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 <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.
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, $T:Xto X$ <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.
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 <br />contains $d$-trees and show that their complement are vertex <br />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 <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.
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 <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.
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 $xy^{n}<br />eq y^{n}x$ 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.
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 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.
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 <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.
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 is<br />verified 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 <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.
$p$-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 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.
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 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.
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