2013
39
4
4
0
Fiber bundles and Lie algebras of top spaces
2
2
In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.
1

589
598


M. R.
Farhangdoost
Department of Mathematics, College of Sciences, Shiraz University, P.O.Box 7145744776, Shiraz, IRAN.
Department of Mathematics, College of Sciences,
Iran
farhang@shirazu.ac.ir
Lie group
top space
fiber bundle
Lie algebra
Hybrid steepestdescent method with sequential and functional errors in Banach space
2
2
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 steepestdescent 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.
1

599
617


S.
Saeidi
University of Kurdistan
University of Kurdistan
Iran
shahram_saeidi@yahoo.com


H.
Haydari
University of Kurdistan
University of Kurdistan
Iran
hussein.haydari@yahoo.com
fixed point
hybrid steepestdescent method
Nonexpansive mapping
variational inequality
Complement of Special Chordal Graphs and Vertex Decomposability
2
2
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 CohenMacaulay.
1

619
625


M.
Alizadeh
Assistant Professor at University of Tehran
Assistant Professor at University of Tehran
Iran
malizadeh@khayam.ut.ac.ir


A.
Goodarzi
MSc Student at University of Tehran
MSc Student at University of Tehran
Iran
af.goodarzi@gmail.com
CohenMacaulay
sequentially CohenMacaulay
shellable complex
vertex decomposable
chordal graph
On vertex balance index set of some graphs
2
2
Let 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 Vertexfriendly if  v(0) − v(1) ≤ 1. The vertex balance index set is defined by { ef (0) − ef (1)  : f is vertexfriendly}. In this paper we completely determine the vertex balance index set of Kn, Km,n, Cn×P2 and Complete binary tree.
1

627
634


Ch.
Adiga
University of Mysore
University of Mysore
India
c_adiga@hotmail.com


C.
Subbaraya
Adichunchanagiri Institute of Technology
Adichunchanagiri Institute of Technology
India
subrayack@gmail.com


A.
Shrikanth
University of Mysore
University of Mysore
India
shrikanth.ait@gmail.com


M.
Sriraj
University of Mysore
University of Mysore
India
srinivasa_sriraj@yahoo.co.in
Vertex labeling
Vertexfriendly
Vertex balance index set
Jordan derivation on trivial extension
2
2
Let A be a unital Ralgebra and M be a unital Abimodule. 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.
1

635
645


H.
Ghahramani
University of Kurdistan
University of Kurdistan
Iran
h.ghahramani@uok.ac.ir
Jordan derivation
derivation
trivial extension
An Alexandroff topology on graphs
2
2
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.
1

647
662


S.
Jafarian Amiri
Zanjan University
Zanjan University
Iran
sm_jafarian@znu.ac.ir


A.
Jafarzadeh
Ferdowsi University of Mashhad
Ferdowsi University of Mashhad
Iran
abbas.jafarzadeh@gmail.com


H.
Khatibzadeh
Zanjan University, Zanjan
Zanjan University, Zanjan
Iran
hkhatibzadeh@znu.ac.ir
Locally finite graph
Alexandroff topology
finite topological spaces
Relative nth noncommuting graphs of finite groups
2
2
Suppose $n$ is a fixed positive integer. We introduce the relative nth noncommuting graph $Gamma^{n} _{H,G}$, associated to the nonabelian 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 $xy^{n}eq y^{n}x$ or $x^{n}yeq yx^{n}$. In fact, the relative nth commutativity degree, $P_{n}(H,G)$ the probability that nth power of an element of the subgroup $H$ commutes with another random element of the group $G$ and the noncommuting graph were the keys to construct such a graph. It is proved that two isoclinic nonabelian groups have isomorphic graphs under special conditions.
1

663
674


A.
Erfanian
Ferdowsi University of Mashhad
Ferdowsi University of Mashhad
Iran
erfanian@math.um.ac.ir


B.
Tolue
Ferdowsi University of Mashhad
Ferdowsi University of Mashhad
Iran
b.tolue@gmail.com
Isoclinism
nth noncommuting graph
nth commutativity degree
Total domination in $K_r$covered graphs
2
2
The 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 nonadjacent 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 ofvertices 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) 289303]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.
1

