1392
8
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Hilbert modules over pro-C*-algebras
Hilbert modules over pro-C*-algebras
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1
2
In this paper, we generalize some results from Hilbert C*-modules to pro-C*-algebra case. We also give a new proof of the known result that l2(A) is aHilbert module over a pro-C*-algebra A.
1
20
م
آژینی
M.
Azhini
دانشگاه آزاد واحد علوم و تحقیقات تهران
دانشگاه آزاد واحد علوم و تحقیقات تهران
ایران
m.azhini@srbiau.ac.ir
ن.
حداد زاده
N.
Haddadzadeh
دانشگاه آزاد واحد علوم وتحقیقات تهران
دانشگاه آزاد واحد علوم وتحقیقات تهران
ایران
[[1] H. J. Borchers, On the algebra of test function, K.C.P. 25, IRMA, II, 15##(1973), 1-14.##[2] M. Dubois-Violette, A generalization of the classical moment on -algebras##with applications to relativistic quantum theory, I. Comm. Math. Phys. , 43##(1975), 225-254.##[3] A. Inoue, Locally C*-algebras, Mem. Fac. Sci. Kyushu Univ. Ser. A, 25##(1971), No. 2, 197-235.##[4] M. Joita, The stabilization theorem for Hilbert modules over locally C*-##algebras, The 3rd International Conference on Topological Algebra and##Applications, (ICTAA3), Oulu, Finland, July 2-6, 2001.##[5] M. Joita, Strict completely positive linear maps between locally C*-algebras##and representations on Hilbert modules, J. London Math. (2) 66 (2002),##[6] M. Joita, On Hilbert modules over locally C*-algebras, II, Period. Math.##Hungar. 51 (1) (2005) 27-36.##[7] M. Joita, On bounded module maps between Hilbert modules over locally##C*-algebras, Acta Math. Univ. Comenianae. Vol. LXXIV , 1 (2005), pp.##[8] A. Khosravi, M. S. Asgari, Frames and bases in Hilbert modules over##locally C*-algebras, International Journal of Pure and Applied Mathematics,##Volume 14 , No. 2 (2004), 169-187. ##[9] E. C. Lance, Hilbert C*-modules, A toolkit for operator algebraists, London##Math. Soc. Lecture Note Series 210. Cambridge Univ. Press, Cambridge,##[10] A. Mallios, Hermitian K-theory over Topological -Algebras, J. Math.##Anal. Appl., 106 (1985), No. 2, 454-539.##[11] N. C. Phillips, Inverse limits of C*-algebras, J. Operator Theory 19##(1988), 159-195.##[12] Yu. I. Zhuraev, F. Sharipov, Hilbert modules over locally C*-algebra,##Preprint, posted on Arxiv Org. Math. OA/0011053 V3 (2001).##]
Some notes on convergence of homotopy based methods for functional equations
Some notes on convergence of homotopy
based methods for functional equations
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1
2
Although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. Some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.Here, after criticizing previous works, a sucient condition for convergence ofhomotopy methods is presented. Finally, examples are given to show that evenif the homotopy method leads to a convergent series, it may not converge tothe exact solution of the equation under consideration.
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31
آ.
عزیزی
A.
Azizi
دانشگاه پیام نور تهران
دانشگاه پیام نور تهران
ایران
a.azizi@pnu.ac.ir
ج.
سعیدیان
J.
Saiedian
دانشکده ریاضی دانشگاه خوارزمی تهران
دانشکده ریاضی دانشگاه خوارزمی تهران
ایران
ا
بابلیان
E.
