Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
2
2013
05
01
On the spectra of some matrices derived from two quadratic matrices
225
238
EN
H.
Ozdemir
Department of Mathematics, University of Sakarya, TR54187, Sakarya, Turkey
hozdemir@sakarya.edu.tr
T.
Petik
Department of Mathematics, University of Sakarya,TR54187, Sakarya, Turkey
petiktugba@hotmail.com
begin{abstract} The relations between the spectrum of the matrix $Q+R$ and the spectra of the matrices $(gamma + delta)Q+(alpha + beta)R-QR-RQ$, $QR-RQ$, $alpha beta R-QRQ$, $alpha RQR-(QR)^{2}$, and $beta R-QR$ 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}
Quadratic matrix,idempotent matrix,spectrum,linear combination,diagonalization
http://bims.iranjournals.ir/article_337.html
http://bims.iranjournals.ir/article_337_6b4319d54520d67fc847630c7c2cac10.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
2
2013
05
15
The least-square bisymmetric solution to a quaternion matrix equation with applications
239
257
EN
Q.
Wang
Department of Mathematics, Shanghai University
wqw858@yahoo.com.cn
G.
Yu
Department of Mathematics, Shanghai University
yuguihai@126.com
In this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation XA=B to have the least-square 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 least-square bisymmetric solution to this equation. As applications, we derive sufficient and necessary conditions for XA=B to have the positive (nonnegative) definite least-square bisymmetric solution and the maximal (minimal) least-square bisymmetric solution.
Quaternion matrix equation,bisymmetric matrix,least-square solution,Inertia
http://bims.iranjournals.ir/article_340.html
http://bims.iranjournals.ir/article_340_5bfe11787a82c95ca80797926f05c97f.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
2
2013
05
15
Optimal convex combinations bounds of centrodial and harmonic means for logarithmic and identric means
259
269
EN
Y.
Chu
Huzhou Teachers College
chuyuming@hutc.zj.cn
S.
Hou
Huzhou Teachers College
houshouwei2008@163.com
W.
Xia
Huzhou Teachers College
xwf212@hutc.zj.cn
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)+(1-alpha_{1} )H(a,b)
logarithmic mean,identric mean,centroidal mean,harmonic mean
http://bims.iranjournals.ir/article_411.html
http://bims.iranjournals.ir/article_411_ce7ebf9563324f84f8dface04487e196.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
2
2013
05
15
Finite groups with three relative commutativity degrees
271
280
EN
R.
Barzegar
Ferdowsi University of Mashhad
ro.gbps@gmail.com
A.
Erfanian
Ferdowsi University of Mashhad
erfanian@math.um.ac.ir
M.
Farrokhi D. G.
Ferdowsi University of Mashhad
m.farrokhi.d.g@gmail.com
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 non-cyclic group of order $pq$, where $p$ and $q$ are primes. Moreover, we determine all the relative commutativity degrees of some known groups.
Commutativity degree,relative commutativity degree,isoclinism,relative isoclinism
http://bims.iranjournals.ir/article_412.html
http://bims.iranjournals.ir/article_412_c7a8a12e199ac1ff4482cfd330bf4466.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
2
2013
05
15
Gorenstein flat and Gorenstein injective dimensions of simple modules
281
287
EN
A.
Xu
Department of Mathematics,
Nanjing University
xuaimin88888@126.com
X.
Yan
School of Mathematics & Information Technology,
Nanjing Xiaozhuang University
yanxg1109@sina.cn
Let R be a right GF-closed 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 semi-simple ring, then the Gorensntein flat dimensnion of R/I as a right R-module and the Gorensntein injective dimensnnion of R/I as a left R-module 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.
Gorenstein flat dimension,Gorenstein injective dimension,simple module
http://bims.iranjournals.ir/article_413.html
http://bims.iranjournals.ir/article_413_0c2096907897563917352df573b7123b.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
2
2013
05
01
Quasirecognition by the prime graph of L_3(q) where 3 < q < 100
289
305
EN
S. S.
Salehi Amiri
Islamic Azad University
salehisss@yahoo.com
A.
