2013
39
2
2
0
On the spectra of some matrices derived from two quadratic matrices
2
2
begin{abstract} The relations between the spectrum of the matrix $Q+R$ and the spectra of the matrices $(gamma + delta)Q+(alpha + beta)RQRRQ$, $QRRQ$, $alpha beta RQRQ$, $alpha RQR(QR)^{2}$, and $beta RQR$ have been given on condition that the matrix $Q+R$ is diagonalizable, where $Q$, $R$ are ${alpha, beta}$quadratic matrix and ${gamma, delta}$quadratic matrix, respectively, of order $n$. end{abstract}
1

225
238


H.
Ozdemir
Department of Mathematics, University of Sakarya, TR54187, Sakarya, Turkey
Department of Mathematics, University of
Turkey
hozdemir@sakarya.edu.tr


T.
Petik
Department of Mathematics, University of Sakarya,TR54187, Sakarya, Turkey
Department of Mathematics, University of
Turkey
petiktugba@hotmail.com
Quadratic matrix
idempotent matrix
spectrum
linear combination
diagonalization
The leastsquare bisymmetric solution to a quaternion matrix equation with applications
2
2
In this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation XA=B to have the leastsquare bisymmetric solution and give the expression of such solution when the solvability conditions are met. Futhermore, we consider the maximal and minimal inertias of the leastsquare bisymmetric solution to this equation. As applications, we derive sufficient and necessary conditions for XA=B to have the positive (nonnegative) definite leastsquare bisymmetric solution and the maximal (minimal) leastsquare bisymmetric solution.
1

239
257


Q.
Wang
Department of Mathematics, Shanghai University
Department of Mathematics, Shanghai University
China, R. O. C.
wqw858@yahoo.com.cn


G.
Yu
Department of Mathematics, Shanghai University
Department of Mathematics, Shanghai University
China, R. O. C.
yuguihai@126.com
Quaternion matrix equation
bisymmetric matrix
leastsquare solution
Inertia
Optimal convex combinations bounds of centrodial and harmonic means for logarithmic and identric means
2
2
We find the greatest values $alpha_{1} $ and $alpha_{2} $, and the least values $beta_{1} $ and $beta_{2} $ such that the inequalities $alpha_{1} C(a,b)+(1alpha_{1} )H(a,b)<L(a,b)<beta_{1} C(a,b)+(1beta_{1} )H(a,b)$ and $alpha_{2} C(a,b)+(1alpha_{2}) H(a,b)<I(a,b)<beta_{2} C(a,b)+(1beta_{2} )H(a,b)$ hold for all $a,b>0$ with $aneq b$. Here, $C(a,b)$, $H(a,b)$, $L(a,b)$, and $I(a,b)$ are the centroidal, harmonic, logarithmic, and identric means of two positive numbers $a$ and $b$, respectively.
1

259
269


Y.
Chu
Huzhou Teachers College
Huzhou Teachers College
China, R. O. C.
chuyuming@hutc.zj.cn


S.
Hou
Huzhou Teachers College
Huzhou Teachers College
China, R. O. C.
houshouwei2008@163.com


W.
Xia
Huzhou Teachers College
Huzhou Teachers College
China, R. O. C.
xwf212@hutc.zj.cn
logarithmic mean
identric mean
centroidal mean
harmonic mean
Finite groups with three relative commutativity degrees
2
2
For a finite group $G$ and a subgroup $H$ of $G$, the relative commutativity degree of $H$ in $G$, denoted by $d(H,G)$, is the probability that an element of $H$ commutes with an element of $G$. Let $mathcal{D}(G)={d(H,G):Hleq G}$ be the set of all relative commutativity degrees of subgroups of $G$. It is shown that a finite group $G$ admits three relative commutativity degrees if and only if $G/Z(G)$ is a noncyclic group of order $pq$, where $p$ and $q$ are primes. Moreover, we determine all the relative commutativity degrees of some known groups.
1

