2016
42
3
3
0
Total perfect codes, OOirredundant and total subdivision in graphs
2
2
Let $G=(V(G),E(G))$ be a graph, $gamma_t(G)$. Let $ooir(G)$ be the total domination and OOirredundance number of $G$, respectively. A total dominating set $S$ of $G$ is called a $textit{total perfect code}$ if every vertex in $V(G)$ is adjacent to exactly one vertex of $S$. In this paper, we show that if $G$ has a total perfect code, then $gamma_t(G)=ooir(G)$. As a consequence, we determine the value of $ooir(G)$ for some classes of graphs.
1

499
506


H.
Hosseinzadeh
Department of Mathematics, Alzahra University, P.O. Box 19834, Tehran, Iran.
Department of Mathematics, Alzahra
Iran
hamideh.hosseinzadeh@gmail.com


N.
Soltankhah
Department of Mathematics, Alzahra University,
P.O. Box 19834, Tehran, Iran.
Department of Mathematics, Alzahra
Iran
soltan@alzahra.ac.ir
Total domination number
OO irredundance number
total subdivision number
The theory of matrixvalued multiresolution analysis frames
2
2
1

507
519


P.
Zhao
School of Science, Beijing Jiaotong University,
Beijing, 100044, China.
School of Science, Beijing Jiaotong
China (P. R. C.)
pingzhao@bjtu.edu.cn


C.
Zhao
Faculty of Mathematics Science , Tianjin normal
University, Tianjin, 300074, China
Faculty of Mathematics Science , Tianjin
China (P. R. C.)
yczhaochun@163.com
Polynomially bounded solutions of the Loewner differential equation in several complex variables
2
2
We determine the form of polynomially bounded solutions to the Loewner differential equation that is satisfied by univalent subordination chains of the form $f(z,t)=e^{int_0^t A(tau){rm d}tau}z+cdots$, where $A:[0,infty]rightarrow L(mathbb{C}^n,mathbb{C}^n)$ is a locally Lebesgue integrable mapping and satisfying the condition $$sup_{sgeq0}int_0^inftyleftexpleft{int_s^t [A(tau)2m(A(tau))I_n]rm {d}tauright}right{rm d}t<infty,$$ and $m(A(t))>0$ for $tgeq0$, where $m(A)=min{mathfrak{Re}leftlangle A(z),zrightrangle:z=1}$. We also give sufficient conditions for $g(z,t)=M(f(z,t))$ to be polynomially bounded, where $f(z,t)$ is an $A(t)$normalized polynomially bounded Loewner chain solution to the Loewner differential equation and $M$ is an entire function. On the other hand, we show that all $A(t)$normalized polynomially bounded solutions to the Loewner differential equation are Loewner chains.
1

521
537


A.
Ebadian
Department of Mathematics, Payame Noor University, P.O. Box 193953697, Tehran, Iran.
Department of Mathematics, Payame Noor University,
Iran
a.ebadian@urmia.ac.ir


S.
Rahrovi
Department of Mathematics, Faculty of Basic Science, University of Bonab, P.O. Box 5551761167, Bonab, Iran.
Department of Mathematics, Faculty of Basic
Iran
sarahrovi@gmail.com


S.
Shams
Department of Mathematics, Urmia University, Urmia,
Iran.
Department of Mathematics, Urmia
Iran
sa40shams@yahoo.com


J.
Sokol
Department of Mathematics, Rzesz'ow University of Technology, Poland.
Department of Mathematics, Rzesz'ow
Poland
jsokol@prz.edu.pl
Biholomorphic mapping
Loewner differential equation
polynomially bounded
subordination chain
parametric representation.
$k$power centralizing and $k$power skewcentralizing maps on triangular rings
2
2
Let $mathcal A$ and $mathcal B$ be unital rings, and $mathcal M$ be an $(mathcal A, mathcal B)$bimodule, which is faithful as a left $mathcal A$module and also as a right $mathcal B$module. Let ${mathcal U}=mbox{rm Tri}(mathcal A, mathcal M, mathcal B)$ be the triangular ring and ${mathcal Z}({mathcal U})$ its center. Assume that $f:{mathcal U}rightarrow{mathcal U}$ is a map satisfying $f(x+y)f(x)f(y)in{mathcal Z}({mathcal U})$ for all $x, yin{mathcal U}$ and $k$ is a positive integer. It is shown that, under some mild conditions, the following statements are equivalent: (1) $[f(x),x^k]in{mathcal Z}({mathcal U})$ for all $xin{mathcal U}$; (2) $[f(x),x^k]=0$ for all $xin{mathcal U}$; (3) $[f(x),x]=0$ for all $xin{mathcal U}$; (4) there exist a central element $zin{mathcal Z}({mathcal U})$ and an additive modulo ${mathcal Z}({mathcal U})$ map $h:{mathcal U}rightarrow{mathcal Z}({mathcal U})$ such that $f(x)=zx+h(x)$ for all $xin{mathcal U}$. It is also shown that there is no nonzero additive $k$skewcentralizing maps on triangular rings.
1

