ORIGINAL_ARTICLE
On the convergence of the homotopy analysis method to solve the system of partial differential equations
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
2015-11-01T11:23:20
2018-06-23T11:23:20
87
100
Homotopy analysis method
System of partial differential equations
H-surface
A.
Fallahzadeh
true
1
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, Central Tehran Branch,
PO. Code 14168-94351, Iran
LEAD_AUTHOR
M. A.
Fariborzi Araghi
true
2
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, Central Tehran Branch,
PO. Code 14168-94351, Iran
AUTHOR
V.
Fallahzadeh
true
3
Department of Mathematics, Islamic Azad University, Arac Branch, Iran
Department of Mathematics, Islamic Azad University, Arac Branch, Iran
Department of Mathematics, Islamic Azad University, Arac Branch, Iran
AUTHOR
[1] S. Abbasbandy, Homotopy analysis method for the Kawahara equation, Nonlinear Analysis: Real World Applications 11 (2010) 307-312.
1
[2] S. Abbasbandy, Solitary wave solutions to the modied form of CamassaHolm equation by means of the homotopy analysis method, Chaos, Solitons and Fractals 39 (2009) 428-435.
2
[3] J. Biazar, M. Eslami, A new homotopy perturbation method for solving system of partial dierential equations, Computers and Mathematics with Applications 62 (2011) 225-234.
3
[4] J. Biazar, M. Eslami, H. Ghazvini, Homotopy perturbation method for system of partial differential equations, International Journal of Nonlinear Sciences and Numerical simulations 8 (3) (2007) 411-416.
4
[5] M.A. Fariborzi Araghi, A. Fallahzadeh, On the convergence of the Homotopy Analysis method for solving the Schrodinger Equation, Journal of Basic and Applied Scientic Research 2(6) (2012) 6076-6083.
5
[6] M.A. Fariborzi Araghi, A. Fallahzadeh, Explicit series solution of Boussinesq equation by homotopy analysis method, Journal of American Science, 8(11) (2012).
6
[7] T. Hayat, M. Khan, Homotopy solutions for a generalized second-grade uid past a porous plate. Nonlinear Dyn 42 (2005) 395-405.
7
[8] S.J. Liao, Beyond pertubation: Introduction to the homotopy Analysis Method, Chapman and Hall/CRC Press, Boca Raton, (2003).
8
[9] S.J. Liao, Notes on the homotopy analysis method: some denitions and theorems, Communication in Nonlinear Science and Numnerical Simulation, 14 (2009) 983-997.
9
[10] P. Roul, P. Meyer, Numerical solution of system of nonlinear integro-diggerential equation by Homotopy perturbation method, Applied Mathematical Modelling 35 (2011) 4234-4242.
10
[11] A. Sami Bataineh, M.S.M. Noorani, I.Hashim, Approximation analytical solution of system of PDEs by homotopy analysis method, Computers and Mathematics with Applications 55 (2008) 2913-2923.
11
[12] F. Wang, Y. An, Nonnegative doubly periodic solution for nonlinear teleghraph system, J.math.Anal.Appl. 338 (2008) 91-100.
12
[13] A.M. Wazwaz, The variational iteration method for solving linear and nonlinear system of PDEs, Comput, Math, Appl 54 (2007) 895-902.
13
[14] W. Wu, Ch. Liou, Out put regulation of two-time-scale hyperbolic PDE systems, Journal of Process control 11 (2001) 637-647.
14
[15] W. Wu, S. Liao, Solving solitary waves with discontinuity by means of the homotopy analysis method. Chaos, Solitons & Fractals, 26 (2005) 177-185.
15
[16] E. Yusufoglu, An improvment to homotopy perturbation method for solving system of linear equations, Computers and Mathematic with Applications 58 (2009) 2231-2235.
16
ORIGINAL_ARTICLE
Stochastic averaging for SDEs with Hopf Drift and polynomial diffusion coefficients
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
2015-11-01T11:23:20
2018-06-23T11:23:20
101
114
Stochastic differential equation
stochastic ow
stochastic averaging
Cholesky decomposition
system of complex bilinear equations
M.
