2010
7
1
1
0
The behavior of homological dimensions
The behavior of homological dimensions
2
2
Let R be a commutative noetherian ring. We study the behavior of injectiveand at dimension of R-modules under the functors HomR(-,-) and -×R-.
1
Let R be a commutative noetherian ring. We study the behavior of injectiveand at dimension of R-modules under the functors HomR(-,-) and -×R-.
1
10
M.
Ansari
M.
Ansari
Department of Mathematics, Islamic Azad University, Gachsaran branch, Gachsaran, Iran.
Department of Mathematics, Islamic Azad University
Iran
ansari.moh@gmail
E.
Hosseini
E.
Hosseini
Department of Mathematics, Islamic Azad University, Gachsaran branch, Gachsaran, Iran.
Department of Mathematics, Islamic Azad University
Iran
esmaeilmath@gmail.com
[[1] D. A. Buchsbaum, Categories and duality, Trans. Amer. Math. Soc. 80 (1955), 1-34.##[2] H. Cartan, S. Eilenberg, Homological algebra, Princeton University Press, (1956).##[3] H. B. Foxby, A homological theory of complexes of modules, Unpublished Notes,##[4] G. Hochshild, Relative homological algebra, Trans. Amer. Math. Soc. 82 (1956),##[5] B. Iversen, Cohomology of sheaves, Springer-Verlag, New Yourk, (1998).##[6] S. Mac Lane, Categories for the working mathematician, Springer-Verlag, New##Yourk, (1998). ##[7] E. Kirkman, J. Kuzmanovich ,Algebra with larg homological dimensions, Proc.##Amer. Math. Soc. 109, (1990), 903-906.##[8] C. A.Weible, An introduction to homological algebra, Cambridge studies in advanced##mathematics 38, Cambridge, (2003).##]
Some Results for CAT(0) Spaces
Some Results for CAT(0) Spaces
2
2
We shall generalize the concept of z = (1-t)+ty to n times which containsto verify some their properties and inequalities in CAT(0) spaces. In the sequelwith introducing of -nonexpansive mappings, we obtain some xed points andapproximate fixed points theorems.
1
We shall generalize the concept of z = (1-t)+ty to n times which containsto verify some their properties and inequalities in CAT(0) spaces. In the sequelwith introducing of -nonexpansive mappings, we obtain some xed points andapproximate fixed points theorems.
11
19
M.
Asadi
M.
Asadi
Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran.
Department of Mathematics, Zanjan Branch,
Iran
masadi@azu.ac.ir
S.M.
Vaezpour
S.M.
Vaezpour
Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran,
Iran.
Department of Mathematics and Computer Science,
Iran
M.
Soleymani
M.
Soleymani
Department of Mathematics, Malayer Branch, Islamic Azad University, Malayer, Iran.
