2015
41
2
2
254
Stochastic differential inclusions of semimonotone type in Hilbert spaces
2
2
In this paper, we study the existence of generalized solutions for
the infinite dimensional nonlinear stochastic differential
inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$
is semimonotone and hemicontinuous and the operatorvalued multifunction $G$ satisfies a Lipschitz condition.
We define the It^{o} stochastic integral of operator setvalued stochastic processes
with respect to the cylindrical Brownian motion on separable Hilbert spaces.
Then, we generalize the existence results for
differential inclusions in [H. Abedi and R. Jahanipur, Nonlinear differential inclusions of semimonotone and
condensing type in Hilbert spaces,
textit{Bull. Korean Math. Soc.},
{52} (2015), no. 2, 421438.] to the corresponding stochastic differential inclusions
using the methods discussed in [R. Jahanipur, Nonlinear functional differential equations of monotonetype in
Hilbert spaces, {it Nonlinear Analysis} {bf 72} (2010), no. 34, 13931408,
R. Jahanipur, Stability of stochastic delay evolution equations with monotone
nonlinearity, {it Stoch. Anal. Appl.}, {bf 21} (2003), 161181, and
R. Jahanipur, Stochastic functional evolution equations with monotone
nonlinearity: existence and stability of the mild solutions, {it J. Differential Equations} {bf 248} (2010), no. 5, 12301255.]
3

291
306


H.
Abedi
University of Kashan
University of Kashan
Iran
h.abedi7@gmail.com
Stochastic differential inclusions
Stochastic setvalued integrals
Generalized solutions
Semimonotone and hemicontinuous setvalued process
Periodic solutions of fourthorder delay differential equation
2
2
In this paper the periodic solutions of fourth order delay differential equation of the form $ddddot{x}(t)+adddot{x}(t)+f(ddot{x}(ttau(t)))+g(dot{x}(ttau(t)))+h({x}(ttau(t)))=p(t)$ is investigated. Some new positive periodic criteria are given.
3

307
314


S.
Balamuralitharan
SRM UNIVERSITY,
SRM UNIVERSITY,
India
balamurali.maths@gmail.com
Fourthorder delay differential equation
periodic solutions
On group equations
2
2
Suppose $f$ is a map from a nonempty finite set $X$ to a finite group $G$. Define the map $zeta^f_G: Glongrightarrow mathbb{N}cup {0}$ by $gmapsto f^{1}(g)$. In this article, we show that for a suitable choice of $f$, the map $zeta^f_G$ is a character. We use our results to show that the solution function for the word equation $w(t_1,t_2,dots,t_n)=g$ ($gin G$) is a character, where $w(t_1,t_2,dots,t_n)$ denotes the product of $t_1,t_2,dots,t_n,t_1^{1},t_2^{1},dots,t_n^{1}$ in a randomly chosen order.
3

315
324


S. K.
Prajapati
Postdoctoral Fellow, Indian Statistical Institute Bangalore, India
Postdoctoral Fellow, Indian Statistical Institute
India
skprajapati.iitd@gmail.com


R.
Sarma
Assistant Professor in Indian Institute of Technology Delhi, India.
Assistant Professor in Indian Institute of
India
ritumoni@maths.iitd.ac.in
finite groups
word equations
group characters
On convolution properties for some classes of meromorphic functions associated with linear operator
2
2
In this paper, we defined two classes $S_{p}^{ast }(n,lambda ,A,B)$ and\ $ K_{p}(n,lambda ,A,B)$ of meromorphic $p$valent functions associated with a new linear operator. We obtained convolution properties for functions in these classes.
3

325
332


A. O.
Mostafa
Mansoura University
Mansoura University
Egypt
adelaeg254@yahoo.com


M. K.
Aouf
Mansoura University
Mansoura University
Egypt
mkaouf127@yahoo.com
meromorphic functions
Subordination
Hadamard product
Linear operator
SincGalerkin method for solving a class of nonlinear twopoint boundary value problems
2
2
In this article, we develop the SincGalerkin method based on double exponential transformation for solving a class of weakly singular nonlinear twopoint boundary value problems with nonhomogeneous boundary conditions. Also several examples are solved to show the accuracy efficiency of the presented method. We compare the obtained numerical results with results of the other existing methods in the literature. The results of this paper confirm that our method is very fast, simple and considerably accurate.
3

