2015
41
3
3
248
On the bandwidth of Mobius graphs
2
2
Bandwidth labelling is a well known research area in graph theory. We
provide a new proof that the bandwidth of Mobius ladder is 4, if it
is not a $K_{4}$, and investigate the bandwidth of a wider class
of Mobius graphs of even strips.
3

545
550


I.
Ahmad
University of Malakand
University of Malakand
Pakistan
iahmaad@hotmail.com


P. M.
Higgins
University of Essex
University of Essex
United Kingdom
peteh@essex.ac.uk
Mobius graphs
Cartesian product of graphs
labelling of graphs
bandwidth of a graph
Characterization of projective special linear groups in dimension three by their orders and degree patterns
2
2
The prime graph $Gamma(G)$ of a group $G$ is
a graph with vertex set $pi(G)$, the set of primes dividing the
order of $G$, and two distinct vertices $p$ and $q$ are adjacent
by an edge written $psim q$ if there is an element in $G$ of
order $pq$. Let $pi(G)={p_{1},p_{2},...,p_{k}}$. For
$pinpi(G)$, set $deg(p):={q inpi(G) psim q}$, which is
called the degree of $p$. We also set
$D(G):=(deg(p_{1}),deg(p_{2}),...,deg(p_{k}))$, where
$p_{1}<p_{2}<...<p_{k}$, which is called degree pattern of $G$.
The group $G$ is called $k$fold ODcharacterizable if there exists
exactly $k$ nonisomorphic groups $M$ satisfying conditions
$G=M$ and $D(G)=D(M)$. In particular, a $1$fold
ODcharacterizable group is simply called ODcharacterizable. In
this paper, as the main result, we prove that projective special
linear group $L_{3}(2^{n})$ where $nin{4,5,6,7,8,10,12}$ is
ODcharacterizable.
3

551
580


G. R.
Rezaeezadeh
Shahrekord University
Shahrekord University
Iran
rezaeezadeh@sci.sku.ac.ir


M.
Bibak
Shahrekord University
Shahrekord University
Iran
m.bibak62@gmail.com


M.
Sajjadi
Shahrekord University
Shahrekord University
Iran
sajadi_mas@yahoo.com
Prime graph
degree pattern
ODcharacterizable
Volume difference inequalities for the projection and intersection bodies
2
2
In this paper, we introduce a new concept of
volumes difference function of the projection and intersection
bodies. Following this, we establish the Minkowski and
BrunnMinkowski inequalities for volumes difference function of
the projection and intersection bodies.
3

581
590


C. J.
Zhao
Department of Mathematics, China Jiliang University, Hangzhou 310018, China
Department of Mathematics, China Jiliang
China, R. O. C.
chjzhao315@sohu.com


W. S.
Cheung
The University of Hong Kong
The University of Hong Kong
Hong Kong
wscheung@hku.hk
Projection body
intersection body
volume difference
Minkowski inequality
BrunnMinkowski inequality
Almost simple groups with Socle $G_2(q)$ acting on finite linear spaces
2
2
After the classification of the flagtransitive linear spaces, the attention has been turned to linetransitive linear spaces. In this article, we present a
partial classification of the finite linear spaces $mathcal S$ on
which an almost simple group $G$ with the socle $G_2(q)$ acts
linetransitively.
3

591
602


S.
Li
School of Mathematical Sciences Suzhou University Suzhou, 215006 China
School of Mathematical Sciences Suzhou University
China (P. R. C.)
lszfd2004@163.com


X.
Li
School of Mathematics, Central South
University, Changsha, P. R. China
School of Mathematics, Central South
University,
China (P. R. C.)
xhli@suda.edu.cn


W.
Liu
School of Mathematics, Central South
University, Changsha, P. R. China
School of Mathematics, Central South
University,
China (P. R. C.)
wjliu6210@126.com
Linetransitive
linear space
almost simple group
Some results on value distribution of the difference operator
2
2
In this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. Suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $E_k(1, f^{n}(z)f(z+c))=E_k(1, g^{n}(z)g(z+c))$. Then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(z)g(z)=t_2,$
for some constants $t_1$ and $t_2$ that satisfy $t_1^{n+1}=1$
and $t_2^{n+1}=1$. We generalize some previous results of Qi et. al.
3

603
611


Y.
Liu
Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang 312000, China
Department of Mathematics, Shaoxing College
China (P. R. C.)
liuyongsdu@aliyun.com


J. P.
Wang
Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang 312000, China
Department of Mathematics, Shaoxing College
China (P. R. C.)
jpwang@usx.edu.cn


