Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401Topological centers of the n-th dual of module actions116387ENK. Haghnejad AzarUniversity of Mohghegh ArdabiliA. RiaziAmirkabir University of TechnologyJournal Article20100126We study the topological centers of $nth$ dual of Banach $mathcal{A}$-modules and we extend some propositions from Lau and "{U}lger into $n-th$ dual of Banach $mathcal{A}-modules$ where $ngeq 0$ is even number. Let $mathcal{B}$ be a Banach $mathcal{A}-bimodule$. By using some new conditions, we show that<br /> $ Z^ell_{mathcal{A}^{(n)}}(mathcal{B}^{(n)})=mathcal{B}^{(n)}$ and<br /> $ Z^ell_{mathcal{B}^{(n)}}(mathcal{A}^{(n)})=mathcal{A}^{(n)}$. We get some conclusions on group algebras.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401Lie triple derivation algebra of Virasoro-like algebra1726388ENH. T.WangHunan University, ChinaN. JingSouth China University of Technology, ChinaQ. G. LiHunan University, ChinaJournal Article20100130Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ its<br />derived algebra, respectively.<br /> We investigate the structure of the Lie triple<br />derivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We prove<br />that they are both isomorphic to $mathfrak{L}$, which provides two<br />examples of invariance under triple derivation.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401Function spaces of Rees matrix semigroups2738389ENH. RahimiIslamic Azad University, IranJournal Article20090430We characterize function spaces of Rees matrix<br />semigroups. Then we study these spaces by using the topological<br />tensor product technique.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401Construction of a class of trivariate nonseparable compactly
supported wavelets with special dilation matrix3954390ENL. LanXi'an University of Arts and ScienceC. ZhengxingXi'an Jiaotong UniversityH. YongdongThe Northwest Secondly National
CollegeJournal Article20120826We present a method for the construction of compactly<br />supported $left (<br />begin{array}{lll}<br />1 & 0 & -1\<br />1 & 1 & 0 \<br />1 & 0 & 1\<br />end{array}<br />right )$-wavelets under a mild condition. Wavelets inherit the<br />symmetry of the corresponding scaling function and satisfies the<br />vanishing moment condition originating in the symbols of the scaling<br />function. As an application, an example is provided.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401On skew Armendariz and skew quasi-Armendariz
modules5584391ENA. AlhevazTarbiat Modares UniversityA. MoussaviTarbiat Modares UniversityJournal Article20090620Let $alpha$ be an endomorphism and $delta$ an $alpha$-derivation<br />of a ring $R$. In this paper we study the relationship between an<br />$R$-module $M_R$ and the general polynomial module $M[x]$ over the<br />skew polynomial ring $R[x;alpha,delta]$. We introduce the notions<br />of skew-Armendariz modules and skew quasi-Armendariz modules which<br />are generalizations of $alpha$-Armendariz modules and extend the<br />classes of non-reduced skew-Armendariz modules. An equivalent<br />characterization of an $alpha$-skew Armendariz module is given.<br />Some properties of this generalization are established, and<br />connections of properties of a skew-Armendariz module $M_R$ with<br />those of $M[x]_{R[x;alpha,delta]}$ are investigated. As a<br />consequence we extend and unify several known results related to<br />Armendariz modules.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401Compact composition operators on certain analytic Lipschitz spaces8599392ENH. MahyarKharazmi UniversityA. H.SanatpourKharazmi UniversityJournal Article20100619We investigate compact composition operators on ceratin Lipschitz<br />spaces of analytic functions on the closed unit disc of the plane.<br />Our approach also leads to some results about composition<br />operators on Zygmund type spaces.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401On a decomposition of Hardy--Hilbert's type inequality101112393ENR. LashkaripourUniversity of Sistan and BaluchestanA. MoazzenUniversity of Sistan and BaluchestanJournal Article20100523In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401On co-Noetherian dimension of rings113122394ENA. HaghanyIsfahan University of TechnologyM. R.VedadiIsfahan University of TechnologyJournal Article20100305We define and study<br />co-Noetherian dimension of rings for which the injective envelope<br />of simple modules have finite Krull-dimension. This is a Morita<br />invariant dimension that measures how far the ring is from being<br />co-Noetherian. The co-Noetherian dimension of certain rings,<br />including commutative rings, are determined. It is<br /> shown that the class ${mathcal W}_n$ of rings with co-Noetherian dimension $leq<br />n$ is closed under homomorphic images and finite normalizing<br />extensions, and that for each $n$ there exist rings with<br />co-Noetherian dimension $n$. The possible relations between Krull<br /> and co-Noetherian dimensions are investigated, and examples are provided to<br /> show that these<br /> dimensions are independent of each<br />other.