2014
3
1
1
0
On the commuting graph of noncommutative rings of order pnq
2
2
Let R be a noncommutative ring with unity. The commuting graph of R denoted
by (R), is a graph with vertex set RnZ(R) and two vertices a and b are adjacent i ab = ba.
In this paper, we consider the commuting graph of noncommutative rings of order pq and p2q
with Z(R) = 0 and noncommutative rings with unity of order p3q. It is proved that CR(a)
is a commutative ring for every 0 ̸= a 2 R n Z(R). Also it is shown that if a; b 2 R n Z(R)
and ab ̸= ba, then CR(a) CR(b) = Z(R). We show that the commuting graph (R) is the
disjoint union of k copies of the complete graph and so is not a connected graph.
1

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6


E
Vatandoost
Faculty of Basic Science, Imam Khomeini International University,
Qazvin, Iran.
Faculty of Basic Science, Imam Khomeini Internatio
Iran
vatandoost@sci.ikiu.ac.ir


F
Ramezani
Faculty of Basic Science, Imam Khomeini International University,
Qazvin, Iran.
Faculty of Basic Science, Imam Khomeini Internatio
Iran


A
Bahraini
Department of Mathematics, Islamic Azad University, Central Tehran Branch,
Tehran, Iran.
Department of Mathematics, Islamic Azad University
Iran
Commuting graph
noncommutative ring
nonconnected graph
algebraic graph
A note on the convergence of the ZakharovKuznetsov equation by homotopy analysis method
2
2
In this paper, the convergence of ZakharovKuznetsov (ZK) equation by homo
topy analysis method (HAM) is investigated. A theorem is proved to guarantee the conver
gence of HAM and to nd the series solution of this equation via a reliable algorithm.
1

7
13


A
Fallahzadeh
Department of Mathematics, Islamic Azad University,
Central Tehran Branch, PO. Code 13185.768, Tehran, 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, PO. Code 13185.768, Tehran, Iran.
Department of Mathematics, Islamic Azad University
Iran
Homotopy analysis method
ZakharovKuznetsov equation
Convergence
partial dierential equation
recursive method
[[1] S. Abbasbandy, Y. Tan, S. J. Liao, Newtonhomotopy analysis method for nonlinear equations, Appl. Math. ##Comput., 188 (2007) 17941800. ##[2] S. Abbasbandy, Homotopy analysis method for the Kawahara equation, Nonlinear Analysis: Real World ##Applications, 11 (2010) 307312. ##[3] J. Biazar, F. Badpeimaa, F. Azimi, Application of the homotopy perturbation method to ZakharovKuznetsov ##equations, Computers and Mathematics with Applications 58 (2009) 23912394. ##[4] W. Huang, A polynomial expansion method and its application in the coupled ZakharovKuznetsov equations, ##Chaos Solitons Fractals, 29 (2006) 365371. ##[5] S. Hesam, A. Nazemi, A. Haghbin, Analytical solution for the ZakharovKuznetsov equations by dierential ##transform method, International Journal of Engineering and Natural Sciences 4 (4) (2010). ##[6] M. Inc, Exact solutions with solitary patterns for the ZakharovKuznetsov equations with fully nonlinear ##dispersion, Chaos Solitons Fractals, 33 (15) (2007) 17831790. ##A. Fallahzadeh et al. / J. Linear. Topological. Algebra. 03(01) (2014) 713. 13 ##[7] S. J. Liao, Beyond pertubation: Introduction to the homotopy Analysis Method, Chapman and Hall/CRC ##Press, Boca Raton, (2003). ##[8] S.J. Liao, Notes on the homotopy analysis method: some denitions and theorems, Communication in Non ##linear Science and Numnerical Simulation, 14 (2009) 983997. ##[9] 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. ##[10] M. A. Fariborzi Araghi, A. Fallahzadeh, Explicit series solution of Boussinesq equation by homotopy analysis ##method, Journal of American Science, 8(11) 2012. ##[11] M. A. Fariborzi Araghi, S. Naghshband, On convergence of homotopy analysis method to solve the Schrodinger ##equation with a power law nonlinearity, Int. J. Industrial Mathematics, 5 (4) (2013) 367374. ##[12] S. Monro, E. J. Parkes, The derivation of a modied ZakharovKuznetsov equation and the stability of its ##solutions, Journal of Plasma Physics, 62 (3) (1999) 305317. ##[13] S. Monro, E. J. Parkes, Stability of solitarywave solutions to a modied ZakharovKuznetsov equation, Journal ##of Plasma Physics, 64 (3) (2000) 411426. ##[14] M. Usman, I. Rashid, T. Zubair, A. Waheed, S. T. Mohyuddin, Homotopy analysis method for Zakharov ##Kuznetsov (ZK) equation with fully nonlinear dispersion, Scientic Research and Essays, 8(23) 10651072 ##[15] A. M. Wazwaz, The extended tanh method for the ZakharovKuznetsov (ZK) equation, the modied ZK ##equation, and its generalized forms, Communications in Nonlinear Science and Numerical Simulation, 13 ##(2008) 10391047. ##[16] X. Zhao, H. Zhou, Y. Tang, H. Jia, Travelling wave solutions for modied ZakharovKuznetsov equation, ##Applied Mathematics and Computation, 181 (2006) 634648.##]
On the superstability of a special derivation
2
2
The aim of this paper is to show that under some mild conditions a functional
equation of multiplicative (; )derivation is superstable on standard operator algebras.
Furthermore, we prove that this generalized derivation can be a continuous and an inner
(; ) derivation.
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22