F. H.
Liu
Department of Mathematics, Shandon university, Jinan, Shandong 250100, China
Department of Mathematics, Shandon university,
China (P. R. C.)
liufanghong07@126.com
Meromorphic functions
difference equations
uniqueness
finite order
Some properties of extended multiplier transformations to the classes of meromorphic multivalent functions
2
2
In this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda
,l,rho )$ and $mathcal{T}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of pvalent
meromorphic functions defined by using the extended multiplier
transformation operator. We use a strong convolution technique and derive
inclusion results. A radius problem and some other interesting properties of
these classes are discussed.
3

613
624


A.
Muhammad
Department of Basic Sciences, University of Engineering and
Technology, P.O. Box 25000, Peshawar Pakistan
Department of Basic Sciences, University
Pakistan
ali7887@gmail.com


S.
Hussain
Department of
Mathematics, COMSATS Institute of Information Technology, P.O. Box 22010, Abbotabad, Pakistan
Department of
Mathematics, COMSATS Institute
Pakistan
saqibhussain@ciit.net.pk


W.
UlHaq
Mathematics Department
Faculty of Science, main campus Zulfi, P.O. Box 1712, Majmaah University, Saudi Arabia
Mathematics Department
Faculty of Science,
Saudi Arabia
w.ulhaq@mu.edu.sa
multivalent functions
Analytic functions
meromorphic functions
multiplier transformations
Linear operator
functions with positive real part
Hadamard product
Coherence in amalgamated algebra along an ideal
2
2
Let $f: Arightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we investigate the transfer of the property of coherence to the amalgamation $Abowtie^{f}J$. We provide necessary and sufficient conditions for $Abowtie^{f}J$ to be a coherent ring.
3

625
632


K.
Alaoui Ismaili
Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202,
University S.M. Ben Abdellah Fez, Morocco
Department of Mathematics, Faculty of Science
Morocco
alaouikarima2012@hotmail.fr


N.
Mahdou
Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202,
University S.M. Ben Abdellah Fez, Morocco
Department of Mathematics, Faculty of Science
Morocco
mahdou@hotmail.com
Amalgamated algebra
coherent ring
The metric dimension and girth of graphs
2
2
A set $Wsubseteq V(G)$ is called a resolving set for $G$,
if for each two distinct vertices $u,vin V(G)$ there exists $win W$
such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance
between the vertices $x$ and $y$. The minimum cardinality of a
resolving set for $G$ is called the metric dimension of $G$, and
denoted by $dim(G)$. In this paper, it is proved that in a
connected graph $G$ of order $n$ which has a cycle, $dim(G)leq ng(G)+2$,
where $g(G)$ is the length of the shortest cycle in $G$, and the
equality holds if and only if $G$ is a cycle, a complete graph or a
complete bipartite graph $K_{s,t}$, $ s,tgeq 2$.
3

633
638


M.
Jannesari
Shahreza High Education Center, 8614956841, Shahreza, Iran
Shahreza High Education Center, 8614956841,
Iran
m.jannesari@math.iut.ac.ir
Resolving set
metric dimension
girth
A remark on asymptotic enumeration of highest weights in tensor powers of a representation
2
2
We consider the semigroup $S$ of highest weights appearing in tensor powers $V^{otimes k}$ of a finite dimensional representation $V$ of a connected reductive group. We describe the cone generated by $S$ as the cone over the weight polytope of $V$ intersected with the positive Weyl chamber. From this we get a description for the asymptotic of the number of highest weights appearing in $V^{otimes k}$ in terms of the volume of this polytope.
3

639
646


K.
Kaveh
Department of Mathematics, Dietrich School of Arts and Sciences, University of Pittsburgh,
301 Thackeray Hall, Pittsburgh, PA 15260, U.S.A.
Department of Mathematics, Dietrich School
United States of America
kaveh@pitt.edu
Reductive group representation
tensor power
semigroup of integral points
weight polytope
moment polytope
A posteriori $ L^2(L^2)$error estimates with the new version of streamline diffusion method for the wave equation
2
2
In this article, we study the new streamline diffusion finite
element for treating the linear second order hyperbolic
initialboundary value problem. We prove a posteriori $ L^2(L^2)$
and error estimates for this method under minimal regularity
hypothesis. Test problem of an application of the wave equation
in the laser is presented to verify the efficiency and accuracy
of the method.
3

647
664


D.
Rostamy
Department of Mathematics, Imam Khomeini International University,
Qazvin, Iran
Department of Mathematics, Imam Khomeini
Iran
rostamy@khayam.ut.ac.ir