333
352


J.
Rashidinia
Iran University of Science and Technology.
Iran University of Science and Technology.
Iran
rashidinia@iust.ac.ir


M.
Nabati
Iran University of Science and Technology
Iran University of Science and Technology
Iran
m_nabati@iust.ac.ir


S.
Ahanj
Iran University of Science and Technology
Iran University of Science and Technology
Iran
sara_ahj@yahoo.com
SincGalerkin method
double exponential transformation
nonlinear singular boundary value problems
ordinary differential equation
Linear Weingarten hypersurfaces in a unit sphere
2
2
In this paper, by modifying ChengYau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665672].
3

353
362


X.
Chao
Southeast University, 210096, Nanjing, P. R. China
Southeast University, 210096, Nanjing, P.
China (P. R. C.)
xlchao@seu.edu.cn
Linear Weingarten hypersurface
generalized maximum principle
rigidity theorem
The distributional HenstockKurzweil integral and measure differential equations
2
2
In the present paper, measure differential equations involving the distributional HenstockKurzweil integral are investigated. Theorems on the existence and structure of the set of solutions are established by using Schauder$^prime s$ fixed point theorem and Vidossich theorem. Two examples of the main results paper are presented. The new results are generalizations of some previous results in the literatures.
3

363
374


H.
Zhou
ollege of Science,
Hohai University, Nanjing 210098, P. R. China
ollege of Science,
Hohai University, Nanjing
China (P. R. C.)
linyizhouhao@126.com


G.
Ye
College of Science, Hohai University, Nanjing 210098, P. R. China
College of Science, Hohai University, Nanjing
China (P. R. C.)
yegj@hhu.edu.cn


W.
Liu
College of Science, Hohai University, Nanjing 210098, P. R. China
College of Science, Hohai University, Nanjing
China (P. R. C.)
liuw626@163.com


O.
Wang
College of Science, Hohai University, Nanjing 210098, P. R. China
College of Science, Hohai University, Nanjing
China (P. R. C.)
18751985160@163.com
Distributional HenstockKurzweil integral
measure differential equation
HenstockStieltjes integral
distributional derivative
Almost powerHermitian rings
2
2
In this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring R such that, every regular matrix admits a diagonal powerreduction.
3

375
380


N.
Ashrafi
Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
Faculty of Mathematics, Statistics and Computer
Iran
ashrafi49@yahoo.com


M.
Sheibani
Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
Faculty of Mathematics, Statistics and Computer
Iran
m.sheibani1@gmail.com


H.
Dehghany
Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
Faculty of Mathematics, Statistics and Computer
Iran
hajardehghany90@gmail.com
Diagonal powerreduction
exchange ring
regular ring
powersubstitution property
On spectral radius of strongly connected digraphs
2
2
It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral
radius among all strongly connected digraphs of order $nge 3$.
In this paper, among others, we determine the digraphs which achieve the second, the third
and the fourth minimum spectral radii respectively among strongly connected
digraphs of order $nge 4$.
3

381
387


J.
Li
Department of Mathematics, South China Normal University,
and
Faculty of Applied
Mathematics,
Guangdong University of Technology
Department of Mathematics, South China Normal
China (P. R. C.)
lijp06@163.com


B.
Zhou
Department of
Mathematics, South China Normal University, Guangzhou 510631, P. R. China
Department of
Mathematics, South China Normal
China (P. R. C.)
zhoubo@scnu.edu.cn
Spectral radius
strongly connected digraph
nonnegative irreducible matrix
bicyclic digraph
Uncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation
2
2
In this paper we consider the second order nonlinear neutral delay partial difference equation $Delta_nDelta_mbig(x_{m,n}+a_{m,n}x_{mk,nl}big)+ fbig(m,n,x_{mtau,nsigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation. Three nontrivial examples are given to illustrate the advantages of our results.
3

389
405


Z.
Liu
Liaoning Normal University
Liaoning Normal University
China (P. R. C.)
zeqingliu@163.com


Z.
Wu
Liaoning Normal University
Liaoning Normal University
China (P. R. C.)
zhihuawu_dl@163.com


J. S.
Ume
Department of Mathematics, Changwon National University
Department of Mathematics, Changwon National
Korea, Republic of
jsume@changwon.ac.kr


