2013
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3
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Derivations in semiprime rings and Banach algebras
2
2
Let R be a 2torsion free semiprime ring with extended centroid C, U the Utumi quotient ring of R and m; n > 0 are xed integers. We show that if R admits derivation d such that b[[d(x); x]n; [y; d(y)]m] = 0 for all x; y 2 R where 0 ̸= b 2 R, then there exists a central idempotent element e of U such that eU is commutative ring and d induce a zero derivation on (1 e)U. We also obtain some related result in case R is a noncommutative Banach algebra and d continuous or spectrally bounded.
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129
135


Sh
Sahebi
Department of Mathematics, Islamic Azad University, Central Tehran Branch,
P. O. Box 1416894351, Tehran, Iran.
Department of Mathematics, Islamic Azad University
Iran


V
Rahmani
Department of Mathematics, Islamic Azad University, Central Tehran Branch,
P. O. Box 1416894351, Tehran, Iran.
Department of Mathematics, Islamic Azad University
Iran
venosrahmani@yahoo.com
prime ring
semiprime ring
derivation
Utumi quotient ring
Banach algebra
[[1] K. I. Beidar, W. S. Martindale III, A. V. Mikhalev, Rings with generalized identities, Pure and Applied ##Math., Vol. 196, New York, 1996. ##[2] H. E. Bell, W. S. Martindale III, Centeralizing mappings of semiprime rings, Canadian Mathematical Bul ##letin, 30 (1) (1987), pp. 92{101. ##[3] M. Bresar, M. Mathieu, Derivations mapping into the radical III, J. Funct. Anal., 133(1), (1995), pp. 21{29. ##[4] C. L. Chung, GPIs having coecients in Utumi quotient rings, proc.Amer.Math.soc., 103 (1988), pp. 723{728. ##[5] J. S. Ericson, W. S. Martindale III, J. M. Osborn, Prime nonassociative algebras, pascic J. math., 60 (1975), ##pp. 49{63. ##[6] B. E. Jacobson, A. M. Sinclair, Continuity of derivations and problem of kaplansky, Amer. J. Math., 90 ##(1968), pp. 1067{1073. ##[7] V. K. Kharchenko, Dierential identity of prime rings, Algebra and Logic., 17 (1978), pp. 155{168. ##[8] C. Lanski, An Engel condition with derivation, Proc. Amer. Math. Soc., 118 (1993), pp. 731{734. ##[9] T. K. Lee, Semiprime rings with dierential identities, Bull. Inst. Math. Acad. Sinica, 20 (1) (1992), pp. ##[10] W. S. Martindale III, Prime rings satistying a generalized polynomial identity, J. Algebra., 12 (1969), pp. ##[11] M. Mathieu, G. J. Murphy, Derivations mapping into the radical, Arch. Math., 57 (5) (1991), pp. 469{474. ##[12] M. Mathieu, V. Runde, Derivations mapping into the radical II, Bull. london Math. soc., 24 (5)(1992), pp. ##[13] E. C. Posner, Derivation in prime rings, Proc. Amer. Math. Soc., 8 (1957), pp. 1093{1100. ##[14] K. H. Park, On derivations in noncommutative semiprime rings and Banach algebras, Bull. Korean Math. ##Soc., 42 (4)(2005), pp. 671{678. ##[15] A. M. Sinclair, Continuous derivations on Banach algebras, Proc. Amer. Math. Soc., 20 (1969), pp. 166{170. ##[16] I. M. Singer, J. Werner, Derivations on commutative normed algebras, Math. Ann., 129 (1955), pp. 260{264. ##[17] M. P. Thomas, The image of a derivation is contained in the radical, math. Ann., 128 (2) (1988), pp. 435{460.##]
Some results of semilocally simply connected property
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2
If we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. In this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.
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137
143


A
Etemad Dehkordya
Department of Mathematical sciences, Isfahan University of Technology, Isfahan, Iran.
Department of Mathematical sciences, Isfahan
Iran
ae110mat@cc.iut.ac.ir


