2015
4
2
2
0
On the convergence of the homotopy analysis method to solve the system of partial dierential equations
2
2
One of the ecient and powerful schemes to solve linear and nonlinear equationsis homotopy analysis method (HAM). In this work, we obtain the approximate solution ofa system of partial dierential equations (PDEs) by means of HAM. For this purpose, wedevelop the concept of HAM for a system of PDEs as a matrix form. Then, we prove theconvergence theorem and apply the proposed method to nd the approximate solution ofsome systems of PDEs. Also, we show the region of convergence by plotting the Hsurface.
1

87
100


A
Fallahzadeh
Department of Mathematics, Islamic Azad University, Central Tehran Branch,
Iran
Department of Mathematics, Islamic Azad University
Iran
amir falah6@yahoo.com


M. A
Fariborzi Araghi
Department of Mathematics, Islamic Azad University, Central Tehran Branch,
Iran
Department of Mathematics, Islamic Azad University
Iran


V
Fallahzadeh
Department of Mathematics, Islamic Azad University, Arac Branch, Iran
Department of Mathematics, Islamic Azad University
Iran
Homotopy analysis method
System of partial differential equations
Hsurface
[[1] S. Abbasbandy, Homotopy analysis method for the Kawahara equation, Nonlinear Analysis: Real World##Applications 11 (2010) 307312.##[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) 428435. ##[3] J. Biazar, M. Eslami, A new homotopy perturbation method for solving system of partial dierential equations, Computers and Mathematics with Applications 62 (2011) 225234.##[4] J. Biazar, M. Eslami, H. Ghazvini, Homotopy perturbation method for system of partial dierential equations,##International Journal of Nonlinear Sciences and Numerical simulations 8 (3) (2007) 411416.##[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) 60766083.##[6] M.A. Fariborzi Araghi, A. Fallahzadeh, Explicit series solution of Boussinesq equation by homotopy analysis##method, Journal of American Science, 8(11) (2012).##[7] T. Hayat, M. Khan, Homotopy solutions for a generalized secondgrade uid past a porous plate. Nonlinear##Dyn 42 (2005) 395405.##[8] S.J. Liao, Beyond pertubation: Introduction to the homotopy Analysis Method, Chapman and Hall/CRC##Press, Boca Raton, (2003).##[9] S.J. Liao, Notes on the homotopy analysis method: some denitions and theorems, Communication in Nonlinear Science and Numnerical Simulation, 14 (2009) 983997.##[10] P. Roul, P. Meyer, Numerical solution of system of nonlinear integrodierential equation by Homotopy##perturbation method, Applied Mathematical Modelling 35 (2011) 42344242.##[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) 29132923.##[12] F. Wang, Y. An, Nonnegative doubly periodic solution for nonlinear teleghraph system, J.math.Anal.Appl.##338 (2008) 91100.##[13] A.M. Wazwaz, The variational iteration method for solving linear and nonlinear system of PDEs, Comput,##Math, Appl 54 (2007) 895902.##[14] W. Wu, Ch. Liou, Out put regulation of twotimescale hyperbolic PDE systems, Journal of Process control##11 (2001) 637647.##[15] W. Wu, S. Liao, Solving solitary waves with discontinuity by means of the homotopy analysis method. Chaos,##Solitons & Fractals, 26 (2005) 177185.##[16] E. Yusufoglu, An improvment to homotopy perturbation method for solving system of linear equations,##Computers and Mathematic with Applications 58 (2009) 22312235.##]
Stochastic averaging for SDEs with Hopf Drift and polynomial diusion coecients
2
2
It is known that a stochastic dierential equation (SDE) induces two probabilisticobjects, namely a diusion process and a stochastic ow. While the diusion process isdetermined by the innitesimal mean and variance given by the coecients of the SDE,this is not the case for the stochastic ow induced by the SDE. In order to characterize thestochastic ow uniquely the innitesimal covariance given by the coecients of the SDE isneeded in addition. The SDEs we consider here are obtained by a weak perturbation of a rigidrotation by random elds which are white in time. In order to obtain information about thestochastic ow induced by this kind of multiscale SDEs we use averaging for the innitesimalcovariance. The main result here is an explicit determination of the coecients of the averagedSDE for the case that the diusion coecients of the initial SDE are polynomial. To do thiswe develop a complex version of Cholesky decomposition algorithm.
1

101
114


M
Alvand
Department of Mathematical Sciences, Isfahan University of Technology,
Isfahan, Iran
Department of Mathematical Sciences, Isfahan
Iran
Stochastic differential equation
stochastic ow
stochastic averaging
Cholesky decomposition
system of complex bilinear equations
Second order linear dierential equations with generalized trapezoidal intuitionistic Fuzzy boundary value
2
2
In this paper the solution of a second order linear dierential equations with intuitionistic fuzzy boundary value is described. It is discussed for two dierent cases: coecientis positive crisp number and coecient is negative crisp number. Here fuzzy numbers aretaken as generalized trapezoidal intutionistic fuzzy numbers (GTrIFNs). Further a numericalexample is illustrated.
1

