Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301Beyond First Order Logic: From number of structures to structure of
numbers: Part I126320ENJ. BaldwinUniversity of Illinois at ChicagoT. HyttinenDepartment of Mathematics and Statistics
University of HelsinkiM. KesalaDepartment of Mathematics and Statistics
University of HelsinkiJournal Article20101007We study the history and recent developments in nonelementary<br />model theory focusing on the framework of abstract<br />elementary classes. We discuss the role of syntax and semantics<br />and the motivation to generalize first order model theory to nonelementary<br />frameworks and illuminate the study with concrete examples<br />of classes of models. <br /><br />This first part introduces the main conceps and philosophies and<br />discusses two research questions, namely categoricity transfer and<br />the stability classification.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301Beyond first order logic: From number of structures to structure of numbers: Part II2748409ENJ. BaldwinUniversity of Illinois
at Chicago, USAT. HyttinenUniversity of Helsinki, FinlandM. KesalaUniversity of Helsinki, FinlandJournal Article20101017We study the history and recent developments in nonelementary<br />model theory focusing on the framework of abstract<br />elementary classes. We discuss the role of syntax and semantics<br />and the motivation to generalize first order model theory to nonelementary<br />frameworks and illuminate the study with concrete examples<br />of classes of models. <br /><br />This second part continues to study the question of catecoricity<br />transfer and counting the number of structures of certain cardinality.<br />We discuss more thoroughly the role of countable models,<br />search for a non-elementary counterpart for the concept of completeness<br />and present two examples: one example answers a question<br />asked by David Kueker and the other investigates models of<br />Peano Arithmetic and the relation of an elementary end-extension<br />in terms of an abstract elementary class.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301Generalized Rings of Measurable and Continuous Functions4964233ENA. AminiShiraz UniversityB. AminiShiraz UniversityE. MomtahanYasouj UniversityM. H. Shirdareh HaghigiShiraz UniversityJournal Article20100710This paper is an attempt to generalize, simultaneously, the ring <br />of real-valued continuous functions and the ring of real-valued <br />measurable functions.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301Grouplikes6585305ENM. H. HooshmandIslamic Azad University - Shiraz BranchJournal Article20090430In this paper we introduce and study an algebraic structure, namely <br />Grouplike. A grouplike is something between semigroup and group and <br />its axioms are generalizations of the four group axioms. <br />Every grouplike is a semigroup containing the minimum ideal that is also a maximal subgroup (but the converse is not valid). <br />The first idea of grouplikes comes from b-parts and $b$-addition <br />of real numbers introduced by the author. Now, the researches have enabled me to <br />introduce Grouplikes and prove some of their main theorems <br />and construct a vast class of them, here. We prove <br />a fundamental structure theorem for a big class of grouplikes, namely <br />Class United Grouplikes. Moreover, we obtain some other results for <br />binary systems, semigroups and groups in general and exhibit several <br />their important subsets with related diagrams. Finally. we show some of future directions <br />for the researches in grouplikes and semigroup theory.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301Brandt extensions and primitive topologically periodic inverse topological semigroups8795335ENJ. JamalzadehI am phd student in sistan and bluchestan universityGh. RezaeiUniversity of Sistan and Bluchestan, IranJournal Article20101220In this paper we find sufficient conditions on primitive inverse <br />topological semigroup S under which: the inversion inv : (H(S)) (H(S)) <br />is continuous; we show that every topologically periodic countable compact <br />primitive inverse topological semigroups with closed H-classes is topologically <br />isomorphic to an orthogonal sum <br />P <br />i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compact topological groups Gi in the class <br />of topological inverse semigroups for some finite cardinals.