2013
39
1
1
0
Beyond First Order Logic: From number of structures to structure of
numbers: Part I
2
2
We study the history and recent developments in nonelementarymodel theory focusing on the framework of abstractelementary classes. We discuss the role of syntax and semanticsand the motivation to generalize first order model theory to nonelementaryframeworks and illuminate the study with concrete examplesof classes of models. This first part introduces the main conceps and philosophies anddiscusses two research questions, namely categoricity transfer andthe stability classification.
1

1
26


J.
Baldwin
University of Illinois at Chicago
University of Illinois at Chicago
United States of America
jbaldwin@uic.edu


T.
Hyttinen
Department of Mathematics and Statistics
University of Helsinki
Department of Mathematics and Statistics
Universit
Finland
tapani.hyttinen@helsinki.fi


M.
Kesala
Department of Mathematics and Statistics
University of Helsinki
Department of Mathematics and Statistics
Universit
Finland
meeri.kesala@helsinki.fi
Mathematical logic
model theory
Beyond first order logic: From number of structures to structure of numbers: Part II
2
2
We study the history and recent developments in nonelementarymodel theory focusing on the framework of abstractelementary classes. We discuss the role of syntax and semanticsand the motivation to generalize first order model theory to nonelementaryframeworks and illuminate the study with concrete examplesof classes of models. This second part continues to study the question of catecoricitytransfer and counting the number of structures of certain cardinality.We discuss more thoroughly the role of countable models,search for a nonelementary counterpart for the concept of completenessand present two examples: one example answers a questionasked by David Kueker and the other investigates models ofPeano Arithmetic and the relation of an elementary endextensionin terms of an abstract elementary class.
1

27
48


J.
Baldwin
University of Illinois
at Chicago, USA
University of Illinois
at Chicago, USA
United States of America
jbaldwin@uic.edu


T.
Hyttinen
University of Helsinki, Finland
University of Helsinki, Finland
Finland
tapani.hyttinen@helsinki.fi


M.
Kesala
University of Helsinki, Finland
University of Helsinki, Finland
Finland
meeri.kesala@helsinki.fi
Mathematical logic
model theory
Generalized Rings of Measurable and Continuous Functions
2
2
This paper is an attempt to generalize, simultaneously, the ring of realvalued continuous functions and the ring of realvalued measurable functions.
1

49
64


A.
Amini
Shiraz University
Shiraz University
Iran
aamini@shirazu.ac.ir


B.
Amini
Shiraz University
Shiraz University
Iran
bamini@shirazu.ac.ir


E.
Momtahan
Yasouj University
Yasouj University
Iran
momtahan_e@hotmail.com


M. H.
Shirdareh Haghigi
Shiraz University
Shiraz University
Iran
shirdareh@susc.ac.ir
rings of continuous functions
rings of measurable functions
regular rings
$aleph_0$selfinjective rings
Grouplikes
2
2
In this paper we introduce and study an algebraic structure, namely Grouplike. A grouplike is something between semigroup and group and its axioms are generalizations of the four group axioms. Every grouplike is a semigroup containing the minimum ideal that is also a maximal subgroup (but the converse is not valid). The first idea of grouplikes comes from bparts and $b$addition of real numbers introduced by the author. Now, the researches have enabled me to introduce Grouplikes and prove some of their main theorems and construct a vast class of them, here. We prove a fundamental structure theorem for a big class of grouplikes, namely Class United Grouplikes. Moreover, we obtain some other results for binary systems, semigroups and groups in general and exhibit several their important subsets with related diagrams. Finally. we show some of future directions for the researches in grouplikes and semigroup theory.
1

65
85


M. H.
Hooshmand
Islamic Azad University  Shiraz Branch
Islamic Azad University  Shiraz Branch
Iran
hadi.hooshmand@gmail.com
Grouplike
class united grouplike
identitylike
grouplike homomorphism
real bgrouplike
Brandt extensions and primitive topologically periodic inverse topological semigroups
2
2
In this paper we find sufficient conditions on primitive inverse topological semigroup S under which: the inversion inv : (H(S)) (H(S)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed Hclasses is topologically isomorphic to an orthogonal sum P i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compact topological groups Gi in the class of topological inverse semigroups for some finite cardinals.
1