115
129


S. P
Mondal
Department of Mathematics, National Institute of Technology, Agartala,
Jirania799046, Tripura, India
Department of Mathematics, National Institute
Iran


T. K
Roy
Department of Mathematics, Indian Institute of Engineering Science and Technology,
Shibpur, Howrah711103, West Bengal, India
Department of Mathematics, Indian Institute
Iran
fuzzy set
fuzzy differential equation
generalized trapezoidal intutionistic fuzzy number
[[1] L. A. Zadeh, Fuzzy sets, Information and Control, 8, (1965) 338353.##[2] D.Dubois, H.Parade, Operation on Fuzzy Number, International Journal of Fuzzy system, 9, (1978) 613626.##[3] K. T. Atanassov, Intuitionistic fuzzy sets, VII ITKRs Session, Soa, Bulgarian, 1983.##[4] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 20, (1986) 8796.##[5] L. A. Zadeh, Toward a generalized theory of uncertainty (GTU) an outline, Information Sciences 172, (2005)##[6] S. L. Chang, L. A. Zadeh, On fuzzy mapping and control, IEEE Transaction on Systems Man Cybernetics##2, (1972) 3034.##[7] D. Dubois, H. Prade, Towards fuzzy dierential calculus: Part 3, Dierentiation, Fuzzy Sets and Systems 8,##(1982) 225233.##[8] M. L. Puri, D. A. Ralescu, Dierentials of fuzzy functions, Journal of Mathematical Analysis and Application##91, (1983) 552558.##[9] R. Goetschel, W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems 18, (1986) 3143.##[10] O. Kaleva, Fuzzy dierential equations, Fuzzy Sets and Systems 24, (1987) 301317.##[11] B. Bede, A note on twopoint boundary value problems associated with nonlinear fuzzy dierential equations,##Fuzzy Sets. Syst.157, (2006) 986989.##[12] B. Bede,S. G. Gal, Generalizations of the dierentiability of fuzzynumbervalued functions with applications##to fuzzy dierential equations, Fuzzy Sets Syst.151, (2005) 581599.##[13] Y. ChalcoCano, H. RomnFlores, On the new solution of fuzzy dierential equations, Chaos Solitons Fractals##38, (2008) 112119.##[14] B. Bede,I. J. Rudas and A. L. Bencsik, First order linear fuzzy dierential equations under generalized##dierentiability, Inf. Sci. 177, (2007) 16481662.##[15] Y. ChalcoCano, M.A.RojasMedar,H.RomnFlores, Sobre ecuaciones diferencial esdifusas, Bol. Soc. Esp.##Mat. Apl. 41, (2007) 9199.##[16] Y. ChalcoCano, H. RomnFlores and M. A. RojasMedar, Fuzzy dierential equations with generalized##derivative, in:Proceedings of the 27th North American Fuzzy Information Processing Society International##Conference, IEEE, 2008.##[17] L. Stefanini, B. Bede, Generalized Hukuhara dierentiability of intervalvalued functions and interval dierential equations, Nonlinear Anal. 71, (2009) 13111328.##[18] A. Khastan,J. J. Nieto, A boundary value problem for secondorder fuzzy dierential equations, Nonlinear##Anal. 72, (2010) 35833593.##[19] P. Diamond, P. Kloeden, Metric Spaces of Fuzzy Sets, World Scientic, Singapore, 1994.##[20] B. Bede, S. G. Gal, Generalizations of the dierentiability of fuzzynumbervalued functions with applications##to fuzzy dierential equations, Fuzzy Set Systems, 151 (2005) 581599.##[21] L. Stefanini, A generalization of Hukuhara dierence 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] L. Stefanini, B. Bede, Generalized Hukuhara dierentiability of intervalvalued functions and interval dierential equations, Nonlinear Analysis, 71 (2009) 13111328.##[23] A. Armand, Z. Gouyandeh, Solving twopoint fuzzy boundary value problem using the variational iteration##method, Communications on Advanced Computational Science with Applications, Vol. 2013, (2013) 110.##[24] N. Gasilov, S. E. Amrahov, A. G. Fatullayev, Solution of linear dierential equations with fuzzy boundary##values, Fuzzy Sets and Systems 257, (2014) 169183.##[25] N. Gasilov, S. E. Amrahov, A. G. Fatullayev, A. Khastan, A new approach to fuzzy initial value problem ,18(2), (2014) 217225. ##[26] B. Bede, L. Stefanini, Generalized dierentiability of fuzzyvalued functions, Fuzzy Sets and Systems, 230,##(2013) 119141.##[27] R. RodrguezLpez, On the existence of solutions to periodic boundary value problems for fuzzy linear dierential equations, Fuzzy Sets and Systems, 219, (2013) 126.##[28] S. Melliani, L. S. Chadli, Introduction to intuitionistic fuzzy partial dierential Equations, Fifth Int. Conf.##on IFSs, Soa, 2223 Sept. 2001.##[29] S. Abbasbandy, T. Allahviranloo, Numerical Solution of Fuzzy Dierential Equations by RungeKutta and##the Intuitionistic Treatment, Journal of Notes on Intuitionistic Fuzzy Sets, Vol. 8, No. 3, (2002) 4353.##[30] S. Lata, A.Kumar, A new method to solve timedependent intuitionistic fuzzy dierential equation and##its application to analyze the intutionistic fuzzy reliability of industrial system, Concurrent Engineering:##Research and Applications, (2012) 18.##[31] S. P. Mondal and T. K. Roy, First order homogeneous ordinary dierential equation with initial value as##triangular intuitionistic fuzzy number, Journal of Uncertainty in Mathematics Science (2014) 117.##[32] S. P. Mondal. and T. K. Roy, System of Dierential Equation with Initial Value as Triangular Intuitionistic##Fuzzy Number and its Application, Int. J. Appl. Comput. Math, (2010).##[33] L. C. Barros, L. T. Gomes, P. A Tonelli, Fuzzy dierential equations: An approach via fuzzication of the##derivative operator, Fuzzy Sets and Systems, 230, (2013) 3952.##[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) 0813.##[35] H.J.Zimmerman, Fuzzy set theory and its applications, Kluwer Academi Publishers, Dordrecht (1991)##]
New characterizations of fusion bases and Riesz fusion bases in Hilbert spaces
2
2
In this paper we investigate a new notion of bases in Hilbert spaces and similarto fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introducea new denition of fusion dual sequence associated with a fusion basis and show that theoperators of a fusion dual sequence are continuous projections. Next we dene the fusionbiorthogonal sequence, Bessel fusion basis, Hilbert fusion basis and obtain some characterizations of them. we study orthonormal fusion systems and Riesz fusion bases for Hilbertspaces. we consider the stability of fusion bases under small perturbations. We also generalized a result of PaleyWiener [16] to the situation of fusion basis.
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131
142