Department of Mathematics, Malayer Branch,
Iran
[[1] L. Leustean, A quadratic rate of asymptotic regularity for CAT(0)-spaces, J.##Math. Anal. Appl. 325, (2007), 386-399.##[2] S. Dhompongsa and B. Panyanak, On 4-convergence theorems in CAT(0)##spaces, Comput. Math. Appl. 56, (2008), 2572-2579. ##[3] F. Bruhat and J. Tits, Groupes reductifs sur un corps local. I. Donnees radicielles##valuees, Inst. Hautes Etudes Sci. Publ. Math. 41, (1972), 5-251.##[4] M. Bridson and A. Hae iger, Metric Spaces of Non-Positive Curvature, Springer-##Verlag, Berlin, Heidelberg, 1999.##[5] T. Suzuki, Fixed point theorems and convergence theorems for some generalized##nonexpansive mappings,J. Math. Anal. Appl. 340, (2008), 1088-1095.##[6] B. Nanjaras and B. Panyanaka and W. Phuengrattana, Fixed point theorems and##convergence theorems for Suzuki-generalized nonexpansive mappings in CAT(0)##spaces, Nonlinear Anal.: Hybrid Systems, 4, (2010), 25-31.##[7] A. Razani and H. Salahifard, Invariant approximation for CAT(0) spaces, Non-##linear Anal. (TMA), 72, (2010), 2421-2425.##[8] P. Chaoha and A. Phon-on, A note on xed point sets in CAT(0) spaces, J.##Math. Anal. Appl. 320, (2006), 983-987.##[9] K. Goebel and W. A. Kirk, Some problems in metric xed point theory, J. of##Fixed Point Theory and Appl. 4, (2008), 13-25.##[10] M. Asadi, S. M. Vaezpour and H. Soleimani, -Nonexpansive Mappings on##CAT(0) Spaces, World Appl. Sci. J. 11, (2010), 1303-1306.##]
Modeling, simulation and analysis of a multi degree of freedom aircraft wing model
Modeling, simulation and analysis of a multi degree of
freedom aircraft wing model
2
2
This paper presented methods to determine the aerodynamic forces that acton an aircraft wing during flight. These methods are initially proposed for asimplified two degree-of-freedoms airfoil model and then are extensivelyapplied for a multi-degree-of-freedom airfoil system. Different airspeedconditions are considered in establishing such methods. The accuracy of thepresented methods is verified by comparing the estimated aerodynamic forceswith the actual values. A good agreement is achieved through the comparisonsand it is verified that the present methods can be used to correctly identify theaerodynamic forces acting on the aircraft wing models.
1
This paper presented methods to determine the aerodynamic forces that acton an aircraft wing during flight. These methods are initially proposed for asimplified two degree-of-freedoms airfoil model and then are extensivelyapplied for a multi-degree-of-freedom airfoil system. Different airspeedconditions are considered in establishing such methods. The accuracy of thepresented methods is verified by comparing the estimated aerodynamic forceswith the actual values. A good agreement is achieved through the comparisonsand it is verified that the present methods can be used to correctly identify theaerodynamic forces acting on the aircraft wing models.
21
62
Xueguang
Bia
Xueguang
Bia
Stanley Security Solutions, Inc., Shenzhen, Guangdong 518108, China
Stanley Security Solutions, Inc., Shenzhen,
Iran
yucheng.liu@louisiana.edu
Yucheng
Liu
Yucheng
Liu
Department of Mechanical Engineering, University of Louisiana, Lafayette, LA 70504, USA
Department of Mechanical Engineering, University
Iran
[[1] R. M. Kirby, Z. Yosibash, G.E. Karniadakis, “Towards stable coupling##methods for high order discretization of fluid-structure interaction:##Algorithms and observations”, Journal of Computational Physics, 223##(2), 2007, 489-518.##[2] F. Liu, J. Cai, Y. Zhu, H.M. Tsai, A.S.F. Wong, “Calculation of wing flutter##by a coupled fluid-structure method”, Journal of Aircraft, 38 (2), 2001,##[3] J. A. Fabunmi, “Effects of structural modes on vibratory force##determination by the pseudoinverse technique”, AIAA Journal, 24 (3),##1986, 504-509.##[4] R. Kamakoti, Y. Lian, S. Regisford, A. Kurdila, W. Shyy, Computational##aeroelasticity using a pressure-based solver, AIAA-2002-869, AIAA##Aerospace Sciences Meeting and Exhibit, 40th, Reno, NV, Jan. 14-17,##[5] Y. Liu, W.S. Shepard, Jr., “Dynamic force identification based on enhanced##least squares and total least-squares schemes in the frequency domain”,##Journal of Sound and Vibration, 282(1/2), 2005, 37-60.