2016
42
4
4
0
The geometric properties of a degenerate parabolic equation with periodic source term
2
2
In this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the Cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. Our objective is to show that: (1)with continuous variation of time t, the surface ϕ = [u(x,t)]mδq is a complete Riemannian manifold floating in space RN+1and is tangent to the space RN at ∂H0(t); (2)the surface u = u(x,t) is tangent to the hyperplane W(t) at ∂Hu(t).
1

799
808


G.
Guo
Institute of Mathematics, Shanghai Normal University, Shanghai, 200235,
China and
Institute of Mathematics, Jimei University, Xiamen, 361021 China.
Institute of Mathematics, Shanghai
China (P. R. C.)
gwg0518@sina.com


J. Q.
Pan
Institute of Mathematics, Jimei University, Xiamen, 361021 China.
Institute of Mathematics, Jimei
China (P. R. C.)
jqpan@jmu.edu.cn
Degenerate parabolic equation
~Riemannian manifold
~Periodic source term
Constructing vertex decomposable graphs
2
2
Recently, some techniques such as adding whiskers and attaching graphs to vertices of a given graph, have been proposed for constructing a new vertex decomposable graph. In this paper, we present a new method for constructing vertex decomposable graphs. Then we use this construction to generalize the result due to Cook and Nagel.
1

809
817


E.
Lashani
Department of Mathematics, Science and Research
branch, Islamic Azad University(IAU), Tehran, Iran.
Department of Mathematics, Science
Iran
lashani@iaudoroud.ac.ir


A.
Soleyman Jahan
Department of Mathematics, University of Kurdistan,
P.O. Box 6617715175, Sanadaj, Iran.
Department of Mathematics, University
Iran
solymanjahan@gmail.com
Finite graph
wellcovered graph
independence complex
edge ideal
vertex decomposable graph
A limited memory adaptive trustregion approach for largescale unconstrained optimization
2
2
This study concerns with a trustregionbased method for solving unconstrained optimization problems. The approach takes the advantages of the compact limited memory BFGS updating formula together with an appropriate adaptive radius strategy. In our approach, the adaptive technique leads us to decrease the number of subproblems solving, while utilizing the structure of limited memory quasiNewton formulas helps to handle largescale problems. Theoretical analysis indicates that the new approach preserves the global convergence to a firstorder stationary point under classical assumptions. Moreover, the superlinear and the quadratic convergence rates are also established under suitable conditions. Preliminary numerical experiments show the effectiveness of the proposed approach for solving largescale unconstrained optimization problems.
1

819
837


M.
Ahookhosh
Faculty of Mathematics, University of Vienna, OskarMorgensternPlatz 1, 1090 Vienna, Austria.
Faculty of Mathematics, University
Austria
masoud.ahookhosh@univie.ac.at


K.
Amini
Department of
Mathematics, Razi University, Kermanshah, Iran.
Department of
Mathematics,
Iran
kamini@razi.ac.ir


M.
Kimiaei
Department of
Mathematics, Asadabad Branch, Islamic Azad University, Asadabad, Iran.
Department of
Mathematics,
Iran
morteza.kimiaei@gmail.com


M. R.
Peyghami
K.N. Toosi University of Department of
Mathematics, K. N. Toosi University of Technology, P.O. Box 163151618, Tehran, Iran.
K.N. Toosi University of Department of
M
Iran
peyghami@kntu.ac.ir
Unconstrained optimization
trustregion framework
compact quasiNewton representation
limited memory technique
adaptive strategy
Totally umbilical radical transversal lightlike hypersurfaces of KählerNorden manifolds of constant totally real sectional curvatures
2
2
In this paper we study curvature properties of semi  symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahlerNorden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$ by the Norden metrics $overline g$ and $overline {widetilde g}$, respectively). We obtain a condition for $overline {widetilde nu}$ (resp. $overline nu$) which is equivalent to eachof the following conditions: $(M,g)$ $(resp., (M,widetilde g))$ is locally symmetric, semisymmetric, Ricci semisymmetric and almost Einstein. We construct an example of a totally umbilical radical transversal lightlike hypersurface, which is locally symmetric, semisymmetric, Ricci semisymmetric and almost Einstein.
1

