Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
1
2013
03
01
Beyond First Order Logic: From number of structures to structure of
numbers: Part I
1
26
EN
J.
Baldwin
University of Illinois at Chicago
jbaldwin@uic.edu
T.
Hyttinen
Department of Mathematics and Statistics
University of Helsinki
tapani.hyttinen@helsinki.fi
M.
Kesala
Department of Mathematics and Statistics
University of Helsinki
meeri.kesala@helsinki.fi
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.
Mathematical logic,model theory
http://bims.iranjournals.ir/article_320.html
http://bims.iranjournals.ir/article_320_2a3d9a459a6dc5deea92274b7c87226a.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
1
2013
03
01
Beyond first order logic: From number of structures to structure of numbers: Part II
27
48
EN
J.
Baldwin
University of Illinois
at Chicago, USA
jbaldwin@uic.edu
T.
Hyttinen
University of Helsinki, Finland
tapani.hyttinen@helsinki.fi
M.
Kesala
University of Helsinki, Finland
meeri.kesala@helsinki.fi
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 non-elementary 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 end-extensionin terms of an abstract elementary class.
Mathematical logic,model theory
http://bims.iranjournals.ir/article_409.html
http://bims.iranjournals.ir/article_409_972adc8069030d13b7a9ea9a157ed273.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
1
2013
03
01
Generalized Rings of Measurable and Continuous Functions
49
64
EN
A.
Amini
Shiraz University
aamini@shirazu.ac.ir
B.
Amini
Shiraz University
bamini@shirazu.ac.ir
E.
Momtahan
Yasouj University
momtahan_e@hotmail.com
M. H.
Shirdareh Haghigi
Shiraz University
shirdareh@susc.ac.ir
This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.
rings of continuous functions,rings of measurable
functions,regular rings,$aleph_0$-self-injective rings
http://bims.iranjournals.ir/article_233.html
http://bims.iranjournals.ir/article_233_c2ebf0d719858815bd653683ce485ae3.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
1
2013
03
01
Grouplikes
65
85
EN
M. H.
Hooshmand
Islamic Azad University - Shiraz Branch
hadi.hooshmand@gmail.com
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 b-parts 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.
Grouplike,class united grouplike,identity-like,grouplike homomorphism,real b-grouplike
http://bims.iranjournals.ir/article_305.html
http://bims.iranjournals.ir/article_305_daa595cb8449dd1f6b4a0cb354aefa32.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
1
2013
03
01
Brandt extensions and primitive topologically periodic inverse topological semigroups
87
95
EN
J.
Jamalzadeh
I am phd student in sistan and bluchestan university
jamalzadeh1980@yahoo.com
Gh.
Rezaei
University of Sistan and Bluchestan, Iran
grezaei@hamoon.usb.ac.ir
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 H-classes 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.
inverse topological semigroup,Topological inverse semigroup,0-
simple group,completely 0-simple semigroup
http://bims.iranjournals.ir/article_335.html
http://bims.iranjournals.ir/article_335_d5c026c53354c9bcbfe4d7fe7e5c649e.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
1
2013
03
01
On the relations between the point spectrum of A and invertibility of I + f(A)B
97
106
EN
H.
Larki
Islamic Azad University, Parand Branch
h.larki@gmail.com
A.
Riazi
Amirkabir University of Technology
riazi@aut.ac.ir
Let A be a bounded linear operator on a Banach space X. We investigate the conditions of existing rank-one 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.
point spectrum,rank-one operator,invariant subspaces
http://bims.iranjournals.ir/article_239.html
http://bims.iranjournals.ir/article_239_aa94bb32deb5aba560c323c06fd34102.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
1
2013
03
01
On a subclass of multivalent analytic functions associated with an extended fractional differintegral operator
107
124
EN
J.-L.
Liu
Department of Mathematics, Yangzhou University
jlliu@yzu.edu.cn
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.
analytic function,Multivalent function,fractional differintegral operator,convex univalent function,Subordination
http://bims.iranjournals.ir/article_222.html
http://bims.iranjournals.ir/article_222_b55977251c75b2af4170f508df58c24c.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
1
2013
03
01
The two parameter quantum groups
$U_{r,s}(mathfrak{g})$ associated to generalized Kac-Moody algebra
and their equitable presentation
125
149
EN
Q.
Sun
Zhejiang University of Science and Technology, China
qxsun@126.com
H.
