A class of Sierpinski carpets with overlaps

Based on a scheme by Lau and Ngai, a sufficient and necessary condition for an IFS of contractive similitudes to satisfy the open set condition is given. A class of Sierpinski carpets with parameters (λ₁,λ₂) is then investigated.     

On automorphisms of finite Abelian <Emphasis Type="Italic">p</Emphasis>-groups

Let A be a finitely generated abelian group. We describe the automorphism group Aut(A) using the rank of A and its torsion part p-part A _p . For a finite abelian p-group A of type (k ₁, ..., k _n ), simple necessary and sufficient conditions for an n × n-matrix over integers to be associated with an automorphism of A are presented. Then, the automorphism group Aut(A) for a finite p-group A of type (k ₁, k ₂) is analyzed. This work has begin during the visit of the second author to the Faculty of Mathematics and Computer Science, Nicolaus Copernicus University during the period July 31–August 13, 2005. This visit was supported by the Nicolaus Copernicus University and a grant from Cnpq.     

BECOOL: Ballooning eigensolver with COOL finite elements

An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equation to a special block pentadiagonal matrix equation that is solved using an inverse vector iteration method. A benchmark test of BECOOL (Ballooning Eigensolver using COOL finite elements) with second order Legendre polynomials recovers precisely the eigenvalues computed by the VVBAL shooting code. Timing runs reveal the need to determine an optimal lower order case. Eigenvalue convergence runs show that cubic Legendre polynomials construct the optimal ballooning mode equation for intensive computations.     

Periodic orbits around the collinear libration points in the restricted three body problem when the smaller primary is a triaxial rigid body and bigger primary is a source of radiation pressure

Periodic orbits belonging to the stromgren families A, B and C around the collinear libration points in the restricted three body problem have been studied when the smaller primary is a triaxial rigid body and more massive body is a source of radiation pressure. These families are determined in three different cases: (i) classical case, (ii) when bigger primary is a source of radiation pressure, (iii) when smaller primary is a triaxial rigid body and bigger primary is a source of radiation pressure. The Liapunov stability of each periodic solution has also been examined.      

Ab initio study of long-range electron transfer between biphenyl anion radical and naphthalene

After the separation of the donor, the aeceptor, and the σ-type bridge from the π-σ-π system, the geometries of biphenyl, biphenyl anion radical, naphthalene, and naphthalene anion radical are optimized, and then the reorganization energy for the intermolecular electron transfer (ET) at the levels of HF/4-31G and HF/DZP is calculated. The ET matrix elements of the self-exchange reactions of the π-σ-π systems have been calculated by means of both the direct calculation based on the variational principle, and the transition energy between the molecular orbitals at the linear coordinate R=0.5. For the cross reactions, the ET matrix element and the geometry of the transition state are determined by searching the minimum energy splitting △_(min) along the reaction coordinate. In the evaluation of the solvent reorganization energy of the ET in solution, the Marcus' two-sphere model has been invoked. A few of ET rate constants for the intramolecular ET reactions for the π-σ-π systems, which contain     

On the Isometry Groups of Hyperbolic Orbifolds

A generic, geometrically finite, hyperbolic n-orbifold is proved to have a finite group of isometries.     

Flange earing and its control on deepdrawing of anisotropy circular sheets

The Hill's quadric anisotropy yield function and the Barlat-Lian anisotropy yield function describing well anisotropy sheet metal with stronger texture are introduced into a quadric-flow corner constitutive theory of elastic-plastic finite deformation suitable for deformation localization analysis. And then, the elastic-plastic large deformation finite element formulation based on the virtual power principle and the discrete Kirchhoff shell element model including the yield functions and the constitutive theory are established. The focus of the present research is on the numerical simulation of the flange earing of the deep-drawing of anisotropy circular sheets, based on the investigated results, the schemes for controlling the flange earing are proposed. Supported by NSFC(No. 19832020) and National Automobile Dynamic Simulation Laboratory of China.     

A SUPERONVERGENCE ANALYISIS FOR FINITE ELEMENT SOLUTION BY THE INTERPOLANT POSTPROCESSING ON IRREGULAR MESHES FOR SMOOTH PROBLEM

1. IntroductionThe results in this paper are based on the idea of interpolation postprocessing in [11 andthe techniques of LZ projection processing in [2]For simlicity) we consider the model problem: Finds e Hi(fl),such thatSuppose that Jh and JH are irregular triangulations (or quadrilateral partitions). Theirsizes satisfy h << H, (H - 0). Construct piecewise k-order and r-order finite element spaceSh and SH respectively. Let ah E Sh be the Galerkin approximation of u E HJ(fl), andbe …     

Light Element Analysis of Individual Microparticles Using Thin-Window EPMA

 The determination of the concentration of light elements, such as carbon, nitrogen and oxygen, in e.g. atmospheric aerosol particles is important to study the chemical behaviour of atmospheric pollution. The knowledge of low-Z element concentrations gives us information on the speciation of nutrients (species having nutritional value for plants) and toxic heavy metals in the particles. The capability of the conventional energy-dispersive EPMA is strongly limited for the analysis of low-Z elements, mainly because the Be window in the EDX detector hinders the detection of characteristic X-rays of light elements such as C, N, O and Na. WDS is suitable for analysis of light elements, but the measurement of beam sensitive microparticles requires the minimisation of the beam current and the measurement time. A semi-quantitative analytical method based on EPMA using an ultra-thin window EDX detector was developed. It was found that the matrix and geometric effects that are important for low-energy X-rays can be reliably evaluated by Monte Carlo calculations. Therefore, the quantification part of the method contains reverse Monte Carlo calculation done by iterative simulations. The method was standardised and tested by measurements on single particles with known chemical compositions. Beam-sensitive particles such as ammonium-sulphate and ammonium-nitrate were analysed using a liquid nitrogen cooled sample stage. The shape and size of the particles, which are important for the simulations, were determined using a high-magnification secondary electron image. Individual marine aerosol particles collected over the North Sea by a nine-stage Berner cascade impactor were analysed using this new method. Preliminary results on five samples and 4500 particles show that the method can be used to study the modification of sea-salt particles in the troposphere.     

A time-stepping procedure based on convolution for the mixed finite element approximation for porous media flow

A time-stepping procedure is established and analyzed for the problem of miscible displacement in porous medium. The fluid velocity based on mixed element method is post-processed by the convolution with Bramble-Schatz kernel. Convergence analysis shows that the property of superconvergence, originally held for the approximation of velocity, can be retained for the approximation of concentration variable. Compared with the traditional results in references, the constraint conditions between parameters in this paper are improved essentially.