F.
Zabihi
Department of Mathematics, Kashan University, Kashan, Iran
Department of Mathematics, Kashan University,
Iran
zabihi@kashanu.ac.ir
Streamline diffusion method
finite element method
a posteriori error estimates
On weakly $mathfrak{F}_{s}$quasinormal subgroups of finite groups
2
2
Let $mathfrak{F}$ be a formation and $G$ a finite group. A subgroup $H$ of $G$ is said to be weakly $mathfrak{F}_{s}$quasinormal in $G$ if $G$ has an $S$quasinormal subgroup $T$ such that $HT$ is $S$quasinormal in $G$ and $(Hcap T)H_{G}/H_{G}leq Z_{mathfrak{F}}(G/H_{G})$, where $Z_{mathfrak{F}}(G/H_{G})$ denotes the $mathfrak{F}$hypercenter of $G/H_{G}$. In this paper, we study the structure of finite groups by using the concept of weakly $mathfrak{F}_{s}$quasinormal subgroup.
3

665
675


Y.
Mao
Department of Mathematics, University of Science and Technology of China, Hefei,
230026, P. R. China
Department of Mathematics, University of
China (P. R. C.)
maoym@mail.ustc.edu.cn


X.
Chen
Department of Mathematics, University of Science and Technology of China, Hefei,
230026, P. R. China
Department of Mathematics, University of
China (P. R. C.)
jelly@mail.ustc.edu.cn


W.
Guo
Department of Mathematics, University of Science and Technology of China, Hefei,
230026, P. R. China
Department of Mathematics, University of
China (P. R. C.)
wbguo@ustc.edu.cn
Fhypercenter
weakly Fsquasinormal subgroups
Sylow subgroups
pnilpotence
supersolubility
On meromorphically multivalent functions defined by multiplier transformation
2
2
The purpose of this paper is to derive various useful subordination properties and
characteristics for certain subclass of multivalent meromorphic functions, which
are defined here by the multiplier transformation. Also, we obtained inclusion
relationship for this subclass.
3

677
697


M. P.
Jeyaraman
Department of Mathematics, L. N. Government College, Ponneri, Chennai, 601 204, Tamilnadu, India
Department of Mathematics, L. N. Government
India
{jeyaraman_mp@yahoo.co.in


T. K.
Suresh
Department of
Mathematics, Easwari Engineering College, Ramapuram, Chennai, 600089, Tamilnadu, India
Department of
Mathematics, Easwari Engineering
India
tksuresh73@yahoo.com
Analytic functions
multivalent functions
differential subordination
Gauss hypergeometric function
multiplier transformation
On convergence of certain nonlinear Durrmeyer operators at Lebesgue points
2
2
The aim of this paper is to study the behaviour of certain sequence of nonlinear Durrmeyer operators $ND_{n}f$ of the form
$$(ND_{n}f)(x)=intlimits_{0}^{1}K_{n}left( x,t,fleft( tright) right)
dt,,,0leq xleq 1,,,,,,nin mathbb{N},
$$
acting on bounded functions on an interval $left[ 0,1right] ,$ where $%
K_{n}left( x,t,uright) $ satisfies some suitable assumptions. Here we
estimate the rate of convergence at a point $x$, which is a Lebesgue point
of $fin L_{1}left( [0,1]right) $ be such that $psi oleftvert
frightvert in BVleft( [0,1]right) $, where $psi oleftvert
frightvert $ denotes the composition of the functions $psi $ and $%
leftvert frightvert $. The function $psi :mathbb{R}_{0}^{+}rightarrow
mathbb{R}_{0}^{+}$ is continuous and concave with $psi (0)=0,$ $psi (u)>0$
for $u>0$, which appears from the $left( Lpsi right) $ Lipschitz
conditions.
3

699
711


H.
Karsli
Department of
Mathematics, Abant Izzet Baysal University,
Faculty of Science and Arts, P.O. Box 14280, Bolu, Turkey
Department of
Mathematics, Abant Izzet Baysal
Turkey
karsli_h@ibu.edu.tr
nonlinear Durrmeyer operators
bounded variation
Lipschitz condition
pointwise convergence
On uniqueness of meromorphic functions sharing five small functions on annuli
2
2
The purpose of this article is
to investigate the uniqueness of meromorphic functions sharing
five small functions on annuli.
3

713
722


N.
Wu
Department of Mathematics, School of Science, China University of Mining and Technology(Beijing)
Department of Mathematics, School of Science,
China (P. R. C.)
wunan2007@163.com


Q.
Ge
Department of Mathematics, School of Science, China University of Mining and Technology (Beijing), Beijing,
100083, People's Republic of China.
Department of Mathematics, School of Science,
China (P. R. C.)
geqin0113@163.com
meromorphic function
Nevanlinna theory
small functions
uniqueness
annulus
Stochastic functional population dynamics with jumps
2
2
In this paper we use a class of stochastic functional
Kolmogorovtype model with jumps to describe the evolutions of
population dynamics. By constructing a special Lyapunov function, we
show that the stochastic functional differential equation associated
with our model admits a unique global solution in the positive
orthant, and, by the exponential martingale inequality with jumps,
we discuss the asymptotic pathwise estimation of such a model.
3