539
554


X. F.
Qi
Department of Mathematics, Shanxi University, Taiyuan 030006, P. R. China.
Department of Mathematics, Shanxi
China (P. R. C.)
xiaofeiqisxu@aliyun.com
Triangular rings
centralizing maps
$k$skewcentralizing maps
nest algebras
On radical formula and Prufer domains
2
2
In this paper we characterize the radical of an arbitrary submodule $N$ of a finitely generated free module $F$ over a commutatitve ring $R$ with identity. Also we study submodules of $F$ which satisfy the radical formula. Finally we derive necessary and sufficient conditions for $R$ to be a Pr$ddot{mbox{u}}$fer domain, in terms of the radical of a cyclic submodule in $Rbigoplus R$.
1

555
563


R.
Nekooei
Department of Pure
Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar
University
of Kerman, P.O. Box 76169133, Kerman, Iran.
Department of Pure
Mathematics,
Iran
rnekooei@uk.ac.ir


F.
Mirzaei
Department of Pure
Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar
University
of Kerman, P.O. Box 76169133, Kerman, Iran.
Department of Pure
Mathematics,
Iran
mirzaee0269@yahoo.com
Prime submodules
Radical of a submodule
Radical formula
Pr$ddot{mbox{u}}$fer domains
Dedekind domains
On cohomogeneity one nonsimply connected 7manifolds of constant positive curvature
2
2
In this paper, we give a classification of non simply connected seven dimensional Reimannian manifolds of constant positive curvature which admit irreducible cohomogeneityone actions. We characterize the acting groups and describe the orbits. The first and second homotopy groups of the orbits have been presented as well.
1

565
584


M.
Zarei
Department of Pure Mathematics,
Faculty of Mathematical Sciences,
Tarbiat Modares University,
P.O. Box 14115134,
Tehran, Iran.
Department of Pure Mathematics,
Faculty
Iran
masoumeh.zarei@modares.ac.ir


S.M.B.
Kashani
Tarbiat Modares University
Tarbiat Modares University
Iran
kashanism@yahoo.com


H.
Abedi
Mathematics Group, School of Sciences BuAli Sina University, Hamedan, Iran.
Mathematics Group, School of Sciences
Iran
h.abedi@basu.ac.ir
Positively curved manifold
irreducible representation
cohomogeneity one action
Complete characterization of the MordellWeil group of some families of elliptic curves
2
2
The MordellWeil theorem states that the group of rational points on an elliptic curve over the rational numbers is a finitely generated abelian group. In our previous paper, H. Daghigh, and S. Didari, On the elliptic curves of the form $ y^2=x^33px$, Bull. Iranian Math. Soc. 40 (2014), no. 5, 11191133., using Selmer groups, we have shown that for a prime $p$ the rank of elliptic curve $y^2=x^33px$ is at most two. In this paper we go further, and using height function, we will determine the MordellWeil group of a family of elliptic curves of the form $y^2=x^33nx$, and give a set of its generators under certain conditions. We will introduce an infinite family of elliptic curves with rank at least two. The full MordellWeil group and the generators of a family (which is expected to be infinite under the assumption of a standard conjecture) of elliptic curves with exact rank two will be described.
1

585
594


H.
Daghigh
Faculty of Mathematical Sciences, University of Kashan, P.O. Box 8731751167, Kashan, Iran.
Faculty of Mathematical Sciences, University
Iran
hassan@kashanu.ac.ir


S.
Didari
Faculty of Mathematical Sciences, University of Kashan, P.O. Box 8731751167, Kashan, Iran.
Faculty of Mathematical Sciences, University
Iran
somayeh_didari@yahoo.com
Elliptic Curve
MordellWeil Group
Generators
Height Function
Involutiveness of linear combinations of a quadratic or tripotent matrix and an arbitrary matrix
2
2
In this article, we characterize the involutiveness of the linear combination of the forma1A1 +a2A2 when a1, a2 are nonzero complex numbers, A1 is a quadratic or tripotent matrix,and A2 is arbitrary, under certain properties imposed on A1 and A2.
1