M
Malek Mohamad
Department of Mathematical sciences, Isfahan University of Technology, Isfahan, Iran.
Department of Mathematical sciences, Isfahan
Iran
Semilocally simply connected
topological fundamental group
discrete space
[[1] D.K. Biss, The topological fundamental group and generalization covering space, Topology and its application ##124(2002), 355371. ##[2] W.A. Bogley and A.J. Sieradski, Wieghted combinatorial group theory and wiled metric complexces A.C. ##Kim(Ed) GroupsKorea'98 de Gruyter, Pusan(2005), 5380. ##[3] J.S. Calcut and J.D. McCarthy, Discreteness and homogeneity of the topological fundamental group, Topology ##Proc. 34(2009) 339349. ##[4] P. Fabel, Metric spaces with discrete topological fundamental group, Topology Appl., 154(2007), 635638. ##[5] R. Fritsch and R.A. Piccinini, Cellular Structures in Topology, Cambridge University press(1990). ##[6] A. Hatcher, Algebraic Topology, Cambridge University press(2002). ##[7] E.H. Spanier, Algebraic Topology, McGrawHill, New york(1966).##]
A generalization of Bertrand's test
2
2
One of the most practical routine tests for convergence of a positive series makes use of the ratio test. If this test fails, we can use Rabbe's test. When Rabbe's test fails the next sharper criteria which may sometimes be used is the Bertrand's test. If this test fails, we can use a generalization of Bertrand's test and such tests can be continued innitely. For simplicity, we call ratio test, Rabbe's test, Bertrand's test as the Bertrand's test of order 0, 1 and 2, respectively. In this paper, we generalize Bertrand's test in order k for natural k > 2. It is also shown that for any k, there exists a series such that the Bertrand's test of order fails, but such test of order k + 1 is useful, furthermore we show that there exists a series such that for any k, Bertrand's test of order k fails. The only prerequisite for reading this article is a standard knowledge of advanced calculus.
1

145
151


A. A.
Tabatabai Adnani
Islamic Azad University, Central Tehran Branch, Tehran, Iran.
Islamic Azad University, Central Tehran Branch,
Iran
a.t.adnani@gmail.com


A
Reza
Islamic Azad University, Central Tehran Branch, Tehran, Iran.
Islamic Azad University, Central Tehran Branch,
Iran


M
Morovati
School of Automotive Engineering, Iran University of Science and Technology, Tehran, Iran.
School of Automotive Engineering, Iran University
Iran
Bertrand's test
Convergence test
Series test
[[1] J. M. H. Olmsted, Advanced Calculus, Prentice Hall. (1961). ##[2] J. Wen, T. Han, C. Gao, Convergence tests on constant Dirichlet series, Computers and Mathematics with ##Applications. 62 (2011) 34723489. ##[3] J. S. Chen, C. W. Liu, C. M. Liao, Twodimensional Laplacetransformed power series solution for solute ##transport in a radially convergent ##ow eld, Advances in Water Resources. 26 (2003) 11131124. ##[4] P. Wonzy, Ecient algorithm for summation of some slowly convergent series, Applied Numerical Mathemat ##ics. 60 (2010) 14421453. ##yand, S. Tikhonov, M. Zeltser, Extending tests for convergence of number series, Journal of Mathe ##matical Analysis and Applications. 377 (2011) 194206. ##[6] A. Bartoszewicz, S. Glab, T. Poreda, On algebrability of nonabsolutely convergent series, Linear Algebra and ##its Applications. 435 (2011) 10251028. ##A. A. Tabatabai Adnani et al. / J. Linear. Topological. Algebra. 02(03) (2013) 141147. ##[7] F. Moricz, A Quantitative Version of the DirichletJordan Test for Double Fourier Series, Journal of Approx ##imation Theory. 71(1992) 344358.##]
On the Finite Groupoid G(n)
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2
In this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid G(n) . Also we show that G(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid G(n) to be commuting regular.
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153
159


M
Azadi
Department of Mathematics, Islamic Azad University, Centeral Tehran Branch, Tehran, Iran.
Department of Mathematics, Islamic Azad University
Iran
meh.azadi@iauctb.ac.ir