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401On topological transitive maps on operator algebras123130395ENH. RezaeiUniversity of YasoujJournal Article20100417We consider the transitive linear maps on the operator algebra $B(X)$<br />for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,<br />then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitive<br />linear map without being hypercyclic in the strong operator topology.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401Ranks of the common solution to some quaternion matrix equations
with applications131157396ENQ. WangShanghai UniversityS. YuEast China University of Science and TechnologyJournal Article20100810We derive the formulas of the maximal and<br />minimal ranks of four real matrices $X_{1},X_{2},X_{3}$ and $X_{4}$<br />in common solution $X=X_{1}+X_{2}i+X_{3}j+X_{4}k$ to quaternion<br />matrix equations $A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3}$. As<br />applications, we establish necessary and sufficient conditions for<br />the existence of the common real and complex solutions to the matrix<br />equations. We give the expressions of such solutions to this system<br />when the solvability conditions are met. Moreover, we present<br />necessary and sufficient conditions for the existence of real and<br />complex solutions to the system of quaternion<br />matrix equations $A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3},A_{4}%<br />XB_{4}=C_{4}$. The findings of this paper extend some known results<br />in the literature.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401On Heyting algebras and dual BCK-algebras159168397ENY. YonMokwon UniversityK. H.KimChungju National UniversityJournal Article20090430A 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 prove 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401Application of fundamental relations on n-ary polygroups169184398ENS. MirvakiliPayame Noor UniversityB. DavvazYazd UniversityJournal Article20090430The class of $n$-ary polygroups is a certain subclass of $n$-ary hypergroups, a generalization of D{"o}rnte $n$-ary<br />groups and a generalization of polygroups. The<br />$beta^*$-relation and the $gamma^*$-relation are the smallest<br />equivalence relations on an $n$-ary polygroup $P$ such that<br />$P/beta^*$ and $P/gamma^*$ are an $n$-ary group and a<br />commutative $n$-ary group, respectively.<br /> We use the $beta^*$-relation and the $gamma^*$-relation on a given<br />$n$-ary polygroup and obtain some new results and some<br />fundamental theorems in this respect. In particular, we prove that the relation $gamma$ is transitive on an $n$-ary<br />polygroup.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401Bivariate mean value interpolation on circles of the same radius185192399ENKh. Rahsepar FardUniversity of QomJournal Article20100505We consider bivariate mean-value interpolation<br />problem, where the integrals over circles are interpolation data.<br /> In this case the problem is described over circles of the same radius and with centers are on a<br />straight line and it is shown that in this case the interpolation is not correct.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401k-forested choosability of graphs with bounded maximum average degree193201400ENX. ZhangXidian UniversityG. LiuShandong UniversityJ. L.WuShandong UniversityJournal Article20100421A 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401c-Frames and c-Bessel mappings203222401ENM. FaroughiIslamic Azad UniversityE. OsgooeiUniversity of TabrizJournal Article20100515The theory of c-frames and c-Bessel mappings are the generalizations<br />of the theory of frames and Bessel sequences. In this paper, we<br />obtain several equivalent conditions for dual of c-Bessel mappings.<br />We show that for a c-Bessel mapping $f$, a retrieval<br />formula with respect to a c-Bessel mapping $g$ is satisfied if and<br />only if $g$ is sum of the canonical dual of $f$ with a c-Bessel<br />mapping which weakly belongs to the null space of the pre-frame operator<br />of $f$. Also, we prove that composition of pre-frame operator with<br />analysis operator of two square norm integrable c-Bessel mappings<br />are trace class operators.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401A variational approach to the problem of oscillations of an