839
854


G.
Nakova
Department of Algebra and Geometry,
Faculty of Mathematics and Informatics,
University of Veliko Tarnovo "St. Cyril and St. Methodius",
2 T. Tarnovski Str., 5003
Department of Algebra and Geometry,
Bulgaria
gnakova@gmail.com
KählerNorden manifold
totally real sectional curvature
radical transversal lightlike hypersurface
totally umbilical lightlike hypersurface
A note on inequalities for Tsallis relative operator entropy
2
2
In this short note, we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy, {em Math. Inequal. Appl.} {18} (2015), no. 2, 401406]. Meanwhile, we also show some new lower and upper bounds for relative operator entropy and Tsallis relative operator entropy.
1

855
859


L.
Zou
School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, P. R. China.
School of Mathematics and Statistics,
China (P. R. C.)
liminzou@163.com


Y.
Jiang
School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, P. R. China.
School of Mathematics and Statistics,
China (P. R. C.)
yyy_j123456@163.com
Relative operator entropy
Tsallis relative operator entropy
operator inequalities
A module theoretic approach to zerodivisor graph with respect to (first) dual
2
2
Let $M$ be an $R$module and $0 neq fin M^*={rm Hom}(M,R)$. We associate an undirected graph $gf$ to $M$ in which nonzero elements $x$ and $y$ of $M$ are adjacent provided that $xf(y)=0$ or $yf(x)=0$. Weobserve that over a commutative ring $R$, $gf$ is connected anddiam$(gf)leq 3$. Moreover, if $Gamma (M)$ contains a cycle,then $mbox{gr}(gf)leq 4$. Furthermore if $gfgeq 1$, then$gf$ is finite if and only if $M$ is finite. Also if $gf=emptyset$, then $f$ ismonomorphism (the converse is true if $R$ is a domain). If $M$ iseither a free module with ${rm rank}(M)geq 2$ or anonfinitely generated projective module there exists $fin M^*$with ${rm rad}(gf)=1$ and ${rm diam}(gf)leq 2$. We prove thatfor a domain $R$ the chromatic number and the clique number of $gf$ are equal.
1

861
872


E.
Momtahan
Department of Mathematics,
Yasouj University, Yasouj,75914, Iran.
Department of Mathematics,
Yasouj
Iran
momtahan_e@hotmail.com


M.
Baziar
Department of Mathematics,
Yasouj University, Yasouj,75914, Iran.
Department of Mathematics,
Yasouj
Iran
mbaziar@yu.ac.ir


S.
Safaeeyan
Department of Mathematics,
Yasouj University, Yasouj,75914, Iran.
Department of Mathematics,
Yasouj
Iran
safaeeyan@yu.ac.ir
Zerodivisor graph
Clique number
Chromatic number
Module
Centerlike subsets in rings with derivations or epimorphisms
2
2
We introduce centerlike subsets Z*(R,f), Z**(R,f) and Z1(R,f), where R is a ring and f is a map from R to R. For f a derivation or a nonidentity epimorphism and R a suitablychosen prime or semiprime ring, we prove that these sets coincide with the center of R.
1

873
878


H. E.
Bell
Department of Mathematics, Brock University, St. Catharines, Ontario L2S 3A1, Canada.
Department of Mathematics, Brock
Canada
hbell@brocku.ca


M. N.
Daif
Department of Mathematics, AlAzhar University, Nasr City(11884), Cairo, Egypt.
Department of Mathematics, AlAzhar
Egypt
nagydaif@yahoo.com
Prime ring
semiprime ring
derivation
epimorphism
centerlike subset
The Ramsey numbers of large trees versus wheels
2
2
For two given graphs G1 and G2, the Ramseynumber R(G1,G2) is the smallest integer n such that for anygraph G of order n, either $G$ contains G1 or the complementof G contains G2. Let Tn denote a tree of order n andWm a wheel of order m+1. To the best of our knowledge, only R(Tn,Wm) with small wheels are known.In this paper, we show that R(Tn,Wm)=3n2 for odd m with n>756m^{10}.
1