##[6] E. Parloo, P. Verboven, P. Guillaume, M.V. Overmeire, “Force##identification by means of in-operation modal models”, Journal of Sound##and Vibration, 262 (1), 2003, 161-173.##[7] I. Lee, S.-H. Kim, “Aeroelastic analysis of a flexible control surface with##structural nonlinearity”, Journal of Aircraft, 32(4), 1995, 868-874.##[8] S. -H. Kim, I. Lee, “Aeroelastic analysis of a flexible airfoil with a freeplay##nonlinearity”, Journal of Sound and Vibration, 193 (4), 1996, 823-846. ##[9] B. H. K. Lee, S.J. Price, Y.S. Wong, “Nonlinear aeroelastic analysis of##airfoils: bifurcation and chaos”, Progress in Aerospace Sciences, 35 (3),##1999, 205-334.##[10] I. D. Roy, W. Eversman, “Adaptive flutter suppression of an unswept##wing”, Journal of Aircraft, 33 (4), 1996, 775-783##[11] W. Eversman, I.D. Roy, “Adaptive flutter suppression using multiinput/##multi-output adaptive least mean square control”, Journal of##Aircraft, 34 (2), 1997, 244-250.##[12] G. Dimitriadis, J. E. Cooper, “A method for identification of non-linear##multi-degree-of-freedom systems”, Proceedings of the Institution of##Mechanical Engineers, Part G: Journal of Aerospace Engineering, 212##(4), 1998, 287-298.##]
Random fixed point of Meir-Keeler contraction mappings and its application
Random xed point of Meir-Keeler contraction
mappings and its application
2
2
In this paper we introduce a generalization of Meir-Keeler contraction forrandom mapping T : Ω×C → C, where C be a nonempty subset of a Banachspace X and (Ω,Σ) be a measurable space with being a sigma-algebra of sub-sets of. Also, we apply such type of random fixed point results to prove theexistence and unicity of a solution for an special random integral equation.
1
In this paper we introduce a generalization of Meir-Keeler contraction forrandom mapping T : Ω×C → C, where C be a nonempty subset of a Banachspace X and (Ω,Σ) be a measurable space with being a sigma-algebra of sub-sets of. Also, we apply such type of random fixed point results to prove theexistence and unicity of a solution for an special random integral equation.
63
67
H.
Dibachi
H.
Dibachi
Department of Mathematics, Islamic Azad University, Arak-Branch, Arak, Iran.
Department of Mathematics, Islamic Azad University
Iran
h-dibachi@iau-arak.ac.ir
[[1] A. Meir, E. Keeler. A theorem on contraction mapping, J. Math. Anal. Appl.##28 (1969), 326-329.##[2] A. Branciari. A xed point theorem for mapping satisfying a general contractive##condition of integral type, Int. J. Math. Math. Sci. 29 (2002), 531-536.##[3] I. Beg, Minimal displacement of random variables under lipschitz random maps,##Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Cen-##ter 19(2002), 391397##[4] S. Plubtieng, P. Kumam, R. Wangkeeree, Approximation of a common random##xed point for a nite family of random operators, Inter. J. Math. Math. Sci.##Volume 2007, Article ID 69626, 12 pages##]
Numerical solution of seven-order Sawada-Kotara equations by homotopy perturbation method
Numerical solution of seven-order Sawada-Kotara
equations by homotopy perturbation method
2
2
In this paper, an application of homotopy perturbation method is appliedto nding the solutions of the seven-order Sawada-Kotera (sSK) and a Lax'sseven-order KdV (LsKdV) equations. Then obtain the exact solitary-wave so-lutions and numerical solutions of the sSK and LsKdV equations for the initialconditions. The numerical solutions are compared with the known analyticalsolutions. Their remarkable accuracy are nally demonstrated for the bothseven-order equations.
1
In this paper, an application of homotopy perturbation method is appliedto nding the solutions of the seven-order Sawada-Kotera (sSK) and a Lax'sseven-order KdV (LsKdV) equations. Then obtain the exact solitary-wave so-lutions and numerical solutions of the sSK and LsKdV equations for the initialconditions. The numerical solutions are compared with the known analyticalsolutions. Their remarkable accuracy are nally demonstrated for the bothseven-order equations.
