Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215Annihilator-small submodules10531063460ENT.Amouzegar KalatiMazandaran University, Department of mathematicD.Keskin TutuncuHacettepe University, Mathematics DepartmentJournal Article20111202Let $M_R$ be a module with $S=End(M_R)$. We call a submodule $K$ of <br />$M_R$ annihilator-small if $K+T=M$, $T$ a submodule of $M_R$, <br />implies that $ell_S(T)=0$, where $ell_S$ indicates the left <br />annihilator of $T$ over $S$. The sum $A_R(M)$ of all such submodules <br />of $M_R$ contains the Jacobson radical $Rad(M)$ and the left <br />singular submodule $Z_S(M)$. If $M_R$ is cyclic, then $A_R(M)$ is <br />the unique largest annihilator-small submodule of $M_R$. We study <br />$A_R(M)$ and $K_S(M)$ in this paper. Conditions when $A_R(M)$ is <br />annihilator-small and $K_S(M)=J(S)=Tot(M, M)$ are given.http://bims.iranjournals.ir/article_460_cc483dbffd072a63c2e7822e0bcb3c67.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215Determinants and permanents of Hessenberg matrices and generalized Lucas polynomials10651078461ENK.KaygisizGaziosmanpasa University
Faculty of Science and Art
Department of MathematicsA.SahinGaziosmanpasa UniversityJournal Article20120511In this paper, we give some determinantal and permanental representations of generalized Lucas polynomials, which are a general form of generalized bivariate Lucas p-polynomials, ordinary Lucas and Perrin sequences etc., by using various Hessenberg matrices. In addition, we show that determinant and permanent of these Hessenberg matrices can be obtained by using combinations. Then we show, the conditions under which the determinants of the Hessenberg matrix become its permanents.http://bims.iranjournals.ir/article_461_614511c7f595e147b7d12b7d884a46e1.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215Gorenstein projective objects in Abelian categories10791097462ENH.ChengDepartment of Mathematics, Nanjing University,
Nanjing 210093, ChinaX.ZhuDepartment of Mathematics, Nanjing University,
Nanjing 210093, ChinaJournal Article20120701Let $mathcal {A}$ be an abelian category with enough projective <br />objects and $mathcal {X}$ be a full subcategory of <br />$mathcal {A}$. We define Gorenstein projective objects with respect <br />to $mathcal {X}$ and $mathcal{Y}_{mathcal{X}}$, respectively, where $mathcal{Y}_{mathcal{X}}$=${ Yin Ch(mathcal {A})| Y$ is acyclic and $Z_{n}Yinmathcal{X}}$. We point out that under certain hypotheses, these two <br />Gorensein projective objects are related in a nice way. In <br />particular, if $mathcal {P}(mathcal {A})subseteqmathcal {X}$, we <br />show that $Xin Ch(mathcal {A})$ is Gorenstein projective with respect to $mathcal{Y}_{mathcal{X}}$ if and only if $X^{i}$ is Gorenstein <br />projective with respect to $mathcal {X}$ for each $i$, when $mathcal {X}$ is a self-orthogonal <br />class or $X$ is $Hom(-,mathcal {X})$-exact. Subsequently, we <br />consider the relationships of Gorenstein projective dimensions between them. As an <br />application, if $mathcal {A}$ is of finite left Gorenstein projective <br />global dimension with respect to $mathcal{X}$ and contains an injective <br />cogenerator, then we find a new <br />model structure on $Ch(mathcal {A})$ by Hovey's results in cite{Ho} .http://bims.iranjournals.ir/article_462_bdb19acaedd836465e241a86c9c3a04e.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215Some classes of strongly clean rings10991115463ENH.ChenDepartment of Mathematics, Hangzhou Normal University, 310036, Hangzhou, ChinaJournal Article20110920A ring $R$ is a strongly clean ring if every element in <br />$R$ is the sum of an idempotent and a unit that commutate. We <br />construct some classes of strongly clean rings which have stable <br />range one. It is shown that such cleanness of $2 imes 2$ matrices <br />over commutative local rings is completely determined in terms of <br />solvability of quadratic equations.http://bims.iranjournals.ir/article_463_8ef77b04cf0305fbaba0af11fc78b480.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215Characteristic function of a meromorphic function and its derivatives11171123464ENJ.WuXianning Vocational and Technical College,
P.O. Box 437100, Xianning, P. R. ChinaZ.WuSchool of Mathematics and Statistics, Hubei University of Science and Technology,
P.O. Box 437100, Xianning, P. R. ChinaJournal Article20110720In this paper, some results of Singh, Gopalakrishna and <br />Kulkarni (1970s) have been extended to higher order derivatives. It <br />has been shown that, if $sumlimits_{a}Theta(a, f)=2$ holds for a <br />meromorphic function $f(z)$ of finite order, then for any positive <br />integer $k,$ $T(r, f)sim T(r, f^{(k)}), rrightarrowinfty$ if <br />$Theta(infty, f)=1$ and $T(r, f)sim (k+1)T(r, f^{(k)}), <br />rrightarrowinfty$ if $Theta(infty, f)=0.$http://bims.iranjournals.ir/article_464_28b526931ff60ee50847aaedcce35cc0.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215Common fixed points of a finite family of multivalued quasi-nonexpansive mappings in uniformly convex Banach spaces11251135465ENA.BunyawatDepartment of Mathematics, Faculty of Science, Chiang Mai University 50200, Chiang