595
610


X.
Liu
College of Science, Guangxi
University for Nationalities, Nanning 530006, P. R. China.
College of Science, Guangxi
Un
China (P. R. C.)
xiaojiliu72@126.com


J.
Benitez
Departamento de Matematica Aplicada, Instituto de Matematica Multidisciplinar,
Universidad Politecnica de Valencia, Valencia 46022, Spain.
Departamento de Matematica Aplicada,
Spain
jbenitez@mat.upv.es


M.
Zhang
College of Science, Guangxi
University for Nationalities, Nanning 530006, P. R. China.
College of Science, Guangxi
U
China (P. R. C.)
zhangmiao198658@163.com
Quadratic matrix
involutive matrix
linear combination
Infinitely many solutions for a binonlocal equation with signchanging weight functions
2
2
In this paper, we investigate the existence of infinitely many solutions for a binonlocal equation with signchanging weight functions. We use some natural constraints and the LjusternikSchnirelman critical point theory on C1manifolds, to prove our main results.
1

611
626


Y.
Jalilian
Department of Mathematics, Razi University,
Kermanshah, Iran.
Department of Mathematics, Razi
Iran
y.jalilian@razi.ac.ir
Infinitely many solutions
Nehari manifold
signchanging weight function
Binonlocal equation
Tdual Rickart modules
2
2
We introduce the notions of Tdual Rickart and strongly Tdual Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that every free (resp. finitely generated free) $R$module is Tdual Rickart if and only if $overline{Z}^2(R)$ is a direct summand of $R$ and End$(overline{Z}^2(R))$ is a semisimple (resp. regular) ring. It is shown that, while a direct summand of a (strongly) Tdual Rickart module inherits the property, direct sums of Tdual Rickart modules do not. Moreover, when a direct sum of Tdual Rickart modules is Tdual Rickart, is included. Examplesillustrating the results are presented.
1

611
642


S.
Ebrahimi Atani
Department of Mathematics, University
of Guilan, P.O. Box 1914, Rasht, Iran.
Department of Mathematics, University
of
Iran
ebrahimi@guilan.ac.ir


M.
Khoramdel
Department of
Mathematics, University
of Guilan, P.O. Box 1914, Rasht, Iran.
Department of
Mathematics, University&lr
Iran
mehdikhoramdel@gmail.com


S.
Dolati Pish Hesari
Department of Mathematics, University
of Guilan, P.O. Box 1914, Rasht, Iran.
Department of Mathematics, University
&l
Iran
saboura_dolati@yahoo.com
Dual Rickart modules
tlifting modules
tdual Baer modules
Tdual Rickart modules
strongly Tdual Rickart modules
The existence of global attractor for a CahnHilliard/AllenCahn equation
2
2
In this paper, we consider a CahnHillard/AllenCahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in H^k(0<=k<5) space of this equation, and it attracts any bounded subset of H^k(omega) in the H^knorm.
1

643
658


H.
Tang
Department of Mathematics, Jilin University, Changchun 130012,
P.R. China
and
School of Science, Changchun University, Changchun 130022, P.R. China.
Department of Mathematics, Jilin
China (P. R. C.)
tangtangth83@163.com


C.
Liu
Department of Mathematics, Jilin University, Changchun 130012,
P.R. China.
Department of Mathematics, Jilin
China, R. O. C.
liucc@jlu.edu.cn


Z.
Zhao
Department of Mathematics, Changchun Normal University, Changchun
130032, P.R. China
and
Academy of Mathematics and Systems Science,
Chinese Academy of Sciences, Beijing, 100190,
Department of Mathematics, Changchun
China (P. R. C.)
jczzx10@163.com
CahnHilliard/AllenCahn equation
existence
global attractor
Nonlinear $*$Lie higher derivations on factor von Neumann algebras
2
2
Let $mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$Lie higher derivation$D={phi_{n}}_{ninmathbb{N}}$ on $mathcal M$ is additive. In particular, if $mathcal M$ is infinite type $I$factor, a concrete characterization of $D$ is given.
1

659
678


F.
Zhang
School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, P. R. China.
School of Science, Xi'an University
China (P. R. C.)
zhfj888@126.com


X.
Qi
Department of Mathematics, Shanxi University, Taiyuan 030006, P. R. China.
Department of Mathematics, Shanxi
China (P. R. C.)
xiaofeiqisxu@aliyun.com


