2013
39
6
6
249
Annihilatorsmall submodules
2
2
Let $M_R$ be a module with $S=End(M_R)$. We call a submodule $K$ of $M_R$ annihilatorsmall 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 annihilatorsmall submodule of $M_R$. We study $A_R(M)$ and $K_S(M)$ in this paper. Conditions when $A_R(M)$ is annihilatorsmall and $K_S(M)=J(S)=Tot(M, M)$ are given.
3

1053
1063


T.
Amouzegar Kalati
Mazandaran University, Department of mathematic
Mazandaran University, Department of mathematic
Iran
t.amoozegar@umz.ac.ir


D.
Keskin Tutuncu
Hacettepe University, Mathematics Department
Hacettepe University, Mathematics Department
Turkey
keskin@hacettepe.edu.tr
small submodules
annihilators
annihilatorsmall submodules
Determinants and permanents of Hessenberg matrices and generalized Lucas polynomials
2
2
In this paper, we give some determinantal and permanental representations of generalized Lucas polynomials, which are a general form of generalized bivariate Lucas ppolynomials, 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.
3

1065
1078


K.
Kaygisiz
Gaziosmanpasa University
Faculty of Science and Art
Department of Mathematics
Gaziosmanpasa University
Faculty of Science
Turkey
kenankaygisiz@yahoo.com


A.
Sahin
Gaziosmanpasa University
Gaziosmanpasa University
Turkey
adem.sahin@gop.edu.tr
Generalized Lucas polynomials
generalized Perrin polynomials
Hessenberg matrix
determinant
permanent
Gorenstein projective objects in Abelian categories
2
2
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 $Z_{n}Yinmathcal{X}}$. We point 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 selforthogonal 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} .
3

1079
1097


H.
Cheng
Department of Mathematics, Nanjing University,
Nanjing 210093, China
Department of Mathematics, Nanjing University,
Nan
China (P. R. C.)
xiangyun23@sina.com.cn


X.
Zhu
Department of Mathematics, Nanjing University,
Nanjing 210093, China
Department of Mathematics, Nanjing University,
Nan
China (P. R. C.)
zhuxs@nju.edu.cn
$mathcal {X}$Gorenstein projective object
$mathcal {X}$Gorenstein projective dimension
$mathcal {F}$preenvelope
cotorsion pair
Some classes of strongly clean rings
2
2
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.
3

1099
1115


H.
Chen
Department of Mathematics, Hangzhou Normal University, 310036, Hangzhou, China
Department of Mathematics, Hangzhou Normal
China (P. R. C.)
huanyinchen@aliyun.com
strongly $J_n$clean ring, $2 imes 2$ matrix
Local ring
Characteristic function of a meromorphic function and its derivatives
2
2
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 $Theta(infty, f)=0.$
3

1117
1123


J.
Wu
Xianning Vocational and Technical College,
P.O. Box 437100, Xianning, P. R. China
Xianning Vocational and Technical College,
P.O.
China, R. O. C.
44976882@qq.com


Z.
Wu
School of Mathematics and Statistics, Hubei University of Science and Technology,
P.O. Box 437100, Xianning, P. R. China
School of Mathematics and Statistics, Hubei
China, R. O. C.
wuzj52@hotmail.com
characteristic function
Nevanlinna's deficiency
maximum deficiency sum
Common fixed points of a finite family of multivalued quasinonexpansive mappings in uniformly convex Banach spaces
2
2
In this paper, we introduce a onestep iterative scheme for finding a common fixed point of a finite family of multivalued quasinonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.
3

1125
1135


A.
Bunyawat
Department of Mathematics, Faculty of Science, Chiang Mai University 50200, Chiang
Mai, Thailand
Department of Mathematics, Faculty of Science,
Thailand
aunyarat@mwit.ac.th


S.
Suantai
Department of Mathematics, Faculty of Science, Chiang Mai University 50200, Chiang
Mai, Thailand
Department of Mathematics, Faculty of Science,
Thailand
suthep.s@cmu.ac.th
Finite family of multivalued quasinonexpansive mappings
common fixed point
onestep iterative
Module approximate amenability of Banach algebras
2
2
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.
3

1137
1158


H.
PourmahmoodAghababa
Tabriz University, Tabriz, Iran
Tabriz University, Tabriz, Iran
Iran
h_p_aghababa@tabrizu.ac.ir


A.
Bodaghi
Islamic Azad University of Garmsar, Garmsar, Iran
Islamic Azad University of Garmsar, Garmsar,
Iran
abasalt.bodaghi@gmail.com
Module derivation
Module amenability
Approximately inner
Inverse semigroups
The streamline diffusion method with implicit integration for the multidimensional Fermi Pencil Beam equation
2
2
We derive error estimates in the appropriate norms, for the streamlinediffusion (SD) finite element methods for steady state, energy dependent,Fermi equation in three space dimensions. These estimates yield optimal convergencerates due to the maximal available regularity of the exact solution.High order SD method together with implicit integration are used. The formulationis strongly consistent in the sense that the time derivative is includedin the stabilization term. Here our focus is on theoretical aspects of the h andhp approximations in SD settings.
3