69
77
M.
Ghasemi
M.
Ghasemi
Department of Applied Mathematics, Faculty of Science, Shahrekord University, Shahrekord, P. O.
Box 115, Iran.
Department of Applied Mathematics, Faculty
Iran
meh_ghasemi@yahoo.com
A.
Azizi
A.
Azizi
Department of Mathematics, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran.
Department of Mathematics, Sanandaj Branch,
Iran
aramazizi@yahoo.com
M.
Fardi
M.
Fardi
Department of Mathematics, Islamic Azad University, Boroujen Branch, Boroujen, Iran.
Department of Mathematics, Islamic Azad University
Iran
[[1] M. Ghasemi, M. Tavassoli Kajani, Application of He's homotopy perturbation##method for linear and nonlinear heat equations, Math. Scientic J. 1 (2008)##[2] M. Ghasemi, M. Tavassoli Kajani, A. Azizi, The application of homotopy pertur-##bation method for solving Schrodinger equation, Math. Scientic J. 1 (5) (2009)##[3] M. Ghasemi, M. Tavassoli Kajani, A. Davari, Numerical solution of two-##dimensional nonlinear dierential equation by homotopy perturbation method,##Appl. Math. Comput. 189 (2007) 341-345.##[4] M. Ghasemi, M. Tavassoli Kajani, E. Babolian, Numerical solutions of the non-##linear Volterra-Fredholm integral equations by using Homotopy perturbation##method, Appl. Math. Comput. 188 (2007) 446-449. ##[5] M. Ghasemi, M. Tavassoli Kajani, E. Babolian, Application of He's homotopy##perturbation method to nonlinear integro-dierential equations, Appl. Math.##Comput. 188 (2007) 538-548.##[6] M. Ghasemi, M. Tavassoli Kajani, Application of He's homotopy perturbation##method to solve a diusion-convection problem, Math. Sci. Quarterly J. 4 (2010)##[7] M. Ghasemi, M. Tavassoli Kajani, R. Khoshsiar Ghaziani, Numerical solution of##fth order KdV equations by homotopy perturbation method, Math. Sci. Quar-##terly J. (2011) In Press.##[8] S. Vahdati, Z. Abbas, M. Ghasemi, Application of Homotopy Analysis Method##to Fredholm and Volterra integral equations, Math. Sci. Quarterly J. 4 (2010)##[9] J.H. He, Application of homotopy perturbation method to nonlinear wave equa-##tions, Chaos Solitons & Fractals 26 (2005) 695-700.##[10] J.H. He, Variational iteration method: a kind of nonlinear analytical technique:##some examples, Int. J. Nonlinear Mech. 34 (1999) 699-708.##[11] J.H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. En-##gng. 178 (1999) 257-262.##[12] J.H. He, Homotopy perturbation method: a new nonlinear analytical technique,##Appl. Math. Comput. 135 (2003) 73-79.##[13] J.H. He, A coupling method of homotopy technique and perturbation technique##for nonlinear problems, Int. J. Nonlinear Mech. 35 (2000) 37-43.##[14] J.H. He, A review on some new recently developed nonlinear analytical tech-##niques, Int. J. Nonlinear Sci. Numer. Simul. 1 (2000) 51-70.##[15] J.H. He, The homotopy perturbation method for nonlinear oscillators with dis-##continuities, Appl. Math. Comput. 151 (2004) 287-292.##[16] J.H. He, Comparison of homotopy perturbation method and homotopy analysis##method, Appl. Math. Comput. 156 (2004) 527-539.##[17] J.H. He, Bookkeeping parameter in perturbation methods, Int. J. Nonlinear Sci.##Numer. Simul. 2 (2001) 257-264.##[18] A.H. Nayfeh, Problems in Perturbation, John Wiley, New York, (1985).##[19] E.J. Parkes, B.R. Duy, An automated tanh-function method for nding solitary##wave solutions to non-linear evolution equations, Comput. Phys. Commun. 98##(1996), 288-300. ##[20] W. Hereman, P.P. Banerjee, A. Korpel, G. Assanto, A. van Immerzeele, A. Meer-##poel, Exact solitary wave solutions of nonlinear evolution and wave equations##using a direct algebraic method, J. Phys. A: Math. Gen. 19 (1986) 607-628.##]
A comment on “Supply chain DEA: production possibility set and performance evaluation model
A comment on “Supply chain DEA: production
possibility set and performance evaluation model
2
2
In a recent paper in this journal, Yang et al. [Feng Yang, Dexiang Wu,Liang Liang, Gongbing Bi & Desheng Dash Wu (2009), supply chainDEA:production possibility set and performance evaluation model] definedtwo types of supply chain production possibility set which were proved to beequivalent to each other. They also proposed a new model for evaluatingsupply chains. There are, however, some shortcomings in their paper. In thecurrent paper, we correct the model, the theorems, and their proofs.
