eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-09-01
39
4
589
598
433
Fiber bundles and Lie algebras of top spaces
M. R. Farhangdoost
farhang@shirazu.ac.ir
1
Department of Mathematics, College of Sciences, Shiraz University, P.O.Box 71457-44776, Shiraz, IRAN.
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.
http://bims.iranjournals.ir/article_433_60e83e555afcee71f46a98403fdecd4b.pdf
Lie group
top space
fiber bundle
Lie algebra
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-09-01
39
4
599
617
230
Hybrid steepest-descent method with sequential and functional errors in Banach space
S. Saeidi
shahram_saeidi@yahoo.com
1
H. Haydari
hussein.haydari@yahoo.com
2
University of Kurdistan
University of Kurdistan
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.
http://bims.iranjournals.ir/article_230_c22700f2141e4eab510b5c02df17748f.pdf
fixed point
hybrid steepest-descent method
Nonexpansive mapping
variational inequality
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-09-01
39
4
619
625
256
Complement of Special Chordal Graphs and Vertex Decomposability
M. Alizadeh
malizadeh@khayam.ut.ac.ir
1
A. Goodarzi
af.goodarzi@gmail.com
2
Assistant Professor at University of Tehran
MSc Student at University of Tehran
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.
http://bims.iranjournals.ir/article_256_ff24e61eaa775eccea5724d832798ec8.pdf
Cohen-Macaulay
sequentially Cohen-Macaulay
shellable complex
vertex decomposable
chordal graph
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-09-01
39
4
627
634
434
On vertex balance index set of some graphs
Ch. Adiga
c_adiga@hotmail.com
1
C. Subbaraya
subrayack@gmail.com
2
A. Shrikanth
shrikanth.ait@gmail.com
3
M. Sriraj
srinivasa_sriraj@yahoo.co.in
4
University of Mysore
Adichunchanagiri Institute of Technology
University of Mysore
University of Mysore
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.
http://bims.iranjournals.ir/article_434_8a847dac9d4c818761d9e8df959e4b3a.pdf
Vertex labeling
Vertex-friendly
Vertex balance index set
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-09-01
39
4
635
645
251
Jordan derivation on trivial extension
H. Ghahramani
h.ghahramani@uok.ac.ir
1
University of Kurdistan
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.
http://bims.iranjournals.ir/article_251_562a2d6f67396e816d3d6bebc0ecb30e.pdf
Jordan derivation
derivation
trivial extension
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-09-01
39
4
647
662
266
An Alexandroff topology on graphs
S. Jafarian Amiri
sm_jafarian@znu.ac.ir
1
A. Jafarzadeh
abbas.jafarzadeh@gmail.com
2
H. Khatibzadeh
hkhatibzadeh@znu.ac.ir
3
Zanjan University
Ferdowsi University of Mashhad
Zanjan University, Zanjan
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.
http://bims.iranjournals.ir/article_266_e1ff26c6f7b350afcde8bd3ec3654132.pdf
Locally finite graph
Alexandroff topology
finite topological spaces
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-09-01
39
4
663
674
435
Relative n-th non-commuting graphs of finite groups
A. Erfanian
erfanian@math.um.ac.ir
1
B. Tolue
b.tolue@gmail.com
2
Ferdowsi University of Mashhad
Ferdowsi University of Mashhad
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.
http://bims.iranjournals.ir/article_435_b9212cae8b75cb41a3069a14c760e131.pdf
Isoclinism
n-th non-commuting graph
n-th commutativity degree
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-09-01
39
4
675
680
436
Total domination in $K_r$-covered graphs
A. P. Kazemi
adelpkazemi@yahoo.com
1
University of Mohaghegh Ardabili
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.
http://bims.iranjournals.ir/article_436_675fe49c341f8166308a56c5462b2fc2.pdf
Total domination number
inflated graph
$K_r$-covered graph
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-09-01
39
4
681
706
437
On reverse degree distance of unicyclic graphs
Z. Du
zhibindu@126.com
1
B. Zhou
zhoubo@scnu.edu.cn
2
Northeast Normal University
Northeast Normal University
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.
http://bims.iranjournals.ir/article_437_7a694edd090f25ab56c01b6e0653732b.pdf
reverse degree distance
diameter
pendant vertices
maximum degree
unicyclic graphs
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-09-01
39
4
707
724
438
A new block by block method for solving two-dimensional linear
and nonlinear Volterra integral equations of the first and second kinds
R. Katani
katani@tabrizu.ac.ir
1
S. Shahmorad
shahmorad@tabrizu.ac.ir
2
PhD student
supervisor
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.
http://bims.iranjournals.ir/article_438_91365a3b3d0f8f725e928d5050269c79.pdf
Two-dimensional Volterra integral equations
Romberg quadrature rule
Block by block method
Gronwall inequality
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-09-01
39
4
725
742
439
On p-semilinear transformations
Y. Ma
may703@nenu.edu.cn
1
L. Chen
chenly640@nenu.edu.cn
2
Northeast Normal University
Department of Mathematics, Northeast Normal University
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.
http://bims.iranjournals.ir/article_439_a072c328c221cd2140b9c1991f0c1313.pdf
$p$-semilinear transformation
the matrix
Rank-nullity
theorem
Jordan-Chevalley decomposition
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-09-01
39
4
743
764
440
Solutions of variational inequalities on fixed points of nonexpansive mappings
H. Piri
hossein_piri1979@yahoo.com
1
Department of Mathematics, University of Bonab, Bonab 5551761167, Iran
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.
http://bims.iranjournals.ir/article_440_17bed45c0dac6526de73e5e4fdbb8abc.pdf
fixed point
strongly monotone
$lambda$- strictly pseudo-contractive
Strongconvergence
Nonexpansive mapping
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-09-01
39
4
765
777
441
Strong convergence theorem for finite family of
m-accretive operators in Banach spaces
N. Gurudwan
niyati.kuhu@gmail.com
1
B. Sharma
sharmabk07@gmail.com
2
S.O.S. in Mathematics, Pt. Ravishankar Shukla University.
Pt. Ravishankar Shukla University, Raipur
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.
http://bims.iranjournals.ir/article_441_71f5511fa84e314d6e95a38b64d6b0f1.pdf
m-accretive operators
strictly convex Banach space
uniformly Gateaux differentiable norm
composite iteration
resolvent
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2013-09-01
39
4
779
788
442
More about measures and Jacobians of singular random matrices
J. Diaz-Garcia
jadiaz@uaaan.mx
1
Universidad Autonoma Agraria Antonio Narro
In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.
http://bims.iranjournals.ir/article_442_82fada08780c2db3a8633e602662b532.pdf
Singular random matrices
Jacobian of transformation
Hausdorff measure, Lebesgue measure, multiplicity