2011
7
2
2
0
Some notes on the existence of an inequality in Banach algebra
Some notes on the existence of an
inequality in Banach algebra
2
2
We shall prove an existence inequality for two maps on Banach algebra, withan example and in sequel we have some results on R and Rn spaces. This waycan be applied for generalization of some subjects of mathematics in teachingwhich how we can extend a math problem to higher level.
1
We shall prove an existence inequality for two maps on Banach algebra, withan example and in sequel we have some results on R and Rn spaces. This waycan be applied for generalization of some subjects of mathematics in teachingwhich how we can extend a math problem to higher level.
1
3
M.
Asadi
M.
Asadi
Department of Mathematics, Zanjan Branch, Islamic Azad University,
Zanjan, Iran.
Department of Mathematics, Zanjan Branch,
Iran
masadi@azu.ac.ir
[[1] G. Klambauer, Mathematical Analysis, Marcel Dekker, Inc., New York,##[2] R. G. Douglas, Banach Algebra Techniques in Operator Theory, Springer-##Verlag, New York, 1998.##]
Module contractibility for semigroup algebras
Module contractibility for semigroup
algebras
2
2
In this paper, we nd the relationships between module contractibility of aBanach algebra and its ideals. We also prove that module contractibility ofa Banach algebra is equivalent to module contractibility of its module uniti-zation. Finally, we show that when a maximal group homomorphic image ofan inverse semigroup S with the set of idempotents E is nite, the moduleprojective tensor product l1(S)×l1(E)l1(S) is l1(E)-module contractible.
1
In this paper, we nd the relationships between module contractibility of aBanach algebra and its ideals. We also prove that module contractibility ofa Banach algebra is equivalent to module contractibility of its module uniti-zation. Finally, we show that when a maximal group homomorphic image ofan inverse semigroup S with the set of idempotents E is nite, the moduleprojective tensor product l1(S)×l1(E)l1(S) is l1(E)-module contractible.
5
18
Abasalt
Bodaghi
Abasalt
Bodaghi
Department of Mathematics, Islamic Azad University, Garmsar Branch,
Garmsar, Iran.
Department of Mathematics, Islamic Azad University
Iran
abasalt.bodaghi@gmail.com
[[1] M. Amini, Module amenability for semigroup algebras, Semigroup Forum,##69 (2004), 243{254.##[2] M. Amini, A. Bodaghi and D. Ebrahimi Bagha, Module amenability of##the second dual and module topological center of semigroup algebras,##Semigroup Forum, 80 (2010), 302{312.##[3] A. Bodaghi, Module amenability and tensor product of semigroup##algebras, J. Math. Extension, 4 (2010), 97{106.##[4] A. Bodaghi, The structure of module contractible Banach algebras, Int.##J. Nonlinear Anal., 1 (2010), 6{11.##[5] A. Bodaghi, Module amenability of the projective module tensor product,##Malaysian J. Math. Sci., 5 (2011), 257{265. ##[6] H. G. Dales, Banach Algebras and Automatic Continuity, Oxford##University Press, Oxford, 2000.##[7] J. Duncan, I. Namioka, Amenability of inverse semigroups and their##semigroup algebras, Proc. Roy. Soc. Edinburgh, 80 (1988), 309-321.##[8] G. H. Esslamzadeh and T. Esslamzadeh, Contractability of `1-Munn##Algebras with Applications, Semigroup Forum, 63 (2001), 1{10.##[9] N. Grnbk, Amenability of weighted discrete convolution algebras on##cancellative semigroups, Proc. Roy. Soc. Edinburgh, 110 (1998), 351{360.##[10] B. E. Johnson, Cohomology in Banach algebras, Memoirs Amer. Math.##Soc. 127, Amer. Math. Soc., Providence, 1972.##[11] W.D. Munn, A class of irreducible matrix representations of an arbitrary##inverse semigroup, Proc. Glasgow Math. Assoc., 5 (1961), 41{48.##[12] H. Pourmahmood-Aghababa, (Super) module amenability, module##topological centre and semigroup algebras, Semigroup Forum, 81 (2010),##[13] H. Pourmahmood-Aghababa, A note on two equivalence relations on##inverse semigroups, Semigroup Forum, DOI 10.1007/s00233-011-##[14] R. Rezavand, M. Amini, M. H. Sattari, and D. Ebrahimi Bagha, Module##Arens regularity for semigroup algebras, Semigroup Forum, 77 (2008),##[15] V. Runde, Lectures on Amenability, Lecture Notes in Mathematics 1774,##Springer-Verlag, Berlin-Heidelberg-New York, 2002.##[16] Yu. V. Selivanov, Banach algebras of small global dimension zero, Uspekhi##Mat. Nauk., 31 (1976), 227{228.##]
A goal programming procedure for ranking decision making units in DEA
A goal programming procedure for ranking
decision making units in DEA
2
2
This research proposes a methodology for ranking decision making units byusing a goal programming model.We suggest a two phases procedure. In phase1, by using some DEA problems for each pair of units, we construct a pairwisecomparison matrix. Then this matrix is utilized to rank the units via the goalprogramming model.