J.
Zhang
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, P. R China.
College of Mathematics and Information Science&lrm
China, R. O. C.
jhzhang@snnu.edu.cn
von Neumann algebra
nonlinear $*$Lie higher derivation
additive $*$higher derivation
Bounding cochordal cover number of graphs via vertex stretching
2
2
It is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (CastelnuovoMumford) regularity. As a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph G are equal provided G is wellcovered bipartite or weakly chordal graph.
1

679
685


M. R.
Fander
Science and Research Branch, Islamic Azad University
(IAU), Tehran, Iran.
Science and Research Branch,
Iran
mohamadrezafander@yahoo.com
CastelnuovoMumford regularity
Induced matching number
Cochordal cover number
Pstability, TF and VSDPL technique in Obrechkoff methods for the numerical solution of the Schrodinger equation
2
2
Many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. For the efficient solution of the above mentioned problems, linear multistep methods or RungeKutta technique are used. For the simulation of chemical procedures the radial Schrodinger equation is used frequently. In the present paper we will study a symmetric twostep Obrechkoff method, in which we will use of technique of VSDPL (vanished some of derivatives ofphaselag), for the numerical integration of the onedimensional Schrodinger equation. We will show superiority of new method in stability, accuracy and efficiency. So we present a stability analysis and an error analysis based on the radial Schrodinger equation. Also we will apply the new proposed method to the resonance problem of the radial Schrodinger equation.
1

687
706


A.
Shokri
Department of Mathematics, Faculty of Basic Science, University
of Maragheh, P.O. Box 5518183111, Maragheh, Iran.
Department of Mathematics, Faculty
Iran
shokri@maragheh.ac.ir


H.
Saadat
Department of Mathematics, Faculty of Basic Science, University
of Maragheh, P.O. Box 5518183111, Maragheh, Iran.
Department of Mathematics, Faculty
Iran
hosein67saadat@yahoo.com
Pstable
Phaselag
Schr"{o}dinger equation
trigonometrically fitted
On subdifferential in Hadamard spaces
2
2
In this paper, we deal with the subdierential concept onHadamard spaces. Flat Hadamard spaces are characterized, and necessary and sucient conditions are presented to prove that the subdifferential set in Hadamard spaces is nonempty. Proximal subdierentialin Hadamard spaces is addressed and some basic properties are highlighted. Finally, a density theorem for subdierential set is established.
1

707
717


M.
Soleimanidamaneh
{School of Mathematics, Statistics and Computer Science, College of Science, University of
Tehran, Enghelab Avenue, Tehran, Iran.
{School of Mathematics, Statistics
Iran
soleimani@khayam.ut.ac.ir


M.
Movahedi
Department of Mathematics, Faculty of Sciences, Alzahra University, Tehran, Iran.
Department of Mathematics, Faculty
Iran
m.movahedi18@yahoo.com


D.
Behmardi
Department of Mathematics, Faculty of Sciences, Alzahra University, Tehran, Iran.
Department of Mathematics, Faculty
Iran
behmardi@alzahra.ac.ir
Subdifferential
Hadamard Space
Flat space
Hilbert space
Convexity
Iterative scheme based on boundary point method for common fixed point of strongly nonexpansive sequences
2
2
Let $C$ be a nonempty closed convex subset of a real Hilbert space $H$. Let ${S_n}$ and ${T_n}$ be sequences of nonexpansive selfmappings of $C$, where one of them is a strongly nonexpansive sequence. K. Aoyama and Y. Kimura introduced the iteration process $x_{n+1}=beta_nx_n+(1beta_n)S_n(alpha_nu+(1alpha_n)T_nx_n)$ for finding the common fixed point of ${S_n}$ and ${T_n}$, where $uin C$ is an arbitrarily (but fixed) element in $C$, $x_0in C$arbitrarily, ${alpha_n}$ and ${beta_n}$ are sequences in $[0,1]$. But in the case where $unotin C$, the iterative scheme above becomes invalid because $x_n$ may not belong to $C$. To overcome this weakness, a new iterative scheme based on the thought of boundary point method is proposed and the strong convergence theorem is proved. As a special case, we can find the minimumnorm common fixed point of ${S_n}$ and ${T_n}$ whether $0in C$ or $0notin C$.
1

719
730


W.
Zhu
College of Management and Economics, Tianjin University,
Tianjin 300072, China.
College of Management and Economics,
China (P. R. C.)
wlzhu152@163.com


