2016
42
2
2
0
Radical of $cdot$ideals in $PMV$algebras
2
2
In this paper, we introduce the notion of the radical of a $PMV$algebra $A$ and we charactrize radical $A$ via elements of $A$. Also, we introduce the notion of the radical of a $cdot$ideal in $PMV$algebras. Several characterizations of this radical is given. We define the notion of a semimaximal $cdot$ideal in a $PMV$algebra. Finally we show that $A/I$ has no nilpotent elements if and only if $I$ is a semimaximal $cdot$ideal of $A$.
1

233
246


F.
Forouzesh
Faculty of Mathematics and computing, Higher Education complex of Bam, Bam, Iran.
Faculty of Mathematics and computing,
Iran
frouzesh@bam.ac.ir
$PMV$algebra
$cdot$ideal
$cdot$prime ideal
radical
Existence of solutions of boundary value problems for Caputo fractional differential equations on time scales
2
2
In this paper, we study the boundaryvalue problem of fractional
order dynamic equations on time scales,
$$
^c{Delta}^{alpha}u(t)=f(t,u(t)),;;tin
[0,1]_{mathbb{T}^{kappa^{2}}}:=J,;;1<alpha<2,
$$
$$
u(0)+u^{Delta}(0)=0,;;u(1)+u^{Delta}(1)=0,
$$
where $mathbb{T}$ is a general time scale with $0,1in mathbb{T}$,
$^c{Delta}^{alpha}$ is the Caputo $Delta$fractional derivative. We investigate the existence and uniqueness of solution for the problem by Banach's fixed point theorem and Schaefer's fixed point
theorem. We also discuss the existence of positive solutions of the
problem by using the Krasnoselskii theorem.
1

247
262


R. A.
Yan
School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P R China
School of Mathematical Sciences, University
China (P. R. C.)
yanrian89@163.com


S. R.
Sun
School of Mathematical Sciences, University of Jinan, Jinan,
Shandong 250022, P R China
School of Mathematical Sciences, University
China (P. R. C.)
sshrong@163.com


Z. L.
Han
School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P R China
School of Mathematical Sciences, University
China (P. R. C.)
hanzhenlai@163.com
Fractional differential equation
Time scales
Boundaryvalue problem
Fixedpoint theorem
Locally GCD domains and the ring $D+XD_S[X]$
2
2
An integral domain $D$ is called a emph{locally GCD domain} if $D_{M}$ is aGCD domain for every maximal ideal $M$ of $D$. We study someringtheoretic properties of locally GCD domains. E.g., we show that $%D$ is a locally GCD domain if and only if $aDcap bD$ is locally principalfor all $0neq a,bin D$, and flat overrings of a locally GCD domain arelocally GCD. We also show that the tclass group of a locally GCD domain isjust its Picard group. We study when a locally GCD domain is Pr"{u}fer or ageneralized GCD domain.We also characterize locally factorial domains as domains $D$ whose minimal prime idealsof a nonzero principal ideal are locally principal and discuss conditions that make them Krull domains.We use the $D+XD_{S}[X]$ construction to give someinteresting examples of locally GCD domains that are not GCD domains.
1

263
284


G. W.
Chang
Department of Mathematics Education, Incheon National University,
Incheon 406772, Republic of Korea.
Department of Mathematics Education,
South Korea
whan@incheon.ac.kr


T.
Dumitrescu
Facultatea de Matematica si Informatica, University of Bucharest, 14 Academiei Str., Bucharest, RO 010014, Romania
Facultatea de Matematica si Informatica,
Romania
tiberiu@fmi.unibuc.ro


M.
Zafruhhah
Department of Mathematics, Idaho State University, Pocatello, ID 83209, USA
Department of Mathematics, Idaho
United States of America
mzafrullah@usa.net
locally GCD domain
generalized GCD domain
$D+XD_S[X]$
Sufficiency and duality for a nonsmooth vector optimization problem with generalized $alpha$$d_{I}$typeI univexity over cones
2
2
In this paper, using Clarke’s generalized directional derivative and dIinvexity we introduce new concepts of nonsmooth KαdIinvex and generalized type I univex functions over cones for a nonsmooth vector optimization problem with cone constraints. We obtain some sufficient optimality conditions and MondWeir type duality results under the foresaid generalized invexity and type I coneunivexity assumptions.
1