M
Hassani
Department of Mathematics, Mashhad Branch, Islamic Azad University,
Mashhad 91735, Iran.
Department of Mathematics, Mashhad Branch,
Iran
mhassanimath@gmail.com


E
Keyhani
Department of Mathematics, Mashhad Branch, Islamic Azad University,
Mashhad 91735, Iran.
Department of Mathematics, Mashhad Branch,
Iran
Ring (
)derivations, Linear (
)derivations, Stable, Superstable, Multiplicative (
)derivations, Multiplicative Derivations
[[1] B. Aupetit, A primer on spectral theory, Springer Verlag, New York, 1990. ##[2] J. A. Baker, The stability of the cosine equation, Proc. Amer. Math. Soc. 80 (1980), 411416. ##[3] A. Bodaghi, Cubic derivations on Banach algebras, Acta Mathematica Vietnamica, 38, No.2 (2013),517528. ##[4] D. G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, ##Duke math, J. 16 (1949), 385397. ##[5] A. Hosseini, M. Hassani, A. Niknam, Generalized derivation on Banach algebras, Bulletin of the Iranian ##Mathematical Society, 37 No. 4 (2011), 8194. ##[6] A. Hosseini, M. Hassani, A. Niknam, S. Hejazian, Some results on derivations, Ann. Funct. Anal, No. 2 ##(2011), 7584. ##[7] Ch. Hou, W. Zhang, Q. Meng, A note on (; )derivations, Linear Algebra and its Applications, 432(2010), ##26002607. ##[8] Ch. Hou, Q. Meng, Continuity of (; )derivation of operator algebras, J. Korean Math. Soc. 48(2011),823 ##[9] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat'e. A cad. Sci. U. S. A. 27 (1941), ##[10] W. S. Martindale, when are multiplicative mappings additive, proceeding of the American Mathematical Soc. ##21 No. 3(1969), 695698. ##[11] L. Molanar, On isomorphisms on standard operators algebras,ar Xiv Preprint Math,2000. ##[12] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), ##[13] P. Semrl, Approximate homomorphisms, Proc 34th Internat. Symp. On Functional Equations,Wisa Jaronik, ##Poland, June 1019 (1996) . ##[14] P. Semrl, The functional equation of multiplicative derivation is superstable on standard operator algebras, ##Integr Equat oper th, Vol. 18 (1994). ##[15] S. M. Ulam, A Collection of Mathematical Problems, Inter Science, New York, 1960. ##[16] S. Y. Yang, A. Bodaghi, K. A. M. Atan, Approximate cubic derivations on Banach algebras. Abstract ##and Applied Analysis, Volume 2012, Article ID 684179, 12 pages, doi:10.1155/2012/684179##]
Positive solution of nonsquare fully Fuzzy linear system of equation in general form using least square method
2
2
In this paper, we propose the leastsquares method for computing the positive
solution of a m n fully fuzzy linear system (FFLS) of equations, where m > n, based on
Kaman's arithmetic operations on fuzzy numbers that introduced in [18]. First, we consider
all elements of coecient matrix are nonnegative or nonpositive. Also, we obtain 1cut of the
fuzzy number vector solution of the nonsquare FFLS of equations by using pseudoinverse.
If 1cuts vector is nonnegative, we solve constrained least squares problem for computing
left and right spreads. Then, in the special case, we consider 0 is belong to the support of
some elements of coecient matrix and solve three overdetermined linear systems and if the
solutions of these systems held in nonnegative fuzzy solutions then we compute the solution
of the nonsquare FFLS of equations. Else, we solve constrained least squares problem for
obtaining an approximated nonnegative fuzzy solution. Finally, we illustrate the eciency
of the proposed method by solving some numerical examples.
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33