Mai, ThailandS.SuantaiDepartment of Mathematics, Faculty of Science, Chiang Mai University 50200, Chiang
Mai, ThailandJournal Article20120502In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.http://bims.iranjournals.ir/article_465_9924dedbbb514316780466391a2a981d.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215Module approximate amenability of Banach algebras11371158466ENH.Pourmahmood-AghababaTabriz University, Tabriz, IranA.BodaghiIslamic Azad University of Garmsar, Garmsar, IranJournal Article20111029In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same properties. It is also shown that module uniform approximate (contractibility) amenability and module (contractibility, respectively) amenability for commutative Banach modules are equivalent. Applying these results to l^1 (S) as an l^1 (E)-module, for an inverse semigroup S with the set of<br />idempotents E, it is shown that l^1(S) is module approximately amenable (contractible) if and only if it is module uniformly approximately amenable if and only if S is amenable.<br />Moreover, l^1(S)^{**} is module (uniformly) approximately amenable if and only if an appropriate group homomorphic image of S is finite.http://bims.iranjournals.ir/article_466_605a2ac8ad2936a6371f9bda251cbb65.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215The streamline diffusion method with implicit integration for the multi-dimensional Fermi Pencil Beam equation11591180467ENE.KazemiIsfahan University of Technology, Isfahan, IranJournal Article20120621We derive error estimates in the appropriate norms, for the streamline<br />diffusion (SD) finite element methods for steady state, energy dependent,<br />Fermi equation in three space dimensions. These estimates yield optimal convergence<br />rates due to the maximal available regularity of the exact solution.<br />High order SD method together with implicit integration are used. The formulation<br />is strongly consistent in the sense that the time derivative is included<br />in the stabilization term. Here our focus is on theoretical aspects of the h and<br />hp approximations in SD settings.http://bims.iranjournals.ir/article_467_6a62e34662811d8fa55d39ce9ae949e3.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215Some properties of marginal automorphisms of groups11811188468ENM. R. R.MoghaddamKhayyam Higher Education Institute, Mashhad , IranH.SafaDepartment of Pure Mathematics, Faculty of Mathematical Sciences, Ferdowsi University
of Mashhad, P.O. Box 1159, Mashhad, IranJournal Article20120607Abstract<br />Let W be a non-empty subset of a free group. The automorphism <br />of a group G is said to be a marginal automorphism, if for all x in G,<br />x^−1alpha(x) in W^*(G), where W^*(G) is the marginal subgroup of G.<br />In this paper, we give necessary and sufficient condition for a purely<br />non-abelian p-group G, such that the set of all marginal automorphisms<br />of G forms an elementary abelian p-group.http://bims.iranjournals.ir/article_468_508d725781c352662ec2e65218cfc8da.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215On the non-split extension group $2^{6}{^{cdot}}Sp(6,2)$11891212470ENA.BasheerUniversities of KwaZulu-Natal & KhartoumJ.MooriNorth-West UniversityJournal Article20120507In this paper we first construct the non-split extension $overline{G}= 2^{6} {^{cdot}}Sp(6,2)$ as a permutation group acting on 128 points. We then determine the conjugacy classes using the coset analysis technique, inertia factor groups and Fischer matrices, which are required for the computations of the character table of $overline{G}$ by means of Clifford-Fischer Theory. There are two inertia factor groups namely $H_{1} = Sp(6,2)$ and $H_{2} = 2^{5}{:}S_{6},$ the Schur multiplier and hence the character table of the corresponding covering group of $H_{2}$ were calculated. Using information on<br />conjugacy classes, Fischer matrices and ordinary and projective tables of $H_{2},$ we concluded that we only need to use the ordinary character table of $H_{2}$ to construct the character table of $overline{G}.$ The Fischer matrices of $overline{G}$ are all listed in this paper. The character table of $overline{G}$ is a $67 times 67$ integral matrix, it has been supplied in the PhD Thesis of the first author, which could be accessed online.http://bims.iranjournals.ir/article_470_17caff41609267a65438eee7c4988ea4.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215The nc-supplemented subgroups of finite groups12131222471ENS.GuoSchool of Science, Sichuan University of Science & Engineering, 643000, Zigong, P.