Alvand
true
1
Department of Mathematical Sciences, Isfahan University of Technology,
Isfahan, Iran
Department of Mathematical Sciences, Isfahan University of Technology,
Isfahan, Iran
Department of Mathematical Sciences, Isfahan University of Technology,
Isfahan, Iran
AUTHOR
[1] N. Abourashchi, A. Yu Veretennikov. On stochastic averaging and mixing, Theory Stoch. Process. 16, (1), (2010) 111-129.
1
[2] M. Alvand, Constructing an SDE from its two-point generator, Stoch. Dyn. DOI: 10.1142/S0219493715500252
2
[3] L. Arnold, Random Dynamical Systems, Springer-Verlag, 1998.
3
[4] P. H. Baxendale, Stochastic averaging and asymptotic behaviour of the stochastic Duffing - Van der Pol equation, Stochastic Process. Appl. 113, No. 2 (2004) 235-272.
4
[5] ———, Brownian motion in the diffeomorphisms group, Compositio Math. 53, No.1 (1984) 19-50.
5
[6] P. Bernard, Stochastic averaging, Nonlinear Stochastic Dynamics, (2002) 29-42.
6
[7] M. I. Freıdlin, The factorization of nonnegative definite matrices, Teor. Verojatnost. i Primenen. 13 (1968) 375-378.
7
[8] Z. L. Huang and W. Q. Zhu, Stochastic averaging of quasi-generalized Hamiltonian systems, Int. J. Nonlinear Mech. No.44 (2009) 71-80.
8
[9] H. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, 1990.
9
[10] J. A. Sanders, F. Verhulst and J. Murdack, Averaging Methods in Nonlinear Dynamical Systems, 2nd edition, Springer, 2007.
10
[11] R. B. Sowers, Averaging of stochastic flows: Twist maps and escape from resonance, Stochastic Process. Appl. No. 119, (2009) 3549-3582.
11
[12] S. Wiggins, An Introduction to Applied Nonlonear Dynamical Systems and Chaos, second edition, SpringerVerlag, 2009.
12
[13] W.Q. Zhu, Z.L. Huang and Y. Suzuki, Stochastic averaging and Lyapunov exponent of quasi partially integrable Hamiltonian systems, Int. J. Nonlinear Mech. No.37 (2002) 419-437.
13
ORIGINAL_ARTICLE
Second order linear differential equations with generalized trapezoidal intuitionistic Fuzzy boundary value
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
2015-11-01T11:23:20
2018-06-23T11:23:20
115
129
fuzzy set
fuzzy differential equation
generalized trapezoidal intutionistic fuzzy number
S. P.
Mondal
true
1
Department of Mathematics, National Institute of Technology, Agartala,
Jirania-799046, Tripura, India
Department of Mathematics, National Institute of Technology, Agartala,
Jirania-799046, Tripura, India
Department of Mathematics, National Institute of Technology, Agartala,
Jirania-799046, Tripura, India
LEAD_AUTHOR
T. K.
Roy
true
2
Department of Mathematics, Indian Institute of Engineering Science and Technology,
Shibpur, Howrah-711103, West Bengal, India
Department of Mathematics, Indian Institute of Engineering Science and Technology,
Shibpur, Howrah-711103, West Bengal, India
Department of Mathematics, Indian Institute of Engineering Science and Technology,
Shibpur, Howrah-711103, West Bengal, India
AUTHOR
[1] L. A. Zadeh, Fuzzy sets, Information and Control, 8, (1965) 338-353.
1
[2] D.Dubois, H.Parade, Operation on Fuzzy Number, International Journal of Fuzzy system, 9, (1978) 613-626.
2
[3] K. T. Atanassov, Intuitionistic fuzzy sets, VII ITKRs Session, Soa, Bulgarian, 19-83.
3
[4] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 20, (1986) 87-96.
4
[5] L. A. Zadeh, Toward a generalized theory of uncertainty (GTU) an outline, Information Sciences 172, (2005) 1-40.