1
This research proposes a methodology for ranking decision making units byusing a goal programming model.We suggest a two phases procedure. In phase1, by using some DEA problems for each pair of units, we construct a pairwisecomparison matrix. Then this matrix is utilized to rank the units via the goalprogramming model.
19
38
Farhad
Hosseinzadeh-Lotfi
Farhad
Hosseinzadeh-Lotfi
Department of Mathematics, Islamic Azad University, Science and Research
Branch, Tehran, Iran.
Department of Mathematics, Islamic Azad University
Iran
Mohammad
Izadikhah
Mohammad
Izadikhah
Department of Mathematics, Islamic Azad University, Arak Branch, Arak
Branch, Iran.
Department of Mathematics, Islamic Azad University
Iran
m-izadikhah@iau-arak.ac.ir,m izadikhah@yahoo.com
R.
Roostaee
R.
Roostaee
Department of Mathematics, Islamic Azad University, Arak Branch, Arak
Branch, Iran.
Department of Mathematics, Islamic Azad University
Iran
Mohsen
Rostamy-Malkhalifeh
Mohsen
Rostamy-Malkhalifeh
Department of Mathematics, Islamic Azad University, Science and Research
Branch, Tehran, Iran.
Department of Mathematics, Islamic Azad University
Iran
[[1] N. Adler, L. Friedman, Z. Sinuany-Stern, Review of ranking methods in##data envelopment analysis context, European J. Operational Research 140##(2002) 249{265.##[2] P. Andersen, N.C. Petersen, A procedure for ranking ecient units in data##envelopment analysis, Management Sci. 39 (1993) 1261{1264. ##[3] V. Belton, An IDEA-integrating data envelopment analysis with multiple##criteria analysis In: Goicochea, A., Duckstein, L., Zionts, S. (Eds.),##Proceedings of the Ninth International Conference on Multiple Criteria##Decision Making: Theory and Applications in Business, Industry and##Commerce. Springer Verlag, Berlin, (1992) 71{79.##[4] V. Belton and S.P. Vickers, Demystifying DEA -a visual interactive##approach based on multiple criteria analysis, J. Opl. Res. Soc. 44 (1993),##[5] C-T. Chang, A modied goal programming model for piecewise linear##functions, Euro. J. Operatational Research 139 (2002) 62{67.##[6] A. Charnes, W. W. Cooper and E. Rhodes, Measuring the eciency of##decision making units, Euro. J. Operatational Research 2 (1978) 429{444.##[7] A. Charnes, W. W. Cooper, Management Model and Industrial##Application of Linear Programming, vol. 1, Wiley, New York, (1961).##[8] G.X. Chen and M. Deng, A cross-dependence based ranking system for##ecient and inecient units in DEA, Expert Sys. Appl. 38 (2011) 9648{##[9] W.D. Cook and M. Kress, Data envelopment model for aggregating##preference ranking, Management Sci. 36 (1990) 1302{1310.##[10] W. D. Cook, M. Kress and L. Seiford, Prioritization models for frontier##decision making units in DEA, Euro. J. Operatational Research 59 (1992)##[11] J.R. Doyle and R.H Green, Data envelopment analysis and multiple##criteria decision making. Omega 21 (1993) 713{715.##[12] P.C. Fishburn, Expected utility: an anniversary and a new era. J. Risk##and Uncertainty, 1 (1988) 267{283.##[13] R.B. Flavell, A new goal programming, Omega 4 (1976) 731{732.