R. ChinaS.LiuSchool of Science, Sichuan University of Science & Engineering, 643000, Zigong, P.
R. ChinaW. J.ShiSchool of Mathematics and Statistics, Chongqing University of Arts and Sciences,
402160, Chongqing, P. R. ChinaJournal Article20110910A subgroup $H$ is said to be <br />$nc$-supplemented in a group $G$ if there exists a subgroup $Kleq G$ <br />such that $HKlhd G$ and $Hcap K$ is contained in $H_{G}$, the core <br />of $H$ in $G$. We characterize the supersolubility of finite groups $G$ <br />with that every maximal subgroup of the Sylow subgroups is $nc$-supplemented in $G$.http://bims.iranjournals.ir/article_471_8d89af79f6fda3147747ae4a8991ca77.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215Bifurcation of limit cycles from a quadratic reversible center with the unbounded elliptic separatrix12231248472ENL.PengSchool of Mathematics and System Sciences, Beihang UniversityY.LeiSchool of Mathematics and System Sciences, Beihang University/The 24th Middle School of BeijingJournal Article20110525The paper is concerned with the bifurcation of limit cycles in general quadratic <br />perturbations of a quadratic reversible and non-Hamiltonian system, whose period annulus is bounded by an elliptic separatrix <br />related to a singularity at infinity in the poincar'{e} disk. <br />Attention goes to the number of limit cycles produced by the period <br />annulus under perturbations. By using the appropriate Picard-Fuchs <br />equations and studying the geometric properties of two planar <br />curves, we prove that the maximal number of limit cycles bifurcating <br />from the period annulus under small quadratic perturbations is two.http://bims.iranjournals.ir/article_472_a02b2450a1b3745f35b4010b9b0ab4d3.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215An iterative method for the Hermitian-generalized Hamiltonian solutions to the inverse problem AX=B with a submatrix constraint12491260473ENJ.CaiHuzhou Teachers CollegeJournal Article20120807In this paper, an iterative method is proposed for solving the matrix inverse problem $AX=B$ for Hermitian-generalized Hamiltonian matrices with a submatrix constraint. By this iterative method, for any initial matrix $A_0$, a solution $A^*$ can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of initial matrix. Furthermore, in the solution set of the above problem, the unique optimal approximation solution to a given matrix can also be obtained. A numerical example is presented to show the efficiency of the proposed algorithm.http://bims.iranjournals.ir/article_473_ef7d4a2fd05bb1efdab593d07d72c417.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215Fixed points for E-asymptotic contractions and Boyd-Wong type E-contractions in uniform spaces12611272474ENA.AghaniansK.N. Toosi University of TechnologyK.FallahiK.N. Toosi University of TechnologyK.NourouziK.N. Toosi University of TechnologyJournal Article20120601In this paper we discuss on the fixed points of asymptotic contractions and Boyd-Wong type contractions in uniform spaces equipped with an E-distance. A new version of<br />Kirk's fixed point theorem is given for asymptotic contractions and Boyd-Wong type contractions is investigated in uniform spaces.http://bims.iranjournals.ir/article_474_a4fea9f574e47dc292fc6e7f8ec1a8a0.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X396201312152-recognizability of the simple groups $B_n(3)$ and $C_n(3)$ by prime graph12731281346ENM.Foroudi GhasemabadiTarbiat Modares UniversityA.IranmaneshTarbiat Modares UniversityN.AhanjidehUniversity of Shahre-kordJournal Article20110525Let $G$ be a finite group and let $GK(G)$ be the prime graph of $G$. We assume that <br /> <br /> $ngeqslant 5 $ is an odd number. In this paper, we show that the simple groups <br /> <br />$B_n(3)$ and $C_n(3)$ are 2-recognizable by their prime graphs. As consequences of the <br /> <br />result, the characterizability of the groups $B_n(3)$ and $C_n(3)$ by their spectra and <br /> <br />by the set of orders of maximal abelian subgroups are obtained. Also, we can conclude <br /> <br />that the AAM's conjecture is true for the groups under study.http://bims.iranjournals.ir/article_346_1295fb2d30416b6530013ae8d990f863.pdf