eng
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
2015-11-01
04
02
87
100
516220
On the convergence of the homotopy analysis method to solve the system of partial differential equations
A. Fallahzadeh
1
M. A. Fariborzi Araghi
2
V. Fallahzadeh
3
Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Iran
Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Iran
Department of Mathematics, Islamic Azad University, Arac Branch, Iran
One of the efficient and powerful schemes to solve linear and nonlinear equations is homotopy analysis method (HAM). In this work, we obtain the approximate solution of a system of partial differential equations (PDEs) by means of HAM. For this purpose, we develop the concept of HAM for a system of PDEs as a matrix form. Then, we prove the convergence theorem and apply the proposed method to find the approximate solution of some systems of PDEs. Also, we show the region of convergence by plotting the H-surface.
http://jlta.iauctb.ac.ir/article_516220_1605dc7b2bf5c8c23ae5bee34af9bf90.pdf
Homotopy analysis method
System of partial differential equations
H-surface
eng
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
2015-11-01
04
02
101
114
516221
Stochastic averaging for SDEs with Hopf Drift and polynomial diffusion coefficients
M. Alvand
1
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran
It is known that a stochastic differential equation (SDE) induces two probabilistic objects, namely a difusion process and a stochastic flow. While the diffusion process is determined by the innitesimal mean and variance given by the coefficients of the SDE, this is not the case for the stochastic flow induced by the SDE. In order to characterize the stochastic flow uniquely the innitesimal covariance given by the coefficients of the SDE is needed in addition. The SDEs we consider here are obtained by a weak perturbation of a rigid rotation by random elds which are white in time. In order to obtain information about the stochastic flow induced by this kind of multiscale SDEs we use averaging for the innitesimal covariance. The main result here is an explicit determination of the coefficients of the averaged SDE for the case that the diffusion coefficients of the initial SDE are polynomial. To do this we develop a complex version of Cholesky decomposition algorithm.
http://jlta.iauctb.ac.ir/article_516221_950328e4fa2b2305abbf280dea57cc07.pdf
Stochastic differential equation
stochastic ow
stochastic averaging
Cholesky decomposition
system of complex bilinear equations
eng
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
2015-11-01
04
02
115
129
516222
Second order linear differential equations with generalized trapezoidal intuitionistic Fuzzy boundary value
S. P. Mondal
1
T. K. Roy
2
Department of Mathematics, National Institute of Technology, Agartala, Jirania-799046, Tripura, India
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India
In this paper the solution of a second order linear differential equations with intuitionistic fuzzy boundary value is described. It is discussed for two different cases: coefficient is positive crisp number and coefficient is negative crisp number. Here fuzzy numbers are taken as generalized trapezoidal intutionistic fuzzy numbers (GTrIFNs). Further a numerical example is illustrated.
http://jlta.iauctb.ac.ir/article_516222_85264e2e63892ac4aba31bf9090e6f90.pdf
fuzzy set
fuzzy differential equation
generalized trapezoidal intutionistic fuzzy number
eng
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
2015-11-01
04
02
131
142
516223
New characterizations of fusion bases and Riesz fusion bases in Hilbert spaces
F. Aboutorabi Goudarzi
1
M. S. Asgari
2
Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran
Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran
In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hilbert fusion basis and obtain some character-izations of them. we study orthonormal fusion systems and Riesz fusion bases for Hilbert spaces. we consider the stability of fusion bases under small perturbations. We also general-ized a result of Paley-Wiener [16] to the situation of fusion basis.
http://jlta.iauctb.ac.ir/article_516223_057e1dfab6e832d236ceaed097dd5a92.pdf
Fusion Frame
Riesz fusion basis
Exact fusion frame
Orthonormal fusion basis
eng
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
2015-11-07
04
02
143
152
516224
On the boundedness of almost multipliers on certain Banach algebras
E. Ansari-Piri
1
M. Shams Yousefi
2
S. Nouri
3
Department of Pure Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran
Department of Pure Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran
Department of Pure Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran
Almost multiplier is rather a new concept in the theory of almost functions. In this paper we discussion the boundedness of almost multipliers on some special Banach algebras, namely stable algebras. We also define an adjoint and extension for almost multiplier.
http://jlta.iauctb.ac.ir/article_516224_7c536d01c1997dca5ee114453373d97e.pdf
Almost multipliers
almost additive maps
dual map
stable normed algebras
eng
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
2015-11-03
04
02
153
158
516225
s-Topological vector spaces
M. Khan
moiz@comsats.edu.pk
1
S. Azam
2
S. Bosan
3
Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan
Punjab Education Department, Pakistan
Punjab Education Department, Pakistan
In this paper, we have dened and studied a generalized form of topological vector spaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-topological vector space is generalized homogeneous space. Every open subspace of an s-topological vector space is an s-topological vector space. A homomorphism between s-topological vector spaces is semi-continuous if it is s-continuous at the identity.
http://jlta.iauctb.ac.ir/article_516225_45ed430709aa3906872fd36f0f79a9ff.pdf
s-Topological vector space
Semi-open set
semi-closed set
semi-continuous mapping
s-continuous mapping
left (right) translation
generalized homeomorphism
generalized homogeneous space
eng
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
2015-11-19
04
02
159
163
516226
On dual shearlet frames
M. Amin khah
1
A. Askari Hemmat
2
R. Raisi Tousi
3
Department of Application Mathematics, Kerman Graduate University of High Technology, PO. Code 76315-115, Iran
Department of Mathematics, Shahid Bahonar University of Kerman, PO. Code 76175-133, Iran
Department of Mathematics, Ferdowsi University of Mashhad, PO. Code 1159-91775, Iran
In This paper, we give a necessary condition for function in $L^2$ with its dual to generate a dual shearlet tight frame with respect to admissibility.
http://jlta.iauctb.ac.ir/article_516226_9092f14f6ed90992c840b306c272e5de.pdf
Dual shearlet frame
Bessel sequence
admissible shearlet