H
Amadi
Department of Mathematics, Islamic Azad University, Centeral Tehran Branch, Tehran, Iran.
Department of Mathematics, Islamic Azad University
Iran
Commuting regular semigroup
semigroup
groupoid
[[1] H. Doostie, L. Pourfaraj, On the minimal ideals of commuting regularrings and semigroups, Internat. J. ##Appl. Math, 19, NO.2(2006), 201216. ##[2] H. Doostie, L. Pourfaraj, Finite rings and loop rings involving the commutingregular elements, International ##Mathematical Forum, Vol. 2, NO.52(2007), 25792586. ##[3] J. M. Howie, Fundamental of Semigroup Theory, Clarendon Prees. Oxford,New York, 1995. ##[4] L. Pourfaraj, On the nite groupoid, International Mathematical Forum Vol. 7,2012, no. 23, 11051114. ##[5] W. B. Vasantha Kandasmy, Groupoids and Smarandachegroupoids, Publishedby the American Reserch Press, ##2002, math. GM.##]
ODcharacterization of S4(4) and its group of automorphisms
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2
Let G be a nite group and (G) be the set of all prime divisors of jGj. The prime graph of G is a simple graph (G) with vertex set (G) and two distinct vertices p and q in (G) are adjacent by an edge if an only if G has an element of order pq. In this case, we write p q. Let jGj = p1 1 p2 2 pk k , where p1 < p2 < : : : < pk are primes. For p 2 (G), let deg(p) = jfq 2 (G)jp qgj be the degree of p in the graph (G), we dene D(G) = (deg(p1); deg(p2); : : : ; deg(pk)) and call it the degree pattern of G. A group G is called kfold ODcharacterizable if there exist exactly k nonisomorphic groups S such that jGj = jSj and D(G) = D(S). Moreover, a 1fold ODcharacterizable group is simply called an ODcharacterizable group. Let L = S4(4) be the projective symplectic group in dimension 4 over a eld with 4 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to L. Since Aut(L) = Z4 hence almost simple groups related to L are L, L : 2 or L : 4. In fact, we prove that L, L : 2 and L : 4 are ODcharacterizable.
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161
166


P
Nosratpour
Department of mathematics, Ilam Branch, Islamic Azad university, Ilam, Iran.
Department of mathematics, Ilam Branch, Islamic
Iran
p.nosratpour@ilamiau.ac.ir
Finite simple group
ODcharacterization
group of lie type
[[1] M. Akbari and A. R. Moghaddamfar, Simple groups which are 2fold ODcharacterizable, Bulletin of the ##Malaysian Mathematical Sciences Society, 35(1), 6577(2012). ##[2] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, Atlas of Finite Groups, Clarendon ##Press, Oxford 1985. ##160 P. Nosratpour / J. Linear. Topological. Algebra. 02(03) (2013) 155160. ##[3] G. Y. Chen, On structure of Frobenius and 2Frobenius group, Jornal of Southwest China Normal University, ##20(5), 485487(1995).(in Chinese) ##[4] M. R. Darafsheh, A. R. Moghaddamfar, and A. R. Zokayi, A characterization of nite simple groups by ##degrees of vertices of their prime graphs, Algebra Colloquium, 12(3), 431442(2005). ##[5] D. Gorenstein, Finite Groups, New York, Harpar and Row, (1980). ##[6] B. Huppert, Endlichen Gruppen I, SpringerVerlag,(1988). ##[7] D. S. Passman, Permutation Groups, New York, Benjamin Inc., (1968). ##[8] J. S. Williams, Prime graph components of nite groups, J. Alg. 69, No.2,487513(1981). ##[9] A. V. Zavarnitsine, Finite simple groups with narrow prime spectrum, Siberian Electronic Math. Reports. 6, ##112(2009).##]
On the nonnegative inverse eigenvalue problem of traditional matrices
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2
In this paper, at rst for a given set of real or complex numbers with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.
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167
174


A. M.
Nazari
Department of Mathematics, Faculty of Science, Arak University,
Arak 3815688349, Iran.
Department of Mathematics, Faculty of Science,
Iran
anazari@araku.ac.ir


S
Kamali Maher
Department of Mathematics, Faculty of Science, Arak University,
Arak 3815688349, Iran.
Department of Mathematics, Faculty of Science,
Iran
Inverse eigenvalue problem
Tridiagonal matrix
Nonnegative matrix
[[1] T. J. Laey, Helena. Smigoc, On a Classic Example in the Nonnegative Inverse Eigenvalue Problem, vol. 17, ##ELA, July 2008, pp. 333342. ##[2] R. Lowey, D. London, A note on an inverse problem for nonnegative matrices, Linear and Multilinear Algebra ##6 (1978) 8390. ##[3] Helena Smigoc, The inverse eigenvalue problem for nonnegative matrices, Linear Algebra Appl. 393 (2004) ##[4] T. J. Laey, E. Meehan, A characterization of trace zero nonnegative 55matrices, Linear Algebra Appl. ##302303 (1999) 295302. ##[5] A. M. Nazari, F. Sherafat, On the inverse eigenvalue problem for nonnegative matrices of order two to ve, ##Linear Algebra Appl. 436 (2012) 17711790. ##[6] C. R. Johnson, Rowstochastic matrices similar to doubly stochasticmatrices, Linear and MultilinearAlgebra ##10 (2) (1981) 113130. ##[7] M. T. Chu, G. H. Golub, Inverse Eigenvalue Problems: Theory, Algorithms and Applications, Oxford Uni ##versity Press, New York, 2005. ##[8] H. Hochstadt, On the construction of a Jacobi matrix from mixed given data, Linear Algebra Appl. 28 (1979) ##[9] H. Pickmann, R. L. Soto, J. Egana, M. Salas, An inverse eigenvalue problem for symmetrical tridiagonal ##matrices, Computers and Mathematics with Applications 54 (2007) 699708.##]
Some properties of band matrix and its application to the numerical solution onedimensional Bratu's problem
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2
A Class of new methods based on a septic nonpolynomial spline function for the numerical solution onedimensional Bratu's problem are presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Associated boundary formulas are developed. Convergence analysis of these methods is discussed. Numerical results are given to illustrate the eciency of methods.
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175
189


