Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
6
2013
12
15
Annihilator-small submodules
1053
1063
EN
T.
Amouzegar Kalati
Mazandaran University, Department of mathematic
t.amoozegar@umz.ac.ir
D.
Keskin Tutuncu
Hacettepe University, Mathematics Department
keskin@hacettepe.edu.tr
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.
small submodules,annihilators,annihilator-small submodules
http://bims.iranjournals.ir/article_460.html
http://bims.iranjournals.ir/article_460_cc483dbffd072a63c2e7822e0bcb3c67.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
6
2013
12
15
Determinants and permanents of Hessenberg matrices and generalized Lucas polynomials
1065
1078
EN
K.
Kaygisiz
Gaziosmanpasa University
Faculty of Science and Art
Department of Mathematics
kenankaygisiz@yahoo.com
A.
Sahin
Gaziosmanpasa University
adem.sahin@gop.edu.tr
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 conditions under which the determinants of the Hessenberg matrix become its permanents.
Generalized Lucas polynomials,generalized Perrin polynomials,Hessenberg matrix,determinant,permanent
http://bims.iranjournals.ir/article_461.html
http://bims.iranjournals.ir/article_461_614511c7f595e147b7d12b7d884a46e1.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
6
2013
12
15
Gorenstein projective objects in Abelian categories
1079
1097
EN
H.
Cheng
Department of Mathematics, Nanjing University,
Nanjing 210093, China
xiangyun23@sina.com.cn
X.
Zhu
Department of Mathematics, Nanjing University,
Nanjing 210093, China
zhuxs@nju.edu.cn
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 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} .
$mathcal {X}$-Gorenstein projective object,$mathcal {X}$-Gorenstein projective dimension,$mathcal {F}$-preenvelope,cotorsion pair
http://bims.iranjournals.ir/article_462.html
http://bims.iranjournals.ir/article_462_bdb19acaedd836465e241a86c9c3a04e.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
6
2013
12
15
Some classes of strongly clean rings
1099
1115
EN
H.
Chen
Department of Mathematics, Hangzhou Normal University, 310036, Hangzhou, China
huanyinchen@aliyun.com
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.
strongly $J_n$-clean ring, $2 imes 2$ matrix,Local ring
http://bims.iranjournals.ir/article_463.html
http://bims.iranjournals.ir/article_463_8ef77b04cf0305fbaba0af11fc78b480.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
6
2013
12
15
Characteristic function of a meromorphic function and its derivatives
1117
1123
EN
J.
Wu
Xianning Vocational and Technical College,
P.O. Box 437100, Xianning, P. R. China
44976882@qq.com
Z.
Wu
School of Mathematics and Statistics, Hubei University of Science and Technology,
P.O. Box 437100, Xianning, P. R. China
wuzj52@hotmail.com
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 $Theta(infty, f)=0.$
characteristic function,Nevanlinna's deficiency,maximum deficiency sum
http://bims.iranjournals.ir/article_464.html
http://bims.iranjournals.ir/article_464_28b526931ff60ee50847aaedcce35cc0.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
6
2013
12
15
Common fixed points of a finite family of multivalued quasi-nonexpansive mappings in uniformly convex Banach spaces
1125
1135
EN
A.
Bunyawat
Department of Mathematics, Faculty of Science, Chiang Mai University 50200, Chiang
Mai, Thailand
aunyarat@mwit.ac.th
S.
Suantai
Department of Mathematics, Faculty of Science, Chiang Mai University 50200, Chiang
Mai, Thailand
suthep.s@cmu.ac.th
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.
Finite family of multivalued quasi-nonexpansive mappings,common fixed point,one-step iterative
http://bims.iranjournals.ir/article_465.html
http://bims.iranjournals.ir/article_465_9924dedbbb514316780466391a2a981d.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
6
2013
12
15
Module approximate amenability of Banach algebras
1137
1158
EN
H.
Pourmahmood-Aghababa
Tabriz University, Tabriz, Iran
h_p_aghababa@tabrizu.ac.ir
A.
Bodaghi
Islamic Azad University of Garmsar, Garmsar, Iran
abasalt.bodaghi@gmail.com
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.
Module derivation,Module amenability,Approximately inner,Inverse semigroups
http://bims.iranjournals.ir/article_466.html
http://bims.iranjournals.ir/article_466_605a2ac8ad2936a6371f9bda251cbb65.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
6
2013
12
15
The streamline diffusion method with implicit integration for the multi-dimensional Fermi Pencil Beam equation
1159
1180
EN
E.
Kazemi
Isfahan University of Technology, Isfahan, Iran
e.kazemi@math.iut.ac.ir
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.
