Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901Fiber bundles and Lie algebras of top spaces589598433ENM. R. FarhangdoostDepartment of Mathematics, College of Sciences, Shiraz University, P.O.Box 71457-44776, Shiraz, IRAN.Journal Article20101214In this paper, by using of Frobenius theorem a relation <br />between Lie subalgebras of the Lie algebra of a top space T and Lie <br />subgroups of T(as a Lie group) is determined. As a result we <br />can consider these spaces by their Lie algebras. We show that a top <br />space with the finite number of identity elements is a C^{∞} principal <br />fiber bundle, by this method we can characterize top spaces.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901Hybrid steepest-descent method with sequential and functional errors in Banach space599617230ENS. SaeidiUniversity of KurdistanH. HaydariUniversity of KurdistanJournal Article20100706Let $X$ be a reflexive Banach space, $T:Xto X$ <br />be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto <br />X$ be $delta$-strongly accretive and $lambda$- strictly <br />pseudocotractive with $delta+lambda>1$. In this paper, we present <br /> modified hybrid steepest-descent methods, involving sequential errors and <br />functional errors with functions admitting a center, which generate <br />convergent sequences to the unique solution <br /> of the variational inequality $VI^*(F, C)$. We also present similar results for a strongly monotone and Lipschitzian <br />operator in the context of a Hilbert space and apply the results for <br />solving a minimization problem.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901Complement of Special Chordal Graphs and Vertex Decomposability619625256ENM. AlizadehAssistant Professor at University of TehranA. GoodarziMSc Student at University of TehranJournal Article20110308In this paper, we introduce a subclass of chordal graphs which <br />contains $d$-trees and show that their complement are vertex <br />decomposable and so is shellable and sequentially Cohen-Macaulay.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901On vertex balance index set of some graphs627634434ENCh. AdigaUniversity of MysoreC. K.SubbarayaAdichunchanagiri Institute of TechnologyA. S.ShrikanthUniversity of MysoreM. A.SrirajUniversity of MysoreJournal Article20110111Let Z2 = {0, 1} and G = (V ,E) be a graph. A labeling f : V → Z2 induces an edge labeling f* : E →Z2 defined by f*(uv) = f(u).f (v). For i ε Z2 let vf (i) = v(i) = card{v ε V : f(v) = i} and ef (i) = e(i) = {e ε E : f*(e) = i}. A labeling f is said to be Vertex-friendly if | v(0) − v(1) |≤ 1. The vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. In this paper we completely determine the vertex balance index set of Kn, Km,n, Cn×P2 and Complete binary tree.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901Jordan derivation on trivial extension635645251ENH. GhahramaniUniversity of KurdistanJournal Article20110412Let A be a unital R-algebra and M be a unital A-bimodule. It is <br />shown that every Jordan derivation of the trivial extension of A by M, under <br />some conditions, is the sum of a derivation and an antiderivation.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901An Alexandroff topology on graphs647662266ENS. M.Jafarian AmiriZanjan UniversityA. JafarzadehFerdowsi University of MashhadH. KhatibzadehZanjan University, ZanjanJournal Article20101024Let G = (V,E) be a locally finite graph, i.e. a graph in which <br />every vertex has finitely many adjacent vertices. In this paper, we <br />associate a topology to G, called graphic topology of G and we show <br />that it is an Alexandroff topology, i.e. a topology in which intersec- <br />tion of every family of open sets is open. Then we investigate some <br />properties of this topology. Our motivation is to give an elementary <br />step toward investigation of some properties of locally finite graphs <br />by their corresponding topology which we introduce in this paper.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901Relative n-th non-commuting graphs of finite groups663674435ENA. ErfanianFerdowsi University of MashhadB. TolueFerdowsi University of MashhadJournal Article20120402Suppose $n$ is a fixed positive integer. We introduce the relative n-th non-commuting graph $Gamma^{n} _{H,G}$, associated to the non-abelian subgroup $H$ of group $G$. The vertex set is $Gsetminus C^n_{H,G}$ in which $C^n_{H,G} = {xin G : [x,y^{n}]=1 mbox{~and~} [x^{n},y]=1mbox{~for~all~} yin H}$. Moreover, ${x,y}$ is an edge if $x$ or $y$ belong to $H$ and $xy^{n}<br />eq y^{n}x$ or $x^{n}y<br />eq yx^{n}$. In fact, the relative n-th commutativity degree, $P_{n}(H,G)$ the probability that n-th power of an element of the subgroup $H$ commutes with another random element of the group $G$ and the non-commuting graph were the keys to construct such a graph. It is proved that two isoclinic non-abelian groups have isomorphic graphs under special conditions.