##[14] A. Hadi-Vencheh and M.N. Mokhtarian, On the issue of non-zero weights##in preference voting and aggregation, Math. Sci. J. 5, (2010) 11{19.##[15] N. Hibiki and T. Sueyoshi, DEA sensitivity analysis by changing a##reference set: Regional contribution to Japanese industrial development,##Omega 27 (1999) 139{153. ##[16] J.P. Ignizio, Introduction to Linear Goal Programming, Sage, Beverly,##Hills, CA (1985).##[17] M. Izadikhah, Ranking units with interval data based on ecient and##inecient frontiers, Math. Sci. J. 3(2007) 49{57.##[18] G.R. Jahanshahloo, F. Hosseinzadeh Lot, N. Shoja, G. Tohidi and S.##Razavyan, Ranking using l1-norm in data envelopment analysis, Appl.##Math. Comput. 153 (2004) 215{224.##[19] G.R. Jahanshahloo, H.V. Junior, F. Hosseinzadeh Lot and D. Akbarian,##A new DEA ranking system based on changing the reference set, Euro. J.##Operatational Research 181 (2007) 331{337.##[20] G.R. Jahanshahloo, F. Hosseinzadeh Lot, M. Khanmohammadi, M.##Kazemimanesh and V. Rezaie, Ranking of units by positive ideal DMU##with common weights, Expert Sys. Appl. 37 (2010) 7483{7488.##[21] G.R. Jahanshahloo, M. Rostamy-Malkhalifeh and S. Izadi-Boroumand,##A comment on Supply chain DEA: production possibility set and##performance evaluation model", Math. Sci. J. 7 (2011) 79{87.##[22] R.L. Keeney and H. Raia, Decision Making with Multiple Objectives.##Wiley, New York, (1976).##[23] R.L. Keeney, Decision analysis: an overview, Operations Research, 30##(1982) 803{838.##[24] M. khodabakhshi and N. Aryavash, Input congestion, technical ineciency##and output reduction in fuzzy data envelopment analysis, Math. Sci. J. 6##(2011) 45{60.##[25] Y.J. Lai and C.L. Hwang, Fuzzy Multiple Objective Decision Making-##Methods and Applications, Springer-Verlag, (1994).##[26] S. M. Lee, Goal Programming for Decision Analysis, Auerbach,##Philadelphia, PA, (1972).##[27] S. Li, G. R. Jahanshahloo and M. Khodabakhshi, A super-eciency model##for ranking ecient units in data envelopment analysis, Appl. Math.##Comput. 184 (2007) 638{648.##[28] F-H.F. Liu and H.H. Peng, Ranking of units on the DEA frontier with##common weights, Computers and Operations Research, 35 (2008) 1624{##[29] S. Mehrabian, M.R. Alirezaee and G.R. Jahanshahloo, A complete##eciency ranking of decision making units in data envelopment analysis,##Computational Optimization and Appl., 14 (1999) 261{266.##[30] M. Oral, O. Kettani and P. Lang, A methodology for collective evaluation##and selection of industrial RD projects. Management Sci. 37 (1991) 871-##[31] F. Rezai Balf, H. Zhiani Rezai, G.R. Jahanshahloo and F. Hosseinzadeh##Lot, Ranking ecient DMUs using the Tchebyche norm, Appl. Math.##Mod. 36 (2012) 46{56.##[32] C. Romero, Extended lexicographic goal programming: A unifying##approach, Omega 29 (2001) 63{71.##[33] T.L. Saaty, The Analytic Hierarchy Process. McGraw-Hill, New York,##[34] M.J. Schniederjans, Goal Programming: Methodology and Applications,##Kluwer, Boston, MA, (1995).##[35] L.M. Seiford and J. Zhu, Infeasibility of super eciency data envelopment##analysis models, INFOR, 37 (1999) 174{187.