elastic half cylinder223240402ENM. HasansoyDogus UniversityJournal Article20100707This paper is devoted to the spectral theory (more precisely, to<br />the variational theory of the spectrum) of guided waves in an<br />elastic half cylinder. We use variational methods to investigate<br />several aspects of propagating waves, including localization (see<br />Figure 1), existence criteria and the formulas to find them. We<br />approach the problem using two complementary methods: The<br />variational methods for non-overdamped operator pencils to<br />describe eigenvalues in definite spectral zones, and<br />Ljusternik-Schnirelman critical point theory to investigate<br />eigenvalues in the mixed spectral zone where the classical<br />variational theory of operator pencils is not applicable.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120101On the existence and uniqueness of solution of initial value problem for fractional order differential equations on time scales241252403ENA. AhmadkhanluAzarbayjan University of Tarbiat MoallemM. JahanshahiAzarbayjan University of Tarbiat MoallemJournal Article20100104n this paper, at first the concept of Caputo fractional<br />derivative is generalized on time scales. Then the fractional order<br />differential equations are introduced on time scales. Finally,<br />sufficient and necessary conditions are presented for the existence<br />and uniqueness of solution of initial value<br />problem including fractional order differential equations.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401On the stability of generalized derivations on Banach algebras253263404ENE. Ansari-PiriUniversity of GuilanE. AnjidaniUniversity of GuilanJournal Article20091103We investigate the stability of generalized<br />derivations on Banach algebras with a bounded central approximate<br />identity. We show that every approximate generalized derivation in<br />the sense of Rassias, is an exact generalized derivation. Also the<br />stability problem of generalized derivations on the faithful Banach<br />algebras is investigated.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401Non-regularity of multiplications for general measure algebras265274405ENJ. LaaliKharazmi UniversityM. EttefaghIslamic Azad UniversityJournal Article20090430Let $fM(X)$ be the space of all finite<br /> regular Borel measures on $X$. A general measure algebra is a subspace of<br />$fM(X)$,<br />which is an $L$-space and<br /> has a multiplication preserving the probability measures.<br /> Let $cLsubseteqfM(X)$ be a general measure algebra on a locally<br />compact space<br /> $X$. In this paper, we investigate the relation between Arens<br />regularity of $cL$ and the topology of $X$. We find conditions<br />under which the Arens regularity of $fL$ implies the compactness of $X$.<br />We<br />show that these conditions are necessary.<br />We also present some examples in showing that the new conditions are<br />different from Theorem 3.1 of cite{7}.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401Extensions of strongly alpha-reversible rings275292406ENL. ZhaoNanjing UniversityX. ZhuNanjing UniversityJournal Article20090923We introduce the notion of<br />strongly $alpha$-reversible rings which is a strong version of<br />$alpha$-reversible rings, and investigate its properties. We first<br />give an example to show that strongly reversible rings need not be<br />strongly $alpha$-reversible. We next argue about the strong<br />$alpha$-reversibility of some kinds of extensions. A number of<br />properties of this version are established. It is shown that a ring<br />$R$ is strongly right $alpha$-reversible if and only if its<br />polynomial ring $R[x]$ is strongly right $alpha$-reversible if and<br />only if its Laurent polynomial ring $R[x, x^{-1}]$ is strongly right<br />$alpha$-reversible. Moreover, we introduce the concept of<br />Nil-$alpha$-reversible rings to investigate the nilpotent elements<br />in $alpha$-reversible rings. Examples are given to show that right<br />Nil-$alpha$-reversible rings need not be right $alpha$-reversible.