Babolian
دانشگاه خوارزمی تهران
دانشگاه خوارزمی تهران
ایران
[[1] S.J. Liao, Proposed homotopy analysis technique for the solution of##nonlinear problems, Ph.D. dissertation, Shanghai Jiao Tong University,##[2] J.H. He, Homotopy perturbation technique, Comp. Meth. Appl. Mech.##Eng., 178 (1999) 257-262.##[3] S.J. Liao, E. Magyari, Exponentially decaying boundary layers as limiting##cases of families of algebraically decaying ones, ZAMP, 57 (2006) 777-792.##[4] S.J. Liao, A new branch of solutions of boundary-layer ows over a##permeable stretching plate, Int. J. Non-Linear Mech., 42 (2007) 819-830.##[5] S. Abbasbandy, Y. Tan and S.J. Liao, Newton-homotopy analysis method##for nonlinear equations, Appl. Math. Comput., 188 (2007) 1794-1800.##[6] S.J. Liao, On the relationship between the homotopy analysis method and##Euler transform, Commun. Nonlin. Sci. Num. Simul., 18 (2010) 1421-1431.##[7] S. Abbasbandy, Application of He's homotopy perturbation method for##Laplace transform, Chaos, Solitons and Fractals, 30 (2006) 1206-1212.##[8] M. A. Rana, A. M. Siddiqui, Q. K. Ghori and R. Qamar, Application of##He's homotopy perturbation method to Sumudu transform, Int. J. Nonlinear##Sci. Numer. Simul., 8 (2008) 185-190.##[9] E. Babolian, J. Saeidian, M. Paripour, Computing the Fourier Transform##via Homotopy Perturbation Method, Z. Naturforsch., A: Phys. Sci., 64a##(2009) 671-675.##[10] E. Babolian, J. Saeidian, New application of HPM for quadratic riccati##dierential equation: a comparative study, Math. Sci. J., 3 (2007) ##[11] M. Ghasemi, M. Tavassoli Kajani, A. Azizi, The application of homotopy##perturbation method for solving Schrodinger equation, Math. Sci. J., 1##[12] M. Ghasemi, A. Azizi, M. Fardi, Numerical solution of seven-order##Sawada-Kotara equations by homotopy perturbation method, Math. Sci.##J., 7 (2011) 69-77.##[13] J. Biazar, H. Ghazvini, Convergence of the homotopy perturbation##method for partial dierential equations, Nonlinear Anal. Real World Appl.,##10 (2009) 2633-2640.##[14] J. Biazar, H. Aminikhah, Study of convergence of homotopy perturbation##method for systems of partial dierential equations, Comput. Math. Appl.,##58 (2009) 2221-2230.##[15] Z. Odibat, A study on the convergence of homotopy analysis method,##Appl. Math. Comput., 217 (2010) 782-789.##[16] S.J. Liao, Beyond Perturbation: An Introduction to Homotopy Analysis##Method, Chapman Hall/CRC Press, Boca Raton, 2003.##[17] S.J. Liao, Y. Tan, A general approach to obtain series solutions of##nonlinear dierential equations, Stud. Appl. Math., 119 (2007) 297-354.##[18] E. Babolian, A. Azizi, J. Saeidian, Some notes on using the homotopy##perturbation method for solving time-dependent dierential equations,##Math. Comput. Model., 50 (2009) 213-224.##]
Common xed point theorem for w-distance with new integral type contraction
Common xed point theorem for
w-distance with new integral type
contraction
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1
2
Boujari [5] proved a fixed point theorem with an old version of the integraltype contraction , his proof is incorrect. In this paper, a new generalizationof integral type contraction is introduced. Moreover, a fixed point theorem isobtained.
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39
E.
Firouz
E.
Firouz
Department of Mathematics, Islamic Azad University, Abhar Branch,
Abhar, Iran.
Department of Mathematics, Islamic Azad University
ایران
e_firouz@iau-abhar.ac.ir
S. J.
Hosseini Ghoncheh
S. J.
Hosseini Ghoncheh
Department of Mathematics, Takestan Branch, Islamic Azad University,
Takestan, Iran.