285
295


H.
Jiao
School of Mathematics and Statistics, Yangtze Normal University, Chongqing 408100, P. R. China.
School of Mathematics and Statistics, Yangtze
China (P. R. C.)
jiaohh361@126.com
Vector optimization
Type I univexity
Cones
Optimality
duality
A new approach for solving the firstorder linear matrix differential equations
2
2
Abstract. The main contribution of the current paper is to propose a new effective numerical method for solving the firstorder linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solving the obtained coupled linear matrix equations. Numerical experiments are presented to demonstrate the applicably and efficiency of our method.
1

297
314


A.
Golbabai
School of Mathematics, Iran
University of Science and Technology, P.O. Box 1684613114,
Tehran, Iran.
School of Mathematics, Iran
Un
Iran
golbabai@iust.ac.ir


S.
P. A. Beik
School of Mathematics, Iran
University of Science and Technology, P.O. Box 1684613114,
Tehran, Iran
School of Mathematics, Iran
Un
Iran
panjehali@iust.ac.ir


D.
K. Salkuyeh
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
Faculty of Mathematical Sciences, Univer
Iran
salkuyeh@gmail.com
Linear matrix differential equation
Legendre polynomials
Coupled linear matrix equations
Iterative algorithm
An analytic solution for a nonlocal initialboundary value problem including a partial differential equation with variable coefficients
2
2
This paper considers a nonlocal initialboundary value problem containing a first order partial differential equation with variable coefficients. At first, the nonselfadjoint spectral problem is derived. Then its adjoint problem is calculated. After that, for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined. Finally the convergence of series solution and the uniqueness of this solution will be proved.
1

315
326


M.
Jahanshahi
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
Department of Mathematics, Azarbaijan Shahid
Iran
jahanshahi@azaruniv.edu


M.
Darabadi
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
Department of Mathematics, Azarbaijan Shahid
Iran
m.darabadi@azaruni.edu
Partial Differential Equation
Boundary Value Problem
Self Adjoint Problem
NonSelf Adjoint Operators
NonLocalBoundary Conditions
Trivially related lax pairs of the SawadaKotera equation
2
2
We show that a recently introduced Lax pair of the SawadaKotera equation is nota new one but is trivially related to the known old Lax pair. Using the socalled trivialcompositions of the old Lax pairs with a differentially constrained arbitrary operators,we give some examples of trivial Lax pairs of KdV and SawadaKotera equations.
1

327
330


D.
Talati
Sama Technical and Vocational Training College, Islamic Azad university, Urmia Branch, Urmia, Iran.
Sama Technical and Vocational Training College,
Iran
talati@eng.ankara.edu.tr
SawadaKotera equation
Lax pair
integrability
On Silverman's conjecture for a family of elliptic curves
2
2
Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $E^{(p)}(Bbb{Q})$ has positive rank, and there are infinitely many primes $q$ for which $E^{(q)}(Bbb{Q})$ has rank $0$. In this paper, assuming the parity conjecture, we show that for infinitely many primes $p$, the elliptic curve $E_n^{(p)}: y^2=x^3np^2x$ has odd rank and for infinitely many primes $p$, $E_n^{(p)}(Bbb{Q})$ has even rank, where $n$ is a positive integer that can be written as biquadrates sums in two different ways, i.e., $n=u^4+v^4=r^4+s^4$, where $u, v, r, s$ are positive integers such that $gcd(u,v)=gcd(r,s)=1$. More precisely, we prove that: if $n$ can be written in two different ways as biquartic sums and $p$ is prime, then under the assumption of the parity conjecture $E_n^{(p)}(Bbb{Q})$ has odd rank (and so a positive rank) as long as $n$ is odd and $pequiv5, 7pmod{8}$ or $n$ is even and $pequiv1pmod{4}$. In the end, we also compute the ranks of some specific values of $n$ and $p$ explicitly.
1