F
Aboutorabi Goudarzi
Department of Mathematics, Faculty of Science,
Central Tehran Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Faculty of Science,
Cen
Iran


M. S
Asgari
Department of Mathematics, Faculty of Science,
Central Tehran Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Faculty of Science,
Cen
Iran
Fusion Frame
Riesz fusion basis
Exact fusion frame
Orthonormal fusion basis
On the boundedness of almost multipliers on certain Banach algebras
2
2
Almost multiplier is rather a new concept in the theory of almost functions. In thispaper we discuss on the boundedness of almost multipliers on some special Banach algebras,namely stable algebras. We also dene an adjoint and extension for almost multiplier.
1

143
152


E
AnsariPiri
Department of Pure Mathematics, Faculty of Mathematical Science,
University of Guilan, Rasht, Iran.
Department of Pure Mathematics, Faculty of
Iran


M
Shams Youse
Department of Pure Mathematics, Faculty of Mathematical Science,
University of Guilan, Rasht, Iran.
Department of Pure Mathematics, Faculty of
Iran


S
Nouri
Department of Pure Mathematics, Faculty of Mathematical Science,
University of Guilan, Rasht, Iran.
Department of Pure Mathematics, Faculty of
Iran
Almost multipliers
almost additive maps
dual map
stable normed algebras
[[1] E. AnsariPiri, S. Nouri, Almost multipliers and some of their properties, Preprint.##[2] E. AnsariPiri, S. Nouri, Stable normed algebra, Priprint.##[3] F. Birtal, Isomorphism and isometric multipliers, Proc. Amer. Math. Soc. (1962), no. 13, 204210.##[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, 143164.##[5] S. Helganson, Multipliers of Banach algebras, Ann. Math ,64 (1956), 240254.##[6] R. Larsen, Theory of Multipliers, Springer, Berlin, 1971.##[7] K. B. Laursen, M. Mbekhta, Closed range multipliers and generalized inverses, Stud. Math. 107 (1993)126135.##[8] T. Miura, G. Hirasawa, S. Takahasi, Stability of multipliers on Banach algebras, A.M.S. 45 (2004), 23772381.##[9] A. Ulger, Multipliers with closed range on commutative semsimple Banach algebras, Stud. Math. 153 (2002),##no. 1, 5980.##[10] J. Wang, Multipliers of commutative Banach algebras, Pacic J. Math, 11(1961), 11311149.##[11] Y. Zaiem, Operateurs de convolution d'image femee et unitesapproches, Bull. Sci. Math. 99 (1975), 6574.##]
sTopological vector spaces
2
2
In this paper, we have dened and studied a generalized form of topological vectorspaces called stopological vector spaces. stopological vector spaces are dened by using semiopen sets and semicontinuity in the sense of Levine. Along with other results, it is provedthat every stopological vector space is generalized homogeneous space. Every open subspaceof an stopological vector space is an stopological vector space. A homomorphism betweenstopological vector spaces is semicontinuous if it is scontinuous at the identity.
1