##[36] T.R. Sexton, R.H. Silkman and A.J. Hogan, Data envelopment analysis:##Critique and extensions, in: R.H. Silkman (Ed.), Measuring Eciency: An##Assessment of Data Envelopment Analysis, Jossey-Bass, San Francisco,##CA, (1986) 73{105.##[37] Z. Sinuany-Stern and A. Mehrez, Discrete multiattribute utility approach##to project selection. J. Opl. Res. Soc. 38 (1987) 1135{1139.##[38] Z. Sinuany-Stern, A. Mehrez and Y. Hadad, An AHP/DEA methodology##for ranking decision making units. Intl. Trans. Op. Res.. 7 (2000) 109{124.##[39] T. J. Stewart, Data envelopment analysis and multiple criteria decision##making: a response. Omega, 22 (1994) 205{206.##[40] M. Tamiz, D. Jones and C. Romero, Goal programming for##decision making: An overview of the current state-of-the-art, Euro. J.##Operatational Research 111 (1998) 567{581.##[41] B. Vitoriano and C. Romero, Extended interval goal programming, J. Opl.##Res. Soc. 50 (1999) 1280{1283. ##[42] Y-M. Wang, Y. Luo and L. Liang, Ranking decision making units by##imposing a minimum weight restriction in the data envelopment analysis.##J. Comput. Appl. Math. 223 (2009) 469-484.##[43] Y-M. Wang, Y. Luo and Y-X. Lan, Common weights for fully ranking##decision making units by regression analysis. Expert Sys. Appl. 38 (2011)##9122{9128.##[44] Y-M. Wang and T.M.S. Elhag, A goal programming method for obtaining##interval weights from an interval comparison matrix. Euro. J. Operational##Research, 177 (2007) 458{471.##[45] J. Zhu, Super-eciency and DEA sensitivity analysis, Euro. J. Operational##Research, 129 (2001) 443{455.##]
A numerical approach for solving a nonlinear inverse diusion problem by Tikhonov regularization
A numerical approach for solving a
nonlinear inverse diusion problem by
Tikhonov regularization
2
2
In this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. In additional, the least-squares method is adopted tond the solution. To regularize the resultant ill-conditioned linear system ofequations, we apply the Tikhonov regularization method to obtain the stablenumerical approximation to the solution. Some numerical experiments con-rm the utility of this algorithm as the results are in good agreement with theexact data.
1
In this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. In additional, the least-squares method is adopted tond the solution. To regularize the resultant ill-conditioned linear system ofequations, we apply the Tikhonov regularization method to obtain the stablenumerical approximation to the solution. Some numerical experiments con-rm the utility of this algorithm as the results are in good agreement with theexact data.
39
54
H.
Molhem
H.
Molhem
Department of Physics , Faculty of Science, Islamic Azad University, Karaj
Branch, Karaj, Iran
Department of Physics , Faculty of Science,
Iran
molhem@kiau.ac.ir
R.
Pourgholi
R.
Pourgholi
School of Mathematics and Computer Sciences,
Damghan University, P.O.Box 36715-364, Damghan, Iran.
School of Mathematics and Computer Sciences,
Damgh
Iran
M.
Borghei
M.
Borghei
Department of Physics , Faculty of Science, Islamic Azad University, Karaj
Branch, Karaj, Iran.