1159
1180


E.
Kazemi
Isfahan University of Technology, Isfahan, Iran
Isfahan University of Technology, Isfahan,
Iran
e.kazemi@math.iut.ac.ir
Fermi equation
particle beam
streamline diffusion
Backward Euler
Stability
convergence
Some properties of marginal automorphisms of groups
2
2
AbstractLet W be a nonempty 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 purelynonabelian pgroup G, such that the set of all marginal automorphismsof G forms an elementary abelian pgroup.
3

1181
1188


M. R.
Moghaddam
Khayyam Higher Education Institute, Mashhad , Iran
Khayyam Higher Education Institute, Mashhad
Iran
rezam@ferdowsi.um.ac.ir


H.
Safa
Department of Pure Mathematics, Faculty of Mathematical Sciences, Ferdowsi University
of Mashhad, P.O. Box 1159, Mashhad, Iran
Department of Pure Mathematics, Faculty of
Iran
hesam.safa@gmail.com
Primary
20D45, 20F28. Secondary
20E05, 20E36
On the nonsplit extension group $2^{6}{^{cdot}}Sp(6,2)$
2
2
In this paper we first construct the nonsplit 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 CliffordFischer 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 onconjugacy 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.
3

1189
1212


A.
Basheer
Universities of KwaZuluNatal & Khartoum
Universities of KwaZuluNatal & Khartoum
South Africa
ayoubbasheer@gmail.com


J.
Moori
NorthWest University
NorthWest University
South Africa
jamshid.moori@nwu.ac.za
Group extensions
symplectic group
character table
Clifford theory
inertia groups
Fischer matrices
The ncsupplemented subgroups of finite groups
2
2
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 $G$.
3

1213
1222


S.
Guo
School of Science, Sichuan University of Science & Engineering, 643000, Zigong, P.
R. China
School of Science, Sichuan University of
China, R. O. C.
710442986@qq.com


S.
Liu
School of Science, Sichuan University of Science & Engineering, 643000, Zigong, P.
R. China
School of Science, Sichuan University of
China, R. O. C.
s.t.liu@yandex.com


W.
Shi
School of Mathematics and Statistics, Chongqing University of Arts and Sciences,
402160, Chongqing, P. R. China
School of Mathematics and Statistics, Chongqing
China, R. O. C.
wjshi@suda.edu.cn
soluble group
$nc$supplemented subgroup
Normal subgroup
Supersoluble group
Bifurcation of limit cycles from a quadratic reversible center with the unbounded elliptic separatrix
2
2
The paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and nonHamiltonian 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 PicardFuchs 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.
3

1223
1248


L.
Peng
School of Mathematics and System Sciences, Beihang University
School of Mathematics and System Sciences,
China, R. O. C.
penglp@buaa.edu.cn


Y.
Lei
School of Mathematics and System Sciences, Beihang University/The 24th Middle School of Beijing
School of Mathematics and System Sciences,
China, R. O. C.
yazhi177@126.com
a quadratic reversible and nonHamiltonian center
bifurcation of limit cycles
a period annulus
the Abelian integral
An iterative method for the Hermitiangeneralized Hamiltonian solutions to the inverse problem AX=B with a submatrix constraint
2
2
In this paper, an iterative method is proposed for solving the matrix inverse problem $AX=B$ for Hermitiangeneralized 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.
3

1249
1260


J.
Cai
Huzhou Teachers College
Huzhou Teachers College
China (P. R. C.)
caijing@hutc.zj.cn
Inverse problem
Hermitiangeneralized Hamiltonian matrix
Submatrix constraint
Optimal approximation
Fixed points for Easymptotic contractions and BoydWong type Econtractions in uniform spaces
2
2
In this paper we discuss on the fixed points of asymptotic contractions and BoydWong type contractions in uniform spaces equipped with an Edistance. A new version ofKirk's fixed point theorem is given for asymptotic contractions and BoydWong type contractions is investigated in uniform spaces.
3

1261
1272


A.
Aghanians
K.N. Toosi University of Technology
K.N. Toosi University of Technology
Iran
a.aghanians@dena.kntu.ac.ir


K.
Fallahi
K.N. Toosi University of Technology
K.N. Toosi University of Technology
Iran
k_fallahi@dena.kntu.ac.ir


K.
Nourouzi
K.N. Toosi University of Technology
K.N. Toosi University of Technology
Iran
nourouzi@kntu.ac.ir
Separated uniform space
Easymptotic contraction
BoydWong type Econtraction
fixed point
2recognizability of the simple groups $B_n(3)$ and $C_n(3)$ by prime graph
2
2
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 2recognizable 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.
3

1273
1281


M.
Foroudi Ghasemabadi
Tarbiat Modares University
Tarbiat Modares University
Iran
mahnaz_mat@yahoo.com


A.
Iranmanesh
Tarbiat Modares University
Tarbiat Modares University
Iran
iranmana@yahoo.com


N.
Ahanjideh
University of Shahrekord
University of Shahrekord
Iran
ahanjideh.neda@sci.sku.ac.ir
Prime graph
classification of finite simple groups
recognition
spectrum