1
In a recent paper in this journal, Yang et al. [Feng Yang, Dexiang Wu,Liang Liang, Gongbing Bi & Desheng Dash Wu (2009), supply chainDEA:production possibility set and performance evaluation model] definedtwo types of supply chain production possibility set which were proved to beequivalent to each other. They also proposed a new model for evaluatingsupply chains. There are, however, some shortcomings in their paper. In thecurrent paper, we correct the model, the theorems, and their proofs.
79
87
G.R.
Jahanshahloo
G.R.
Jahanshahloo
Department of Mathematics, science and Research Branch, Islamic Azad
University,Tehran 14515-775, Iran
Department of Mathematics, science and Research
Iran
M.
Rostamy-Malkhalifeh
M.
Rostamy-Malkhalifeh
Department of Mathematics, science and Research Branch, Islamic Azad
University,Tehran 14515-775, Iran
Department of Mathematics, science and Research
Iran
S.
Izadi-Boroumand
S.
Izadi-Boroumand
Department of Mathematics, science and Research Branch, Islamic Azad
University,Tehran 14515-775, Iran
Department of Mathematics, science and Research
Iran
s_izadi1363@yahoo.com
[References##[1] F. Yang, D. Wu, L. Liang, G. Bi, D. D. Wu, Supply chain##DEA:production possibility set and performance evaluation model.Journal of##Ann oper Res, DOI:10.1007/s10479-008-0511-2 (2009).##]
Approximating xed points of generalized non-expansive non-self mappings in CAT(0) spaces
Approximating xed points of generalized
non-expansive non-self mappings in CAT(0) spaces
2
2
Suppose K is a nonempty closed convex subset of a complete CAT(0) spaceX with the nearest point projection P from X onto K. Let T : K → X be anonself mapping, satisfying condition (C) with F(T) :={ x ε K : Tx = x}≠Φ.Suppose fxng is generated iteratively by x1ε K, xn+1 = P((1-αn)xn+αnTP[(1-αn)xn+βnTxn]),n≥1, where {αn }and {βn } are real sequences in[ε,1-ε] for some ε in (0,1). Then {xn} is Δ-convergence to some point x* inF(T). This work extends a result of Laowang and Panyanak [5] to the case ofgeneralized nonexpansive nonself mappings.
1
Suppose K is a nonempty closed convex subset of a complete CAT(0) spaceX with the nearest point projection P from X onto K. Let T : K → X be anonself mapping, satisfying condition (C) with F(T) :={ x ε K : Tx = x}≠Φ.Suppose fxng is generated iteratively by x1ε K, xn+1 = P((1-αn)xn+αnTP[(1-αn)xn+βnTxn]),n≥1, where {αn }and {βn } are real sequences in[ε,1-ε] for some ε in (0,1). Then {xn} is Δ-convergence to some point x* inF(T). This work extends a result of Laowang and Panyanak [5] to the case ofgeneralized nonexpansive nonself mappings.