Department of Physics , Faculty of Science,
Iran
[[1] J. Bear , Dynamics of Fluids in Porous Media, 2nd edn. Elsevier, New##York, 1975.##[2] J. R. Cannon, The One-Dimensional Heat Equation. Addison-Wesley,##Menlo Park, California, 1984.##[3] P. C. Hansen, Analysis of discrete ill-posed problems by means of the##L-curve, SIAM Rev. 34 (1992), 561{80.##[4] A. N. Tikhonov, V. Y. Arsenin, On the solution of ill-posed problems, New##York, Wiley, 1977.##[5] C. L. Lawson, R. J. Hanson, Solving least squares problems, Philadelphia,##PA,SIAM, 1995, First published by Prentice-Hall, 1974.##[6] J. R. Cannon, P. Duchateau, An inverse problem for a nonlinear diusion##equation, SIAM J. appl. Math. 39 (1980), 272{289. ##[7] O. A. Ladyzhenskaya, V. A. Sollonikov, N. N. Uralceva, Linear and##Quasilinear Equations Parabolic Type,Amer. Math. Soc. Providence, RI##[8] H. T. Chen, S. M. Chang, Application of the hybrid method to inverse heat##conduction problems, Int. J. Heat Mass Transfer, 33 (1990), 621{628.##[9] A. Shidfar, R. Pourgholi, M. Ebrahimi, A Numerical Method for Solving##of a Nonlinear Inverse Diusion Problem, Comput. Math. Appl. 52 (2006),##1021{1030.##[10] A. Shidfar, R. Pourgholi, Application of nite dierence method to##analysis an ill-posed problem, Appl. Math. Comput. 168 (2005), 1400{##[11] R. Pourgholi, N. Azizi, Y. S. Gasimov, F. Aliev, H. K. Khala,##Removal of Numerical Instability in the Solution of an Inverse##Heat Conduction Problem, Communications in Nonlinear Science and##Numerical Simulation, (2008) In Press.##[12] F. Durbin, Numerical inversion of Laplace transforms: ecient##improvement to Dubner and Abates method, Comp. J. 17 (1973), 371{##[13] G. Honig and U. Hirdes, A method for the numerical inversion of Laplace##transforms, J. Comp. Appl. Math. 9 (1984), 113-132.##[14] G. H. Golub, C. F. Van Loan, Matrix computations, John Hopkins##university press, Baltimore, MD, 1983.##]
A method for solving fully fuzzy linear system
A method for solving fully fuzzy linear
system
2
2
In this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form Ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where A~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisting of m non-negative fuzzy numbers.
1
In this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form Ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where A~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisting of m non-negative fuzzy numbers.
55
66
M.
Mosleh
M.
Mosleh
Department of Mathematics, Islamic Azad University, Firuozkooh Branch,
Firuozkooh, Iran.
Department of Mathematics, Islamic Azad University
Iran
S.
Abbasbandy
S.
Abbasbandy
Department of Mathematics, Science and Research Branch, Islamic Azad
University, Tehran 14515/775, Iran.
Department of Mathematics, Science and Research
Iran
abbasbandy@yahoo.com
M.
Otadi
M.
Otadi
Department of Mathematics, Islamic Azad University, Firuozkooh Branch,
Firuozkooh, Iran.
Department of Mathematics, Islamic Azad University
Iran
[[1] S. Abbasbandy, A. Jafarian and R. Ezzati, Conjugate gradient method for##fuzzy symmetric positive denite system of linear equations, Appl. Math.##Comput. 171 (2005) 1184-1191.##[2] S. Abbasbandy, R. Ezzati and A. Jafarian, LU decomposition method for##solving fuzzy system of linear equations, Appl. Math. Comput. 172 (2006)##[3] S. Abbasbandy, J.J. Nieto and M. Alavi, Tuning of reachable set in one##dimensional fuzzy dierential inclusions, Chaos, Solitons & Fractals 26##(2005) 1337-1341.##[4] S. Abbasbandy, M. Otadi and M. Mosleh, Minimal solution of general dual##fuzzy linear systems, Chaos Solitons & Fractals 37 (2008) 1113-1124.##[5] S. Abbasbandy, M. Otadi and M. Mosleh, Numerical solution of a system##of fuzzy polynomials by fuzzy neural network, Inform. Sci. 178 (2008)##1948-1960.##[6] T. Allahviranloo, Succesive over relaxation iterative method for fuzzy##system of linear equations, Appl. Math. Comput. 162 (2005) 189-196.##[7] T. Allahviranloo, Numerical methods for fuzzy system of linear equations,##Appl. Math. Comput. 155 (2004) 493-502.##[8] T. Allahviranloo, M. Afshar Kermani, Solution of a fuzzy system of linear##equation,Appl. Math. Comput.175 (2006) 519-531.##[9] B. Asady, S. Abbasbandy and M. Alavi, Fuzzy general linear systems,##Appl. Math. Comput. 169 (2005) 34-40.##[10] S. Barnet, Matrix Methods and Applications, Clarendon Press, Oxford,##[11] M. Caldas and S. Jafari, -Compact fuzzy topological spaces, Chaos##Solitons & Fractals 25 (2005) 229-232.