R
Ezzati
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Department of Mathematics, Karaj Branch,
Iran
ezati@kiau.ac.ir


A
Yousefzadeh
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Department of Mathematics, Karaj Branch,
Iran
Fuzzy linear system
Fuzzy number
Ranking Function
Fuzzy number vector solution
[[1] T. Allahviranloo, Numerical methods for fuzzy system of linear equations, Applied Mathematics and Computation, ##155 (2004) 493502. ##[2] T. Allahviranloo, Successive over relaxation iterative method for fuzzy system of linear equations, Applied ##Mathematics and Computation, 162 (2005) 189196. ##[3] T. Allahviranloo, The Adomian decomposition method for fuzzy system of linear equations, Applied Mathematics ##and Computation, 163 (2005) 553563. ##[4] T. Allahviranloo, E. Ahmady, N. Ahmady and Kh. Shams Alketaby, Block Jacobi twostage method with ##GaussSidel inner iterations for fuzzy system of linear equations, Applied Mathematics and Computation, ##175 (2006) 12171228. ##[5] T. Allahviranloo, N. Mikaeilvand, Non Zero Solutions Of The Fully Fuzzy Linear Systems, Appl. Comput. ##Math, 10 (2) 271282. ##[6] J.J. Buckley and Y. Qu, Solving system of linear fuzzy equations, Fuzzy Sets and Systems, 43 (1991) 3343. ##[7] C. Cheng, A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets Syst. 95 (1998) 307317. ##[8] M. Dehghan, B. Hashemi and M. Ghatee, Solution of the fully fuzzy linear systems using iterative techniques, ##Chaos Solutions and Fractals 34 (2007) 316336. ##[9] M. Dehghan and B. Hashemi, Solution of the fully fuzzy linear systems using the decomposition procedure, ##Applied Mathematics and Computation, 182 (2006) 15681580. ##[10] M. Dehghan, B. Hashemi, M. Ghatee, Computational methods for solving fully fuzzy linear systems, Appl ##Math and Comput 179 (2006) 328343. ##[11] M. Dehghan, B. Hashemi, Iterative solution of fuzzy linear systems, Applied Mathematics and Computation, ##175 (2006) 645674. ##[12] D. Dubois, H. Prade, Fuzzy Sets and Systems; Theory and Applications, Academic Press, New York, 1980. ##[13] M. Friedman, M. Ma, A. Kandel, Fuzzy linear systems, Proc. IEEE Int. Conf. Syst., Man, Cybernet. 1 (1996) ##1417. October 336338. ##[14] M. Friedman, M. Ma, A. Kandel, Fuzzy linear systems, Fuzzy Sets Syst. 96 (1998) 201209. ##[15] R. Ghanbari , N.MahdaviAmiri, New solution of linear systems using ranking functions and ABS algorithms, ##Appl. Math. Comput. 34 (2010) 33633375. ##[16] O. Kaleva, Fuzzy dierential equations, Fuzzy Sets and Systems 24 (1987) 301317. ##[17] A. Kumar, J.Kaur, P.Singh, A new method for solving fully fuzzy linear programming problems, Appl. Math. ##Comput. 35 (2011) 817823. ##[18] A. Kaufmann, M.M. Gupta, Introduction to Fuzzy Arithmetic Theory and Applications, Van Nostrand ##Reinhold, New York,1985. ##[19] M. Ming, M. Friedman, A. Kandel, General fuzzy least squares, Fuzzy Sets and Systems 88 (1997) 107118. ##[20] R. E. Moore, Methods and Applications of Interval Analysis, SIAM, Philadelphia, 1979. ##[21] H. T. Nguyen, E.A. Wallker, A First Course in Fuzzy Logic, Chapman , Hall, 2000. ##[22] V. Sundarapandian, Numerical Linear Algebra,New Dehli, 2008. ##[23] H. J. Zimmermann, Fuzzy Set Theory and its Applications, third ed., Kluwer Academic , Norwell, 1996. ##[24] L. A. Zadeh, A fuzzysettheoretic interpretation of linguistic hedges, Journal of Cybernetics 2 (1972) 434. ##[25] L. A. Zadeh, The concept of the linguistic variable and its application to approximate reasoning, Information ##Sciences 8 (1975) 199249. ##[26] R. Ezzati, S. Khezerloo, A. Yousefzadeh, Solving fully fuzzy linear system of equations in general form, ##Journal of Fuzzy Set Valued Analysis, Volume 2012, Article ID jfsva00117, (2012) 111.##]
Expansion methods for solving integral equations with multiple time lags using Bernstein polynomial of the second kind
2
2
In this paper, the Bernstein polynomials are used to approximate the solutions
of linear integral equations with multiple time lags (IEMTL) through expansion methods
(collocation method, partition method, Galerkin method). The method is discussed in detail
and illustrated by solving some numerical examples. Comparison between the exact and
approximated results obtained from these methods is carried out.
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35
45


