2013
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Generalized notion of character amenability
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2
This paper continues the investigation of the rst author begun in part one. The hereditary properties of nhomomorphism amenability for Banach algebras are investigated and the relations between nhomomorphism amenability of a Banach algebra and its ideals are found. Analogous to the character amenability, it is shown that the tensor product of two unital Banach algebras is nhomomorphism amenable if and only if each one is nhomomorphism amenable.
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191
200


A.
Bodaghi
Department of Mathematics, Garmsar Branch, Islamic Azad University,
Garmsar, Iran
Department of Mathematics, Garmsar Branch,
Iran
abasalt.bodaghi@gmail.com


F.
Anousheh
Department of Mathematics, Islamic Azad University, Central Tehran Branch,
Tehran, Iran
Department of Mathematics, Islamic Azad University
Iran


S.
Etemad
Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran
Department of Mathematics, Tabriz Branch,
Iran
amenability
contractibility
nhomomorphism
[[1] A. Bodaghi, nhomomorphism amenability, Proc. Rom. Aca., Series A, 14, No.2 (2013), 101105. ##[2] J. Duncan and S. A. Hosseiniun, The second dual of a Banach algebra, Proc. Roy. Soc. Edinburgh Soc., 84A (1979), 309325. ##[3] S. Hejazian, M. Mirzavaziri and M. S. Moslehian, nhomomorphisms, Bull. Iran. Math. Soc., 31, No. 1 (2005), 1323. ##[4] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc., 127(Providence, 1972). ##[5] Z. Hu, M. S. Monfared and T. Traynor, On character amenable Banach algebras, Studia Math., 193 (2009), 5378. ##[6] E. Kaniuth, A. T. Lau, and J. Pym, On φamenability of Banach algebras, Math. Proc. Cambridge Philos. Soc., 144 (2008), 8596. ##[7] E. Kaniuth, A. T. Lau and J. Pym, On character amenability of Banach algebras, J. Math. Anal. Appl., 344 (2008), 942955. ##[8] M. S. Monfared, Character amenability of Banach algebras, Math. Proc. Camb. Phil. Soc., 144 (2008), 697706.##]
Operatorvalued bases on Hilbert spaces
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2
In this paper we develop a natural generalization of Schauder basis theory, we term operatorvalued basis or simply ovbasis theory, using operatoralgebraic methods. We prove several results for ovbasis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ovbasis are continuous. We also dene the concepts of Bessel, Hilbert ovbasis and obtain some characterizations of them. We study orthonormal and Riesz ovbases for Hilbert spaces. Finally we consider the stability of ovbases under small perturbations. We generalize a result of PaleyWiener [4] to the situation of ovbasis.
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201
218


M. S.
Asgari
Department of Mathematics, Islamic Azad University, Central Tehran Branch,
PO. Code 13185768, Tehran, Iran
Department of Mathematics, Islamic Azad University
Iran
msasgari@yahoo.com
ovbases
dual ovbases
Bessel ovbases
Hilbert ovbases
ovbiorthogonal sequence
[[1] M. S. Asgari, H. Rahimi, Generalized frames for operators in Hilbert spaces, Inf. Dim. Anal. Quant. Probab. Rel. Topics, Vol. 17, No. 2, (2014), 14500131  145001320. ##[2] W. Rudin, Functional Analysis,McGrawHill. Inc, New York, (1991). ##[3] W. Sun, Gframes and GRiesz bases, J. Math. Anal. Appl. (2006), 322, 437452. ##[4] R. Young, An Introduction to Nonharmonic Fourier Series, Academic Press, New York, (2001).##]
On the Finsler modules over Halgebras
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2
In this paper, applying the concept of generalized Avalued norm on a right $H^*$module and also the notion of ϕhomomorphism of Finsler modules over $C^*$algebras we first improve the definition of the Finsler module over $H^*$algebra and then define ϕmorphism of Finsler modules over $H^*$algebras. Finally we present some results concerning these new ones.
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219
227


F.
Hasanvand
Department of Mathematics, Mashhad Branch, Islamic Azad University,
91735, Mashhad, Iran
Department of Mathematics, Mashhad Branch,
Iran


M.
Khanehgir
Department of Mathematics, Mashhad Branch, Islamic Azad University,
91735, Mashhad, Iran
Department of Mathematics, Mashhad Branch,
Iran
khanehgir@mshdiau.ac.ir


