Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
4
2013
09
01
Fiber bundles and Lie algebras of top spaces
589
598
EN
M. R.
Farhangdoost
Department of Mathematics, College of Sciences, Shiraz University, P.O.Box 71457-44776, Shiraz, IRAN.
farhang@shirazu.ac.ir
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.
Lie group,top space,fiber bundle,Lie algebra
http://bims.iranjournals.ir/article_433.html
http://bims.iranjournals.ir/article_433_60e83e555afcee71f46a98403fdecd4b.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
4
2013
09
01
Hybrid steepest-descent method with sequential and functional errors in Banach space
599
617
EN
S.
Saeidi
University of Kurdistan
shahram_saeidi@yahoo.com
H.
Haydari
University of Kurdistan
hussein.haydari@yahoo.com
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.
fixed point,hybrid steepest-descent method,Nonexpansive mapping,variational inequality
http://bims.iranjournals.ir/article_230.html
http://bims.iranjournals.ir/article_230_c22700f2141e4eab510b5c02df17748f.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
4
2013
09
01
Complement of Special Chordal Graphs and Vertex Decomposability
619
625
EN
M.
Alizadeh
Assistant Professor at University of Tehran
malizadeh@khayam.ut.ac.ir
A.
Goodarzi
MSc Student at University of Tehran
af.goodarzi@gmail.com
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.
Cohen-Macaulay,sequentially Cohen-Macaulay,shellable complex,vertex decomposable,chordal graph
http://bims.iranjournals.ir/article_256.html
http://bims.iranjournals.ir/article_256_ff24e61eaa775eccea5724d832798ec8.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
4
2013
09
01
On vertex balance index set of some graphs
627
634
EN
Ch.
Adiga
University of Mysore
c_adiga@hotmail.com
C.
K.
Subbaraya
Adichunchanagiri Institute of Technology
subrayack@gmail.com
A.
S.
Shrikanth
University of Mysore
shrikanth.ait@gmail.com
M.
A.
Sriraj
University of Mysore
srinivasa_sriraj@yahoo.co.in
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 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.
Vertex labeling,Vertex-friendly,Vertex balance index set
http://bims.iranjournals.ir/article_434.html
http://bims.iranjournals.ir/article_434_8a847dac9d4c818761d9e8df959e4b3a.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
4
2013
09
01
Jordan derivation on trivial extension
635
645
EN
H.
Ghahramani
University of Kurdistan
h.ghahramani@uok.ac.ir
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.
Jordan derivation,derivation,trivial extension
http://bims.iranjournals.ir/article_251.html
http://bims.iranjournals.ir/article_251_562a2d6f67396e816d3d6bebc0ecb30e.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
4
2013
09
01
An Alexandroff topology on graphs
647
662
EN
S.
M.
Jafarian Amiri
Zanjan University
sm_jafarian@znu.ac.ir
A.
Jafarzadeh
Ferdowsi University of Mashhad
abbas.jafarzadeh@gmail.com
H.
Khatibzadeh
Zanjan University, Zanjan
hkhatibzadeh@znu.ac.ir
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.
Locally finite graph,Alexandroff topology,finite topological spaces
http://bims.iranjournals.ir/article_266.html
http://bims.iranjournals.ir/article_266_e1ff26c6f7b350afcde8bd3ec3654132.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
4
2013
09
01
Relative n-th non-commuting graphs of finite groups
663
674
EN
A.
Erfanian
Ferdowsi University of Mashhad
erfanian@math.um.ac.ir
B.
Tolue
Ferdowsi University of Mashhad
b.tolue@gmail.com
Suppose $n$ 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 $xy^{n}eq y^{n}x$ or $x^{n}yeq yx^{n}$. 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.
Isoclinism,n-th non-commuting graph,n-th commutativity degree
http://bims.iranjournals.ir/article_435.html
http://bims.iranjournals.ir/article_435_b9212cae8b75cb41a3069a14c760e131.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
4
2013
09
01
Total domination in $K_r$-covered graphs
675
680
EN
A.
