Bulletin of the Iranian Mathematical Society http://bims.iranjournals.ir/ Thu, 20 Jun 2013 09:20:37 +0100 FeedCreator http://bims.iranjournals.ir/ Feed provided by Bulletin of the Iranian Mathematical Society. Click to visit. http://bims.iranjournals.ir/?_action=articleInfo&article=337 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} Tue, 30 Apr 2013 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=340 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. Tue, 14 May 2013 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=411 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. Tue, 14 May 2013 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=412 ‎‎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. Tue, 14 May 2013 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=413 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. Tue, 14 May 2013 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=414 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. Tue, 30 Apr 2013 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=415 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. Tue, 14 May 2013 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=416 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 Tue, 14 May 2013 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=417 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. Tue, 14 May 2013 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=315 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. Tue, 14 May 2013 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=344 In this paper, we prove a fixed 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. Tue, 30 Apr 2013 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=230 Let $X$ be a reflexive Banach space, $T:Xto X$ be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto X$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. In this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences to the unique solution of the variational inequality $VI^*(F, C)$. We also present similar results for a strongly monotone and Lipschitzian operator in the context of a Hilbert space and apply the results for solving a minimization problem. Mon, 04 Apr 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=244 A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prove that the $k$-forested choosability of a graph with maximum degree $Deltageq kgeq 4$ is at most $leftlceilfrac{Delta}{k-1}rightrceil+1$, $leftlceilfrac{Delta}{k-1}rightrceil+2$ or $leftlceilfrac{Delta}{k-1}rightrceil+3$ if its maximum average degree is less than $frac{12}{5}$, $frac{8}{3}$ or $3$, respectively. Tue, 03 May 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=251 Let A be a unital R-algebra and M be a unital A-bimodule. It is shown that every Jordan derivation of the trivial extension of A by M, under some conditions, is the sum of a derivation and an antiderivation. Thu, 19 May 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=253 $n$-ary polygroups are a certain subclass of $n$-ary hypergroups, a generalization of D{"o}rnte $n$-ary groups and a generalization of polygroups. The $beta^*$-relation and $gamma^*$-relation are the smallest equivalence relations on an $n$-ary polygroup $P$ such that $P/beta^*$ and $P/gamma^*$ are an $n$-ary group and a commutative $n$-ary group, respectively. In this paper, we use the $beta^*$-relation and the $gamma^*$-relation on a given $n$-ary polygroup and obtain some new results and some fundamental theorems in this respect. In particular, we prove the relation $gamma$ is transitive on an $n$-ary polygroup. Tue, 24 May 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=256 In this paper, we introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially Cohen-Macaulay. Wed, 25 May 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=258 In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that, this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula. Wed, 25 May 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=262 This paper is devoted to the spectral theory (more precisely, to the variational theory of the spectrum) of guided waves in an elastic half cylinder. We use variational methods to investigate several aspects of propagating waves, including localization (see Figure 1), existence criteria and the formulas to find them. We approach the problem using two complementary methods: The variational methods for non-overdamped operator pencils to describe eigenvalues in definite spectral zones, and Ljusternik-Schnirelman critical point theory to investigate eigenvalues in the mixed spectral zone where the classical variational theory of operator pencils is not applicable. Fri, 27 May 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=266 Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an elementary step toward investigation of some properties of locally finite graphs by their corresponding topology which we introduce in this paper. Sun, 29 May 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=268 In this paper, at first the concept of Caputo fractional derivative is generalized on time scales. Then the fractional order differential equations are introduced on time scales. Finally, sufficient and necessary conditions are presented for the existence and uniqueness of solution of initial value problem including fractional order differential equations. Mon, 30 May 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=270 A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and show that a Heyting semilattice is equivalent to an $i$-invariant and $m$-invariant dual $BCK$-semilattices, and show that a commutative Heyting algebra is equivalent to a bounded implicative dual $BCK$-algebra. Mon, 30 May 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=271 We define and study co-Noetherian dimension of rings for which the injective envelope of simple modules have