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301On the relations between the point spectrum of A and invertibility of I + f(A)B97106239ENH. LarkiIslamic Azad University, Parand BranchA. RiaziAmirkabir University of TechnologyJournal Article20110426Let A be a bounded linear operator on a Banach space X. We <br />investigate the conditions of existing rank-one operator B such that I+f(A)B is invertible for every analytic function <br />f on sigma(A). Also we compare the invariant subspaces of f(A)B and B. This work is motivated by an <br />operator method on the Banach space ell^2 for solving some PDEs which is extended to general operator space under some <br />conditions in this paper.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301On a subclass of multivalent analytic functions associated with an extended fractional differintegral operator107124222ENJ.-L. LiuDepartment of Mathematics, Yangzhou UniversityJournal Article20100826Making 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301The two parameter quantum groups
$U_{r,s}(mathfrak{g})$ associated to generalized Kac-Moody algebra
and their equitable presentation125149410ENQ. SunZhejiang University of Science and Technology, ChinaH. LiZhejiang International Studies University, ChinaJournal Article20101115We 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301Essential norm of generalized composition operators from
weighted Dirichlet or Bloch type spaces to Q_K type spaces151164342ENSh. RezaeiIslamic Azad University, IranH. MahyarTarbiat Moallem University, IranJournal Article20110414In this paper we obtain lower and upper estimates for the <br />essential norms of generalized composition operators from weighted <br />Dirichlet spaces or Bloch type spaces to $Q_K$ type <br />spaces.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301Existence and uniqueness of solutions for a periodic
boundary value problem165173343ENA. Amini HarandiUniversity of Shahrekord, IranJournal Article20110501In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301The Quasi-morphic Property of Group175185339ENQ. WangDepartment of Mathematics and Systems Science, National University of Defense Technology, P.R.China 410073,Changsha, China.K. LongDepartment of Mathematics and Systems Science, National University of Defense Technology ,P.R.China 410073, Changsha, China.L. FengDepartment of Mathematics and Systems Science, National University of Defense
Technology, P.R.China 410073, Changsha, China.Journal Article20110528A 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301Maximal subsets of pairwise non-commuting elements of some finite p-groups187192341ENA. AzadArak University, IranS. FouladiKharazmi University, IranR. OrfiArak University, IranJournal Article20110301Let G be a group. A subset X of G is a set of pairwise noncommuting <br />elements if xy ̸= yx for any two distinct elements x and y in X. <br />If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, <br />then X is said to be a maximal subset of pairwise non-commuting elements. <br />In this paper we determine the cardinality of a maximal subset of pairwise <br />non-commuting elements in any non-abelian p-groups with central quotient <br />of order less than or equal to p3 for any prime number p. As an immediate <br />consequence we give this cardinality for any non-abelian group of order p4.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301$varepsilon$-Simultaneous approximations
of downward sets193203345ENH. AlizadehIslamic Aazad University, Marand, IranSh. RezapourAzarbaidjan University of Tarbiat Moallem, IranS. M.VaezpourAmirkabir University of Technology, IranJournal Article20110520In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301Spacelike hypersurfaces in Riemannian or Lorentzian space forms satisfying L_k(x)=Ax+b205223338ENF. PashaieTarbiat Modares University, IranS.M.B. KashaniTarbiat Modares UniversityJournal Article20110530We study connected <br />orientable spacelike hypersurfaces <br />$x:M^{n}rightarrowM_q^{n+1}(c)$, isometrically immersed into the <br />Riemannian or Lorentzian space form of curvature $c=-1,0,1$, and <br />index $q=0,1$, satisfying the condition $~L_kx=Ax+b$,~ <br /> where $L_k$ is the $textit{linearized operator}$ of <br />the $(k+1)$-th mean curvature $H_{k+1}$ of the hypersurface for a <br />fixed integer $0leq k<n$, $A$ is a constant matrix and $b$ is a <br />constant vector. <br /> <br />We show that the only hypersurfaces satisfying that condition are <br />hypersurfaces with zero $H_{k+1}$ and constant $H_k$ ( when $cneq <br />0$ ), open pieces of totally umbilic hypersurfaces and open pieces <br />of the standard Riemannian product of two totally umbilic <br />hypersurfaces.