Department of Mathematics, Takestan Branch,
ایران
[[1] M. Asadi, S. Mansour Vaezpour and H. Soleimani, Some Results for CAT(0)##Spaces, Mathematics Scientic Journal, 7 (2011) 11{19.##[2] V. Berinde, A priori and a posteriori error estimates for a class of -##contractions, Bulletins for Applied & Computing Mathematics, (1999), 183-##[3] V. Berinde, Iterative approximation of xed points, Editura Efemeride,##Baia Mare, 2002.##[4] M. Beygmohammadi, A. Razani,Two xed-point theorems for mappings##satisfying a general contractive condition of integral type in the modular##space,Int. J. Math. Math. Sci., Article ID 317107, (2010), 10 pages.##[5] M. Boujari, Common xed point theorem with w-distance, Mathematical##Science, 4 (2010), 135{142.##[6] A. Branciari, A xed point theorem for mapping satisfying a general##contractive condition of integral type,Int. J. Math. Math. Sci., 10 (2002),##[7] S. J. Hosseini Ghoncheh, A. Razani, R. Moradi, B.E. Rhoades, A Fixed##Point Theorem for a General Contractive Condition of Integral Type in##Modular Spaces, J. Sci. I. A. U (JSIAU), 20 (2011), 89{100.##[8] O. Kada, T. Suzuki, W. Takahashi, Nonconvex minimization theorems and##xed point theorems in complete metric spaces, Math. Japonica 44 (1996),##[9] A. Razani and R. Moradi, Common xed point theorems of integral type##in modular spaces,Bulletin of the Iranian Mathematical Society 35 (2009),##[10] B. E. Rhoades, Two xed point theorems for mappings satisfying a general##contractive condition of integral type, Int. J. Math. Math. Sci, 63 (2003),##4007-4013.##[11] S. Shabani and S. J. Hosseini Ghoncheh, Approximating xed points##of generalized non-expansive non-self mappings in CAT(0) spaces,##Mathematics Scientic Journal, 7 (2011) 89{95.##]
Application of iterative Jacobi method for an anisotropic diusion in image processing
Application of iterative Jacobi method for
an anisotropic diusion in image
processing
1
1
Image restoration has been an active research area. Dierent formulations are eective in high qualityrecovery. Partial Dierential Equations (PDEs) have become an important tool in image processingand analysis. One of the earliest models based on PDEs is Perona-Malik model that is a kindof anisotropic diusion (ANDI) lter. Anisotropic diusion lter has become a valuable tool indierent elds of image processing specially denoising. This lter can remove noises without degradingsharp details such as lines and edges. It is running by an iterative numerical method. Therefore, afundamental feature of anisotropic diusion procedure is the necessity to decide when to stop theiterations. This paper proposes the modied stopping criterion that from the viewpoints of complexityand speed is examined. Experiments show that it has acceptable speed without suering from theproblem of computational complexity.
2
Image restoration has been an active research area. Dierent formulations are eective in high qualityrecovery. Partial Dierential Equations (PDEs) have become an important tool in image processingand analysis. One of the earliest models based on PDEs is Perona-Malik model that is a kindof anisotropic diusion (ANDI) lter. Anisotropic diusion lter has become a valuable tool indierent elds of image processing specially denoising. This lter can remove noises without degradingsharp details such as lines and edges. It is running by an iterative numerical method. Therefore, afundamental feature of anisotropic diusion procedure is the necessity to decide when to stop theiterations. This paper proposes the modied stopping criterion that from the viewpoints of complexityand speed is examined. Experiments show that it has acceptable speed without suering from theproblem of computational complexity.
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48
M
Khanian
M.
Knanian
Department of Mathematics, Khorasgan (Isfahan) Branch, Islamic Azad
University, Isfahan, Iran.
Department of Mathematics, Khorasgan (Isfahan)
ایران
mar.khanian@gmail.com
A.
Davari
A.
Davari
Department of Mathematics, Faculty of sciences, University of Isfahan,
Isfahan, Iran.
Department of Mathematics, Faculty of sciences,
ایران
[[1] P. Perona, J. Malik, Scale space and edge detection using anisotropic##diusion, IEEE Trans. Pattern Anal. Mach. Intell.,12,629-639 (1990).##[2] I. Capuzzo Dolcetta, R. Ferretti, Optimal stopping time formulation of##adaptive image ltering, Appl.Math. Optim. 43, 245-258 (2001).##[3] G. Gilboa, N. Sochen, Y.Y. Zeevi, Estimation of optimal PDE-based##denoising in the SNR sense, IEEE Trans. Image Proc. 15, 2269-2280 (2006).##[4] H. Molhem, R. Pourgholi, M. Borghei, A numerical approach for##solving a nonlinear inverse diusion problem by Tikhonov regularization,##Mathematics Scientic Journal, Vol. 7, No. 2, 39-54(2012).##[5] P. Mrazek, M. Navara, Selection of optimal stopping time for nonlinear##diusion ltering, Int. J. Comput. Vision. 52, 189-203 (2003). ##[6] A. Ilyevsky, E. Turkel, Stopping criteria for anisotropic PDEs in image##processing, J. Sci. Compute. 45, 337-347, (2010).##[7] Z. Wang, A.C. Bovick, H.R. Sheikh , E.P. Simoncelli, A novel kernel-##based framework for facial-image hallucination Structural Similarity, IEEE##Transactions on Image Processing. 13, No. 4, pp. 600-612 (2004).##]
The eect of indicial equations in solving inconsistent singular linear system of equations
The eect of indicial equations in solving
inconsistent singular linear system of
equations
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2
The index of matrix A in Cn.n is equivalent to the dimension of largest Jor-dan block corresponding to the zero eigenvalue of A. In this paper, indicialequations and normal equations for solving inconsistent singular linear systemof equations are investigated.