271
280


R.
Barzegar
Ferdowsi University of Mashhad
Ferdowsi University of Mashhad
Iran
ro.gbps@gmail.com


A.
Erfanian
Ferdowsi University of Mashhad
Ferdowsi University of Mashhad
Iran
erfanian@math.um.ac.ir


M.
Farrokhi D. G.
Ferdowsi University of Mashhad
Ferdowsi University of Mashhad
Iran
m.farrokhi.d.g@gmail.com
Commutativity degree
relative commutativity degree
isoclinism
relative isoclinism
Gorenstein flat and Gorenstein injective dimensions of simple modules
2
2
Let R be a right GFclosed ring with finite left and right Gorenstein global dimension. We prove that if I is an ideal of R such that R/I is a semisimple ring, then the Gorensntein flat dimensnion of R/I as a right Rmodule and the Gorensntein injective dimensnnion of R/I as a left Rmodule are identical. In particular, we show that for a simple module S over a commutative Gorensntein ring R, the Gorenstein flat dimension of S equals to the Gorenstein injective dimension of S.
1

281
287


A.
Xu
Department of Mathematics,
Nanjing University
Department of Mathematics,
Nanjing University
China, R. O. C.
xuaimin88888@126.com


X.
Yan
School of Mathematics & Information Technology,
Nanjing Xiaozhuang University
School of Mathematics & Information Technology
China, R. O. C.
yanxg1109@sina.cn
Gorenstein flat dimension
Gorenstein injective dimension
simple module
Quasirecognition by the prime graph of L_3(q) where 3 < q < 100
2
2
Let $G$ be a finite group. We construct the prime graph of $ G $,which is denoted by $ Gamma(G) $ as follows: the vertex set of thisgraph is the prime divisors of $ G $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ G $ contains anelement of order $ pq $.In this paper, we determine finite groups $ G $ with $ Gamma(G) =Gamma(L_3(q)) $, $2 leq q < 100 $ and prove that if $ q neq 2, 3$, then $L_3(q) $ is quasirecognizable by prime graph, i.e., if $G$is a finite group with the same prime graph as the finite simplegroup $L_3(q)$, then $G$ has a unique nonAbelian composition factorisomorphic to $L_3(q)$. As a consequence of our results we provethat the simple group $L_{3}(4)$ is recognizable and the simplegroups $L_{3}(7)$ and $L_{3}(9)$ are $2$recognizable by the primegraph.
1

289
305


S. S.
Salehi Amiri
Islamic Azad University
Islamic Azad University
Iran
salehisss@yahoo.com


A.
Khalili Asboei
Islamic Azad University
Islamic Azad University
Iran
alirezakhas@gmail.com


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


A.
Tehranian
Islamic Azad University
Islamic Azad University
Iran
tehranian1340@yahoo.com
Prime graph
element order
simple group
linear group
Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation
2
2
This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.
1

307
323


F.
Torres
Departamento de Matematica
Universidad de Atacama
Departamento de Matematica
Universidad de
Not listed here
francisco.torres@uda.cl
Caputo derivative
cone
fixed point theorem
Fractional differential equation
positive solutions
On Hcofinitely supplemented modules
2
2
A module $M$ is called $emph{H}$cofinitely supplemented if for every cofinite submodule $E$ (i.e. $M/E$ is finitely generated) of $M$ there exists a direct summand $D$ of $M$ such that $M = E + X$ holds if and only if $M = D + X$, for every submodule $X$ of $M$. In this paper we study factors, direct summands and direct sums of $emph{H}$cofinitely supplemented modules. Let $M$ be an $emph{H}$cofinitely supplemented module and let $N leq M$ be a submodule. Suppose that for every direct summand $K$ of $M$, $(N + K)/N$ lies above a direct summand of $M/N$. Then $M/N$ is $emph{H}$cofinitely supplemented. Let $M$ be an $emph{H}$cofinitely supplemented module. Let $N$ be a direct summand of $M$. Suppose that for every direct summand $K$ of $M$ with $M=N+K$, $Ncap K$ is also a direct summand of $M$. Then $N$ is $emph{H}$cofinitely supplemented. Let $M = M_{1} oplus M_{2}$. If $M_{1}$ is radical $M_{2}$projective (or $M_{2}$ is radical $M_{1}$projective) and $M_{1}$ and $M_{2}$ are $emph{H}$cofinitely supplemented, then $M$ is $emph{H}$cofinitely supplemented
1