M.
Hassani
Department of Mathematics, Mashhad Branch, Islamic Azad University,
91735, Mashhad, Iran
Department of Mathematics, Mashhad Branch,
Iran
$H^*$algebra
full Finsler module
ϕmorphism
trace class
[[1] W. Ambrose, Structure theorems for a special class of Banach algebras. Transactions of the American Mathematical Society 57, (1945), 364386. ##[2] M. Amyari, A. Niknam, A note on Finsler modules. Bulletin of the Iranian Mathematical Society 29, No. 1, (2003) 7781. ##[3] M. Amyari, A. Niknam, On homomorphisms of Finsler modules. International Mathematical Journal 3, No. 3, (2003), 277281. ##[4] V. K. Balachandran, N. Swaminathan, Real H algebras. Journal of Functional Analysis 65, No. 1, (1986), 6475. ##[5] D. Bakic, B. Guljas, Operators on Hilbert Hmodules. Journal of Operator Theory 46, (2001), 123137. ##[6] M. Cabrera, J. Martinez and A. Rodriguez, Hilbert modules revisited: Orthonormal bases and HilbertSchmidt operators. Glasgow Mathematical Journal 37, (1995), 4554. ##[7] N. C. Phillips, N. Weaver, Modules with norms which take values in a Calgebra. Pacic Journal of Mathematics 185, No. 1, (1998), 163181. ##[8] P. P. Saworotnow, A generalized Hilbert space. Duke Mathematical Journal 35, (1968), 191197. ##[9] P. P. Saworotnow, J. C. Friedell, Traceclass for an arbitrary H*algebra. Proceedings of the American Mathematical Society 26, (1970), 95100. ##[10] J. F. Smith, The structure of Hilbert modules. Journal of the London Mathematical Society 8, (1974), 741749. ##[11] A. Taghavi, M. Jafarzadeh, A note on modules maps over Finsler modules. Journal of Advances in Applied Mathematics Analysis 2, No. 2, (2007), 8995. ##[12] B. Zalar, Jordanvon Neumann theorem for Saworotnows generalized Hilbert space. Journal of Acta Mathematica Hungarica 69, (1995), 301325.##]
Numerical solution of secondorder stochastic differential equations with Gaussian random parameters
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2
In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially secondorder with timevarying and Gaussian random coefficients. We indicate a complete analysis for secondorder equations in special case of scalar linear secondorder equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differential equations system from this equation, it could be approximated or solved numerically by different numerical methods. In the case of linear stochastic differential equations system by Computing fundamental matrix of this system, it could be calculated based on the exact solution of this system. Finally, this stochastic equation is solved by numerically method like EulerMaruyama and Milstein. Also its Asymptotic stability and statistical concepts like expectation and variance of solutions are discussed.
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229
241


R.
Farnoosh
School of Mathematics, Iran University of Science and Technology, 16844, Tehran, Iran
School of Mathematics, Iran University of
Iran


H.
Rezazadeh
School of Mathematics, Iran University of Science and Technology, 16844, Tehran, Iran
School of Mathematics, Iran University of
Iran
hr_rezazadeh@mathdep.iust.ac.ir


A.
Sobhani
School of Mathematics, Iran University of Science and Technology, 16844, Tehran, Iran
School of Mathematics, Iran University of
Iran