87
95


J.
Jamalzadeh
I am phd student in sistan and bluchestan university
I am phd student in sistan and bluchestan
Iran
jamalzadeh1980@yahoo.com


Gh.
Rezaei
University of Sistan and Bluchestan, Iran
University of Sistan and Bluchestan, Iran
Iran
grezaei@hamoon.usb.ac.ir
inverse topological semigroup
Topological inverse semigroup
0 simple group
completely 0simple semigroup
On the relations between the point spectrum of A and invertibility of I + f(A)B
2
2
Let A be a bounded linear operator on a Banach space X. We investigate the conditions of existing rankone operator B such that I+f(A)B is invertible for every analytic function f on sigma(A). Also we compare the invariant subspaces of f(A)B and B. This work is motivated by an operator method on the Banach space ell^2 for solving some PDEs which is extended to general operator space under some conditions in this paper.
1

97
106


H.
Larki
Islamic Azad University, Parand Branch
Islamic Azad University, Parand Branch
Iran
h.larki@gmail.com


A.
Riazi
Amirkabir University of Technology
Amirkabir University of Technology
Iran
riazi@aut.ac.ir
point spectrum
rankone operator
invariant subspaces
On a subclass of multivalent analytic functions associated with an extended fractional differintegral operator
2
2
Making use of an extended fractional differintegral operator ( introduced recently by Patel and Mishra), we introduce a new subclass of multivalent analytic functions and investigate certain interesting properties of this subclass.
1

107
124


J.L.
Liu
Department of Mathematics, Yangzhou University
Department of Mathematics, Yangzhou University
China, R. O. C.
jlliu@yzu.edu.cn
analytic function
Multivalent function
fractional differintegral operator
convex univalent function
Subordination
The two parameter quantum groups
$U_{r,s}(mathfrak{g})$ associated to generalized KacMoody algebra
and their equitable presentation
2
2
We construct a family of two parameter quantum grou\ps
$U_{r,s}(mathfrak{g})$ associated with a generalized KacMoody
algebra corresponding to symmetrizable admissible Borcherds Cartan
matrix. We also construct the $textbf{A}$form $U_{textbf{A}}$ and
the classical limit of $U_{r,s}(mathfrak{g})$. Furthermore, we
display the equitable presentation for a subalgebra
$U_{r,s}^{b}(mathfrak{g} )$ of $U_{r,s}(mathfrak{g})$ and show
that this presentation has the attractive feature that all of its
generators act semisimply on finite dimensional irreducible
$U_{r,s}(mathfrak{g})$modules associated with the KacMoody algebra.
1

125
149


Q.
Sun
Zhejiang University of Science and Technology, China
Zhejiang University of Science and Technology,
China (P. R. C.)
qxsun@126.com


H.
Li
Zhejiang International Studies University, China
Zhejiang International Studies University,
China (P. R. C.)
honglli@126.com
Essential norm of generalized composition operators from
weighted Dirichlet or Bloch type spaces to Q_K type spaces
2
2
In this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted Dirichlet spaces or Bloch type spaces to $Q_K$ type spaces.
1

151
164


Sh.
Rezaei
Islamic Azad University, Iran
Islamic Azad University, Iran
Iran
sh.rezaei@srbiau.ac.ir


H.
Mahyar
Tarbiat Moallem University, Iran
Tarbiat Moallem University, Iran
Iran
mahyar@khu.ac.ir
Bloch type space
weighted Dirichlet space
$Q_K$ type space
generalized composition operator
essential norm
Existence and uniqueness of solutions for a periodic
boundary value problem
2
2
In this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a firstorder ordinary differential equation with periodic boundary conditions in Banach spaces admitting the existence of a lower solution.
1

165
173


A.
Amini Harandi
University of Shahrekord, Iran
University of Shahrekord, Iran
Iran
aminih_a@yahoo.com
fixed point
Periodic boundary value problem
Banach lattice
The Quasimorphic Property of Group
2
2
A group is called morphic if for each normal endomorphism α in end(G),there exists β such that ker(α)= Gβ and Gα= ker(β). In this paper, we consider the case that there exist normal endomorphisms β and γ such that ker(α)= Gβ and Gα = ker(γ). We call G quasimorphic, if this happens for any normal endomorphism α in end(G). We get the following results: G is quasimorphic if and only if, for any normal subgroup K and N such that G/K≌N, there exist normal subgroup T and H such that G/T≌K and G/N≌H. Further, we investigate the quasimorphic property of finitely generated abelian group and get that a finitely generated abelian group is quasimorphic if and only if it is finite.
1