331
340


K.
Nabardi
Department of
Mathematics, Azarbaijan Shahid Madani University,
Tabriz 5375171379, Iran.
Department of
Mathematics, Azarbaijan Shahid
Iran
nabardi@azaruniv.edu


F.
Izadi
Department of
Mathematics, Azarbaijan Shahid Madani University, P. O. Box 5375171379,
Tabriz , Iran.
Department of
Mathematics, Azarbaijan Shahid
Iran
izadi@azaruniv.edu
Silverman's Conjecture
Elliptic Curve
Quadratic Twist
Rank
Parity Conjecture
Every class of $S$acts having a flatness property is closed under directed colimits
2
2
Let $S$ be a monoid. In this paper, we prove every class of $S$acts having a flatness property is closed underdirected colimits, it extends some known results. Furthermore thisresult implies that every $S$act has a flatness cover if and only if it has a flatness precover.
1

341
351


H.
Qiao
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.
College of Mathematics and Statistics, Northwest
China (P. R. C.)
qiaohs@nwnu.edu.cn


L.
Wang
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.
College of Mathematics and Statistics, Northwest
China (P. R. C.)
wanglm@nwnu.edu.cn


X.
Ma
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.
College of Mathematics and Statistics, Northwest
China (P. R. C.)
maxin263@126.com
Flatness property
colimit
closed
Partial proof of Graham Higman's conjecture related to coset diagrams
2
2
Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree, there are finite number of such polynomials. In this paper, we consider a family Ϝ of fragments such that each fragment in Ϝ contains one vertex fixed byF_v [(〖xy〗^(1) )^(s_1 ) (xy)^(s_2 ) (〖xy〗^(1) )^(s_3 ),(xy)^(q_1 ) (〖xy〗^(1) )^(q_2 ) (xy)^(q_3 ) ]where s₁,s₂,s₃,q₁,q₂,q₃∈ℤ⁺, and prove Higman's conjecture for the polynomials obtained from the fragments in Ϝ.
1

353
369


Q.
Mushtaq
Vice Chancellor, The Islamia University of Bahawalpur, Pakistan.
Vice Chancellor, The Islamia University of
Pakistan
pir_qmushtaq@yahoo.com


A.
Razaq
Department of Mathematics, Govt. Post Graduate College Jauharabad, Pakistan.
Department of Mathematics, Govt. Post Graduate
Pakistan
makenqau@gmail.com
Modular group
Coset diagrams
projective line over finite field
Toroidalization of locally toroidal morphisms of 3folds
2
2
A toroidalization of a dominant morphism $varphi: Xto Y$ of algebraic varieties over a field of characteristic zero is a toroidal lifting of $varphi$ obtained by performing sequences of blow ups of nonsingular subvarieties above $X$ and $Y$. We give a proof of toroidalization of locally toroidal morphisms of 3folds.
1

371
405


R.
Ahmadian
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 193955746, Tehran, Iran.
School of Mathematics, Institute for Research
Iran
ahmadian@ipm.ir
Toroidalization
resolution of morphisms
principalization
Finite groups with $X$quasipermutable subgroups of prime power order
2
2
Let $H$, $L$ and $X$ be subgroups of a finite group$G$. Then $H$ is said to be $X$permutable with $L$ if for some$xin X$ we have $AL^{x}=L^{x}A$. We say that $H$ is emph{$X$quasipermutable } (emph{$X_{S}$quasipermutable}, respectively) in $G$ provided $G$ has a subgroup$B$ such that $G=N_{G}(H)B$ and $H$ $X$permutes with $B$ and with all subgroups (with all Sylowsubgroups, respectively) $V$ of $B$ such that $(H, V)=1$. Inthis paper, we analyze the influence of $X$quasipermutable and$X_{S}$quasipermutable subgroups on the structure of $G$. Some known results are generalized.
1

407
416


X.
Yi
Department of Mathematics, Zhejiang SciTech University, 310018, Hangzhou, P. R. China.
Department of Mathematics, Zhejiang SciTech
China (P. R. C.)
yxlyixiaolan@163.com