S.
Ling
College of Management and Economics, Tianjin University,
Tianjin 300072, China.
College of Management and Economics,
China (P. R. C.)
lingshuai@tju.edu.cn
minimumnorm common fixed point
strongly nonexpansive mappings
strong convergence
boundary point method
variational inequality
On strongly dense submodules
2
2
The submodules with the property of the title ( a submodule $N$ of an $R$module $M$ is called strongly dense in $M$, denoted by $Nleq_{sd}M$, if for any index set $I$, $prod _{I}Nleq_{d}prod _{I}M$) are introduced and fully investigated. It is shown that for each submodule $N$ of $M$ there exists the smallest subset $D'subseteq M$ such that $N+D'$ is a strongly dense submodule of $M$ and $D'bigcap N=0$. We also introduce a class of modules in which the two concepts of strong essentiality and strong density coincide. It is also shown that for any module $M$, dense submodules in $M$ are strongly dense if and only if $Mleq_{sd} tilde{E}(M)$, where $tilde{E}(M)$ is the rational hull of $M$. It is proved that $R$ has no strongly dense left ideal if and only if no nonzeroelement of every cyclic $R$module $M$ has a strongly dense annihilator in $R$. Finally, some appropriate properties and new concepts related to strong density are defined and studied.
1

731
747


E.
Ghashghaei
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
Department of Mathematics, Shahid
Iran
e.ghashghaei@yahoo.com


M.
Namdari
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
Department of Mathematics, Shahid
Iran
namdari@ipm.ir
Strongly essential submodule
strongly dense submodule
singular submodule
special submodule
column submodule
The power digraphs of safe primes
2
2
A power digraph, denoted by $G(n,k)$, is a directed graph with $Z_{n}={0,1,..., n1}$ as the set of vertices and $L={(x,y):x^{k}equiv y~(bmod , n)}$ as the edge set, where $n$ and $k$ are any positive integers. In this paper, the structure of $G(2q+1,k)$, where $q$ is a Sophie Germain prime is investigated. The primality tests for the integers of the form $n=2q+1$ are established in terms of the structure of components of $G(n,k)$. The digraphs in which all components look like directed star graphs are completely classified. This work generalizes the results of M. Krizekek, L. Somer, Sophie Germain Little Suns, Math. Slovaca 54(5) (2004), 433442.
1

749
759


U.
Ahmad
Department of
Mathematics, University
of the Punjab, New Campus, Lahore, Pakistan.
Department of
Mathematics,
Pakistan
uzma.math@pu.edu.pk


S. M.
Husnine
Department of Humanities
and Sciences, National University
of Computer and Emerging Sciences(FAST), Lahore Campus, Lahore, Pakistan.
Department of Humanities
and Sciences&lr
Pakistan
syed.husnine@nu.edu.pk
Iteration digraph
Carmichael lambda function
fixed point
Sophie Germain primes
Safe primes
Applications of subordination theory to starlike functions
2
2
Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $w^{2}1=1$ when the functions $(1alpha)p(z)+alpha p^{2}(z)+beta zp'(z)$ , $(1alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ or $p(z)+beta zp'(z)/p^{2}(z)$ is subordinate to $varphi_{C}(z)$. Related results for $p$ to be in the parabolic region bounded by the $RE w=w1$ are investigated.
1

761
777


K.
Sharma
Department of Mathematics, Atma Ram Sanatan Dharma College, University of Delhi, Delhi 110021, India.
Department of Mathematics, Atma
India
kanika.divika@gmail.com


V.
Ravichandran
Department of Mathematics, University of Delhi, Delhi110007, India.
Department of Mathematics, University
India
vravi68@gmail.com
convex and starlike functions
differential subordination
univalent functions
Weak $F$contractions and some fixed point results
2
2
In this paper we define weak $F$contractions on a metric space into itself by extending $F$contractions introduced by D. Wardowski (2012) and provide some fixed point results in complete metric spaces and in partially ordered complete generalized metric spaces. Some relationships between weak $F$contractions and $Fi$contractions are highlighted. We also give some applications on fractal theory improving the classical HutchinsonBarnsley's theory of iterated function systems. Some illustrative examples are provided.
1

779
798


N. A.
Secelean
Department of Mathematics and Informatics Faculty of Sciences,
Lucian Blaga University of Sibiu, Romania.
Department of Mathematics and Informatic
Romania
nicolae.secelean@ulbsibiu.ro
Fcontraction
partially ordered metric space
generalized metric
iterated function system
fixed point theorem