175
185


Q.
Wang
Department of Mathematics and Systems Science, National University of Defense Technology, P.R.China 410073,Changsha, China.
Department of Mathematics and Systems Science,
China, R. O. C.
wangqichuan1026@163.com.cn


K.
Long
Department of Mathematics and Systems Science, National University of Defense Technology ,P.R.China 410073, Changsha, China.
Department of Mathematics and Systems Science,
China, R. O. C.
lkkkkkkkk@hotmail.com.cn


L.
Feng
Department of Mathematics and Systems Science, National University of Defense
Technology, P.R.China 410073, Changsha, China.
Department of Mathematics and Systems Science,
China, R. O. C.
fenglg2002@sina.com.cn
quasimorphic group
finitely generated abelian group
normal endomorphism
Maximal subsets of pairwise noncommuting elements of some finite pgroups
2
2
Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If X ≥ Y  for any other set of pairwise noncommuting elements Y in G, then X is said to be a maximal subset of pairwise noncommuting elements. In this paper we determine the cardinality of a maximal subset of pairwise noncommuting elements in any nonabelian pgroups with central quotient of order less than or equal to p3 for any prime number p. As an immediate consequence we give this cardinality for any nonabelian group of order p4.
1

187
192


A.
Azad
Arak University, Iran
Arak University, Iran
Iran
a.azad1347@gmail.com


S.
Fouladi
Kharazmi University, Iran
Kharazmi University, Iran
Iran
s_fouladi@khu.ac.ir


R.
Orfi
Arak University, Iran
Arak University, Iran
Iran
rorfi@araku.ac.ir
pairwise noncommuting elements
Finite pgroup
ACgroup
$varepsilon$Simultaneous approximations
of downward sets
2
2
In this paper, we prove some results on characterization of $varepsilon$simultaneous approximations of downward sets in vector lattice Banach spaces. Also, we give some results about simultaneous approximations of normal sets.
1

193
203


H.
Alizadeh
Islamic Aazad University, Marand, Iran
Islamic Aazad University, Marand, Iran
Iran
halizadeh@marandiau.ac.ir


Sh.
Rezapour
Azarbaidjan University of Tarbiat Moallem, Iran
Azarbaidjan University of Tarbiat Moallem,
Iran
sh.rezapour@azaruniv.edu


S.
Vaezpour
Amirkabir University of Technology, Iran
Amirkabir University of Technology, Iran
Iran
vaez@aut.ac.ir
$varepsilon$simultaneous approximation
Downward set
Lattice Banach space
Spacelike hypersurfaces in Riemannian or Lorentzian space forms satisfying L_k(x)=Ax+b
2
2
We study connected orientable spacelike hypersurfaces $x:M^{n}rightarrowM_q^{n+1}(c)$, isometrically immersed into the Riemannian or Lorentzian space form of curvature $c=1,0,1$, and index $q=0,1$, satisfying the condition $~L_kx=Ax+b$,~ where $L_k$ is the $textit{linearized operator}$ of the $(k+1)$th mean curvature $H_{k+1}$ of the hypersurface for a fixed integer $0leq k<n$, $A$ is a constant matrix and $b$ is a constant vector. We show that the only hypersurfaces satisfying that condition are hypersurfaces with zero $H_{k+1}$ and constant $H_k$ ( when $cneq 0$ ), open pieces of totally umbilic hypersurfaces and open pieces of the standard Riemannian product of two totally umbilic hypersurfaces.
1

205
223


F.
Pashaie
Tarbiat Modares University, Iran
Tarbiat Modares University, Iran
Iran
f_pashaie@yahoo.com


S.M.B.
Kashani
Tarbiat Modares University
Tarbiat Modares University
Iran
kashanism@yahoo.com
Linearized operator $L_k$
Higher order mean curvatures
Lorentzian space forms