Fermi equation,particle beam,streamline diffusion,Backward Euler,Stability,convergence
http://bims.iranjournals.ir/article_467.html
http://bims.iranjournals.ir/article_467_6a62e34662811d8fa55d39ce9ae949e3.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
6
2013
12
15
Some properties of marginal automorphisms of groups
1181
1188
EN
M. R.
R.
Moghaddam
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
hesam.safa@gmail.com
AbstractLet 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 purelynon-abelian p-group G, such that the set of all marginal automorphismsof G forms an elementary abelian p-group.
Primary,20D45, 20F28. Secondary,20E05, 20E36
http://bims.iranjournals.ir/article_468.html
http://bims.iranjournals.ir/article_468_508d725781c352662ec2e65218cfc8da.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
6
2013
12
15
On the non-split extension group $2^{6}{^{cdot}}Sp(6,2)$
1189
1212
EN
A.
Basheer
Universities of KwaZulu-Natal & Khartoum
ayoubbasheer@gmail.com
J.
Moori
North-West University
jamshid.moori@nwu.ac.za
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 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.
Group extensions,symplectic group,character table,Clifford theory,inertia groups,Fischer matrices
http://bims.iranjournals.ir/article_470.html
http://bims.iranjournals.ir/article_470_17caff41609267a65438eee7c4988ea4.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
6
2013
12
15
The nc-supplemented subgroups of finite groups
1213
1222
EN
S.
Guo
School of Science, Sichuan University of Science & Engineering, 643000, Zigong, P.
R. China
710442986@qq.com
S.
Liu
School of Science, Sichuan University of Science & Engineering, 643000, Zigong, P.
R. China
s.t.liu@yandex.com
W.
J.
Shi
School of Mathematics and Statistics, Chongqing University of Arts and Sciences,
402160, Chongqing, P. R. China
wjshi@suda.edu.cn
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 $G$.
soluble group,$nc$-supplemented subgroup,Normal subgroup,Supersoluble group
http://bims.iranjournals.ir/article_471.html
http://bims.iranjournals.ir/article_471_8d89af79f6fda3147747ae4a8991ca77.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
6
2013
12
15
Bifurcation of limit cycles from a quadratic reversible center with the unbounded elliptic separatrix
1223
1248
EN
L.
Peng
School of Mathematics and System Sciences, Beihang University
penglp@buaa.edu.cn
Y.
Lei
School of Mathematics and System Sciences, Beihang University/The 24th Middle School of Beijing
yazhi177@126.com
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.
a quadratic reversible and non-Hamiltonian center,bifurcation of limit cycles,a period annulus,the Abelian integral
http://bims.iranjournals.ir/article_472.html
http://bims.iranjournals.ir/article_472_a02b2450a1b3745f35b4010b9b0ab4d3.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
6
2013
12
15
An iterative method for the Hermitian-generalized Hamiltonian solutions to the inverse problem AX=B with a submatrix constraint
1249
1260
EN
J.
Cai
Huzhou Teachers College
caijing@hutc.zj.cn
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.
Inverse problem,Hermitian-generalized Hamiltonian matrix,Submatrix constraint,Optimal approximation
http://bims.iranjournals.ir/article_473.html
http://bims.iranjournals.ir/article_473_ef7d4a2fd05bb1efdab593d07d72c417.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
6
2013
12
15
Fixed points for E-asymptotic contractions and Boyd-Wong type E-contractions in uniform spaces
1261
1272
EN
A.
Aghanians
K.N. Toosi University of Technology
a.aghanians@dena.kntu.ac.ir
K.
Fallahi
K.N. Toosi University of Technology
k_fallahi@dena.kntu.ac.ir
K.
Nourouzi
K.N. Toosi University of Technology
nourouzi@kntu.ac.ir
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 ofKirk's fixed point theorem is given for asymptotic contractions and Boyd-Wong type contractions is investigated in uniform spaces.
Separated uniform space,E-asymptotic contraction,Boyd-Wong type
E-contraction,fixed point
http://bims.iranjournals.ir/article_474.html
http://bims.iranjournals.ir/article_474_a4fea9f574e47dc292fc6e7f8ec1a8a0.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
6
2013
12
15
2-recognizability of the simple groups $B_n(3)$ and $C_n(3)$ by prime graph
1273
1281
EN
M.
Foroudi Ghasemabadi
Tarbiat Modares University
mahnaz_mat@yahoo.com
A.
Iranmanesh
Tarbiat Modares University
iranmana@yahoo.com
N.
Ahanjideh
University of Shahre-kord
ahanjideh.neda@sci.sku.ac.ir
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.
Prime graph,classification of finite simple groups,recognition,spectrum
http://bims.iranjournals.ir/article_346.html
http://bims.iranjournals.ir/article_346_1295fb2d30416b6530013ae8d990f863.pdf