eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-05-01
39
2
225
238
337
On the spectra of some matrices derived from two quadratic matrices
H. Ozdemir
hozdemir@sakarya.edu.tr
1
T. Petik
petiktugba@hotmail.com
2
Department of Mathematics, University of Sakarya, TR54187, Sakarya, Turkey
Department of Mathematics, University of Sakarya,TR54187, Sakarya, Turkey
begin{abstract} <br /> The relations between the spectrum of the matrix $Q+R$ and the spectra of the matrices <br /> $(gamma + delta)Q+(alpha + beta)R-QR-RQ$, $QR-RQ$, $alpha beta R-QRQ$, $alpha RQR-(QR)^{2}$, <br /> and $beta R-QR$ have been given on condition that the matrix $Q+R$ is diagonalizable, where $Q$, <br /> $R$ are ${alpha, beta}$-quadratic matrix and ${gamma, delta}$-quadratic matrix, respectively, of order $n$. <br />end{abstract}
http://bims.iranjournals.ir/article_337_6b4319d54520d67fc847630c7c2cac10.pdf
Quadratic matrix
idempotent matrix
spectrum
linear combination
diagonalization
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-05-15
39
2
239
257
340
The least-square bisymmetric solution to a quaternion matrix equation with applications
Q. Wang
wqw858@yahoo.com.cn
1
G. Yu
yuguihai@126.com
2
Department of Mathematics, Shanghai University
Department of Mathematics, Shanghai University
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.
http://bims.iranjournals.ir/article_340_5bfe11787a82c95ca80797926f05c97f.pdf
Quaternion matrix equation
bisymmetric matrix
least-square solution
Inertia
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-05-15
39
2
259
269
411
Optimal convex combinations bounds of centrodial and harmonic means for logarithmic and identric means
Y. Chu
chuyuming@hutc.zj.cn
1
S. Hou
houshouwei2008@163.com
2
W. Xia
xwf212@hutc.zj.cn
3
Huzhou Teachers College
Huzhou Teachers College
Huzhou Teachers College
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.
http://bims.iranjournals.ir/article_411_ce7ebf9563324f84f8dface04487e196.pdf
logarithmic mean
identric mean
centroidal mean
harmonic mean
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-05-15
39
2
271
280
412
Finite groups with three relative commutativity degrees
R. Barzegar
ro.gbps@gmail.com
1
A. Erfanian
erfanian@math.um.ac.ir
2
M. Farrokhi D. G.
m.farrokhi.d.g@gmail.com
3
Ferdowsi University of Mashhad
Ferdowsi University of Mashhad
Ferdowsi University of Mashhad
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.
http://bims.iranjournals.ir/article_412_c7a8a12e199ac1ff4482cfd330bf4466.pdf
Commutativity degree
relative commutativity degree
isoclinism
relative isoclinism
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-05-15
39
2
281
287
413
Gorenstein flat and Gorenstein injective dimensions of simple modules
A. Xu
xuaimin88888@126.com
1
X. Yan
yanxg1109@sina.cn
2
Department of Mathematics, Nanjing University
School of Mathematics & Information Technology, Nanjing Xiaozhuang University
Let R be a right GF-closed ring with finite left and right <br />Gorenstein global dimension. We prove that if I is an ideal of <br />R such that R/I is a semi-simple ring, then the Gorensntein flat <br />dimensnion of R/I as a right R-module and the Gorensntein <br />injective dimensnnion of R/I as a left R-module are identical. <br />In particular, we show that for a simple module S over a <br />commutative Gorensntein ring R, the Gorenstein flat dimension of <br />S equals to the Gorenstein injective dimension of S.
http://bims.iranjournals.ir/article_413_0c2096907897563917352df573b7123b.pdf
Gorenstein flat dimension
Gorenstein injective dimension
simple module
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-05-01
39
2
289
305
414
Quasirecognition by the prime graph of L_3(q) where 3 < q < 100
S. S. Salehi Amiri
salehisss@yahoo.com
1
A. Khalili Asboei
alirezakhas@gmail.com
2
A. Iranmanesh
iranmana@yahoo.com
3
A. Tehranian
tehranian1340@yahoo.com
4
Islamic Azad University
Islamic Azad University
Tarbiat Modares University
Islamic Azad University
Let $G$ be a finite group. We construct the prime graph of $ G $,<br />which is denoted by $ Gamma(G) $ as follows: the vertex set of this<br />graph is the prime divisors of $ |G| $ and two distinct vertices $ p<br />$ and $ q $ are joined by an edge if and only if $ G $ contains an<br />element of order $ pq $.<br />In this paper, we determine finite groups $ G $ with $ Gamma(G) =<br />Gamma(L_3(q)) $, $2 leq q < 100 $ and prove that if $ q neq 2, 3<br />$, then $L_3(q) $ is quasirecognizable by prime graph, i.e., if $G$<br />is a finite group with the same prime graph as the finite simple<br />group $L_3(q)$, then $G$ has a unique non-Abelian composition factor<br />isomorphic to $L_3(q)$. As a consequence of our results we prove<br />that the simple group $L_{3}(4)$ is recognizable and the simple<br />groups $L_{3}(7)$ and $L_{3}(9)$ are $2-$recognizable by the prime<br />graph.