153
158


Moiz ud
Din Khan
Department of Mathematics, COMSATS Institute of Information
Technology, Park Road, Islamabad, Pakistan.
Department of Mathematics, COMSATS Institute
Iran


S
Azam
Punjab Education Department, Pakistan.
Punjab Education Department, Pakistan.
Iran
sTopological vector space
Semiopen set
semiclosed set
semicontinuous mapping
scontinuous mapping
left (right) translation
generalized homeomorphism
generalized homogeneous space
[[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), 7686.##[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), 4561.##[3] D. E. Cameron and G. Woods, sContinuous and sOpen Mappings, pre print.##[4] Y. Q. Chen, Fixed Points for Convex Continuous mappings in Topological Vector Space, American Mathematical Society, Vol. 129 (2001), 21572162.##[5] S. T. Clark, A Tangent Cone Analysis of Smooth Preferences on a Topological Vector Space, Economic##Theory, Vol.23 (2004), 337352.##[6] S. G. Crossley, S.K. Hildebrand, Semiclosed sets and semicontinuity in topological spaces, Texas J. Sci.,##Vol. 22 (1971), 123126.##[7] S. G. Crossley, S.K. Hildebrand, Semiclosure, Texas J. Sci. 22 (1971), 99{112.##[8] S. G. Crossley, S.K. Hildebrand, Semitopological properties, Fund. Math. 74 (1972), 233{254.##[9] L. Drewnowski, Resolution of topological linear spaces and continuity of linear maps., Anal. Appl.##335(2)(2007), 11771195.##[10] A. Grothendieck. Topological vector spaces. New York: Gordon and Breach Science Publishers, (1973).##[11] D. H. Hyers, Pseudonormed linear spaces and Abelian groups, Duke Mathematical Journal, Vol. 5 (1939),##[12] J. L. Kelly, General topology, Van Nastrand (New York 1955).##[13] Kolmogro, Zur Normierbarkeit eines topologischen linearen Raumes, Studia Mathematica, Vol. 5 (1934),##[14] N. Levine, Semiopen sets and semicontinuity in topological spaces, Amer. Math. Monthly, Vol. 70 (1963),##[15] J. V. Neuman, On complete topological spaces, Transactions of American Mathematical Society, Vol. 37##(1935), 12.##[16] T. Noiri, On semi continuous mappings, Atti. Accad. Naz. Lin. El. Sci. Fis. mat. Natur. 8(54)(1973), 210214.##[17] A. P. Robertson, W.J. Robertson, Topological vector spaces. Cambridge Tracts in Mathematics. 53. Cambridge University Press, (1964).##[18] J. V. Wehausen, Transformations in Linear Topological Spaces, Duke Mathematical Journal, Vol. 4 (1938),##]
On dual shearlet frames
2
2
In This paper, we give a necessary condition for function in L^2with its dual to generate a dual shearlet tight frame with respect to admissibility.
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159
163


M
Amin khah
Department of Application Mathematics, Kerman Graduate University
of High Technology, Iran.
Department of Application Mathematics, Kerman
Iran


A
Askari Hemmat
Department of Mathematics, Shahid Bahonar University of Kerman, Iran.
Department of Mathematics, Shahid Bahonar
Iran


R
Raisi Tousi
Department of Mathematics, Ferdowsi University of Mashhad, Iran.
Department of Mathematics, Ferdowsi University
Iran
Dual shearlet frame
Bessel sequence
admissible shearlet
[[1] C. K. Chui, X. Shi, On a LittlewoodPaley identity and characterization of wavelets, Math. Anal. Appl. 177##(1993) 608{626.##[2] I. Daubechies, B. Han, Pairs of dual wavelet frames from any two renable functions, Constr. Appr.,to appear.##[3] B. Han, On dual wavelet tight frames, Appl. Comput. Harmon. Anal. 4 (1997) 380{413.##[4] G. Kutyniok, D. Labate, Shearlets: Multiscale Analysis for Multivariate Data, Birkhauser, Basel, 2012.##]