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901Total domination in $K_r$-covered graphs675680436ENA. P. KazemiUniversity of Mohaghegh ArdabiliJournal Article20110426The inflation $G_{I}$ of a graph $G$ with $n(G)$ vertices and $m(G)$ edges is obtained from $G$ by replacing every vertex of degree $d$ of $G$ by a clique, which is isomorph to the complete graph $K_{d}$, and each edge $(x_{i},x_{j})$ of $G$ is replaced by an edge $(u,v)$ in such a way that $uin X_{i}$, $vin X_{j}$, and two different edges of $G$ are replaced by non-adjacent edges of $G_{I}$. The total domination number $gamma _{t}(G)$ of a graph $G$ is the minimum cardinality of a total dominating set, which is a set of<br />vertices such that every vertex of $G$ is adjacent to one vertex of it. A graph is $K_{r}$-covered if every vertex of it is contained in a clique $K_{r}$. Cockayne et al. in [Total domination in $K_{r}$-covered graphs, Ars Combin. textbf{71} (2004) 289-303]<br />conjectured that the total domination number of every $K_{r}$-covered graph with $n$ vertices and no $K_{r}$-component is at most $frac{2n}{r+1}.$ This conjecture has been proved only for $3leq rleq 6$. In this paper, we prove this conjecture for a big family of $K_{r}$-covered graphs.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901On reverse degree distance of unicyclic graphs681706437ENZ. DuNortheast Normal UniversityB. ZhouNortheast Normal UniversityJournal Article20111025The reverse degree distance of a connected graph $G$ is defined <br />in discrete mathematical chemistry as <br />[ <br />r (G)=2(n-1)md-sum_{uin V(G)}d_G(u)D_G(u), <br />] <br />where $n$, $m$ and $d$ are the number of vertices, the number of <br />edges and the diameter of $G$, respectively, $d_G(u)$ is the degree of vertex $u$, <br /> $D_G(u)$ is the sum of distance between vertex $u$ and all other vertices of $G$, and $V(G)$ is the vertex set of $G$. <br />We <br />determine the unicyclic graphs of given girth, number of pendant <br />vertices and maximum degree, respectively, with maximum reverse <br />degree distances. We also determine the <br />unicyclic graphs of given number of vertices, girth and diameter <br />with minimum degree distance.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901A new block by block method for solving two-dimensional linear
and nonlinear Volterra integral equations of the first and second kinds707724438ENR. KataniPhD studentS. ShahmoradsupervisorJournal Article20111201In this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear Volterra integral equations of the first and second kinds, which avoids from using starting values. An existence and uniqueness theorem is proved and convergence is<br />verified by using an appropriate variety of the Gronwall inequality. Application of the method is demonstrated for solving the useful telegraph equation.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901On p-semilinear transformations725742439ENY. MaNortheast Normal UniversityL. ChenDepartment of Mathematics, Northeast Normal UniversityJournal Article20111215In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive <br />characteristic $p$, discuss initially the elementary properties of <br />$p$-semilinear transformations, make use of it to give some <br />characterizations of linear algebras over a field ${bf F}$ of <br />positive characteristic $p$. Moreover, we find a one-to-one <br />correspondence between $p$-semilinear transformations and matrices, and we prove a result which is closely related to the well-known Jordan-Chevalley decomposition of an element.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901Solutions of variational inequalities on fixed points of nonexpansive mappings743764440ENH. PiriDepartment of Mathematics,
University of Bonab, Bonab 5551761167, IranJournal Article20120101n this paper , we propose a generalized iterative method for<br />finding a common element of the set of fixed points of a single<br />nonexpannsive mapping and the set of solutions of two variational<br />inequalities with inverse strongly monotone mappings and strictly<br />pseudo-contractive of Browder-Petryshyn type mapping. Our results<br />improve and extend the results announced by many others.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901Strong convergence theorem for finite family of
m-accretive operators in Banach spaces765777441ENN. GurudwanS.O.S. in Mathematics,
Pt. Ravishankar Shukla University.B. K.SharmaPt. Ravishankar Shukla University, RaipurJournal Article20120412The purpose of this paper is to propose a composite<br />iterative scheme for approximating a common solution for a finite<br />family of m-accretive operators in a strictly convex Banach space<br />having a uniformly Gateaux differentiable norm. As a consequence,<br />the strong convergence of the scheme for a common fixed point of<br />a finite family of pseudocontractive mappings is also obtained.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901More about measures and Jacobians of singular random matrices779788442ENJ. A.Diaz-GarciaUniversidad Autonoma Agraria Antonio NarroJournal Article20120220In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.