325
346


Y.
Talebi
University of Mazandaran, Iran
University of Mazandaran, Iran
Iran
talebi@umz.ac.ir


R.
Tribak
University of Tetouan
University of Tetouan
Morocco
tribak12@yahoo.com


A.
Moniri Hamzekolaei
Univeristy of Mazandaran, Iran
Univeristy of Mazandaran, Iran
Iran
a.monirih@umz.ac.ir
Hsupplemented module
Hcofinitely supplemented module
radicalprojective module
HyersUlamRassias stability of nJordan *homomorphisms on C*algebras
2
2
In this paper, we introduce njordan homomorphisms and njordan *homomorphisms and Also investigate the HyersUlamRassiasstability of njordan *homomorphisms on C*algebras.
1

347
353


Sh.
Ghaffary Ghaleh
Department of Mathematics, Payame Noor University of Zahedan Branch, Zahedan,
Iran
Department of Mathematics, Payame Noor University
Iran
shahram.ghaffary@gmail.com


Kh.
Ghasemi
Department of Mathematics, Payame Noor University of Khash Branch, Khash, Iran
Department of Mathematics, Payame Noor University
Iran
khatere.ghasemi@gmail.com
HyersUlamRassias stability
nJordan *homomorphism
njordan homomorphism
C*algebra
Ore extensions of skew $pi$Armendariz rings
2
2
For a ring endomorphism $alpha$ and an $alpha$derivation $delta$, we introduce a concept, so called skew $pi$Armendariz ring, that is a generalization of both $pi$Armendariz rings, and $(alpha,delta)$compatible skew Armendariz rings. We first observe the basic properties of skew $pi$Armendariz rings, and extend the class of skew $pi$Armendariz rings through various ring extensions. We next show that all $(alpha,delta)$compatible $NI$ rings are skew $pi$Armendariz, and if a ring $R$ is an $(alpha,delta)$compatible $2$$primal$ ring, then the polynomial ring $R[x]$ is skew $pi$Armendariz.
1

355
368


O.
Lunqun
Department of Mathematics, Hunan University of Science and
Technology,
Xiangtan, Hunan 411201, P.R. China
Department of Mathematics, Hunan University
China, R. O. C.
ouyanglqtxy@163.com


L.
Jingwang
Department of Mathematics, Hunan University of Science and Technology Xiangtan,
Hunan 411201, P. R. China
Department of Mathematics, Hunan University
China, R. O. C.
jwliu64@yohoo.com.cn


X.
Yueming
Department of Mathematics and Applied Mathematics, Huaihua University, Huaihua,
418000, P. R. China
Department of Mathematics and Applied Mathematics,
China, R. O. C.
xymls999@126.com
skew Armendariz ring
skew $pi$Armendariz ring
$pi$Armendariz ring
On the fixed point theorems in generalized weakly contractive mappings on partial metric spaces
2
2
In this paper, we prove a fixed point theorem for a pair of generalized weakly contractive mappings in complete partial metric spaces. The theorems presented are generalizations of very recent fixed point theorems due to Abdeljawad, Karapinar and Tas. To emphasize the very general nature of these results, we illustrate an example.
1

369
381


K.
Chi
Vinh University
Vinh University
Vietnam
chidhv@gmail.com


E.
Karapinar
ATILIM UNIVERSITY
ATILIM UNIVERSITY
Turkey
erdalkarapinar@yahoo.com


T.
Thanh
Vinh University
Vinh University
Vietnam
cesurakar@gmail.com
fixed point theorems
partial metric spaces
weakly contractive mappings