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64
M
Nikuei
M.
Nikuei
Young Researchers Club, Tabriz Branch, Islamic Azad University, Tabriz,
Iran.
Young Researchers Club, Tabriz Branch, Islamic
ایران
M.K.
Mirnia
M.K.
Mirnia
Department of Computer engineering, Tabriz Branch, Islamic Azad
University, Tabriz, Iran.
Department of Computer engineering, Tabriz
ایران
[[1] A. Ben, T. Greville, Generalized Inverses: Theory and applications, USA,##[2] S. Abbasbandy, M. Alavi, A new method for solving symmetric fuzzy##linear systems, Mathematics Scientic Journal (Islamic Azad University-##Arak Branch), 1 (2005) 55-62.##[3] A. Jafarian, S. Measoomy Nia, Utilizing a new feed-back fuzzy neural##network for solving a system of fuzzy equations, Communications in##Numerical Analysis, ID cna-00096 (2012).##[4] M. Saravi, E. Babolian, M. Rastegari, Systems of linear dierential##equations and collocation method , Mathematics Scientic Journal(Islamic##Azad University-Arak Branch), 5 (2010) 79-87.##[5] D. Conte, R. D'Ambrosio, B. Paternoster, Two-step diagonally-implicit##collocation based methods for Volterra Integral Equations, Applied##Numerical Mathematics, 62 (2012) 1312-1324.##[6] A. Shahsavaran, Numerical solution of linear Volterra and Fredholm##integro dierential equations using Haar wavelets, J. Mathematics##Scientic Journal, 6 (2010) 85-96.##[7] M. Tavassoli Kajani, S. Mahdavi, Numerical solution of nonlinear integral##equations by Galerkin methods with hybrid Legendre and Block-Pulse##functions, Mathematics Scientic Journal (Islamic Azad University-Arak##Branch), 7 (2011) 97-105.##[8] M. Mosleh, M. Otadi, Fuzzy Fredholm integro-dierential equations with##articial neural networks, Communications in Numerical Analysis, ID cna-##00128, (2012). ##[9] S. Campbell, C. Meyer, Generalized Inverses of Linear Transformations,##Pitman London,1979.##[10] B. Detta, Numerical Linear Algebra and Application, Thomson, 1994.##[11] D. Kincaid, W. Cheney, Numerical analysis mathematics of scientic##Computing California,1990.##[12] L. Lin, Y. Wei, N. Zhang, Convergence and quotient convergence of##iterative methods for solving singular linear equations with index one,##Linear Algebra and its Applications, 203 (2008) 35-45.##[13] M. Nikuie, M. K. Mirnia, A method for solving singular linear system of##equations, Journal of Operational Research and its Applications (Journal##of Applied Mathematics), Appl Math Islamic Azad University-Lahijan##Branch, 7 (2010) 79-90.##[14] L. Trefethen, D. Bau, Numerical linear algebra, SIAM, 1997.##[15] L. Zheng, A characterization of the Drazin inverse, Linear Algebra and its##Application, 335 (2001) 183-188.##[16] M. Nikuie, M. K. Mirnia, Y. Mahmoudi, Some results about the index##of matrix and Drazin inverse, Mathematical Sciences Quarterly Journal##(Islamic Azad University-Karaj Branch), 4 (2010) 283-294.##[17] Y. Wei, J. Zhou, A two-step algorithm for solving singular linear systems##with index one, Applied Mathematics and Computation, 174 (2006) 252-##]