Bulletin of Iranian Mathematical Society
Volume:39 Issue: 6, 2013

Let $M_R$ be a module with $S=End(M_R)$. We call a submodule $K$ of $M_R$ annihilator-small if $K+T=M$, $T$ a submodule of $M_R$, implies that $ell_S(T)=0$, where $ell_S$ indicates the left annihilator of $T$ over $S$. The sum $A_R(M)$ of all such submodules of $M_R$ contains the Jacobson radical $Rad(M)$ and the left singular submodule $Z_S(M)$. If $M_R$ is cyclic, then $A_R(M)$ is the unique largest annihilator-small submodule of $M_R$. We study $A_R(M)$ and $K_S(M)$ in this paper. Conditions when $A_R(M)$ is annihilator-small and $K_S(M)=J(S)=Tot(M, M)$ are given.

In 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 conditionsunderwhich the determinants of the Hessenberg matrix become its permanents.

Let $mathcal {A}$ be an abelian category with enough projective objects and $mathcal {X}$ be a full subcategory of $mathcal {A}$. We define Gorenstein projective objects with respect to $mathcal {X}$ and $mathcal{Y}_{mathcal{X}}$, respectively, where $mathcal{Y}{mathcal{X}}$=${Yin Ch(mathcal {A})| Y$ is acyclic and $Z_{n}Yinmathcal{X}$.Wepoint out that under certain hypotheses, these two Gorensein projective objects are related in a nice way. In particular, if $mathcal {P}(mathcal {A})subseteqmathcal {X}$, we show that $Xin Ch(mathcal {A})$ is Gorenstein projective with respect to $mathcal{Y} {mathcal{X}}$ if and only if $X^{i}$ is Gorenstein projective with respect to $mathcal {X}$ for each $i$, when $mathcal {X}$ is a self orthogonal class or $X$ is $Hom(-,mathcal {X})$-exact. Subsequently, we consider the relationships of Gorenstein projective dimensions between them. As an application, if $mathcal {A}$ is of finite left Gorenstein projective global dimension with respect to $mathcal{X}$ and contains an injective cogenerator, then we find a new model structure on $Ch(mathcal {A})$ by Hovey''s results in cite{Ho}.

A ring $R$ is a strongly clean ring if every element in $R$ is the sum of an idempotent and a unit that commutate. We construct some classes of strongly clean rings which have stable range one. It is shown that such cleanness of $2 imes 2$ matrices over commutative local rings is completely determined in terms of solvability of quadratic equations.

In this paper, some results of Singh, Gopalakrishna and Kulkarni (1970s) have been extended to higher order derivatives. It has been shown that, if $sumlimits_{a}Theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $T(r, f)sim T(r, f^{(k)}), rrightarrowinfty$ if $Theta(infty, f)=1$ and $T(r, f)sim (k+1)T(r, f^{(k)}), rrightarrowinfty$ if $Theta(infty, f)=0.$

In 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.

In 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 ofidempotents 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.Moreover, l^1(S)^{**} is module (uniformly) approximately amenable if and only if an appropriate group homomorphic image of S is finite.

We derive error estimates in the appropriate norms, for the streamline diffusion (SD) finite element methods for steady state, energy dependent, Fermi equation in three space dimensions. These estimates yield optimal convergence rates due to the maximal available regularity of the exact solution.High order SD method together with implicit integration are used. The formulation is strongly consistent in the sense that the time derivative is included in the stabilization term. Here our focus is on theoretical aspects of the h and hp approximations in SD settings.

Let W be a non-empty subset of a free group. The automorphism of a group G is said to be a marginal automorphism, if for all x in G, x^−1alpha (x) in W^*(G), where W^*(G) is the marginal subgroup of G. In this paper, we give necessary and sufficient condition for a purely non-abelian p-group G, such that the set of all marginal automorphisms of G forms an elementary abelian p-group.

In 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 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.

A subgroup $H$ is said to be $nc$-supplemented in a group $G$ if there exists a subgroup $Kleq G$ such that $HKlhd G$ and $Hcap K$ is contained in $H_{G}$, the core of $H$ in $G$. We characterize the supersolubility of finite groups $G$ with that every maximal subgroup of the Sylow subgroups is $nc$-supplemented in $G$.

The paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-Hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the poincar''{e} disk. Attention goes to the number of limit cycles produced by the period annulus under perturbations. By using the appropriate Picard-Fuchs equations and studying the geometric properties of two planar curves, we prove that the maximal number of limit cycles bifurcating from the period annulus under small quadratic perturbations is two.

In 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.

In 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 Kirk''s fixed point theorem is given for asymptotic contractions and Boyd-Wong type contractions is investigated in uniform spaces.

Let $G$ be a finite group and let $GK(G)$ be the prime graph of $G$. We assume that $ngeqslant 5 $ is an odd number. In this paper, we show that the simple groups $B_n(3)$ and $C_n(3)$ are 2-recognizable by their prime graphs. As consequences of the result, the characterizability of the groups $B_n(3)$ and $C_n(3)$ by their spectra and by the set of orders of maximal abelian subgroups are obtained. Also, we can conclude that the AAM''s conjecture is true for the groups under study.