M
Paripour
Department of Mathematics, Hamedan University of Technology, Hamedan, 65156579, Iran.
Department of Mathematics, Hamedan University
Iran
paripour@hut.ac.ir, paripour@gmail.com


Z
Shojaei
Department of Mathematics, Lorestan University, Khoramabad, Iran.
Department of Mathematics, Lorestan University,
Iran


S
Abdolahi
Department of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran.
Department of Mathematics, Arak Branch, Islamic
Iran
Integral equation with multiple time lags
Expansion methods
Bernstein polynomial
[[1] A. Jerri, Introduction to Integral equations with application, 1st edition, Marcel Dekker USA, 1985. ##[2] T. A. Burton, Integral equation with delay, Acta Math. Hung. 72 (3) (1998), pp. 233{242. ##M. Paripour et al. / J. Linear. Topological. Algebra. 03(01) (2014) 3545. 45 ##[3] H. Smith, On periodic solution of delay integral equations modeling epidemics, Jr. Math. Biology 4 (1997), ##pp. 69{80. ##[4] D. E. Kamen, P. P. Khargonekar, A. Tannenbaum, Proper factorizations and feedback control of linear time ##delay system, International Jr. of control 43 (2006), pp. 837{857. ##[5] D. D. Bhatta, M. I. Bhatti, Numerical solution of KdV equation using modied Bernstein polynomials, Appl. ##Math. Comput. 174 (2006), pp. 1255{1268. ##[6] M. I. Bhatti, P. Bracken, Solutions of dierential equations in a Bernstein polynomial basis, J. Comput. ##Appl. Math. 205 (2007), pp. 272{280. ##[7] B. N. Mandal, S. Bhattacharya, Numerical solution of some classes of integral equations using Bernstein ##polynomials, Appl. Math. Comput. 190 (2007), pp. 1707{1716. ##[8] A. J. Kadhim, Expansion Methods for Solving Linear Integral Equations with Multiple Time Lags Using ##BSpline and Orthogonal Functions, Eng. Tech. Journal 29 (9) (2011), pp. 1651{1661. ##[9] K. Engelborghs, T. Luzyanina, D. Roose, Colloction Methods for the computation of periodic solution of ##delay dierential equation, SIAM Jr. Sci. Comput. 22 (5) (2000), pp. 1593{1609. ##[10] M. Gelfand, S. Famines, Methods of Numerical approximation, Oxford university computing Laboratory, ##]
Cubic spline Numerov type approach for solution of Helmholtz equation
2
2
We have developed a three level implicit method for solution of the Helmholtz
equation. Using the cubic spline in space and nite dierence in time directions. The approach
has been modied to drive Numerov type nite dierence method. The method yield the tri
diagonal linear system of algebraic equations which can be solved by using a tridiagonal
solver. Stability and error estimation of the presented method are analyzed.The obtained
results satised the ability and eciency of the method.
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47
54


J
Rashidinia
Department of Mathematics,College of basic science, Islamic Azad University, Alborz, Iran.
Department of Mathematics,College of basic
Iran
j.rashidinia@iust.ac.ir


H. S.
Shekarabi
Department of Mathematics,College of basic science, Islamic Azad University, Alborz, Iran.
Department of Mathematics,College of basic
Iran