Li
Zhejiang International Studies University, China
honglli@126.com
We construct a family of two parameter quantum grou-\ps
$U_{r,s}(mathfrak{g})$ associated with a generalized Kac-Moody
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 Kac-Moody algebra.
http://bims.iranjournals.ir/article_410.html
http://bims.iranjournals.ir/article_410_9c4af9233d4d3e488f54d9d44c7ea5bd.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
1
2013
03
01
Essential norm of generalized composition operators from
weighted Dirichlet or Bloch type spaces to Q_K type spaces
151
164
EN
Sh.
Rezaei
Islamic Azad University, Iran
sh.rezaei@srbiau.ac.ir
H.
Mahyar
Tarbiat Moallem University, Iran
mahyar@khu.ac.ir
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.
Bloch type space,weighted Dirichlet space,$Q_K$ type space,generalized composition operator,essential norm
http://bims.iranjournals.ir/article_342.html
http://bims.iranjournals.ir/article_342_7297405479aa435b72d575295ddb0380.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
1
2013
03
01
Existence and uniqueness of solutions for a periodic
boundary value problem
165
173
EN
A.
Amini Harandi
University of Shahrekord, Iran
aminih_a@yahoo.com
In this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in Banach spaces admitting the existence of a lower solution.
fixed point,Periodic boundary value problem,Banach lattice
http://bims.iranjournals.ir/article_343.html
http://bims.iranjournals.ir/article_343_4afacfa2a4973fe9304d888b866fd3ae.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
1
2013
03
01
The Quasi-morphic Property of Group
175
185
EN
Q.
Wang
Department of Mathematics and Systems Science, National University of Defense Technology, P.R.China 410073,Changsha, China.
wangqichuan1026@163.com.cn
K.
Long
Department of Mathematics and Systems Science, National University of Defense Technology ,P.R.China 410073, Changsha, China.
lkkkkkkkk@hotmail.com.cn
L.
Feng
Department of Mathematics and Systems Science, National University of Defense
Technology, P.R.China 410073, Changsha, China.
fenglg2002@sina.com.cn
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 quasi-morphic, if this happens for any normal endomorphism α in end(G). We get the following results: G is quasi-morphic 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 quasi-morphic property of finitely generated abelian group and get that a finitely generated abelian group is quasi-morphic if and only if it is finite.
quasi-morphic group,finitely generated abelian group,normal endomorphism
http://bims.iranjournals.ir/article_339.html
http://bims.iranjournals.ir/article_339_e1fa74b090c7cf943c21d3c24a31908a.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
1
2013
03
01
Maximal subsets of pairwise non-commuting elements of some finite p-groups
187
192
EN
A.
Azad
Arak University, Iran
a.azad1347@gmail.com
S.
Fouladi
Kharazmi University, Iran
s_fouladi@khu.ac.ir
R.
Orfi
Arak University, Iran
r-orfi@araku.ac.ir
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 non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian p-groups 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 non-abelian group of order p4.
pairwise non-commuting elements,Finite p-group,AC-group
http://bims.iranjournals.ir/article_341.html
http://bims.iranjournals.ir/article_341_ed95cc075963c4991eb4ff3398515d7c.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
1
2013
03
01
$varepsilon$-Simultaneous approximations
of downward sets
193
203
EN
H.
Alizadeh
Islamic Aazad University, Marand, Iran
halizadeh@marandiau.ac.ir
Sh.
Rezapour
Azarbaidjan University of Tarbiat Moallem, Iran
sh.rezapour@azaruniv.edu
S.
M.
Vaezpour
Amirkabir University of Technology, Iran
vaez@aut.ac.ir
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.
$varepsilon$-simultaneous approximation,Downward set,Lattice Banach space
http://bims.iranjournals.ir/article_345.html
http://bims.iranjournals.ir/article_345_3d1cd47063aa5b80dbcd37a8684f8675.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
1
2013
03
01
Spacelike hypersurfaces in Riemannian or Lorentzian space forms satisfying L_k(x)=Ax+b
205
223
EN
F.
Pashaie
Tarbiat Modares University, Iran
f_pashaie@yahoo.com
S.M.B.
Kashani
Tarbiat Modares University
kashanism@yahoo.com
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
Linearized operator $L_k$,Higher order mean
curvatures,Lorentzian space forms
http://bims.iranjournals.ir/article_338.html
http://bims.iranjournals.ir/article_338_564a4b1f52aa0e44c763a92cfc8189b5.pdf