5
[6] S. L. Chang, L. A. Zadeh, On fuzzy mapping and control, IEEE Transaction on Systems Man Cybernetics 2, (1972) 30 34.
6
[7] D. Dubois, H. Prade, Towards fuzzy dierential calculus: Part 3, Dierentiation, Fuzzy Sets and Systems 8, (1982) 225-233.
7
[8] M. L. Puri, D. A. Ralescu, Dierentials of fuzzy functions, Journal of Mathematical Analysis and Application
8
91, (1983) 552558.
9
[9] R. Goetschel, W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems 18, (1986) 31-43.
10
[10] O. Kaleva, Fuzzy dierential equations, Fuzzy Sets and Systems 24, (1987) 301-317.
11
[11] B. Bede, A note on two-point boundary value problems associated with non-linear fuzzy differential equations, Fuzzy Sets. Syst.157, (2006) 986-989.
12
[12] B. Bede,S. G. Gal, Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations, Fuzzy Sets Syst.151, (2005) 581-599.
13
[13] Y. Chalco-Cano, H. Romn-Flores, On the new solution of fuzzy dierential equations, Chaos Solitons Fractals 38, (2008) 112-119.
14
[14] B. Bede,I. J. Rudas and A. L. Bencsik, First order linear fuzzy dierential equations under generalized differentiability, Inf. Sci. 177, (2007) 1648-1662.
15
[15] Y. Chalco-Cano, M.A.Rojas-Medar,H.Romn-Flores, Sobre ecuaciones differencial esdifusas, Bol. Soc. Esp. Mat. Apl. 41, (2007) 91-99.
16
[16] Y. Chalco-Cano, H. Romn-Flores and M. A. Rojas-Medar, Fuzzy dierential equations with generalized derivative, in:Proceedings of the 27th North American Fuzzy Information Processing Society International Conference, IEEE, 2008.
17
[17] L. Stefanini, B. Bede, Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Anal. 71, (2009) 1311-1328.
18
[18] A. Khastan,J. J. Nieto, A boundary value problem for second-order fuzzy dierential equations, Nonlinear Anal. 72, (2010) 3583-3593.
19
[19] P. Diamond, P. Kloeden, Metric Spaces of Fuzzy Sets, World Scientic, Singapore, 1994.
20
[20] B. Bede, S. G. Gal, Generalizations of the dierentiability of fuzzy-number-valued functions with applications to fuzzy differential equations, Fuzzy Set Systems, 151 (2005) 581-599.
21
[21] L. Stefanini, A generalization of Hukuhara difference for interval and fuzzy arithmetic, in: D. Dubois, M.A. Lubiano, H. Prade, M. A. Gil, P. Grzegorzewski, O. Hryniewicz (Eds.), Soft Methods for Handling Variability and Imprecision, in: Series on Advances in Soft Computing, 48 (2008).
22
[22] L. Stefanini, B. Bede, Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Analysis, 71 (2009) 1311-1328.
23
[23] A. Armand, Z. Gouyandeh, Solving two-point fuzzy boundary value problem using the variational iteration method, Communications on Advanced Computational Science with Applications, Vol. 2013, (2013) 1-10.
24
[24] N. Gasilov, S. E. Amrahov, A. G. Fatullayev, Solution of linear dierential equations with fuzzy boundary values, Fuzzy Sets and Systems 257, (2014) 169-183.
25
[25] N. Gasilov, S. E. Amrahov, A. G. Fatullayev, A. Khastan, A new approach to fuzzy initial value problem ,18(2), (2014) 217-225.
26
[26] B. Bede, L. Stefanini, Generalized dierentiability of fuzzy-valued functions, Fuzzy Sets and Systems, 230 (2013) 119-141.
27
[27] R. Rodrguez-Lpez, On the existence of solutions to periodic boundary value problems for fuzzy linear differential equations, Fuzzy Sets and Systems, 219, (2013) 1-26.
28
[28] S. Melliani, L. S. Chadli, Introduction to intuitionistic fuzzy partial differential Equations, Fifth Int. Conf. on IFSs, Sofia, 22-23 Sept. 2001.