879
880


D.
Zhu
School of Economics and Management, Southeast University, Nanjing 210093, P.R. China.
School of Economics and Management,
China (P. R. C.)
dongmeizhu2013@126.com


L.
Zhang
School of Management and Engineering,
Nanjing University, Nanjing 210093, P.R. China.
School of Management and Engineering,
Na
China (P. R. C.)
zhanglm@nju.edu.cn


D.
Li
School of Management and Engineering,
Nanjing University, Nanjing 210093, P.R. China.
School of Management and Engineering,
Na
China (P. R. C.)
leedongxin@163.com
Ramsey number
tree
wheel
Coefficient estimates for a subclass of analytic and biunivalent functions
2
2
In this paper, we introduce and investigate a subclass of analytic and biunivalent functions in the open unit disk. Upper bounds for the second and third coefficients of functions in this subclass are founded. Our results, which are presented in this paper, generalize and improve those in related works of several earlier authors.
1

881
889


A.
Zireh
Department of Mathematics, Shahrood University Of Technology, P.O. Box 31636155, Shahrood, Iran.
Department of Mathematics, Shahrood
Iran
azireh@shahroodut.ac.ir


E.
Analouei Audegani
Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Mobarakeh, P.O. Box 8481997817, Isfahan, Iran.
Department of Mathematics, Mobarakeh
Iran
e_analoei@ymail.com
Analytic functions
BiUnivalent Functions
Coefficient estimates
starlike functions
Koebe onequarter theorem
Relative (co)homology of $F$Gorenstein modules
2
2
We investigate the relative cohomology and relative homology theories of $F$Gorenstein modules, consider the relations between classical and $F$Gorenstein (co)homology theories.
1

891
902


C.
Zhang
Department of Mathematics, Northwest
School of Mathematics Sciences, Chongqing Normal University, Chongqing 400000, China.
Department of Mathematics, Northwest
School
China (P. R. C.)
zhangcx@nwnu.edu.cn


Z.
Li
Department of Mathematics, Northwest
Normal University, Lanzhou 730070, China.
Department of Mathematics, Northwest&lrm
China (P. R. C.)
792252531@qq.com
$F$Gorenstein projective module
$F$Gorenstein injective module
relative cohomology
relative homology
On BlackScholes equation; method of Heirequations, nonlinear selfadjointness and conservation laws
2
2
In this paper, Heirequations method is applied to investigate nonclassical symmetries and new solutions of the BlackScholes equation. Nonlinear selfadjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.
1

903
921


M. S.
Hashemi
Department of Mathematics, Basic Science Faculty,
University of Bonab, P.O. Box 5551761167, Bonab, Iran.
Department of Mathematics, Basic
Iran
hashemi_math396@yahoo.com
BlackScholes equation
Heirequation
nonclassical symmetry
Nonlinear selfadjointness
Conservation law
On the order of a module
2
2
Abstract. Let (R,P) be a Noetherian unique factorization domain (UFD) and M be a finitely generated Rmodule. Let I(M)be the first nonzero Fitting ideal of M and the order of M, denotedord_R(M), be the largest integer n such that I(M) ⊆ P^n. In thispaper, we show that if M is a module of order one, then either Mis isomorphic with direct sum of a free module and a cyclic moduleor M is isomorphic with a special module represented in the text.We also assert some properties of M while ord_R(M) = 2.
1

923
931


S.
Hadjirezaei
Department of
Mathematics, ValieAsr University of Rafsanjan, P.O. Box 7718897111, Rafsanjan, Iran.
Department of
Mathematics,
Iran
s.hajirezaei@vru.ac.ir