R
Jalilian
Department of Mathematics, Razi University Tagh Bostan, Kermanshah P.O. Box 6714967346 Iran;
Department of Mathematics, Razi University
Iran
rezajalilian@iust.ac.ir


Y
Jalilian
Department of Mathematics, Razi University Tagh Bostan, Kermanshah P.O. Box 6714967346 Iran;
Department of Mathematics, Razi University
Iran


H
Jalilian
School of Mathematics, Iran University of Science and Technology Narmak, Tehran 16844, Iran
School of Mathematics, Iran University of
Iran
Twopoint boundary value problem
Nonpolynomial spline
Convergence analysis
Bratu's problem
[[1] G. Akram, and S. S. Siddiqi, End conditions for interpolatory septic splines, International Journal of Computer ##Mathematics, Vol. 82, No. 12 (2005), pp. 15251540. ##[2] G. Akram, and S. S. Siddiqi, Solution of sixth order boundary value problems using nonpolynomial spline ##technique, Appl. Math. Comput. 181( 2006), pp. 708720. ##[3] Y.A.S. Aregbesola, Numerical solution of Bratu problem using the method of weighted residual, Electron. J. ##South. Afr. Math. Sci. 3(1)(2003), pp. 17. ##[4] J. P. Boyd, Chebyshev polynomial expansions for simultaneous approximation of two branches of a function ##with application to the onedimensional Bratu equation, Appl. Math. Comput. 142(2003), pp. 189200. ##[5] A. Boutayeb, and E. H. Twizell, Numerical methods for the solution of special sixthorder boundaryvalue ##problems, Intern. J. Computer Math. 45(1992), pp. 207223. ##[6] A. Boutayeb, and E. H. Twizell, Finitedierence methods for the solution of special eighthorder boundary ##value problems, International Journal of Computer Mathematics, Volume 48(1993 ), pp. 6375, . ##[7] R., Buckmire, Application of a Mickens nitedierence scheme to the cylindrical BratuGelfand problem, ##Numer. Methods Partial Dieren. Eqns 20(3)(2004), pp. 327337. ##182 R. Jalilian et al. / J. Linear. Topological. Algebra. 02(03) (2013) 169183. ##Table 5. Observed maximum absolute errors for = 2 ##n Secondorder Fourthorder Eightorder Tenthorder ##16 1.39102 3.68104 3.26109 1.131010 ##32 3.81103 2.28105 7.071012 1.931014 ##64 9.72104 1.42106 2.961014 5.251019 ##128 2.44104 8.86108 1.141016 6.491024 ##256 6.11105 5.53109 4.431019 2.671028 ##512 1.52105 3.451010 1.721021 3.301032 ##1024 3.82106 2.161011 6.751024 2.431036 ##[8] H. Caglar, N. Caglar, and M. Ozer, Antonios Valaristos and Antonios N. Anagnostopoulos, Bspline method ##for solving Bratus problem, International Journal of Computer Mathematics, 87(2010), pp. 18851891. ##[9] E. Deeba, S. A. Khuri, and S. Xie, An algorithm for solving boundary value problems, J. Comput. Phys. ##159(2000), pp. 125138. ##[10] D. A. FrankKamenetski, Diusion and Heat Exchange in Chemical Kinetics, Princeton University Press, ##Princeton, NJ, 1955. ##[11] P. Henrici, Discrete Variable Methods in Ordinary Dierential Equations, Wiley, New York, 1961. ##[12] I.H.A.H. Hassan, and V. S. Erturk, Applying dierential transformation method to the onedimensional ##planar Bratu problem, Int. J. Contemp. Math. Sci. 2(2007), pp. 14931504. ##[13] J.H. He, Variational Approach to the Bratu's problem, Journal of Physics: Conference Series 96(2008), pp. ##[14] J.H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B 20(10)(2006), pp. ##11411199. ##[15] R. Jalilian, Nonpolynomial spline method for solving Bratus problem, Computer Physics Communications, ##181(2010),pp. 18681872. ##[16] R. Jalilian, and J. Rashidinia, Convergence analysis of nonicspline solutions for special nonlinear sixthorder ##boundary value problems, Commun Nonlinear Sci Numer Simulat, 15(2010), pp. 38053813. ##[17] J. Jacobsen, and K. Schmitt, The LiouvilleBratuGelfand problem for radial operators, J. Dieren. Eqns. ##184(2002), pp. 283298. ##[18] S. A. Khuri, A new approach to Bratus problem, Appl. Math. Comput. 