675
680


A.
P. Kazemi
University of Mohaghegh Ardabili
University of Mohaghegh Ardabili
Iran
adelpkazemi@yahoo.com
Total domination number
inflated graph
$K_r$covered graph
On reverse degree distance of unicyclic graphs
2
2
The reverse degree distance of a connected graph $G$ is defined in discrete mathematical chemistry as [ r (G)=2(n1)mdsum_{uin V(G)}d_G(u)D_G(u), ] where $n$, $m$ and $d$ are the number of vertices, the number of edges and the diameter of $G$, respectively, $d_G(u)$ is the degree of vertex $u$, $D_G(u)$ is the sum of distance between vertex $u$ and all other vertices of $G$, and $V(G)$ is the vertex set of $G$. We determine the unicyclic graphs of given girth, number of pendant vertices and maximum degree, respectively, with maximum reverse degree distances. We also determine the unicyclic graphs of given number of vertices, girth and diameter with minimum degree distance.
1

681
706


Z.
Du
Northeast Normal University
Northeast Normal University
China, R. O. C.
zhibindu@126.com


B.
Zhou
Northeast Normal University
Northeast Normal University
China (P. R. C.)
zhoubo@scnu.edu.cn
reverse degree distance
diameter
pendant vertices
maximum degree
unicyclic graphs
A new block by block method for solving twodimensional linear
and nonlinear Volterra integral equations of the first and second kinds
2
2
In this paper, we propose a new method for the numerical solution of twodimensional 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 isverified by using an appropriate variety of the Gronwall inequality. Application of the method is demonstrated for solving the useful telegraph equation.
1

707
724


R.
Katani
PhD student
PhD student
Iran
katani@tabrizu.ac.ir


S.
Shahmorad
supervisor
supervisor
Iran
shahmorad@tabrizu.ac.ir
Twodimensional Volterra integral equations
Romberg quadrature rule
Block by block method
Gronwall inequality
On psemilinear transformations
2
2
In this paper, we introduce $p$semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a onetoone correspondence between $p$semilinear transformations and matrices, and we prove a result which is closely related to the wellknown JordanChevalley decomposition of an element.
1

725
742


Y.
Ma
Northeast Normal University
Northeast Normal University
China, R. O. C.
may703@nenu.edu.cn


L.
Chen
Department of Mathematics, Northeast Normal University
Department of Mathematics, Northeast Normal
China, R. O. C.
chenly640@nenu.edu.cn
$p$semilinear transformation
the matrix
Ranknullity theorem
JordanChevalley decomposition
Solutions of variational inequalities on fixed points of nonexpansive mappings
2
2
n this paper , we propose a generalized iterative method forfinding a common element of the set of fixed points of a singlenonexpannsive mapping and the set of solutions of two variationalinequalities with inverse strongly monotone mappings and strictlypseudocontractive of BrowderPetryshyn type mapping. Our resultsimprove and extend the results announced by many others.
1

743
764


H.
Piri
Department of Mathematics,
University of Bonab, Bonab 5551761167, Iran
Department of Mathematics,
University of
Iran
hossein_piri1979@yahoo.com
fixed point
strongly monotone
$lambda$ strictly pseudocontractive
Strongconvergence
Nonexpansive mapping
Strong convergence theorem for finite family of
maccretive operators in Banach spaces
2
2
The purpose of this paper is to propose a compositeiterative scheme for approximating a common solution for a finitefamily of maccretive operators in a strictly convex Banach spacehaving a uniformly Gateaux differentiable norm. As a consequence,the strong convergence of the scheme for a common fixed point ofa finite family of pseudocontractive mappings is also obtained.
1

765
777


N.
Gurudwan
S.O.S. in Mathematics,
Pt. Ravishankar Shukla University.
S.O.S. in Mathematics,
Pt. Ravishankar Shukla
India
niyati.kuhu@gmail.com


B.
Sharma
Pt. Ravishankar Shukla University, Raipur
Pt. Ravishankar Shukla University, Raipur
India
sharmabk07@gmail.com
maccretive operators
strictly convex Banach space
uniformly Gateaux differentiable norm
composite iteration
resolvent
More about measures and Jacobians of singular random matrices
2
2
In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.
1

779
788


J.
DiazGarcia
Universidad Autonoma Agraria Antonio Narro
Universidad Autonoma Agraria Antonio Narro
Mexico
jadiaz@uaaan.mx
Singular random matrices
Jacobian of transformation
Hausdorff measure, Lebesgue measure, multiplicity