29
[29] S. Abbasbandy, T. Allahviranloo, Numerical Solution of Fuzzy Differential Equations by Runge-Kutta and the Intuitionistic Treatment, Journal of Notes on Intuitionistic Fuzzy Sets, Vol. 8, No. 3, (2002) 43-53.
30
[30] S. Lata, A.Kumar, A new method to solve time-dependent intuitionistic fuzzy differential equation and its application to analyze the intutionistic fuzzy reliability of industrial system, Concurrent Engineering: Research and Applications, (2012) 1-8.
31
[31] S. P. Mondal and T. K. Roy, First order homogeneous ordinary differential equation with initial value as triangular intuitionistic fuzzy number, Journal of Uncertainty in Mathematics Science (2014) 1-17.
32
[32] S. P. Mondal. and T. K. Roy, System of Differential Equation with Initial Value as Triangular Intuitionistic Fuzzy Number and its Application, Int. J. Appl. Comput. Math, (2010).
33
[33] L. C. Barros, L. T. Gomes, P. A Tonelli, Fuzzy differential equations: An approach via fuzzification of the derivative operator, Fuzzy Sets and Systems, 230, (2013) 39-52.
34
[34] M.R.Seikh, P.K.Nayak and M.Pal, Generalized Triangular Fuzzy Numbers In Intuitionistic Fuzzy Environment, International Journal of Engineering Research and Development, Volume 5, Issue 1 (2012) 08-13.
35
[35] H.J.Zimmerman, Fuzzy set theory and its applications, Kluwer Academi Publishers, Dordrecht (1991).
36
ORIGINAL_ARTICLE
New characterizations of fusion bases and Riesz fusion bases in Hilbert spaces
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
2015-11-01T11:23:20
2018-06-23T11:23:20
131
142
Fusion Frame
Riesz fusion basis
Exact fusion frame
Orthonormal fusion basis
F.
Aboutorabi Goudarzi
true
1
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
Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran
LEAD_AUTHOR
M. S.
Asgari
true
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
Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran
AUTHOR
[1] M. S. Asgari, G. Kavian, Expansion of Bessel and g-Bessel sequences to dual frames and dual g-frames, J. Linear and Topological Algebra, Vol. 02, No. 01, 2013, 51- 57
1
[2] M. S. Asgari, New characterizations of fusion frames (frames of subspaces), Proc. Indian Acad. Sci. (Math. Sci.) 119 No. 3 (2009), 1-14.
2
[3] M. S. Asgari, On the stability of fusion frames (frames of subspaces), Acta Math. Sci. Ser. B, 31(4), (2011), 1633-1642.
3
[4] M. S. Asgari, Operator-valued bases on Hilbert spaces, J. Linear and Topological Algebra, Vol. 02, No. 04, (2013), 201-218.
4
[5] P. G. Casazza and G. Kutyniok, Frames of subspaces, in Wavelets, Frames and Operator Theory (College Park, MD, 2003), Contemp. Math. 345, Amer. Math. Soc. Providence, RI, 2004, 87-113.
5
[6] O. Christensen, An Introduction to frames and Riesz Bases, Birkhauser, Boston, 2003.
6
[7] I. Daubechies, A. Grossmann and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys. 27(1986), 1271-1283.
7
[8] R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72,(2), (1952), 341-366.
8
[9] M. Fornasier, Quasi-orthogonal decompositions of structured frames, J. Math. Anal. Appl. 289 (2004), 180- 199.
9
[10] P. Gavruta, On the duality of fusion frames, J. Math. Anal. Appl. 333 (2007), 871-879.
10
[11] J.R. Holub, Pre-frame operators, Besselian frames and near-Riesz bases in Hilbert spaces, Proc. Amer. Math. Soc. 122 (1994) 779-785.
11
[12] V. Kaftal, D. R. Larson and Sh. Zhang, Operator-valued frames, Trans. Amer. Math. Soc. 361 (2009), 6349- 6385.