##[12] M. Dehghan, B. Hashemi, M. Ghatee, Solution of the fully fuzzy linear##systems using iterative techniques, Chaos Solitons & Fractals 34 (2007)##[13] M. Dehghan, B. Hashemi, M. Ghatee, Computational mathods for solving##fully fuzzy linear systems, Appl. Math. Comput. 179 (2006) 328-343.##[14] D. Dubois and H. Prade, Operations on fuzzy numbers, J. Systems Sci. 9##(1978) 613-626.##[15] D. Dubois and H. Prade, Systems of linear fuzzy constraints. Fuzzy Sets##Sys. 3 (1980) 37-48.##[16] G. Feng and G. Chen, Adaptive control of discrete-time chaotic systems:##a fuzzy control approach, Chaos Solitons & Fractals 23 (2005) 459-467. ##[17] M. Friedman, Ma Ming and A. Kandel, Fuzzy linear systems, Fuzzy Sets##Sys. 96 (1998) 201-209.##[18] M. Friedman, Ma Ming and A. Kandel, Duality in fuzzy linear systems,##Fuzzy Sets and Sys. 109 (2000) 55-58.##[19] R. Goetschel, W. Voxman, Elementary calculus, Fuzzy Sets and Systems##18 (1986) 31-43.##[20] W. Jiang and Q. Guo-Dong and D. Bin, H1 Variable universe adaptive##fuzzy control for chaotic system, Chaos Solitons & Fractals 24 (2005)##1075-1086.##[21] A. Kaufmann and M. M. Gupta, Introduction Fuzzy Arithmetic, Van##Nostrand Reinhold, New York, 1985.##[22] S . Muzzioli and H. Reynaerts, Fuzzy linear systems of the form A1x+b1 =##A2x + b2, Fuzzy Sets and Sys. 157 (2006) 939-951.##[23] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons & Fractals##22 (2004) 1039-1046.##[24] X. Wang, Z. Zhong and M. Ha, Iteration algorithms for solving a system##of fuzzy linear equations, Fuzzy Sets and Sys. 119 (2001) 121-128.##[25] L. A. Zadeh, The concept of a linguistic variable and its application to##approximate reasoning, Inform. Sci. 8 (1975) 199-249.##]
Positive solution for boundary value problem of fractional dierential equation
Positive solution for boundary value
problem of fractional dierential equation
2
2
In this paper, we prove the existence of the solution for boundary value prob-lem(BVP) of fractional dierential equations of order q 2 (2; 3]. The Kras-noselskii's xed point theorem is applied to establish the results. In addition,we give an detailed example to demonstrate the main result.
1
In this paper, we prove the existence of the solution for boundary value prob-lem(BVP) of fractional dierential equations of order q 2 (2; 3]. The Kras-noselskii's xed point theorem is applied to establish the results. In addition,we give an detailed example to demonstrate the main result.
67
78
Haidong
Qu
Haidong
Qu
Department of Mathematics and Information, Hanshan Normal University,
Chaozhou, Guangdong, 521041, P. R. China
Department of Mathematics and Information,
Iran
qhaidong@163.com
[[1] N. Kosmatov, A singular boundary value problem for nonlinear dierential##equations of fractional order, J. Appl. Math. Comput. 29 (2009), 125-135.##[2] S. Zhang, Positive solutions for boundary value problem of nonlinear##fractional dierential equations, Electric. J. Di. Equs. 36 (2006),1-12.##[3] A. P. Chen, Y. S. Tian, Existence of Three Positive Solutions to##Three-Point Boundary Value Problem of Nonlinear Fractional Dierential##Equation, Dier. Equ. Dyn. Syst. 18 (2010), 327-339.##[4] A.A. Kilbsa, H. M. Srivastava, J.J. Trujillo. Theory and Applications of##Fractional Dierential Equations, Elsevier, Amsterdam, 2006.##[5] S. Q. Zhang, Existence results of positive solutions to boundary value##problem for fractional dierential equation, ,Positivity 13(2009), 583-599.##[6] S. Zhang, The existence of a positive solution for a nonlinear fractional##dierential equation, J. Math. Anal. Appl. 252 (2000), 804-812.##[7] S. Zhang, Positive solution for some class of nonlinear fractional##dierential equation, J. Math. Anal. Appl. 278 (2003), 136-148.##[8] M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahab, Existence results##for fractional order functional dierential equations with innite delay, J.##Math. Anal. Appl. 338 (2008), 1340-1350.##[9] D.J. Guo, L. Lakshmikantham, Nonlinear Problems in Abstract Cones,##Academic Press, New York, 1988.##]
An approach for simultaneously determining the optimal trajectory and control of a cancerous model
An approach for simultaneously
determining the optimal trajectory and
control of a cancerous model
2
2
The main attempt of this article is extension the method so that it generallywould be able to consider the classical solution of the systems and moreover,produces the optimal trajectory and control directly at the same time. There-fore we consider a control system governed by a bone marrow cancer equation.Next, by extending the underlying space, the existence of the solution is con-sidered and pair of the solution are identied simultaneously. In this mannera numerical example is also given.