R.
Khalili Asboei
Islamic Azad University
alirezakhas@gmail.com
A.
Iranmanesh
Tarbiat Modares University
iranmana@yahoo.com
A.
Tehranian
Islamic Azad University
tehranian1340@yahoo.com
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 non-Abelian 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.
Prime graph,element order,simple group,linear group
http://bims.iranjournals.ir/article_414.html
http://bims.iranjournals.ir/article_414_abb286fd32fe231f0647dce9cdb1cae2.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
2
2013
05
15
Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation
307
323
EN
F.
J.
Torres
Departamento de Matematica
Universidad de Atacama
francisco.torres@uda.cl
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.
Caputo derivative,cone,fixed point theorem,Fractional differential equation,positive solutions
http://bims.iranjournals.ir/article_415.html
http://bims.iranjournals.ir/article_415_bcc9076ae61d66e52701f70a718d0c42.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
2
2013
05
15
On H-cofinitely supplemented modules
325
346
EN
Y.
Talebi
University of Mazandaran, Iran
talebi@umz.ac.ir
R.
Tribak
University of Tetouan
tribak12@yahoo.com
A.
R.
Moniri Hamzekolaei
Univeristy of Mazandaran, Iran
a.monirih@umz.ac.ir
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
H-supplemented module,H-cofinitely supplemented module,radical-projective module
http://bims.iranjournals.ir/article_416.html
http://bims.iranjournals.ir/article_416_a39509657a78fc90c5d27db44e1ed1d3.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
2
2013
05
15
Hyers-Ulam-Rassias stability of n-Jordan *-homomorphisms on C*-algebras
347
353
EN
Sh.
Ghaffary Ghaleh
Department of Mathematics, Payame Noor University of Zahedan Branch, Zahedan,
Iran
shahram.ghaffary@gmail.com
Kh.
Ghasemi
Department of Mathematics, Payame Noor University of Khash Branch, Khash, Iran
khatere.ghasemi@gmail.com
In this paper, we introduce n-jordan homomorphisms and n-jordan *-homomorphisms and Also investigate the Hyers-Ulam-Rassiasstability of n-jordan *-homomorphisms on C*-algebras.
Hyers-Ulam-Rassias stability,n-Jordan *-homomorphism,n-jordan homomorphism,C*-algebra
http://bims.iranjournals.ir/article_417.html
http://bims.iranjournals.ir/article_417_c380aae386a841b43bbf3cd5bd085049.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
2
2013
05
15
Ore extensions of skew $pi$-Armendariz rings
355
368
EN
O.
Lunqun
Department of Mathematics, Hunan University of Science and
Technology,
Xiangtan, Hunan 411201, P.R. China
ouyanglqtxy@163.com
L.
Jingwang
Department of Mathematics, Hunan University of Science and Technology Xiangtan,
Hunan 411201, P. R. China
jwliu64@yohoo.com.cn
X.
Yueming
Department of Mathematics and Applied Mathematics, Huaihua University, Huaihua,
418000, P. R. China
xymls999@126.com
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.
skew Armendariz ring,skew $pi$-Armendariz ring,$pi$-Armendariz ring
http://bims.iranjournals.ir/article_315.html
http://bims.iranjournals.ir/article_315_670f68e3782d06daa57d42c7aaf944da.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
2
2013
05
01
On the fixed point theorems in generalized weakly contractive mappings on partial metric spaces
369
381
EN
K.
P.
Chi
Vinh University
chidhv@gmail.com
E.
Karapinar
ATILIM UNIVERSITY
erdalkarapinar@yahoo.com
T.
D.
Thanh
Vinh University
cesurakar@gmail.com
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.
fixed point theorems,partial metric spaces,weakly contractive mappings
http://bims.iranjournals.ir/article_344.html
http://bims.iranjournals.ir/article_344_9cee21f500eec7a4df3245b5b9a8734e.pdf