12
[13] S. S. Karimizad, G-frames, g-orthonormal bases and g-Riesz bases, J. Linear and Topological Algebra, Vol. 02, No. 01, 2013, 25-33.
13
[14] W. Rudin, Functional Analysis, McGrawHill. Inc, New York, (1991).
14
[15] W. Sun, G-frames and G-Riesz bases, J. Math. Anal. Appl. (2006), 322, 437-452.
15
[16] R. Young, An Introduction to Nonharmonic Fourier Series, Academic Press, New York, 2001.
16
ORIGINAL_ARTICLE
On the boundedness of almost multipliers on certain Banach algebras
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
2015-11-07T11:23:20
2018-06-23T11:23:20
143
152
Almost multipliers
almost additive maps
dual map
stable normed algebras
E.
Ansari-Piri
true
1
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
LEAD_AUTHOR
M.
Shams Yousefi
true
2
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
AUTHOR
S.
Nouri
true
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
AUTHOR
[1] E. Ansari-Piri, S. Nouri, Almost multipliers and some of their properties, Preprint.
1
[2] E. Ansari-Piri, S. Nouri, Stable normed algebra, Priprint.
2
[3] F. Birtal, Isomorphism and isometric multipliers, Proc. Amer. Math. Soc. (1962), no. 13, 204-210.
3
[4] B. Host, F. Parreau, Sur un probleme de I. Glicksberg: les ideauxfermes de type ni deM(G), Ann. Inst. Fourier (Grenoble) 28(1978), no.3, 143-164.
4
[5] S. Helganson, Multipliers of Banach algebras, Ann. Math ,64 (1956), 240-254.
5
[6] R. Larsen, Theory of Multipliers, Springer, Berlin, 1971.
6
[7] K. B. Laursen, M. Mbekhta, Closed range multipliers and generalized inverses, Stud. Math. 107 (1993)126-135.
7
[8] T. Miura, G. Hirasawa, S. Takahasi, Stability of multipliers on Banach algebras, A.M.S. 45 (2004), 2377-2381.
8
[9] A. Ulger, Multipliers with closed range on commutative semsimple Banach algebras, Stud. Math. 153 (2002), no. 1, 59-80.
9
[10] J. Wang, Multipliers of commutative Banach algebras, Pacic J. Math, 11(1961), 1131-1149.
10
[11] Y. Zaiem, Operateurs de convolution d'image femee et unitesapproches, Bull. Sci. Math. 99 (1975), 65-74.
11
ORIGINAL_ARTICLE
s-Topological vector spaces
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
2015-11-03T11:23:20
2018-06-23T11:23:20
153
158
s-Topological vector space
Semi-open set
semi-closed set
semi-continuous mapping
s-continuous mapping
left (right) translation
generalized homeomorphism
generalized homogeneous space
M.
Khan
moiz@comsats.edu.pk
true
1
Department of Mathematics, COMSATS Institute of Information
Technology, Park Road, Islamabad, Pakistan
Department of Mathematics, COMSATS Institute of Information
Technology, Park Road, Islamabad, Pakistan
Department of Mathematics, COMSATS Institute of Information
Technology, Park Road, Islamabad, Pakistan
LEAD_AUTHOR
S.
Azam
true
2
Punjab Education Department, Pakistan
Punjab Education Department, Pakistan
Punjab Education Department, Pakistan
AUTHOR
S.
Bosan
true
3
Punjab Education Department, Pakistan
Punjab Education Department, Pakistan
Punjab Education Department, Pakistan
AUTHOR
[1] S. M. Alsulami and L. A. Khan, Weakly Almost Periodic Functions in Topologicl Vector Spaces, Afr. Diaspora J. Math.. (N.S.), 15(2)(2013), 76-86.
1
[2] G. Bosi, J.C. Candeal,; E. Indurain,; M. Zudaire, Existence of Homogenous Representations of interval Orders on a Cone in Topological Vector Space, Social Choice and welfare, Vol.24 (2005), 45-61.
2
[3] D. E. Cameron and G. Woods, s-Continuous and s-Open Mappings, preprint.
