2014
3
1
1
60
On the commuting graph of noncommutative rings of order $p^nq$
2
2
Let $R$ be a noncommutative ring with unity. The commuting graph of $R$ denoted by $Gamma(R)$, is a graph with vertex set $RZ(R)$ and two vertices $a$ and $b$ are adjacent iff $ab=ba$. In this paper, we consider the commuting graph of noncommutative rings of order pq and $p^2q$ with Z(R) = 0 and noncommutative rings with unity of order $p^3q$. It is proved that $C_R(a)$ is a commutative ring for every $0neq a in RZ(R)$. Also it is shown that if $a,bin RZ(R)$ and $abneq ba$, then $C_R(a)cap C_R(b)= Z(R)$. We show that the commuting graph $Gamma(R)$ is the disjoint union of $k$ copies of the complete graph and so is not a connected graph.
1

1
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
[[1] A. Abdollahi, Commuting graphs of full matrix rings over finite fields, Linear Algebra Appl. 422 (2008), 654–658. ##[2] S. Akbari, M. Ghandehari, M. Hadian, and A. Mohammadian, On commuting graphs of semisimple rings, Linear Algebra and its Applications, 390 (2004), 345355. ##[3] S. Akbari, A. Mohammadian, H. Radjavi, and P. Raja, On the diameters of commuting graphs, Linear Algebra and its Applications, 418 (2006), 161176. ##[4] S. Akbari and P. Raja, Commuting graphs of some subsets in simple rings, Linear Algebra and its Applications, 416 (2006), 10381047. ##[5] N. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge, 1993. ##[6] D. M. Cvetkovi´c, M. Doob, and H. Sachs, Spectra of graphs  Theory and applications, 3rd edition, Johann Ambrosius Barth Verlag, HeidelbergLeipzig, 1995. ##[7] J. B. Derr, G. F. Orr, and Paul S. Peck, Noncommutative rings of order p 4 , Journal of Pure and Applied Algebra, 97 (1994), 109116. ##[8] K. E. Eldridge, Orders for finite noncommutative rings with unity, The American Mathematical Monthly, 75(5). (May, 1968), 512514. ##[9] G. R. Omidi, E. Vatandoost, On the commuting graph of rings, Journal of Algebra and Its Applications. 10 (2011), 521–527.##]
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 homotopy analysis method (HAM) is investigated. A theorem is proved to guarantee the convergence 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


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 differential 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 differential 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. ##[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 Nonlinear 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 ZakharovKuznetsov (ZK) equation with fully nonlinear dispersion, Scientic Research and Essays, 8 (23) (2013) 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 $(alpha,beta)$derivation is superstable on standard operator algebras. Furthermore, we prove that this generalized derivation can be a continuous and an inner $(alpha,beta)$derivation.
1

15
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 $(alpha,beta)$
Linear $(alpha,beta)$derivations
Stable
Superstable
Multiplicative $(alpha,beta)$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),823835. ##[9] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat'e. A cad. Sci. U. S. A. 27 (1941), 222224. ##[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), 297300. ##[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 $mtimes n$ fully fuzzy linear system (FFLS) of equations, where $m > n$, based on Kaffman's arithmetic operations on fuzzy numbers that introduced in [18]. First, we consider all elements of coefficient 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 coefficient 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 efficiency of the proposed method by solving some numerical examples.
1

23
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. ##[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.
1

35
45


M.
Paripour
Department of Mathematics, Hamedan University of Technology, Hamedan, 65156579, Iran
Department of Mathematics, Hamedan University
Iran


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. 233242. ##[3] H. Smith, On periodic solution of delay integral equations modeling epidemics, Jr. Math. Biology 4 (1997), pp. 6980. ##[4] D. E. Kamen, P. P. Khargonekar, A. Tannenbaum, Proper factorizations and feedback control of linear timedelay system, International Jr. of control 43 (2006), pp. 837857. ##[5] D. D. Bhatta, M. I. Bhatti, Numerical solution of KdV equation using modied Bernstein polynomials, Appl. Math. Comput. 174 (2006), pp. 12551268. ##[6] M. I. Bhatti, P. Bracken, Solutions of dierential equations in a Bernstein polynomial basis, J. Comput. Appl. Math. 205 (2007), pp. 272280. ##[7] B. N. Mandal, S. Bhattacharya, Numerical solution of some classes of integral equations using Bernstein polynomials, Appl. Math. Comput. 190 (2007), pp. 17071716. ##[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. 16511661. ##[9] K. Engelborghs, T. Luzyanina, D. Roose, Colloction Methods for the computation of periodic solution of delay differential equation, SIAM Jr. Sci. Comput. 22 (5) (2000), pp. 15931609. ##[10] M. Gelfand, S. Famines, Methods of Numerical approximation, Oxford university computing Laboratory, 2006.##]
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 finite difference in time directions. The approach has been modied to drive Numerov type nite difference method. The method yield the tridiagonal 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 effciency of the method.
1

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 difference
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 flow 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 preconditioned 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), 287314. ##[8] G. M. L. Gladwell, N. B. Willms, On the mode shape of the Helmholtz equation, J. Sound Vib. 188(1995), 419433. ##[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 fluid 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 fluid 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 engineering analysis with boundary elements. 26 (2002), 205225. ##[16] R. K. Mohanty, Stability interval for explicit difference 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), 42344244. ##[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 $M_n(R)$ 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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55
60


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.##]