http://bims.iranjournals.ir/article_414_abb286fd32fe231f0647dce9cdb1cae2.pdf
Prime graph
element order
simple group
linear group
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-05-15
39
2
307
323
415
Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation
F. Torres
francisco.torres@uda.cl
1
Departamento de Matematica Universidad de Atacama
This paper presents conditions for the existence and <br />multiplicity of positive solutions for a boundary value problem of <br />a nonlinear fractional differential equation. We show that it has at <br />least one or two positive solutions. The main tool is Krasnosel'skii <br />fixed point theorem on cone and fixed point index theory.
http://bims.iranjournals.ir/article_415_bcc9076ae61d66e52701f70a718d0c42.pdf
Caputo derivative
cone
fixed point theorem
Fractional differential equation
positive solutions
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-05-15
39
2
325
346
416
On H-cofinitely supplemented modules
Y. Talebi
talebi@umz.ac.ir
1
R. Tribak
tribak12@yahoo.com
2
A. Moniri Hamzekolaei
a.monirih@umz.ac.ir
3
University of Mazandaran, Iran
University of Tetouan
Univeristy of Mazandaran, Iran
A module $M$ is called $emph{H}$-cofinitely supplemented if for <br />every cofinite submodule $E$ (i.e. $M/E$ is finitely generated) of $M$ there exists a direct summand <br />$D$ of $M$ such that $M = E + X$ holds if and only if $M = D + <br />X$, for every submodule $X$ of $M$. In this paper we study factors, direct summands and direct sums of $emph{H}$-cofinitely supplemented modules. <br /> <br />Let $M$ be an $emph{H}$-cofinitely supplemented module <br />and let $N leq M$ be a submodule. Suppose that for every direct summand $K$ of $M$, $(N <br />+ K)/N$ lies above a direct summand of $M/N$. Then <br />$M/N$ is $emph{H}$-cofinitely supplemented. <br /> <br />Let $M$ be an $emph{H}$-cofinitely supplemented module. <br />Let $N$ be a direct summand of $M$. <br />Suppose that for every direct summand $K$ of $M$ with $M=N+K$, $Ncap K$ is also a direct summand of $M$. <br />Then $N$ is $emph{H}$-cofinitely supplemented. <br /> <br />Let $M = M_{1} oplus M_{2}$. <br />If $M_{1}$ is radical $M_{2}$-projective (or $M_{2}$ is <br />radical $M_{1}$-projective) and $M_{1}$ and $M_{2}$ are <br />$emph{H}$-cofinitely supplemented, then $M$ is <br />$emph{H}$-cofinitely supplemented
http://bims.iranjournals.ir/article_416_a39509657a78fc90c5d27db44e1ed1d3.pdf
H-supplemented module
H-cofinitely supplemented module
radical-projective module
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-05-15
39
2
347
353
417
Hyers-Ulam-Rassias stability of n-Jordan *-homomorphisms on C*-algebras
Sh. Ghaffary Ghaleh
shahram.ghaffary@gmail.com
1
Kh. Ghasemi
khatere.ghasemi@gmail.com
2
Department of Mathematics, Payame Noor University of Zahedan Branch, Zahedan, Iran
Department of Mathematics, Payame Noor University of Khash Branch, Khash, Iran
In this paper, we introduce n-jordan homomorphisms and n-jordan *-homomorphisms and Also investigate the Hyers-Ulam-Rassias<br />stability of n-jordan *-homomorphisms on C*-algebras.
http://bims.iranjournals.ir/article_417_c380aae386a841b43bbf3cd5bd085049.pdf
Hyers-Ulam-Rassias stability
n-Jordan *-homomorphism
n-jordan homomorphism
C*-algebra
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-05-15
39
2
355
368
315
Ore extensions of skew $pi$-Armendariz rings
O. Lunqun
ouyanglqtxy@163.com
1
L. Jingwang
jwliu64@yohoo.com.cn
2
X. Yueming
xymls999@126.com
3
Department of Mathematics, Hunan University of Science and Technology, Xiangtan, Hunan 411201, P.R. China
Department of Mathematics, Hunan University of Science and Technology Xiangtan, Hunan 411201, P. R. China
Department of Mathematics and Applied Mathematics, Huaihua University, Huaihua, 418000, P. R. China
For a ring endomorphism <br />$alpha$ and an $alpha$-derivation $delta$, we introduce a <br />concept, so called skew $pi$-Armendariz ring, that is a <br />generalization of both $pi$-Armendariz rings, <br />and $(alpha,delta)$-compatible skew Armendariz rings. We first <br />observe the basic properties of skew $pi$-Armendariz rings, and <br />extend the class of skew $pi$-Armendariz rings through various ring <br />extensions. We next show that all $(alpha,delta)$-compatible <br />$NI$ rings are skew $pi$-Armendariz, and if a ring $R$ is an <br />$(alpha,delta)$-compatible $2$-$primal$ ring, then the polynomial <br />ring $R[x]$ is skew $pi$-Armendariz.
http://bims.iranjournals.ir/article_315_670f68e3782d06daa57d42c7aaf944da.pdf
skew Armendariz ring
skew $pi$-Armendariz ring
$pi$-Armendariz ring
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-05-01
39
2
369
381
344
On the fixed point theorems in generalized weakly contractive mappings on partial metric spaces
K. Chi
chidhv@gmail.com
1
E. Karapinar
erdalkarapinar@yahoo.com
2
T. Thanh
cesurakar@gmail.com
3
Vinh University
ATILIM UNIVERSITY
Vinh University
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.
http://bims.iranjournals.ir/article_344_9cee21f500eec7a4df3245b5b9a8734e.pdf
fixed point theorems
partial metric spaces
weakly contractive mappings