Department of Pure Mathematics (2003 - Present)
Math
, Illinois, U.S.A
Math
, kharazmi University,
Math
, Mashhad Ferdowsi University,
I got my B.Sc. in Mathematics from Ferdowsi University of Mashhad in 1988 and M.Sc. in Mathematics from Kharazmi University in 1991. I got my Ph.D. from University of Illinois at Urbana in January 1998. I have been a faculty member in Shahid Behshti and Tarbiat Modares Universities and Senior Research Fellow in IPM since then.
Let R be a unitary ring of finite cardinality pk, where p is a prime and p k. We show that if the group of units of R has at most one subgroup of order p, then,
Let be a tilting module. In this paper, Gorenstein -projective modules are introduced and some of their basic properties are studied. Moreover, some characterizations of rings over which all modules are Gorenstein -projective are given. For instance, on the -cocoherent rings, it is proved that the Gorenstein -projectivity of all -modules is equivalent to the -projectivity of -injective as a module.
In this article, we study chain conditions for graph C*-algebras. We show that there are infinitely many mutually non isomorphic Noetherian (and Artinian) purely infinite graph C*-algebras with infinitely many ideals. We prove that if E is a graph, then C*(E) is a Noetherian (resp. Artinian) C*-algebra if and only if E satisfies condition (K) and each ascending (resp. descending) sequence of admissible pairs of E stabilizes.
In this paper, we use the convolution of sets to define a canonical coarse structure on a locally compact hypergroup. We also define invariant metrics using the maximal subgroup (center) of the hypergroup, and study the coarse structures induced by invariant metrics. We give some sufficient conditions for these structures to have a Higson compactification for the hypergroup.
In this article, we present a trichotomy (a division into three classes) on Noetherian and Artinian C*-algebras and obtain some structural results about Noetherian (and/or Artinian) C*-algebras. We show that every Noetherian, purely infinite and σ-unital C*-algebra A is generated as a C*-ideal by a single projection. We show that if A is a purely infinite, nuclear, separable, Noetherian and Artinian C*-algebra, then . This is a partial extension of Kirchberg's -absorption theorem and Kirchberg's exact embedding theorem. Finally, we show that each Noetherian AF-algebra has a full finite-dimensional C*-subalgebra.
We give a set of axioms for the notion of locally compact hypergroupoids, as an extension of both groupoids and hypergroups, and study their basic properties. We show that, adding a natural condition on the continuity of support, one of the axioms assumed by Renault on the left Haar system automatically follows. We show that an irreducible representation of a compact hypergroupoid is fiberwise finite dimensional.
We show that the universal groupoid of an inverse semigroup is topologically (measurewise) amenable if and only if is hyperfinite and all members of a family of subsemigroups of indexed by the spectrum of the commutative -algebra on the idempotents of are amenable. Thereby we solve some problems raised by ALT Paterson.
We show that the dynamic asymptotic dimension of a minimal free action of an infinite virtually cyclic group on a compact Hausdorff space is always one. This extends a well-known result of Guentner, Willett, and Yu for minimal free actions of infinite cyclic groups. Furthermore, the minimality assumption can be replaced by the marker property, and we prove the marker property for all free actions of countable groups on finite dimensional compact Hausdorff spaces, generalising a result of Szabo in the metrisable setting.
In this paper, the commutative module amenable Banach algebras are characterized. The hereditary and permanence properties of module amenability and the relations between module amenability of a Banach algebra and its ideals are explored. Analogous to the classical case of amenability, it is shown that the projective tensor product and direct sum of module amenable Banach algebras are again module amenable. By an application of Ryll-Nardzewski fixed point theorem, it is shown that for an inverse semigroup S, every module derivation of 1 (S) into a reflexive module is inner.
In this research we investigated female elementary students’ level of mastery over science and mathematics content and explained the nature of relationship between students’ level of mastery and learnability of content in elementary level science and mathematics. This research is mixed-method in nature. The quantitative analyses are based on correlation method, Structural Equation Modeling and comparing means. 914 female students of public senior elementary schools in Kashan were recruited. Minimum sample size determined by GPower software for each grade and students were selected by cluster random sampling method. The needed data for fourth and fifth graders were gathered through researcher-made cumulative tests; the data related to si
Let be a finite unitary ring such that , where is the prime ring and is not a nilpotent group. We show that if all proper subgroups of are nilpotent groups, then the cardinality of is a power of 2. In addition, if is not a -group, then either or , where is the ring of matrices over the finite field and is a direct sum of copies of the finite field .
We extend the reduction method of Juzvinskiĭ to non compact dynamics. We show that the method could be used to prove results on entropies of transformations on non compact metric or Polish spaces. This is illustrated in three situations. First we extend the results of P. Walters on transformations with complete positive entropy. Then we extend the Abramov-Rohlin addition formula of R. K. Thomas. Finally we use the addition formula to extend the results of Walters on the uniqueness of invariant measures with maximal entropy.
The selective attention for identification model (SAIM) is an established model of selective visual attention. SAIM implements translation-invariant object recognition, in scenes with multiple objects, using the parallel distributed processing (PDP) paradigm. Here, we show that SAIM can be formulated as Bayesian inference. Crucially, SAIM uses excitatory feedback to combine top-down information (i.e. object knowledge) with bottom-up sensory information. By contrast, predictive coding implementations of Bayesian inference use inhibitory feedback. By formulating SAIM as a predictive coding scheme, we created a new version of SAIM that uses inhibitory feedback. Simulation studies showed that both types of architectures can reproduce the respon
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