1
The main attempt of this article is extension the method so that it generallywould be able to consider the classical solution of the systems and moreover,produces the optimal trajectory and control directly at the same time. There-fore we consider a control system governed by a bone marrow cancer equation.Next, by extending the underlying space, the existence of the solution is con-sidered and pair of the solution are identied simultaneously. In this mannera numerical example is also given.
79
92
Hamid Reza
Sahebi
Hamid Reza
Sahebi
Department of Mathematics, Islamic Azad University, Ashtian Branch,
Ashtian, Iran.
Department of Mathematics, Islamic Azad University
Iran
sahebi@mail.aiau.ac.ir
S.
Ebrahimi
S.
Ebrahimi
Department of Mathematics, Islamic Azad University, Ashtian Branch,
Ashtian, Iran.
Department of Mathematics, Islamic Azad University
Iran
[[1] G. Chqquet, Lectures on Analysis, Benjamin, New York , 1969.##[2] R.E. Edwards,Functional Analysis Theory and Application, Holt, Rinehart##and Winston, New York, 1965.##[3] Fakharzadeh J., A. and J. E. Rubio, Global Solution of Optimal Shape##Designe Problems, ZAA Journal for Analysis and its Applications. 16,##(1999), 143-155.##[4] Rubio, J. E., Control and Optimization: the Linear Treatment of Non-##linear Problems, Manchester University Press, Manchester, (1986).##[5] Rubio, J. E., The Global Control of Non-linear Elliptic Equation, Journal##of Franklin Institute, 330(1), pp. 29-35, (1993). ##[6] Rosenbloom, P. C., Qudques Classes de Problems Exteremaux, Bulltein de##Societe Mathematique de France, 80 , pp.183-216, (1952).##[7] A. Swierniak, A. Polanski, and M. Kimmel,Optimal control problems##arising in cell-cyclespecic cancer chemotherapy, Cell Prolif., 29 , pp. 117-##139 (1996).##[8] G. W. Swan, Role of Optimal Control Theory in Cancer Chemotherapy,##Math. Biosci.,101, pp.237-284 (1990).##[9] H. Schattler, Optimal##controls for a model with pharmacokinetics maximizing bone marrow in##cancer chemotherapy,Mathematical Biosciences Volume 206, Issue 2,pp.##320-342 (2007).##[10] Xia, X,Modelling of bone marrow cancer. Vaccine readiness, drug##eectiveness and therapeutical failures, Journal of Process Control. No##17.pp. 253-260 (2007).##[11] G.F. Webb, Resonance phenomena in cell population chemotherapy##models, Rocky Mountain J. of Mathematics., 20, pp. 1195-1216 (1990).##]
Numerical solution of Hammerstein Fredholm and Volterra integral equations of the second kind using block pulse functions and collocation method
Numerical solution of Hammerstein
Fredholm and Volterra integral equations
of the second kind using block pulse
functions and collocation method
2
2
In this work, we present a numerical method for solving nonlinear Fredholmand Volterra integral equations of the second kind which is based on the useof Block Pulse functions(BPfs) and collocation method. Numerical examplesshow eciency of the method.
