capability for approximating of different functions. Since for Shannon-type wavelets, the scaling function and the mother wavelet are not necessarily absolutely integrable, the partial sums of the wavelet series behave differently and a more stringent condition, such as bounded variation, is needed for convergence of Shannon wavelet series. With nominate Shannon wavelet operational matrices of integration, the solutions are approximated in the form of convergent series with easily computable terms. Also, by applying collocation points the exact solutions of fractional differential equations can be achieved by well-known series solutions. Illustrative examples are presented to demonstrate the applicability and validity of the wavelet base technique. To highlight the convergence, the numerical experiments are solved for different values of bounded series approximation.
Boundary value problems
Fractional differential
equations
Shannon wavelet
Operational matrix
http://wala.vru.ac.ir/article_6349.html
http://wala.vru.ac.ir/article_6349_a879aab68ceb63c1143db65fbc4b6bc7.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
1
1
2014
08
01
Linear preservers of two-sided matrix majorization
43
50
EN
F.
Khalooei
Department of Mathmatics, Faculty of Mathmatics, Shahid Bahonar University of Kerman,
Kerman, Islamic Republic of Iran
For vectors X, Y ∈ Rn, it is said that X is left matrix majorized by Y if for some row stochastic matrix R; X = RY. The relation X ∼` Y, is defined as follows: X ∼` Y if and only if X is left matrix majorized by Y and Y is left matrix majorized by X. A linear operator T : Rp → Rn is said to be a linear preserver of a given relation ≺ if X ≺ Y on Rp implies that T X ≺ TY on Rn. The linear preservers of ≺` from Rp to Rn are characterized before. In this parer we characterize the linear preservers of ∼` from Rp to Rn, p ≥ 3. In fact we show that the linear preservers of ∼` from Rp to Rn are the same as the linear preservers of ≺` from Rp to Rn, but for p = 2, they are not the same.
Linear preservers,Matrix majorization,Row stochastic matrix
http://wala.vru.ac.ir/article_6350.html
http://wala.vru.ac.ir/article_6350_cfc0204b394816145bc22b5af538dfde.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
1
1
2014
08
01
Property (T) for C*-dynamical systems
51
62
EN
H.
Abbasi
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Islamic
Republic of Iran.
afrouzi@umz.ac.ir
Gh.
Haghighatdoost
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Islamic
Republic of Iran.
I.
Sadeqi
Faculty of Sciences, Sahand University of Technology, Tabriz, Islamic Republic of Iran.
In this paper, we introduce a notion of property (T) for a C∗- dynamical system (A, G, α) consisting of a unital C∗-algebra A, a locally compact group G, and an action α on A. As a result, we show that if A has strong property (T) and G has Kazhdan’s property (T), then the triple (A, G, α) has property (T).
Kazhdan’s property (T)
Hilbert bimodule
C*-dynamical system
http://wala.vru.ac.ir/article_6351.html
http://wala.vru.ac.ir/article_6351_a1b72b21c66debb8390ddfc5ae6cadad.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
1
1
2014
08
01
Two-wavelet constants for square integrable representations of G/H
63
73
EN
R. A.
Kamyabi Gol
Department of Mathematics, Center of Excellency in Analysis on Algebraic
Structures(CEAAS), Ferdowsi University Of Mashhad, Mashhad, Islamic Republic of Iran.
F.
Esmaeelzadeh
Department of Mathematics, Bojnourd Branch, Islamic Azad University, Bojnourd, Islamic
Republic of Iran.
R.
Raisi Tousi
Department of Mathematics, Ferdowsi University Of Mashhad, Mashhad, Islamic Republic
of Iran.
In this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. We establish the orthogonality relations for square integrable representations of homogeneous spaces which give rise to the existence of a unique self adjoint positive operator on the set of admissible wavelets. Finally, we show that this operator is a constant multiple of identity operator when G is a semidirect product group of a unimodular subgroup K and a closed subgroup H.
Homogenous space
Irreducible representation
http://wala.vru.ac.ir/article_6352.html
http://wala.vru.ac.ir/article_6352_1a0047fe61bbe9c10151dbc7795a6868.pdf