S. M.
Kang
Gyeongsang National University
Gyeongsang National University
Korea, Republic of
smkang@gnu.ac.kr
Uncountably many bounded positive solutions
second order nonlinear neutral delay partial difference equation
Banach fixed point theorem
Random coincidence point results for weakly increasing functions in partially ordered metric spaces
2
2
The aim of this paper is to establish random coincidence
point results for weakly increasing random operators in the setting
of ordered metric spaces by using generalized altering distance
functions. Our results present random versions and extensions of
some wellknown results in the current literature.
3

407
422


A. R.
Khan
Department of Mathematics and Statistics, King Fahd University of
Petroleum and Minerals, Dhahran, 3126, Saudia Arabia
Department of Mathematics and Statistics,
Saudi Arabia
arahim@kfupm.edu.sa


N.
Hussain
Department of Mathematics, King Abdulaziz University, P.O.
Box 80203, Jeddah, 21589, Saudi Arabia
Department of Mathematics, King Abdulaziz
Saudi Arabia
nhusain@kau.edu.sa


N.
Yasmin
Centre for Advanced Studies
in Pure and Applied Mathematics, Bahauudin Zakariya University, Multan, 60800, Pakistan
Centre for Advanced Studies
in Pure and Applied
Saudi Arabia
usyasmin@yahoo.com


N.
Shafqat
entre for Advanced Studies
in Pure and Applied Mathematics, Bahauudin Zakariya University, Multan, 60800, Pakistan
entre for Advanced Studies
in Pure and Applied
Saudi Arabia
naeem781625@yahoo.com
Random coincidence point
altering distance function
partially ordered metric space
The Artinian property of certain graded generalized local chohomology modules
2
2
Let $R=oplus_{nin Bbb N_0}R_n$ be a Noetherian homogeneous ring with local base ring $(R_0,frak{m}_0)$, $M$ and $N$ two finitely generated graded $R$modules. Let $t$ be the least integer such that $H^t_{R_+}(M,N)$ is not minimax. We prove that $H^j_{frak{m}_0R}(H^t_{R_+}(M,N))$ is Artinian for $j=0,1$. Also, we show that if ${rm cd}(R_{+},M,N)=2$ and $tin Bbb N_0$, then $H^t_{frak{m}_0R}(H^2_{R_+}(M,N))$ is Artinian if and only if $H^{t+2}_{frak{m}_0R}(H^1_{R_+}(M,N))$ is Artinian.
3

423
428


Y.
Gu
Department of Mathematics, Soochow University
Department of Mathematics, Soochow University
China (P. R. C.)
guyan@suda.edu.cn


L.
Chu
Department of Mathematics, Soochow University
Department of Mathematics, Soochow University
China (P. R. C.)
chulizhong@suda.edu.cn
Graded local cohomology modules
Artinian modules
minimax
On certain subclasses of univalent $p$harmonic mappings
2
2
Inthis paper, the main aim is to introduce the class $mathcal{U}_p(lambda,alpha,beta,k_0)$ of $p$harmonic mappings togetherwith its subclasses $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p$ and $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p^0$, andinvestigate the properties of the mappings in these classes. First,we give a sufficient condition for mappings to be in $mathcal{U}_p(lambda,alpha,beta,k_0)$ and also the characterization ofmappings in $mathcal {U}_p(lambda,alpha,beta,k_0)capmathcal{T}_p$ for $max{0,frac{lambdafrac{1}{2}}{lambda+1}}leqalphaleq lambda$. Second, we consider the starlikeness ofmappings in $mathcal {U}_p(lambda,alpha,beta,k_0)capmathcal{T}_p^0$ for $max{0,frac{lambdafrac{1}{2}}{lambda+1}}leqalphaleq lambda$. Third, extreme points of $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p$ for$max{0,frac{lambdafrac{1}{2}}{lambda+1}}leq alphaleqlambda$ are found. The support points of $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p$ for$max{0,frac{lambdafrac{1}{2}}{lambda+1}}leq alphaleqlambda$ and convolution of mappings in $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p$ for$max{0,frac{lambdafrac{1}{2}}{lambda+1}}leq alphaleqlambda$ are also discussed.
3

