On the spectra of some matrices derived from two quadratic matrices
H.
Ozdemir
Department of Mathematics, University of Sakarya, TR54187, Sakarya, Turkey
author
T.
Petik
Department of Mathematics, University of Sakarya,TR54187, Sakarya, Turkey
author
text
article
2013
eng
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}
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
39
v.
2
no.
2013
225
238
http://bims.iranjournals.ir/article_337_6b4319d54520d67fc847630c7c2cac10.pdf
The least-square bisymmetric solution to a quaternion matrix equation with applications
Q.
Wang
Department of Mathematics, Shanghai University
author
G.
Yu
Department of Mathematics, Shanghai University
author
text
article
2013
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
39
v.
2
no.
2013
239
257
http://bims.iranjournals.ir/article_340_5bfe11787a82c95ca80797926f05c97f.pdf
Optimal convex combinations bounds of centrodial and harmonic means for logarithmic and identric means
Y.
Chu
Huzhou Teachers College
author
S.
Hou
Huzhou Teachers College
author
W.
Xia
Huzhou Teachers College
author
text
article
2013
eng
We find the greatest values $alpha_{1} $ and $alpha_{2} $, and the least values $beta_{1} $ and $beta_{2} $ such that the inequalities $alpha_{1} C(a,b)+(1-alpha_{1} )H(a,b)<L(a,b)<beta_{1} C(a,b)+(1-beta_{1} )H(a,b)$ and $alpha_{2} C(a,b)+(1-alpha_{2}) H(a,b)<I(a,b)<beta_{2} C(a,b)+(1-beta_{2} )H(a,b)$ 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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
39
v.
2
no.
2013
259
269
http://bims.iranjournals.ir/article_411_ce7ebf9563324f84f8dface04487e196.pdf
Finite groups with three relative commutativity degrees
R.
Barzegar
Ferdowsi University of Mashhad
author
A.
Erfanian
Ferdowsi University of Mashhad
author
M.
Farrokhi D. G.
Ferdowsi University of Mashhad
author
text
article
2013
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
39
v.
2
no.
2013
271
280
http://bims.iranjournals.ir/article_412_c7a8a12e199ac1ff4482cfd330bf4466.pdf
Gorenstein flat and Gorenstein injective dimensions of simple modules
A.
Xu
Department of Mathematics,
Nanjing University
author
X.
Yan
School of Mathematics & Information Technology,
Nanjing Xiaozhuang University
author
text
article
2013
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
39
v.
2
no.
2013
281
287
http://bims.iranjournals.ir/article_413_0c2096907897563917352df573b7123b.pdf
Quasirecognition by the prime graph of L_3(q) where 3 < q < 100
S. S.
Salehi Amiri
Islamic Azad University
author
A.
Khalili Asboei
Islamic Azad University
author
A.
Iranmanesh
Tarbiat Modares University
author
A.
Tehranian
Islamic Azad University
author
text
article
2013
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
39
v.
2
no.
2013
289
305
http://bims.iranjournals.ir/article_414_abb286fd32fe231f0647dce9cdb1cae2.pdf
Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation
F.
Torres
Departamento de Matematica
Universidad de Atacama
author
text
article
2013
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
39
v.
2
no.
2013
307
323
http://bims.iranjournals.ir/article_415_bcc9076ae61d66e52701f70a718d0c42.pdf
On H-cofinitely supplemented modules
Y.
Talebi
University of Mazandaran, Iran
author
R.
Tribak
University of Tetouan
author
A.
Moniri Hamzekolaei
Univeristy of Mazandaran, Iran
author
text
article
2013
eng
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
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
39
v.
2
no.
2013
325
346
http://bims.iranjournals.ir/article_416_a39509657a78fc90c5d27db44e1ed1d3.pdf
Hyers-Ulam-Rassias stability of n-Jordan *-homomorphisms on C*-algebras
Sh.
Ghaffary Ghaleh
Department of Mathematics, Payame Noor University of Zahedan Branch, Zahedan,
Iran
author
Kh.
Ghasemi
Department of Mathematics, Payame Noor University of Khash Branch, Khash, Iran
author
text
article
2013
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
39
v.
2
no.
2013
347
353
http://bims.iranjournals.ir/article_417_c380aae386a841b43bbf3cd5bd085049.pdf
Ore extensions of skew $pi$-Armendariz rings
O.
Lunqun
Department of Mathematics, Hunan University of Science and
Technology,
Xiangtan, Hunan 411201, P.R. China
author
L.
Jingwang
Department of Mathematics, Hunan University of Science and Technology Xiangtan,
Hunan 411201, P. R. China
author
X.
Yueming
Department of Mathematics and Applied Mathematics, Huaihua University, Huaihua,
418000, P. R. China
author
text
article
2013
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
39
v.
2
no.
2013
355
368
http://bims.iranjournals.ir/article_315_670f68e3782d06daa57d42c7aaf944da.pdf
On the fixed point theorems in generalized weakly contractive mappings on partial metric spaces
K.
Chi
Vinh University
author
E.
Karapinar
ATILIM UNIVERSITY
author
T.
Thanh
Vinh University
author
text
article
2013
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
39
v.
2
no.
2013
369
381
http://bims.iranjournals.ir/article_344_9cee21f500eec7a4df3245b5b9a8734e.pdf