1
In this work, we present a numerical method for solving nonlinear Fredholmand Volterra integral equations of the second kind which is based on the useof Block Pulse functions(BPfs) and collocation method. Numerical examplesshow eciency of the method.
93
103
M. M.
Shamivand
M. M.
Shamivand
Department of Mathematics, Islamic Azad University, Borujerd Branch,
Borujerd, Iran.
Department of Mathematics, Islamic Azad University
Iran
m.shamivand@yahoo.com
A.
Shahsavaran
A.
Shahsavaran
Department of Mathematics, Islamic Azad University, Borujerd Branch,
Borujerd, Iran.
Department of Mathematics, Islamic Azad University
Iran
[[1] K. E. Atkinson, The numerical solution of integral equations of the second##kind, Cambridge University Press, 1997.##[2] K. E. Atkinson, A survey of numerical methods for solving nonlinear##integral equations, J. Integral Equations Appl. 4 (1992) 15{46.##[3] E. Babolian, Z. Masouri, S. H. Varmazyar, Introdusing a direct method to##solve nonlinear Volterra and Fredholm integral equations using orthogonal##triangular functions, Math. Sci. J., 5 (2009) 11{26.##[4] M. Ghasemi, M. T. Kajani, A. Azizi, The application of homotopy##perturbation method for solving Schrodinger equation, Math. Sci. J., 5##(2009) 47{55.##[5] J. Kondo, Integral equations, Oxford University Press, 1991. ##[6] K. Maleknejad, M. Hadizadeh, Algebraic nonlinearity in Volterra-##Hammerstein equations, J. Sci. I. R. Iran, 10 (1999).##[7] K. Maleknejad, M. Karami, N. Aghazadeh, Numerical solution of##Hammerstein equations via an interpolation method, Applied Mathematics##and Compution 168 (2005) 141{145.##[8] K. Maleknejad, M. Karami, Numerical solution of nonlinear Fredholm##integral equations by using multiwavelets in the Petrov-Galerkin method,##Appl. Math. Comput. 168 (2005) 102{110.##[9] N. Parandin, Numerical solution of linear and nonlinear Fredholm integral##equation of the second kind using nite dierences method, Math. Sci. J.,##5 (2009) 113{122.##[10] A. Shahsavaran, E. Babolian, Computational method for solving nonlinear##Fredholm integral equations of Hammerstein type based on Lagrange##interpolation and quadrature method, Math. Sci. J., 5 (2009) 137{145.##[11] T. Cardinali, N. S. Papageorgiou, Hammerstein integral inclusions in##re exive banach spaces, Amer. Math. Soc. 127 (1999) 95{103.##]
A three-step method based on Simpson's 3/8 rule for solving system of nonlinear Volterra integral equations
A three-step method based on Simpson's
3/8 rule for solving system of nonlinear
Volterra integral equations
2
2
This paper proposes a three-step method for solving nonlinear Volterra integralequations system. The proposed method convents the system to a (3 × 3)nonlinear block system and then by solving this nonlinear system we ndapproximate solution of nonlinear Volterra integral equations system. To showthe advantages of our method some numerical examples are presented.
1
This paper proposes a three-step method for solving nonlinear Volterra integralequations system. The proposed method convents the system to a (3 × 3)nonlinear block system and then by solving this nonlinear system we ndapproximate solution of nonlinear Volterra integral equations system. To showthe advantages of our method some numerical examples are presented.
105
130
M.
Tavassoli-Kajani
M.
Tavassoli-Kajani
Department of Mathematics, Islamic Azad University, Khorasgan Branch,
Isfahan, Iran.
Department of Mathematics, Islamic Azad University
Iran
mtavassoli@khuisf.ac.ir
L.
Kargaran-Dehkordi
L.
Kargaran-Dehkordi
Department of Mechanic, Shahr-e-Kord University, Shahr-e-Kord, Iran.
Department of Mechanic, Shahr-e-Kord University,
Iran
Sh.
Hadian-Jazi
Sh.
Hadian-Jazi
Department of Mechanic, Shahr-e-Kord University, Shahr-e-Kord, Iran.
Department of Mechanic, Shahr-e-Kord University,
Iran
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