429
451


J.
Qiao
Department of Mathematics,
Hebei University, Baoding, Hebei 071002, People&#039;s Republic of China
Department of Mathematics,
Hebei University,
China (P. R. C.)
mathqiao@126.com


J.
Chen
School of Science,
Hebei University of Engineering, Handan, Hebei 056038, People's
Republic of China
School of Science,
Hebei University of Engineering
China (P. R. C.)
jiqiang516@163.com


M.
Shi
Department of Mathematics,
Hebei University, Baoding, Hebei 071002, People's Republic of China
Department of Mathematics,
Hebei University,
China, R. O. C.
mingyulj08@163.com
$p$harmonic mapping
uniform convexity
uniform starlikeness
extreme point
support point
On constant products of elements in skew polynomial rings
2
2
Let $R$ be a reversible ring which is $alpha$compatible for an endomorphism $alpha$ of $R$ and $f(X)=a_0+a_1X+cdots+a_nX^n$ be a nonzero skew polynomial in $R[X;alpha]$. It is proved that if there exists a nonzero skew polynomial $g(X)=b_0+b_1X+cdots+b_mX^m$ in $R[X;alpha]$ such that $g(X)f(X)=c$ is a constant in $R$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $R$ such that $rf(X)=ac$. In particular, $r=ab_p$ for some $p$, $0leq pleq m$, and $a$ is either one or a product of at most $m$ coefficients from $f(X)$. Furthermore, if $b_0$ is a unit in $R$, then $a_1,a_2,cdots, a_n$ are all nilpotent. As an application of the above result, it is proved that if $R$ is a weakly 2primal ring which is $alpha$compatible for an endomorphism $alpha$ of $R$, then a skew polynomial $f(X)$ in $R[X;alpha]$ is a unit if and only if its constant term is a unit in $R$ and other coefficients are all nilpotent.
3

453
462


W.
Chen
School of Mathematics and Information Science, Shandong Institute of Business
and Technology, Yantai, 264005)
School of Mathematics and Information Science,
China, R. O. C.
wxchen5888@163.com
Constant products
skew polynomial rings
reversible rings
weakly 2primal rings
Conformal mappings preserving the Einstein tensor of Weyl manifolds
2
2
In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds related by a conformal mapping preserving the Einstein tensor with a gradient covector field. Then, we prove that a Weyl manifold $W_n$ and a flat Weyl manifold $tilde{W}_n$, which are in a conformal correspondence preserving the Einstein tensor are EinsteinWeyl manifolds. Moreover, we show that an isotropic Weyl manifold is an EinsteinWeyl manifold with zero scalar curvature and we obtain that a Weyl manifold $W_n$ and an isotropic Weyl manifold related by the conformal mapping preserving the Einstein tensor are EinsteinWeyl manifolds.
3

463
475


M.
Gürlek
Istanbul Technical university
Maslak
Istanbul Technical university
Maslak
Turkey
mgurlek@itu.edu.tr


G.
Çivi
Istanbul technical university
Faculty of Science and letters, dept . of Math., maslak
Istanbul technical university
Faculty of
Turkey
civi@itu.edu.tr
Weyl manifold
Einstein tensor
conformal mapping
flat Weyl manifold
isotropic Weyl manifold
On difference sequence spaces defined by Orlicz functions without convexity
2
2
In this paper, we first define spaces of single difference sequences defined by a sequence of Orlicz functions without convexity and investigate their properties. Then we extend this idea to spaces of double sequences and present a new matrix theoretic approach construction of such double sequence spaces.
3

477
489


H.
Dutta
Department of Mathematics, Gauhati University,
Guwahati781014, Assam, India
Department of Mathematics, Gauhati University,
Guw
India
hemen_dutta08@rediffmail.com


L.
Kočinac
Univeristy of East Sarajevo
Bosnia and Herzegovina
Univeristy of East Sarajevo
Bosnia and Herzegovina
Serbia
lkocinac@gmail.com
Difference sequence space
$K$function
$F$space
$AK$space
Frechet space
Explicit multiple singular periodic solutions and singular soliton solutions to KdV equation
2
2
Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Kortewegde Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude depend on some rational functions.
3