723
737


L.
Tan
School of Statistics, Jiangxi University of Finance and Economics, Nanchang, 330013, China
and
Research Center of Applied statistics, Jiangxi University of Finance and Economics, Nanchang, 330013, China
School of Statistics, Jiangxi University
China (P. R. C.)
tltanli@126.com


Z.
Hou
Mathematics Department, Central South University
Mathematics Department, Central South University
China (P. R. C.)
zthou@csu.edu.cn


X.
Yang
School of Mathematics and Statistics, Central South
University, Changsha, 410075, China
School of Mathematics and Statistics, Central
China (P. R. C.)
yangxiaoxia0731@163.com
Kolmogorovtype population dynamics
jumps
exponential martingale inequality with jumps
asymptotic pathwise estimation
A certain convolution approach for subclasses of univalent harmonic functions
2
2
In the present paper we study convolution properties for subclasses of
univalent harmonic functions in the open unit disc and obtain some basic
properties such as coefficient characterization and extreme points.
3

739
747


R. M.
ElAshwah
Department of Mathematics,
Faculty of Science,
Damietta University,
New Damietta 34517, Egypt
Department of Mathematics,
Faculty of
Egypt
r_elashwah@yahoo.com


M. K.
Aouf
Department of Mathematics,
Faculty of Science,
Mansoura University,
Mansoura 35516, Egypt
Department of Mathematics,
Faculty of Science,
Egypt
mkaouf127@yahoo.com
Analytic
harmonic
Convolution
Notes on amalgamated duplication of a ring along an ideal
2
2
In this paper, we study some ring theoretic properties of the
amalgamated duplication ring $Rbowtie I$ of a commutative
Noetherian ring $R$ along an ideal $I$ of $R$ which was introduced by
D'Anna and Fontana. Indeed, it is determined that when $Rbowtie I$
satisfies Serre's conditions $(R_n)$ and $(S_n)$, and when is a
normal ring, a generalized CohenMacaulay ring and finally a filter
ring.
3

749
757


P.
Sahandi
Department of Mathematics, University of Tabriz
Department of Mathematics, University of
Iran
sahandi@tabrizu.ac.ir


N.
Shirmohammadi
Department of Mathematics, University of Tabriz
Department of Mathematics, University of
Iran
shirmohammadi@tabrizu.ac.ir
Amalgamated ring
CohenMacaulay ring
Serre condition
normal ring
filter ring
Optimality conditions for Pareto efficiency and proper ideal point in setvalued nonsmooth vector optimization using contingent cone
2
2
In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a starshaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex setvalued map, in general real normed spaces.
3

759
770


Y. F.
Chai
Department of
Mathematics, Xidian University, Xi'an 710071, China
Department of
Mathematics, Xidian University,
China (P. R. C.)
chyf_0923@163.com


S. Y.
Liu
Department of
Mathematics, Xidian University, Xi'an 710071, China
Department of
Mathematics, Xidian University,
China, R. O. C.
liusanyang@126.com
Starshaped set
Bouligand tangent cone
generalized cone convex maps
optimality conditions
Integration formulas for the conditional transform involving the first variation
2
2
In this paper, we show that the conditional transform with respect to the Gaussian process
involving the first variation can be expressed in terms of the conditional transform without the first variation.
We then use this result to obtain various integration formulas involving the conditional $diamond$product and the first variation.
3

771
783


I. Y.
Lee
Department of Mathematics, Dankook University, Cheonan 330714, Korea
Department of Mathematics, Dankook University,
Korea, Republic of
iylee@dankook.ac.kr


H. S.
Chung
Department of Mathematics, Dankook University, Cheonan 330714, Korea
Department of Mathematics, Dankook University,
Korea, Republic of
hschung@dankook.ac.kr


S. J.
Chang
Department of Mathematics, Dankook University, Cheonan 330714, Korea
Department of Mathematics, Dankook University,
Korea, Republic of
sejchang@dankook.ac.kr
Brownian motion process
Gaussian process
simple formula
conditional transform with respect to Gaussian process
conditional $diamond$product
first variation
Approximate multiadditive mappings in 2Banach spaces
2
2
A mapping $f:V^n longrightarrow W$, where $V$ is a commutative
semigroup, $W$ is a linear space and $n$ is a positive integer, is
called multiadditive if it is additive in each variable. In this
paper we prove the HyersUlam stability of
multiadditive mappings in 2Banach spaces. The corollaries from our
main results correct some outcomes from [W.G. Park, Approximate additive mappings in 2Banach spaces and related
topics, J. Math. Anal. Appl. 376 (2011) 193202].
3

785
792


K.
Cieplinski
AGH University of Science and Technology, Faculty of Applied Mathematics,
al. A. Mickiewicza 30,
30059 Krakow, Poland
AGH University of Science and Technology,
Poland
cieplin@agh.edu.pl
Stability
multiadditive mapping
linear 2normed space