D.
Ebrahimibagha
Department of Mathematics, Center Branch, Islamic Azad university, Tehran, Iran
Department of Mathematics, Center Branch,
Iran
Stochastic differential equation
Linear equations system
Gaussian random variables
damped harmonic oscillators with noise
multiplicative noise
[[1] M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Oxford University Press, Oxford, UK, (1997). ##[2] L. Arnold, Stochastic Differential Equations: Theory and Applications, Wiley, (1974). ##[3] K. Burrage, I. Lenane, and G. Lythe, Numerical methods for secondorder stochastic differential equations, SIAM J. SCI. Compute., Vol. 29, No. 1, pp. 245264, (2007). ##[4] R. Cairoli, J. Walsh, Stochastic integrals in the plane, in Acta Math., 134, pp. 111183., (1975). ##[5] Dongbin Xiu, D Daniel M. Tartakovsky, Numerical solution for differential equation in random domain, SIAM J. Sci. Compute. Vol. 28, No. 3, pp. 11671185 (2006). ##[6] Lawrence C. Evans.:An Introduction to Stochastic Dierential Equations Version 1.2 (2004). ##[7] C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences, 3rd ed., SpringerVerlag, Berlin, (2004). ##[8] D. J. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Review 43, 525546, (2001). ##[9] E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Dierential Equations I: Nonstiff Problems, 2nd ed., SpringerVerlag, Berlin, (1993). ##[10] N. V. Krylov, Introduction to the Theory of Diusion Processes, American Math Society, (1995). ##[11] J. Lamperti, A simple construction of certain diusion processes, J. Math. Kyoto, 161170, (1964). ##[12] G. N. Milstein and M. V. Tretyakov, Quasisymplectic methods for Langevintype equations, IMA J. Numer. Anal., 23, pp. 593626, (2003). ##[13] H. McKean, Stochastic Integrals, Academic Press, (1969). ##[14] C. A. Marsh and J. M. Yeomans, Dissipative particle dynamics: The equilibrium for nite time steps, Europhys. Lett., 37, pp. 511516, (1997). ##[15] B. K. Oksendal, Stochastic Dierential Equations: An Introduction with Applications, 4th ed., Springer, (1995). ##[16] H. R. Rezazadeha, M. Magasedib, B. Shojaeec.Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation, Journal of Linear and Topological Algebra Vol. 01, No. 02, 79 89, (2012). ##[17] Wuan Luo. Wiener Chaos Expansion and Numerical Solutions of Stochastic Partial Differential Equations. California Institute of Technology Pasadena, California,(2006).##]
Approximate solution of fourth order differential equation in Neumann problem
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Generalized solution on Neumann problem of the fourth order ordinary differential equation in space $W^2_alpha(0,b)$ has been discussed, we obtain the condition on B.V.P when the solution is in classical form. Formulation of Quintic Spline Function has been derived and the consistency relations are given.Numerical method,based on Quintic spline approximation has been developed. Spline solution of the given problem has been considered for a certain value of $alpha$. Error analysis of the spline method is given and it has been tested by an example.
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254


J.
Rashidinia
School of Mathematics, Iran University of Science and Technology, Tehran, Iran
School of Mathematics, Iran University of
Iran
rashidinia@iust.ac.ir


D.
Kalvand
Faculty of Mathematics, Yerevan state University , Yerevan, Armenia
Faculty of Mathematics, Yerevan state University
Armenia