finite Krull-dimension. This is a Morita invariant dimension that measures how far the ring is from being co-Noetherian. The co-Noetherian dimension of certain rings, including commutative rings, are determined. It is shown that the class ${mathcal W}_n$ of rings with co-Noetherian dimension $leq n$ is closed under homomorphic images and finite normalizing extensions, and that for each $n$ there exist rings with co-Noetherian dimension $n$. The possible relations between Krull and co-Noetherian dimensions are investigated, and examples are provided to show that these dimensions are independent of each other. Tue, 31 May 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=293 Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ its derived algebra respectively. In this paper, we investigate the structure of the Lie triple derivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We prove that they are both isomorphic to $mathfrak{L}$, which provides two examples of invariance under triple derivation. Thu, 02 Jun 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=295 We investigate compact composition operators on ceratin Lipschitz spaces of analytic functions on the closed unit disc of the plane. Our approach also leads to some results about composition operators on Zygmund type spaces. Thu, 02 Jun 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=300 We in this paper derive the formulas of the maximal and minimal ranks of four real matrices $X_{1},X_{2},X_{3}$ and $X_{4}$ in solution $X=X_{1}+X_{2}i+X_{3}j+X_{4}k$ to the common solution of quaternion matrix equations $A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3}$. As applications, we establish necessary and sufficient conditions for the existence of the common real and complex solutions to the matrix equations. We give the expressions of such solutions to this system when the solvability conditions are met. Moreover, we present necessary and sufficient conditions for the existence of real and complex solutions to the system of quaternion matrix equations $A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3},A_{4}% XB_{4}=C_{4}$. The findings of this paper extend some known results in the literature. Fri, 10 Jun 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=301 In this study, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities. As mentioned, we consider some kinds of Hilbert' s inequality Sun, 12 Jun 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=307 The theory of c-frames and c-Bessel mappings are the generalizations of the theory of frames and Bessel sequences. In this article, we obtain several equivalence conditions for dual of c-Bessel mappings. We show that for a c-Bessel mapping $f$, an retrieval formula with respect to a c-Bessel mapping $g$ is satisfied if and only if $g$ is sum of the canonical dual of $f$ with a c-Bessel mapping which is weakly in the null space of the pre-frame operator of $f$. Also, we prove that composition of pre-frame operator with analysis operator of two square norm integrable c-Bessel mappings are trace class operators. Sun, 19 Jun 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=311 In this paper we consider bivariate mean-value interpolation‎ ‎problem‎, ‎where the integrals over circles are interpolation data.‎ ‎In this case the problem is described over circles with same radius and centers are on a‎ ‎straight line when it is not correct.‎ Tue, 21 Jun 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=313 We investigate the stability of generalized derivations on Banach algebras with a bounded central approximate identity. We show that every approximate generalized derivation in the sense of Rassias, is an exact generalized derivation. Also the stability problem of generalized derivations on the faithful Banach algebras is investigated. Mon, 27 Jun 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=316 In the present paper we consider the transitive linear maps on the operator algebra B(X) for a separable Banach space X. We show if a bounded linear map is norm transitive on B(X), then it must be hypercyclic with strong operator topology. Also we provide a norm transitive linear map without being hypercyclic in the strong operator topology. Wed, 29 Jun 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=318 Let $alpha$ be an endomorphism and $delta$ an $alpha$-derivation of a ring $R$. In this paper we study the relationship between an $R$-module $M_R$ and the general polynomial module $M[x]$ over the skew polynomial ring $R[x;alpha,delta]$. We introduce the notions of skew-Armendariz modules and skew quasi-Armendariz modules which are generalizations of $alpha$-Armendariz modules and extend the classes of non-reduced skew-Armendariz modules. An equivalent characterization of an $alpha$-skew Armendariz module is given. Some properties of this generalization are established, and connections of properties of a skew-Armendariz module $M_R$ with those of $M[x]_{R[x;alpha,delta]}$ are investigated. As a consequence we extend and unify several known results related to Armendariz modules. Mon, 04 Jul 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=319 In this paper we characterize function spaces of Rees matrix semigroups. Then we study these spaces by using the topological tensor product technique. Mon, 04 Jul 2011 19:30:00 +0100 http://bims.iranjournals.ir/?_action=articleInfo&article=346 Let $G$ be a finite group and let $GK(G)$ be the prime graph of $G$. We assume that $ngeqslant 5 $ is an odd number. In this paper, we show that the simple groups $B_n(3)$ and $C_n(3)$ are 2-recognizable by their prime graphs. As consequences of the result, the characterizability of the groups $B_n(3)$ and $C_n(3)$ by their spectra and by the set of orders of maximal abelian subgroups are obtained. Also, we can conclude that the AAM's conjecture is true for the groups under study. Thu, 22 Dec 2011 20:30:00 +0100