S.
Karimzadeh
Department of
Mathematics, ValieAsr University of Rafsanjan, P.O. Box 7718897111, Rafsanjan, Iran.
Department of
Mathematics,
Iran
karimzadeh@vru.ac.ir
Fitting ideals
minimal free presentation
order of a module
Sufficient conditions for univalence and starlikeness
2
2
It is known that the condition $mathfrak {Re} left{zf'(z)/f(z)right}>0$, $z<1$ is a sufficient condition for $f$, $f(0)=f'(0)1$ to be starlike in $z<1$. The purpose of this work is to present some new sufficient conditions for univalence and starlikeness.
1

933
939


M. N.
Nunokawa
University of Gunma, Hoshikukicho 7988, ChuouWard, Chiba 2600808, Japan.
University of Gunma, Hoshikukicho
Japan
mamoru_nuno@doctor.nifty.jp


J.
Sokol
Department of Mathematics, Rzeszow University of Technology, Al. Powstancow Warszawy 12, 35959 Rzeszow, Poland.
Department of Mathematics, Rzeszow
Poland
jsokol@prz.edu.pl


N. E.
Cho
Department of Applied Mathematics, College of Natural Sciences,
Pukyong National University, Busan 608737, Korea.
Department of Applied Mathematics, Colle
Korea, Republic of
necho@pknu.ac.kr
Analytic functions
convex functions
starlike functions
univalent functions
On two problems concerning the Zariski topology of modules
2
2
Let $R$ be an associative ring and let $M$ be a left $R$module.Let $Spec_{R}(M)$ be the collection of all prime submodules of $M$ (equipped with classical Zariski topology). There is a conjecture which says that every irreducible closed subset of $Spec_{R}(M)$ has a generic point. In this article we give an affirmative answer to this conjecture and show that if $M$ has a Noetherian spectrum, then $Spec_{R}(M)$ is a spectral space.
1

941
948


H.
AnsariToroghy
Department of pure Mathematics,
Faculty of mathematical Sciences, University of Guilan,
P.O. Box 4133519141, Rasht, Iran.
Department of pure Mathematics,
Faculty
Iran
ansari@guilan.ac.ir


R.
OvlyaeeSarmazdeh
Department of pure Mathematics,
Faculty of mathematical Sciences, University of Guilan,
P.O. Box 4133519141, Rasht, Iran.
Department of pure Mathematics,
Faculty
Iran
ovlyaee@guilan.ac.ir


Seyed Sajad
Pourmortazavi
Department of pure Mathematics,
Faculty of mathematical Sciences, University of Guilan,
P. O. Box 4133519141 Rasht, Iran.
Department of pure Mathematics,
Faculty
Iran
mortazavi@phd.guilan.ac.ir
Prime spectrum
classical Zariski topology
spectral space
Complexes of $C$projective modules
2
2
Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule $C$, $C$perfect complexes have the ability to detect when a ring is strongly regular.It is shown that there exists a class of modules which admit minimal resolutions of $C$projective modules.
1

949
958


E.
Amanzadeh
Faculty of Mathematical Sciences and Computer,
Kharazmi University, Tehran, Iran.
Faculty of Mathematical Sciences and Computer
Iran
en.amanzadeh@gmail.com


M. T.
Dibaei
Faculty of Mathematical Sciences and Computer,
Kharazmi University, Tehran, Iran
and
School of Mathematics,
Institute for Research in Fundamental Sciences (IPM), P.O. Box
Faculty of Mathematical Sciences and Computer
Iran
dibaeimt@ipm.ir
Semidualizing
$C$projective
$mathcal P_C$resolution
$C$perfect complex
strongly regular
Hyperstability of some functional equation on restricted domain: direct and fixed point methods
2
2
The study of stability problems of functional equations was motivated by a question of S.M. Ulam asked in 1940. The first result giving answer to this question is due to D.H. Hyers. Subsequently, his result was extended and generalized in several ways.We prove some hyperstability results for the equation g(ax+by)+g(cx+dy)=Ag(x)+Bg(y)on restricted domain. Namely, we show, under some weak natural assumptions, that functions satisfying the above equation approximately (in some sense) must be actually solutions to it.
1