89
95
Saeed
Saeed Shabani
Saeed
Saeed Shabani
Department of Mathematics, Izeh Branch, Islamic Azad University, Izeh, Iran.
Department of Mathematics, Izeh Branch, Islamic
Iran
shabani60@gmail.com
S.J.
Hoseini Ghoncheh
S. J.
Hoseini Ghoncheh
Department of Mathematics, Takestan Branch, Islamic Azad University, Takestan, Iran.
Department of Mathematics, Takestan Branch,
Iran
sjhghoncheh@gmail.com
[[1] M. Bridson and A. Hae iger, Metric Spaces of Non-Positive Curvature, vol. 319##of Fundamental Principles of Mathematical Sciences, Berlin, Germany, 1999.##[2] S. Dhompongsa and W. Kirk and B. Sims, xed point of uniformly lipschitzian##mappings, Nonlinear Anal. 65 (2006), 762{772.##[3] S. Dhompongsa and B. Panyanak, On -convergence theorems in CAT(0)##spaces. Computers and Mathematics with Applications. 56 (2008), 2572{2579.##[4] W. Kirk and B. Panyanak, A concept of convergence in geodesic spaces. Nonlinear##Anal. 68 (2008), 3689{3696.##[5] W. Laowang and B. Panyanak, Approximating xed points of nonexpansive non-##self mappings in CAT(0) spaces. Fixed Point Theory Appl. Article ID 367274##(2010), 11 pages.##[6] T. Suzuki, Fixed point theorems and convergence theorems for some generalized##nonexpansive mapping, Math. Anal. Appl. 340 (2008), 1088{1095.##[7] A. Razani and H. Salahifard, Invariant approximation for CAT(0) spaces, Non-##linear Anal. 72 (2010), 2421{2425.##[8] S. Dhompongsa, W. A. Kirk and B. Panyanak, Nonexpansive set-valued mappings##in metric and Banach spaces, J. Nonlinear and Convex Anal. 8 (2007), 35-45.##]
Numerical solution of nonlinear integral equations by Galerkin methods with hybrid Legendre and Block-Pulse functions
Numerical solution of nonlinear integral equations
by Galerkin methods with hybrid Legendre and
Block-Pulse functions
2
2
In this paper, we use a combination of Legendre and Block-Pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.The nonlinear part of the integral equation is approximated by Hybrid Legen-dre Block-Pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. We give some numerical examples. To showapplicability of the proposed method.
1
In this paper, we use a combination of Legendre and Block-Pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.The nonlinear part of the integral equation is approximated by Hybrid Legen-dre Block-Pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. We give some numerical examples. To showapplicability of the proposed method.
97
105
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
S.
Mahdavi
S.
Mahdavi
Department of Mathematics, Islamic Azad University, , Khorasgan Branch, Isfahan, Iran.