L.
Tepoyan
Faculty of Mathematics, Yerevan state University , Yerevan, Armenia
Faculty of Mathematics, Yerevan state University
Armenia
Fourth order ordinary differential equation
Neumann problem
generalized solution
quintic spline function
Error Analysis
[[1] Berezanski.J.M,Expansion in Eigenfunctions of Selfadjoint Operators.,Transl.Math. Monographs 17, American Mathematical Soc, Providence,1968. ##[2] Bicadze.A.V, Equations of mixed type.,M. Izd. AN SSSR,1959 (Russian). ##[3] Burenko. V.V, Sobolev Spaces on Domains., Teubner, 1999. ##[4] Dezin. A.A,Partial Differential Equations.(An Introduction to a General Theory of Linear Boundary Value Problems),Springer,1987. ##[5] Fichera. G, On a unied theory of boundary value problems for ellipticparabolic equations of second order., Boundary Problems of Differential Equations, The Univ. of Wisconsin Press,pp. 97120 , 1960. ##[6] Kalvand. Daryoush, Neumann problem for the degenerate differentialoperator equations of the fourth order., Vestnik RAU, PhysicalMathematical and Natural Sciences, No. 2,pp. 3441, 2010 (Russian). ##[7] Kalvand. Daryoush, Tepoyan. L, Neumann problem for the fourth order degenerate ordinary differential equation., Proceedings of the Yerevan State University, Physical and Mathematical Sciences, No. 1,pp. 2226, 2010. ##[8] Kalvand. Daryoush, Tepoyan. L, Rashidinia. J, Existence and uniqueness of the fourth order boundary value problem and quintic Spline solution., Proceeding of 9th Seminar on Differential Equations and Dynamical Systems, 1113 July, Iran,pp. 133136, 2012. ##[9] Keldi. M. V, Fis, On certain cases of degeneration of equations of elliptic type on the boundary of a domain., Dokl. Akad. Nauk. SSSR, 77,pp. 181183, 1951 (Russian). ##[10] Rashidinia,J.Direct methods for solution of a linear fourthorder twopoint boundary value problem.,J. Intern.Eng.Sci., Vol.13,pp.3748(2002). ##[11] Rashidinia, J.Jalilian,R. Nonpolynomial spline for solution of boundary value problems in plate defection theory., J. Comput. Math., 84(10), pp.14831494.(2007) ##[12] Rashidinia,J.Mahmoodi,R.Jalilian,R.Quintic spline solution of Boundary value problem in plate Defection., ##J. Comput. Sci.Eng.,Vol.16,No.1,pp.5359(2009). ##[13] Romanko. V.K, On the theory of the operators of the form, Differential Equations,Vol. 3,No. 11, pp. 19571970, 1967 (Russian). ##[14] Showalter. R.E, Hilbert Space Methods for Partial Differential Equations., Electronic Journal of Differential Equations, Monograph 01, 1994. ##[15] Tepoyan. L, Degenerate fourthorder dierentialoperator equations.,Differ. Urav, Vol. 23(8), 1987, pp. 1366 1376, (Russian); English Transl. in Amer. Math. Soc.,No. 8, 1988. ##[16] Tepoyan. L, On a degenerate dierentialoperator equation of higher order., Izvestiya Natsionalnoi AkademiiNauk Armenii. Matematika, Vol.34(5), pp. 4856,1999. ##[17] Tepoyan. L, On the spectrum of a degenerate operator., Izvestiya Natsionalnoi Akademii Nauk Armenii. Matematika,Vol. 38,No. 5,pp. 5357, 2003. ##[18] Tepoyan. L, The Neumann problem for a degenerate dierentialoperator equation., Bulletin of TICMI (Tbilisi International Centre of Mathematics and Informatics),Vol. 14, pp. 19, 2010. ##[19] Tricomi, F, On linear partial dierential equations of second order of mixed type., M., Gostexizdat, 1947 (Russian). ##254 J. Rashidinia et al. / J. Linear. Topological. Algebra. 02(04) (2013) 243254. ##[20] Usmani,R.A. Discrete methods for boundary value problems with applications in plate defection the ##ory.,J.Appl.Math.Phys., 30 ,pp.8799(1979). ##[21] Visik. M.I, Boundaryvalue problems for elliptic equations degenerate on the boundary of a region., Mat. Sb., ##35(77), pp. 513568,1954 (Russian); Amer. Math. Soc,Vol. 35,No. 2,(English) 1964. ##[22] Zahra ,W.K,Ashraf, M.El,Mhlawy. Numerical solution of twoparameter singularly perturbed boundary vproblems via exponential spline, Journal of King Saudi University Science January(2013).##]
Some algebraic properties of Lambert Multipliers on $L^2$ spaces
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In this paper, we determine the structure of the space of multipliers of the range of a composition operator $C_varphi$ that induces by the conditional expectation between two $L^p(Sigma)$ spaces.
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261


A.
Zohri
Faculty of Mathematical Sciences, Payame Noor University, P. O. BOX 193953697, Tehran, I. R. Iran
Faculty of Mathematical Sciences, Payame
Iran


S.
Khalil Sarbaz
Faculty of Mathematical Sciences, Payame Noor University, P. O. BOX 193953697, Tehran, I. R. Iran
Faculty of Mathematical Sciences, Payame
Iran
conditional expectation
multipliers
multiplication operators
composition operators
[[1] C. Burnap, I. L. B. Jung and A. Lambert, Separating partial normality classes with composition operators, J. Operator Theory 53, No. 2 (2005), 381397. ##[2] J. T. Campbell, M. EmbryWardrop, R. J. Fleming, and S. K. Narayan, Normal and quasinormal weighted composition operators, Glasgow Math. J. 33, No. 3 (1991), 275279. ##[3] J. D. Herron, Weighted conditional expectation operators on Lpspaces, UNC Charlotte Doctoral Dissertation. ##[4] M. R. Jabbarzadeh and S. Khalil Sarbaz, Lambert multipliers between Lpspaces, Czech. Math. J. 60 (135), No. 1 (2010), 3143. ##[5] A. Lambert, Hyponormal composition operators, Bull. London Math. Soc. 18, No. 4 (1986), 395400. ##[6] A. Lambert and T. G. Lucas, Nagatas principle of idealization in relation to module homomorphisms and conditional expectations, Kyungpook Math. J. 40, No. 2 (2000), 327337.##]