نشریه علوم دانشگاه خوارزمی
سال سیزدهم شماره 2 (تابستان 1392)

An automorphism $theta$ of a group $G$ is pointwise inner if$theta(x)$ is conjugate to $x$ for any $xin G$. It is interesting and natural to discuss the question of ``finding necessary and sufficient conditions for a group $G$ such that certain subgroups of $tex {Aut}(G)$ be equal''. There are some well-known results in this regard for finite groups. In this paper, we find a necessary and sufficient condition in certain finitely generatednilpotent groups of class 2 for which $mathrm{Aut}_{pwi}(G)simeq mathr {Inn}(G)$. We also prove that in a nilpotent group of class 2 with cyclic commutator subgroup $mathrm{Aut}_{pwi}(G simeq mathrm{Inn}(G)$ and the quotient$mathrm{Aut}_{pwi}(G)/mathrm{Inn}(G)$ is torsion. In particular if $G'$ is a finite cyclic group then $mathrm{Aut}_{pwi}(G)= mathr {Inn}(G)$.

In this research work nano porous silicon layers with different porosity were prepared by using electrochemical etching. Surface morphology and size of pores were investigated by scanning electron microscopy (SEM).TiO2 thin films with EBPVD method have been deposited on the surface of PSi layers. The influence of anodization conditions such as anodization time interval and current density on electrical properties and surface morphology of sandwich devices were carried out using I-V measurement. The results showed that, electrical properties were influenced by changes of current density and anodization time interval. We also investigated the AC electrical conductivity of Al/TiO2/PSi/Al sandwich devices over the range of frequency 102 to 105 Hz and temperature range 300 to 378 K. It is known that, over the range of frequency < 103Hz the band theory and over the range of frequency > 103Hz hopping mechanism is applicable in explaining the conductivity of TiO2/PSi thin films nano structures with aluminum electrodes.

In this article‎, ‎the efficient numerical methods for finding solution of the linear and nonlinear Fredholm integral equations of the second kind on base of Bernstein multi scaling functions are being presented‎. ‎In the beginning the properties of these functions‎, ‎which are a combination of block-pulse functions on ‎, ‎and Bernstein polynomials with the dual operational matrix are presented‎. ‎Then these properties are used for the purpose of conversion of the mentioned integral equation to a matrix equation that are compatible to a algebraic equations system‎. ‎The imperative of the Bernstein multi scaling functions are‎, ‎for the proper quantitative value of and have a high accuracy and specifically the relative errors of the numerical solutions will be minimum‎. ‎The presented methods from the standpoint of computation are very simple and attractive and the numerical examples which were presented at the end shows the efficiency and accuracy of these methods‎.

In this paper, we study the Arens regularity properties of module actions and we extend some proposition from Baker, Dales, Lau and others into general situations. We establish some relationships between the topological centers of module actions and factorization properties of them with some results in group algebras. In 1951 Arens shows that the second dual of Banach algebra endowed with the either Arens multiplications is a Banach algebra, see [1]. The constructions of the two Arens multiplications in lead us to definition of topological centers for with respect to both Arens multiplications. The topological centers of Banach algebras, module actions and applications of them were introduced and discussed in [3, 5, 6, 9, 15, 16, 17, 18, 19, 24, 25]. In this paper, we extend some problems from [3, 5, 6, 16, 22] to the general criterion on module actions with some applications in group algebras. Baker, Lau and Pym in [3] proved that for Banach algebra with bounded right approximate identity, is an ideal of right annihilators in and. In the following, for a Banach, we study the similar discussion on the module actions and for Banach, we show that

Let (R,m) be a Noetherian local ring, a an ideal of R and M a finitely generated R- module. We investigate some properties of formal local cohomology modules with respect to a Serre subcategory. We provide a common language to indicate some properties of formal local cohomology modules.Let (R,m) be a Noetherian local ring, a an ideal of R and M a finitely generated R- module. We investigate some properties of formal local cohomology modules with respect to a Serre subcategory. We provide a common language to indicate some properties of formal local cohomology modules.

In this paper, a collocation method based on the Bessel polynomials is used for the solution of nonlinear Fredholm-Volterra-Hammerstein integro-differential equations (FVHIDEs) under mixed condition. This method of estimating the solution, transforms the nonlinear (FVHIDEs) to matrix equations with the help of Bessel polynomials of the first kind and collocation points. The matrix equations correspond to a system of nonlinear algebraic equations with the unknown Bessel coefficients. Present results and comparisons demonstrate that our estimate has good degree of accuracy and this method is more valid and useful than other methods.In this paper, a collocation method based on the Bessel polynomials is used for the solution of nonlinear Fredholm-Volterra-Hammerstein integro-differential equations (FVHIDEs) under mixed condition. This method of estimating the solution, transforms the nonlinear (FVHIDEs) to matrix equations with the help of Bessel polynomials of the first kind and collocation points. The matrix equations correspond to a system of nonlinear algebraic equations with the unknown Bessel coefficients. Present results and comparisons demonstrate that our estimate has good degree of accuracy and this method is more valid and useful than other methods.

Inverse time - dependent heat source problems have an important role in many branches of science and technology. The aim of this paper is to solve these classes of problems using a variational iteration method(VIM). The method applied does not require discretization of the region, as in the case of classical methods based on the finite difference method, the boundary element method or the other methods. Applying this method, we obtain a stable approximation to an unknown source term in an inverse heat equation from over-specified data that the source term is only time - dependent. Some numerical examples using this approach are presented and discussed