M
Aghamohamadi
Department of Mathematics,College of basic science, Islamic Azad University, Alborz, Iran.
Department of Mathematics,College of basic
Iran
Cubic spline
Finite dierence
Numerov type
Stability
Helmholtz equation
[[1] Carlos J. S. Alves, Svilen S. Valtchev,Numerical simulation of acoustic wave scattering using a meshfree plane ##waves method,International Workshop on MeshFree Methods( 2003),16. ##[2] K. Atkinson, W. Han, Theoretical Numerical Analysis: A Functional Analysis Framework, Springer,(2005). ##[3] R. J. Astley, P. Gamallo, Special short elements for ##ow acoustics, Comput. Method Appl. Mech. Engrg. 194 ##(2005), 341353. ##[4] R. K. Beatson, J. B. Cherrie, C. T. Mouat, Fast tting of radial basis functions: method based on precondi ##tioned GMRES iteration, Adv. Comput. Math. 11 (1999), 253270. ##[5] R. K. Beatson, W. A. Light, S. Billings, Fast solution of the radial basis function interpolation equations: ##domain decomposition methods, SIAM J. Sci. Comput. 5 (2000),17171740. ##[6] A. I. Bouhamid, A. Le Mhaut, Spline curves and surfaces under tension, (1994),5158. ##[7] A. I. Bouhamid, A. Le Mhaut, Multivariate interpolating (m;s)spline, Adv. Comput. Math. 11 (1999),287 ##[8] G. M. L. Gladwell, N. B. Willms, On the mode shape of the Helmholtz equation, J. Sound Vib. 188(1995),419 ##[9] Charles I. Goldstein, A Finite Element Method for Solving Helmholtz,Type Equationsin Waveguides and ##Other Unbounded Domains, mathematics of computation,39(160),(1982),309324. ##[10] F. Ihlenburg, I. Babusk. Finite element solution of the Helmholtz equation with high wave number part I: ##the hversion of the FEM. Computers Mathematics with Applications, 30(9),(1995),937. ##[11] F. Ihlenburg, I. Babuska. Finite element solution of the Helmholtz equation with high wave number part II: ##the hp version of the FEM. SIAM Journal of Numerical Analysis, 34(1),(1997)315358. ##[12] M. K. Jain, Numerical Solution of Dierential Equations, 2nd edn. Wiley, New Delhi (1984). ##[13] E. J. Kansa, A scattered data approximation scheme with applications to computational ##uid dynamics. I. ##Surface approximations and partial derivative estimates, Comput. Math. Appl. 19 (8,9) (1990),127145. ##[14] E. J. Kansa, Multiquadrics a scattered data approximation scheme with applications to computational ##dynamics. II. Solutions to parabolic, hyperbolic partial dierential equations, Comput. Math. Appl. 19 (8,9) ##(1990), 127145. ##[15] Y. C. Hon,C. S. Chen, Numerical comparisons of two meshless methods using radial basis functions engineer ##ing analysis with boundary elements. 