X.
Yang
Department of Mathematics, Zhejiang SciTech University, 310018, Hangzhou, P. R. China.
Department of Mathematics, Zhejiang SciTech
China (P. R. C.)
yangxue0222@126.com
$X$quasipermutable subgroup
Sylow subgroup
$p$soluble group
$p$supersoluble group
$p$nilpotent group
The augmented Zagreb index, vertex connectivity and matching number of graphs
2
2
Let $Gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. Denote by $Upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. In the classes of graphs $Gamma_{n,kappa}$ and $Upsilon_{n,beta}$, the elements having maximum augmented Zagreb index are determined.
1

417
425


A.
Ali
Department of Mathematics, National University of Computer and
Emerging Sciences, BBlock, Faisal Town, Lahore, Pakistan.
Department of Mathematics, National University
Pakistan
akbarali.maths@gmail.com


A.
Bhatti
Department of Mathematics, National University of Computer and
Emerging Sciences, BBlock, Faisal Town, Lahore, Pakistan.
Department of Mathematics, National University
Pakistan
akhlaq.ahmad@nu.edu.pk


Z.
Raza
Department of Mathematics, National University of Computer
and Emerging Sciences, BBlock, Faisal Town, Lahore, Pakistan.and Department of Mathematics, College of Sciences, University
of Sharjah, Sharjah, United Arab Emirates.
Department of Mathematics, National University
Pakistan
zahid.raza@nu.edu.pk
augmented Zagreb index
vertex connectivity
matching number
spanning subgraph
The unit sum number of Baer rings
2
2
In this paper we prove that each element of any regular Baer ring is a sum of two units if no factor ring of R is isomorphic to Z_2 and we characterize regular Baer rings with unit sum numbers $omega$ and $infty$. Then as an application, we discuss the unit sum number of some classes of group rings.
1

427
434


N.
Ashrafi
Semnan UniversityFaculty of Mathematics, Statistics and
Computer Science,
Semnan University, Semnan, Iran.
Semnan UniversityFaculty of Mathematics,
Iran
nashrafi@semnan.ac.ir


N.
Pouyan
Faculty of Mathematics, Statistics and Computer Science,
Semnan
University, Semnan, Iran.
Faculty of Mathematics, Statistics and Computer
Iran
neda.pouyan@gmail.com
unit sum number
regular Baer ring
$pi$regular Baer ring
right perpetual ideal
Existence of ground states for approximately inner twoparameter $C_0$groups on $C^*$algebras
2
2
In this paper, we generalize the definitions of approximately inner $C_0$groups and their ground states to the two parameter case and study necessary and sufficient conditions for a state to be ground state. Also we prove that any approximately inner two parameter $C_0$group must have at least one ground state. Finally some applications are given.
1

435
446


R.
Abazari
Department of
Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
Department of
Mathematics, Mashhad Branch,
Iran
rasoolabazari@gmail.com


A.
Niknam
Department of
Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
Department of
Mathematics, Mashhad Branch,
Iran
niknam@um.ac.ir
Twoparameter group
Approximately inner dynamical system
Tensor product
Ground state
Remarks on microperiodic multifunctions
2
2
It is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. We introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. We deal with Vietoris and Hausdorff continuity concepts.Stability of microperiodic multifunctions is considered, namely we show that an approximately microperiodic multifunction is close to a constant one, provided it is continuous at some point. As a consequence we obtain stability result for an approximately microperiodic singlevalued function.
1

447
459


J.
Olko
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30059 Kraków, Poland.
AGH University of Science and Technology,
Poland
olko@agh.edu.pl
multifunction
microperiodic function
functional inequality
functional inclusion
On cycles in intersection graphs of rings
2
2
Let $R$ be a commutative ring with nonzero identity. We describe all $C_3$ and $C_4$free intersection graph of nontrivial ideals of $R$ as well as $C_n$free intersection graph when $R$ is a reduced ring. Also, we shall describe all complete, regular and $n$clawfree intersection graphs. Finally, we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. We show that such graphs are indeed pancyclic.
1

461
470


N.
Hoseini
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
Department of Pure Mathematics, Ferdowsi
Iran
nesa.hoseini@gmail.com