959
974


A.
Bahyrycz
AGH University of Science and Technology, Faculty of Applied Mathematics, Mickiewicza 30, 30059 Krakow, Poland.
AGH University of Science and Technology,
Poland
bahyrycza@gmail.com
hyperstability
linear equation
quadratic equation
pWright affine function
fixed point theorem
On statistical type convergence in uniform spaces
2
2
The concept of ${mathscr{F}}_{st}$fundamentality is introduced in uniform spaces, generated by some filter ${mathscr{F}}$. Its equivalence to the concept of ${mathscr{F}}$convergence in uniform spaces is proved. This convergence generalizes many kinds of convergence, including the wellknown statistical convergence.
1

975
986


B. T.
Bilalov
Department of
Nonharmonic analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, 9, B.Vahabzade Str., AZ 1141, Baku, Azerbaijan.
Department of
Nonharmonic analysis
Azerbaijan
b_bilalov@mail.ru


T. Y.
Nazarova
Department of
Nonharmonic analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, 9, B. Vahabzade Str., AZ 1141, Baku, Azerbaijan.
Department of
Nonharmonic analysis
Azerbaijan
tubunazarova@mail.ru
${mathscr{F}}$convergence
${mathscr{F}}_{st}$ fundamentality
statistical convergence
a uniform space
Polynomial evaluation groupoids and their groups
2
2
In this paper, we show how certain metabelian groups can be found within polynomial evaluation groupoids. We show that every finite abelian group can beobtained as a polynomial evaluation groupoid.
1

987
997


H. S.
Kim
Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea.
Department of Mathematics, Research
Korea, Republic of
heekim@hanyang.ac.kr


P. J.
Allen
Department of Mathematics, University of Alabama, Tuscaloosa, AL 354870350, USA.
Department of Mathematics, University
United States of America
pallen@as.ua.edu


J.
Neggers
Department of Mathematics, University of Alabama, Tuscaloosa, AL 354870350, USA.
Department of Mathematics, University
United States of America
jneggers@as.ua.edu
polynomial evaluation groupoids
group evaluation polynomial
group
Strongly noncosingular modules
2
2
An Rmodule M is called strongly noncosingular if it has no nonzero Radsmall (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an Rmodule M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingular Rmodules; (3)absolutely coneat modules are strongly noncosingular if and only if R is a right Maxring and injective modules are strongly noncosingular; (4) a commutative ring R is semisimple if and only if the class of injective modules coincides with the class of strongly noncosingular Rmodules.
1

999
1013


Y.
Alagöz
İzmir Institute of Technology, Department
of Mathematics, 35430, İzmir, Turkey.
İzmir Institute of Technology, Departmen
Turkey
yusufalagoz@iyte.edu.tr


Y.
Durğun
Bitlis Eren University, Department of Mathematics, 13000, Bitlis, Turkey.
Bitlis Eren University, Department
Turkey
yilmaz.durgun@math.uzh.ch
coclosed submodules
(non) cosingular modules
coatomic modules
On certain semigroups of transformations that preserve double direction equivalence
2
2
Let TX be the full transformation semigroups on the set X. For an equivalence E on X, let TE(X) = {α ∈ TX : ∀(x, y) ∈ E ⇔ (xα, yα) ∈ E}It is known that TE(X) is a subsemigroup of TX. In this paper, we discussthe Green's *relations, certain *ideal and certain Rees quotient semigroup for TE(X).
1

1015
1024


L.
Deng
School of Mathematical Science, Guizhou Normal University, Guiyang 550001, China.
School of Mathematical Science, Guizhou
China (P. R. C.)
denglunzhi@163.com
Transformation semigroups
Equivalence
Green's *relations
*Ideal
Rees quotient semigroup