26 (2002), 205225. ##[16] R. K. Mohanty, Stability interval for explicit dierence schemes for multidimensional second order hyperbolic ##equations with signicant rst order space derivative terms, Appl. Math. Comput. 190 (2007),16831690. ##[17] R. K. Mohanty, Venu Gopal, High accuracy cubic spline nite dierence approximation for the solution of ##onespace dimensional nonlinear wave equations,Applied Mathematics and Computation 218 (2011), 4234 ##[18] C. C. Paige, M. A. Saunders, LSQR: an algorithm for sparse linear equations and sparse least squares, ACM ##Trans. Math. Softw. 8 (1982) ,4371. ##[19] J. Rashidinia, R. Jalilian, V. Kazemi, Spline methods for the solutions of hyperbolic equations, Appl. Math. ##Comput. 190 (2007), 882886. ##[20] A. S. Wood, G. E. Tupholme, M. I. H. Bhatti, P. J. Heggs, Steadystate heattransfer through extended plane ##surfaces, Int. Commun. Heat Mass Transfer 22 (1995), 99109.##]
Generalized fclean rings
2
2
In this paper, we introduce the new notion of nfclean rings as a generalization
of fclean rings. Next, we investigate some properties of such rings. We prove that Mn(R) is
nfclean for any nfclean ring R. We also, get a condition under which the denitions of
ncleanness and nfcleanness are equivalent.
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S
Jamshidvand
Department of Mathematics, Shahed University, Tehran, Iran.
Department of Mathematics, Shahed University,
Iran
jamshidvand1367@gmail.com


H
Haj Seyyed Javadi
Department of Mathematics, Shahed University, Tehran, Iran.
Department of Mathematics, Shahed University,
Iran


N
Vahedian Javaheri
Department of Mathematics, Shahed University, Tehran, Iran.
Department of Mathematics, Shahed University,
Iran
Full element
clean ring
nclean ring
nfclean ring
[[1] P. Ara, The exchange property for purely inite simple rings, Proc. Amer. Math. Soc, 132, No. 9, (2004) ##25432547. ##[2] P. Ara, K. R. Goodearl, and E. Pardo, K0 of purely inite simple regular rings, KTheory, 26, No. 1, ##(2002) 69100. ##[3] V. P. Camillo and H. P. Yu, Exchange rings, units and idempotents, Comm. Algebra, 22, N0. 12, (1994) ##47374749. ##[4] H. Chen and Morita Contexts with many units, Algebra, 30, No. 3, (2002) 14991512. ##[5] A. Haghany, Hopcity and coHopsity for Morita Contexts, Comm. Algebra, 27, (1), (1999) 477492. ##[6] B. Li and L. Feng, fclean rings and rings having many full elements, J. Korean Math. Soc, 47, (2010) 247261. ##[7] W. K. Nicholson, Liftig Idempotents and exchang rings, Trans. Amer. Math. Soc, 229, (1977) 269278. ##[8] G. Xiao and W. Tong, nclean rings and weakly unit stable range rings,Comm. Algebra, 33, No. 5, (2005) ##15011517. ##[9] H. Yu, On quasiduo rings, Glasgow Math. J, 37, No. 1, (1995) 2131.##]