491
498


Y.
Huang
Chuxiong Normal University
Chuxiong Normal University
China (P. R. C.)
huang11261001@163.com
Lax system
KdV equation
Darboux transformation
singular periodic solution
On the nonsplit extension $2^{2n}{^{cdot}}Sp(2n,2)$
2
2
In this paper we give some general results on the nonsplitextension group $overline{G}_{n} = 2^{2n}{^{cdot}}Sp(2n,2), ngeq2.$ We then focus on the group $overline{G}_{4} =2^{8}{^{cdot}}Sp(8,2).$ We construct $overline{G}_{4}$ as apermutation group acting on 512 points. The conjugacy classes aredetermined using the coset analysis technique. Then we determine theinertia factor groups and Fischer matrices, which are required forthe computations of the character table of $overline{G}_{4}$ bymeans of CliffordFischer Theory. There are two inertia factorgroups namely $H_{1} = Sp(8,2)$ and $H_{2} = 2^{7}{:}Sp(6,2),$ theSchur multiplier and hence the character table of the correspondingcovering group of $H_{2}$ were calculated. Using the information onconjugacy classes, Fischer matrices and ordinary and projectivetables of $H_{2},$ we concluded that we only need to use theordinary character table of $H_{2}$ to construct the character tableof $overline{G}_{4}.$ The Fischer matrices of $overline{G}_{4}$are all listed in this paper. The character table of$overline{G}_{4}$ is a $195 times 195$ complex valued matrix, ithas been supplied in the PhD Thesis of the firstauthor, which could be accessed online.
3

499
518


A. B. M.
Basheer
School of Mathematical Sciences, NorthWest University (Mafikeng)
School of Mathematical Sciences, NorthWest
South Africa
ayoubbasheer@gmail.com


J.
Moori
NorthWest University
NorthWest University
South Africa
jamshid.moori@nwu.ac.za
Group extensions
symplectic group
character table
inertia groups
Fischer matrices
Application of measures of noncompactness to infinite system of linear equations in sequence spaces
2
2
G. Darbo [Rend. Sem. Math. Univ. Padova, 24 (1955) 8492] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. In this paper, we apply the Darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.
3

519
527


A.
Alotaibi
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia, and,
Operator Theory and its Applications Research Group, King Abdulaziz University, Jeddah, Saudi Arabia
Department of Mathematics, Faculty of Science,
Saudi Arabia
mathker11@hotmail.com


M.
Mursaleen
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India, and,
Operator Theory and its Applications Research Group, King Abdulaziz University, Jeddah, Saudi Arabia
Department of Mathematics, Aligarh Muslim
India
mursaleenm@gmail.com


S. A.
Mohiuddine
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia, and,
Operator Theory and its Applications Research Group, King Abdulaziz University, Jeddah, Saudi Arabia
Department of Mathematics, Faculty of Science,
Saudi Arabia
mohiuddine@gmail.com
Sequence spaces
matrix transformations
Hausdorff measure of noncompactness
Darbo's fixed point theorem
infinite system of linear equations
Generalized Drazin inverse of certain block matrices in Banach algebras
2
2
Several representations of the generalized Drazin inverse of an antitriangular block matrix in Banach algebra are given in terms of the generalized BanachiewiczSchur form.
3

529
542


M. Z.
Kolundžija
University of Nis,
Faculty of Science and Mathematics
University of Nis,
Faculty of Science and
Serbia
mkolundzija@pmf.ni.ac.rs


D.
Mosić
University of Niš,
Faculty of Science and Mathematics
University of Niš,
Faculty of Science
Serbia
dijana@pmf.ni.ac.rs


D. S.
Djordjević
University of Nis, Faculty of Science and Mathematics
University of Nis, Faculty of Science and
Serbia
dragan@pmf.ni.ac.rs
Generalized Drazin inverse
Schur complement
block matrix
Erratum: Applications of epiretractable and coepiretractable modules
2
2
In this errata, we reconsider and modify two propositions and their corollaries which were written on epiretractable and coepiretractable modules.
3

543
544


H.
Mostafanasab
University of Mohaghegh Ardabili
University of Mohaghegh Ardabili
Iran
h.mostafanasab@gmail.com
Epiretractable modules
coepiretractable modules
Hereditary rings