P. Kazemi
University of Mohaghegh Ardabili
adelpkazemi@yahoo.com
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 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 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) 289-303]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.
Total domination number,inflated graph,$K_r$-covered graph
http://bims.iranjournals.ir/article_436.html
http://bims.iranjournals.ir/article_436_675fe49c341f8166308a56c5462b2fc2.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
4
2013
09
01
On reverse degree distance of unicyclic graphs
681
706
EN
Z.
Du
Northeast Normal University
zhibindu@126.com
B.
Zhou
Northeast Normal University
zhoubo@scnu.edu.cn
The reverse degree distance of a connected graph $G$ is defined in discrete mathematical chemistry as [ r (G)=2(n-1)md-sum_{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.
reverse degree distance,diameter,pendant vertices,maximum degree,unicyclic graphs
http://bims.iranjournals.ir/article_437.html
http://bims.iranjournals.ir/article_437_7a694edd090f25ab56c01b6e0653732b.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
4
2013
09
01
A new block by block method for solving two-dimensional linear
and nonlinear Volterra integral equations of the first and second kinds
707
724
EN
R.
Katani
PhD student
katani@tabrizu.ac.ir
S.
Shahmorad
supervisor
shahmorad@tabrizu.ac.ir
In 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 isverified by using an appropriate variety of the Gronwall inequality. Application of the method is demonstrated for solving the useful telegraph equation.
Two-dimensional Volterra integral equations,Romberg quadrature rule,Block by block method,Gronwall inequality
http://bims.iranjournals.ir/article_438.html
http://bims.iranjournals.ir/article_438_91365a3b3d0f8f725e928d5050269c79.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
4
2013
09
01
On p-semilinear transformations
725
742
EN
Y.
Ma
Northeast Normal University
may703@nenu.edu.cn
L.
Chen
Department of Mathematics, Northeast Normal University
chenly640@nenu.edu.cn
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 one-to-one 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.
$p$-semilinear transformation,the matrix,Rank-nullity
theorem,Jordan-Chevalley decomposition
http://bims.iranjournals.ir/article_439.html
http://bims.iranjournals.ir/article_439_a072c328c221cd2140b9c1991f0c1313.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
4
2013
09
01
Solutions of variational inequalities on fixed points of nonexpansive mappings
743
764
EN
H.
Piri
Department of Mathematics,
University of Bonab, Bonab 5551761167, Iran
hossein_piri1979@yahoo.com
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 strictlypseudo-contractive of Browder-Petryshyn type mapping. Our resultsimprove and extend the results announced by many others.
fixed point,strongly monotone,$lambda$- strictly pseudo-contractive,Strongconvergence,Nonexpansive mapping
http://bims.iranjournals.ir/article_440.html
http://bims.iranjournals.ir/article_440_17bed45c0dac6526de73e5e4fdbb8abc.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
4
2013
09
01
Strong convergence theorem for finite family of
m-accretive operators in Banach spaces
765
777
EN
N.
Gurudwan
S.O.S. in Mathematics,
Pt. Ravishankar Shukla University.
niyati.kuhu@gmail.com
B.
K.
Sharma
Pt. Ravishankar Shukla University, Raipur
sharmabk07@gmail.com
The purpose of this paper is to propose a compositeiterative scheme for approximating a common solution for a finitefamily of m-accretive 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.
m-accretive operators,strictly convex Banach space,uniformly Gateaux differentiable norm,composite iteration,resolvent
http://bims.iranjournals.ir/article_441.html
http://bims.iranjournals.ir/article_441_71f5511fa84e314d6e95a38b64d6b0f1.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
4
2013
09
01
More about measures and Jacobians of singular random matrices
779
788
EN
J.
A.
Diaz-Garcia
Universidad Autonoma Agraria Antonio Narro
jadiaz@uaaan.mx
In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.
Singular random matrices,Jacobian of transformation,Hausdorff measure, Lebesgue measure, multiplicity
http://bims.iranjournals.ir/article_442.html
http://bims.iranjournals.ir/article_442_82fada08780c2db3a8633e602662b532.pdf