3
[4] Y. Q. Chen, Fixed Points for Convex Continuous mappings in Topological Vector Space, American Mathematical Society, Vol. 129 (2001), 2157-2162.
4
[5] S. T. Clark, A Tangent Cone Analysis of Smooth Preferences on a Topological Vector Space, Economic Theory, Vol.23 (2004), 337-352.
5
[6] S. G. Crossley, S.K. Hildebrand, Semi-closed sets and semi-continuity in topological spaces, Texas J. Sci., Vol. 22 (1971), 123-126.
6
[7] S. G. Crossley, S.K. Hildebrand, Semi-closure, Texas J. Sci. 22 (1971), 99-112.
7
[8] S. G. Crossley, S.K. Hildebrand, Semi-topological properties, Fund. Math. 74 (1972), 233-254.
8
[9] L. Drewnowski, Resolution of topological linear spaces and continuity of linear maps., Anal. Appl. 335 (2) (2007), 1177-1195.
9
[10] A. Grothendieck. Topological vector spaces. New York: Gordon and Breach Science Publishers, (1973).
10
[11] D. H. Hyers, Pseudo-normed linear spaces and Abelian groups, Duke Mathematical Journal, Vol. 5 (1939), 628-634.
11
[12] J. L. Kelly, General topology, Van Nastrand (New York 1955).
12
[13] Kolmogro, Zur Normierbarkeit eines topologischen linearen Raumes, Studia Mathematica, Vol. 5 (1934), 29-33.
13
[14] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, Vol. 70 (1963), 36-41.
14
[15] J. V. Neuman, On complete topological spaces, Transactions of American Mathematical Society, Vol. 37 (1935), 1-2.
15
[16] T. Noiri, On semi continuous mappings, Atti. Accad. Naz. Lin. El. Sci. Fis. mat. Natur. 8(54)(1973), 210-214.
16
[17] A. P. Robertson, W.J. Robertson, Topological vector spaces. Cambridge Tracts in Mathematics. 53. Cam-bridge University Press, (1964).
17
[18] J. V. Wehausen, Transformations in Linear Topological Spaces, Duke Mathematical Journal, Vol. 4 (1938), 157-169.
18
ORIGINAL_ARTICLE
On dual shearlet frames
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
2015-11-19T11:23:20
2018-06-23T11:23:20
159
163
Dual shearlet frame
Bessel sequence
admissible shearlet
M.
Amin khah
true
1
Department of Application Mathematics, Kerman Graduate University of High Technology, PO. Code 76315-115, Iran
Department of Application Mathematics, Kerman Graduate University of High Technology, PO. Code 76315-115, Iran
Department of Application Mathematics, Kerman Graduate University of High Technology, PO. Code 76315-115, Iran
LEAD_AUTHOR
A.
Askari Hemmat
true
2
Department of Mathematics, Shahid Bahonar University of Kerman, PO. Code 76175-133, Iran
Department of Mathematics, Shahid Bahonar University of Kerman, PO. Code 76175-133, Iran
Department of Mathematics, Shahid Bahonar University of Kerman, PO. Code 76175-133, Iran
AUTHOR
R.
Raisi Tousi
true
3
Department of Mathematics, Ferdowsi University of Mashhad, PO. Code 1159-91775, Iran
Department of Mathematics, Ferdowsi University of Mashhad, PO. Code 1159-91775, Iran
Department of Mathematics, Ferdowsi University of Mashhad, PO. Code 1159-91775, Iran
AUTHOR
[1] C. K. Chui, X. Shi, On a LittlewoodPaley identity and characterization of wavelets, Math. Anal. Appl. 177 (1993) 608-626.
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[2] I. Daubechies, B. Han, Pairs of dual wavelet frames from any two renable functions, Constr. Appr.,to appear.
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[3] B. Han, On dual wavelet tight frames, Appl. Comput. Harmon. Anal. 4 (1997) 380-413.
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[4] G. Kutyniok, D. Labate, Shearlets: Multiscale Analysis for Multivariate Data, Birkhauser, Basel, 2012.
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