Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39220130501On the spectra of some matrices derived from two quadratic matrices225238337ENH. OzdemirDepartment of Mathematics, University of Sakarya, TR54187, Sakarya, TurkeyT. PetikDepartment of Mathematics, University of Sakarya,TR54187, Sakarya, TurkeyJournal Article20110614begin{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}Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39220130515The least-square bisymmetric solution to a quaternion matrix equation with applications239257340ENQ. WangDepartment of Mathematics, Shanghai UniversityG. YuDepartment of Mathematics, Shanghai UniversityJournal Article20110127In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39220130515Optimal convex combinations bounds of centrodial and harmonic means for logarithmic and identric means259269411ENY. ChuHuzhou Teachers CollegeS. HouHuzhou Teachers CollegeW. XiaHuzhou Teachers CollegeJournal Article20110611We 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39220130515Finite groups with three relative commutativity degrees271280412ENR. BarzegarFerdowsi University of MashhadA. ErfanianFerdowsi University of MashhadM. Farrokhi D. G.Ferdowsi University of MashhadJournal Article20110718For 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39220130515Gorenstein flat and Gorenstein injective dimensions of simple modules281287413ENA. XuDepartment of Mathematics,
Nanjing UniversityX. YanSchool of Mathematics & Information Technology,
Nanjing Xiaozhuang UniversityJournal Article20110730Let 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39220130501Quasirecognition by the prime graph of L_3(q) where 3 < q < 100289305414ENS. S. Salehi AmiriIslamic Azad UniversityA. R.Khalili AsboeiIslamic Azad UniversityA. IranmaneshTarbiat Modares UniversityA. TehranianIslamic Azad UniversityJournal Article20110920Let $G$ 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39220130515Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation307323415ENF. J.TorresDepartamento de Matematica
Universidad de AtacamaJournal Article20111123This 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39220130515On H-cofinitely supplemented modules325346416ENY. TalebiUniversity of Mazandaran, IranR. TribakUniversity of TetouanA. R.Moniri HamzekolaeiUniveristy of Mazandaran, IranJournal Article20110816A 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 supplementedIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39220130515Hyers-Ulam-Rassias stability of n-Jordan *-homomorphisms on C*-algebras347353417ENSh. Ghaffary GhalehDepartment of Mathematics, Payame Noor University of Zahedan Branch, Zahedan,
IranKh. GhasemiDepartment of Mathematics, Payame Noor University of Khash Branch, Khash, IranJournal Article20111118In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39220130515Ore extensions of skew $pi$-Armendariz rings355368315ENO. LunqunDepartment of Mathematics, Hunan University of Science and
Technology,
Xiangtan, Hunan 411201, P.R. ChinaL. JingwangDepartment of Mathematics, Hunan University of Science and Technology Xiangtan,
Hunan 411201, P. R. ChinaX. YuemingDepartment of Mathematics and Applied Mathematics, Huaihua University, Huaihua,
418000, P. R. ChinaJournal Article20110514For 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39220130501On the fixed point theorems in generalized weakly contractive mappings on partial metric spaces369381344ENK. P.ChiVinh UniversityE. KarapinarATILIM UNIVERSITYT. D.ThanhVinh UniversityJournal Article20110516In 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.