A.
Erfanian
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
Department of Pure Mathematics, Ferdowsi
Iran
erfanian@math.um.ac.ir


A.
Azimi
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
Department of Pure Mathematics, Ferdowsi
Iran
ali.azimi61@gmail.com


M.
Farrokhi D. G.
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
Department of Pure Mathematics, Ferdowsi
Japan
m.farrokhi.d.g@gmail.com
Intersection graph
cycle
claw
Hamiltonian
pancyclic
On linear preservers of sgutmajorization on $textbf{M}_{n,m}$
2
2
Abstract. Let Mn;m be the set of nbym matrices with entries inthe field of real numbers. A matrix R in Mn = Mn;n is a generalizedrow substochastic matrix (grow substochastic, for short) if Re e, where e = (1; 1; : : : ; 1)t. For X; Y 2 Mn;m, X is said to besgutmajorized by Y (denoted by X sgut Y ) if there exists annbyn upper triangular grow substochastic matrix R such thatX = RY . This paper characterizes all linear preservers and stronglinear preservers of sgut on Rn and Mn;m respectively.
1

471
481


A.
Ilkhanizadeh Manesh
Department of
Mathematics, ValieAsr
University of Rafsanjan, P.O. Box 7713936417, Rafsanjan, Iran.
Department of
Mathematics, ValieAsr
University
Iran
a.ilkhani@vru.ac.ir
Linear preserver
Strong linear preserver
grow substochastic matrices
sgut majorization
Examples of nonquasicommutative semigroups decomposed into unions of groups
2
2
Decomposability of an algebraic structure into the union of its substructures goes back to G. Scorza's Theorem of 1926 for groups. An analogue of this theorem for rings has been recently studied by A. Lucchini in 2012. On the study of this problem for nongroup semigroups, the first attempt is due to Clifford's work of 1961 for the regular semigroups. Since then, N.P. Mukherjee in 1972 studied the decomposition of quasicommutative semigroups where, he proved that: a regular quasicommutative semigroup is decomposable into the union of groups. The converse of this result is a natural question. Obviously, if a semigroup $S$ is decomposable into a union of groups then $S$ is regular so, the aim of this paper is to give examples of nonquasicommutative semigroups which are decomposable into the disjoint unions of groups. Our examples are the semigroups presented by the following presentations: $$pi_1 =langle a,bmid a^{n+1}=a, b^3=b, ba=a^{n1}brangle,~(ngeq 3),$$ $$pi_2 =langle a,bmid a^{1+p^alpha}=a, b^{1+p^beta}=b, ab=ba^{1+p^{alphagamma}}rangle$$where, $p$ is an odd prime, $alpha, beta$ and $gamma$ are integers such that $alpha geq 2gamma$, $beta geq gamma geq 1$ and $alpha +beta > 3$.
1

483
487


N.
Hosseinzadeh
Department of
Mathematics, Tehran Science and Research Branch, Islamic Azad
University, P.O. Box 14515/1775, Tehran, Iran.
Department of
Mathematics, Tehran Science
Iran
narges.hosseinzadeh@gmail.com


H.
Doostie
Department of
Mathematics, Tehran Science and Research Branch, Islamic Azad
University, P.O. Box 14515/1775, Tehran, Iran.
Department of
Mathematics, Tehran Science
Iran
doostih@khu.ac.ir
quasicommutative semigroups
finitely presented semigroups
decomposition
Pseudo Ricci symmetric real hypersurfaces of a complex projective space
2
2
Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.
1

489
497


S. k.
Hui
Department of Mathematics, Sidho Kanho Birsha University, Purulia723104, West Bengal, India.newline
Department of Mathematics, Bankura University, Bankura722155, West Bengal, India.
Department of Mathematics, Sidho Kanho Birsha
India
shyamal_hui@yahoo.co.in


Y.
Matsuyama
Department of Mathematics, Chuo University, Faculty of Science and Engineering, 11327 Kasuga, Bunkyoku, Tokyo 1128551, Japan.
Department of Mathematics, Chuo University,
Japan
matuyama@math.chuou.ac.jp
real hypersurface
complex projective space
pseudo Ricci symmetric