147(2004), pp. 131136. ##[19] S. Li, and S. J. Liao, An analytic approach to solve multiple solutions of a strongly nonlinear problem, Appl. ##Math. Comput. 169(2005), pp. 854865. ##[20] S. Liao, and Y. Tan, A general approach to obtain series solutions of nonlinear dierential equations, Stud. ##Appl. Math. 119(2007), pp. 297354. ##[21] J. S. McGough, Numerical continuation and the Gelfand problem, Appl. Math. Comput. 89(1998), pp. 225 ##[22] A. S. Mounim, and B. M. de Dormale, From the tting techniques to accurate schemes for the Liouville ##BratuGelfand problem, Numer. Methods Partial Dieren.Volume 22, Issue 4(2006), pp. 761775. ##[23] A. Mohsen, L.F. Sedeek, and S.A. Mohamed, New smoother to enhance multigridbased methods for Bratu ##problem, Applied Mathematics and Computation 204(2008), pp. 325339. ##[24] j. Rashidinia, and R. Jalilian, Nonpolynomial spline for solution of boundaryvalue problems in plate de ##tion theory, International Journal of Computer Mathematics, 84(2007), pp. 14831494. ##[25] J. Rashidinia, R. Jalilian, and R. Mohammadi, Nonpolynomial spline methods for the solution of a system ##of obstacle problems, Appl. Math. Comput. 188(2007), pp. 19841990. ##[26] M. A. Ramadan, I. F. Lashien, and W. K. Zahra, A class of methods based on a septic nonpolynomial ##spline function for the solution of sixthorder twopoint boundary value problems, International Journal of ##Computer Mathematics Vol. 85, No. 5(2008) 759770. ##[27] M. Ramadan, I. Lashien, and W. Zahra, Quintic nonpolynomial spline solutions for fourth order boundary ##value problem, Commun Nonlinear Sci Numer Simulat, 14(2009), pp. 11051114. ##[28] S. S. Siddiqi, and G. Akram, Septic spline solutions of sixthorder boundary value problems, Journal of ##Computational and Applied Mathematics 215(2008), pp. 288301. ##[29] M. I. Syam, and A. Hamdan, An ecient method for solving Bratu equations, Appl. Math. Comput. ##176(2006), pp. 704713. ##[30] E. H. Twizell, and A. Boutayeb, Numerical methods for the solution of special and general sixthorder ##boundaryvalue problems with applications to Bnard layer eigenvalue problems, Proc. R. Soc. Lond. A, ##431(1990), pp. 433450. ##[31] I. A. Tirmizi, and E. H. Twizell, HigherOrder FiniteDierence Methods for Nonlinear SecondOrder Two ##Point BoundaryValue Problems, Applied Mathematics Letters 15(2002), pp. 89790. ##[32] R. A. Usmani, and S. A. Wasrt, Quintic spline solutions of boundary value problems, Comput. Math. with ##Appl. 6(1980), pp. 197203. ##[33] R. A. Usmani, and M. Sakai, A connection between quartic spline and Numerov solution of a boundary value ##problem, Int. J. Comput. Math. 26(1989), pp. 263273. ##[34] S. Ul Islam, I. A. Tirmizi, F. Haq, and S. K. Taseer, Family of numerical methods based on nonpolynomial ##splines for solution of contact problems, Commun Nonlinear Sci Numer Simulat, 13(2008), pp. 14481460. ##[35] M. Van Daele, G. Vanden berghe, and H. A. De Meyer, Smooth approximation for the solution of a fourth ##order boundary value problem based on nonpolynomial splines, J. Comput. Appl. Math. Vol.pp.51(1994), ##pp. 383394. ##R. Jalilian et al. / J. Linear. Topological. Algebra. 02(03) (2013) 169183. 183 ##[36] A. M. Wazwaz, Adomian decomposition method for a reliable treatment of the Bratutype equations, Appl. ##Math. Comput. 166(2005), pp. 652663.##]