Department of Mathematics, Islamic Azad University
Iran
[[1] B.M. Mohan, K.B. Datta, Orthogonal function in systems and control, 1995.##[2] C. Hwang, Y.P. Shih, 1983, Laguerre series direct method for variational prob-##lems , J. Optimization Theory Appl.39, (?), 143149.##[3] E. Kreyzing, Introduction functional analysis with applications, SIAM, John Wi-##ley & Sons, 1978.##[4] K. Maleknejad, M. Tavassoli K, Y. Mahmoudi, Numarical solution of linear Fred-##holm and Voltera integral equation of the second kind by using Legandre wavelets,##J. Science, Islamic Republic of Iran 13 (?) , 161-166.##[5] K. Maleknejad, M. Tavassoli K, Solving second kind integral equations by##Galerkin methods with hybrid Legendre and Block-pulse functions, , Appl. Math.##Comput. 145 (2003), 623-629.##[6] Y. Mahmoudi, Wavelet Galerkin method for numerical solution of nonlinear in-##tegral equation, Appl. Math. Comput. ? 2005, ?{?.##[7] W. Sweldens, R. Piessens, Quadrature formulae and asymptotic error expansions##for wavelet approximations of smooth function, SIAM J. Numer. Anal. 31 (1994),##1240-1264.##]
Artinianess of Graded Generalized Local Cohomology Modules
Artinianess of Graded Generalized Local
Cohomology Modules
2
2
Let R = L n2N0Rn be a Noetherian homogeneous graded ring with local basering (R0;m0) of dimension d . Let R+ = Ln2NRn denote the irrelevant idealof R and let M and N be two nitely generated graded R-modules. Lett = tR+(M;N) be the rst integer i such that HiR+(M;N) is not minimax.We prove that if i t, then the set AssR0 (HiR+(M;N)n) is asymptoticallystable for n ! 1 and Hjm0 (HiR+(M;N)) is Artinian for 0 j 1. More-over, let s = sR+(M;N) be the largest integer i such that HiR+(M;N) is notminimax. For each i s, we prove that R0m0R0HiR+(M;N) is Artinian andthat Hjm0 (HiR+(M;N)) is Artinian for d 1 j d. Finally we show thatHd2m0 (HsR+(M;N)) is Artinian if and only if Hdm0 (Hs1R+(M;N)) is Artinian.
1
Let R = L n2N0Rn be a Noetherian homogeneous graded ring with local basering (R0;m0) of dimension d . Let R+ = Ln2NRn denote the irrelevant idealof R and let M and N be two nitely generated graded R-modules. Lett = tR+(M;N) be the rst integer i such that HiR+(M;N) is not minimax.We prove that if i t, then the set AssR0 (HiR+(M;N)n) is asymptoticallystable for n ! 1 and Hjm0 (HiR+(M;N)) is Artinian for 0 j 1. More-over, let s = sR+(M;N) be the largest integer i such that HiR+(M;N) is notminimax. For each i s, we prove that R0m0R0HiR+(M;N) is Artinian andthat Hjm0 (HiR+(M;N)) is Artinian for d 1 j d. Finally we show thatHd2m0 (HsR+(M;N)) is Artinian if and only if Hdm0 (Hs1R+(M;N)) is Artinian.
107
117
Sh.
Tahamtan
Sh.
Tahamtan
Department of Mathematics, Islamic Azad University, Borujerd-Branch, Borujerd, iran.
Department of Mathematics, Islamic Azad University
Iran
taham_sh@yahoo.com
[[1] K. Bahmanpour, R. Naghipour, On the coniteness of local cohomology modules,##Amer.Math.Soc.##[2] M. Brodmann, S. Fumasoli and R. Tajarod, Local cohomology over homogenous##rings with one-dimensional local base ring, proceedings of AMS. 131 (2003),##2977-2985.##[3] M. Brodmann, R.Y.Sharp, Local cohomology: an algebraic introduction with##geometric applications, Cambridge Studies in Advanced Mathematics 60, Cam-##bridge University Press (1998).##[4] ] W.Bruns, J.Herzog, Cohen-Macaulay rings, Cambridge stuies in advanced##mathematics, No.39. Cambridge University Press (1993). ##[5] K. Khashayarmanesh, Associated primes of graded components of generalized##local cohomology modules, Comm. Algebra. 33(9) (2005), 3081-3090.##[6] D. Kirby, Artinian modules and Hilbert polynomials, Quarterly Journal Mathe-##matics Oxford (2) 24 (1973), 47-57.##[7] R. Sazeedeh, Finiteness of graded local cohomology modules, J. Pure Appl. Alg.##212(1) (2008), 275-280.##[8] Sh. Tahamtan, H. Zakeri, A note on Artinianess of certain generalized local##cohomology modules, Journal of sciences, Islamic republic of Iran 19(3):265-##272(2008).##]