聚合物假冠醚研究（Ⅰ）单体乙二醇二苯醚的合成与表征

本文以乙二醇为底物,通过中间体乙二醇二苯磺酸酯,合成出了乙二醇二苯醚。对两合成产物进行了红外光谱、薄层色谱。溶解性能及结晶分析,实验结果表明,在乙二醇二苯磺酸酯的合成中,因为使用苯磺酰氯代替了传统的对甲苯磺酰氯磺酰化试剂,并用氯仿做稀释剂以控制催化剂吡啶的恰当使用量,使合成不但经济而且获得82．5％,的较高收率,在乙二醇二苯醚的合成中,采用回流,蒸馏交替使用的实验方法,同时用馏出物沸点数值监控和及时排除体系的水份,使产率达到78．0％。     

Analysis of a kinematic dynamo model with FEM–BEM coupling

We consider a kinematic dynamo model in a bounded interior simply connected region Ω and in an insulating exterior region . In the so‐called direct problem, the magnetic field B and the electric field E are unknown and are driven by a given incompressible flow field w . After eliminating E , a vector and a scalar potential ansatz for B in the interior and exterior domains, respectively, are applied, leading to a coupled interface problem. We apply a finite element approach in the bounded interior domain Ω, whereas a symmetric boundary element approach in the unbounded exterior domain Ω^c is used. We present results on the well‐posedness of the continuous coupled variational formulation, prove the well‐posedness and stability of the semi‐discretized and fully discretized schemes, and provide quasi‐optimal error estimates for the fully discretized scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

The fast multipole method for the symmetric boundary integral formulation

^** Email: of{at}mathematik.uni-stuttgart.de^*** Email: o.steinbach{at}tugraz.at^**** Email: wendland{at}mathematik.uni-stuttgart.de A symmetric Galerkin boundary-element method is used for thesolution of boundary-value problems with mixed boundary conditionsof Dirichlet and Neumann type. As a model problem we considerthe Laplace equation. When an iterative scheme is employed forsolving the resulting linear system, the discrete boundary integraloperators are realized by the fast multipole method. While thesingle-layer potential can be implemented straightforwardlyas in the original algorithm for particle simulation, the double-layerpotential and its adjoint operator are approximated by the applicationof normal derivatives to the multipole series for the kernelof the single-layer potential. The Galerkin discretization ofthe hypersingular integral operator is reduced to the single-layerpotential via integration by parts. We finally present a correspondingstability and error analysis for these approximations by thefast multipole method of the boundary integral operators. Itis shown that the use of the fast multipole method does notharm the optimal asymptotic convergence. The resulting linearsystem is solved by a GMRES scheme which is preconditioned bythe use of hierarchical strategies as already employed in thefast multipole method. Our numerical examples are in agreementwith the theoretical results.     

A boundary element method for homogenization of periodic structures

Homogenized coefficients of periodic structures are calculated via an auxiliary partial differential equation in the periodic cell. Typically, a volume finite element discretization is employed for the numerical solution. In this paper, we reformulate the problem as a boundary integral equation using Steklov–Poincaré operators. The resulting boundary element method only discretizes the boundary of the periodic cell and the interface between the materials within the cell. We prove that the homogenized coefficients converge super-linearly with the mesh size, and we support the theory with examples in two and three dimensions.     

线性算子方程广义解的存在性

本文中我们研究并得到了线性算子方程的Moore-Penrose广义解的稳定性性质。     

电脑加速度传感器标定仪

介绍了一种新的加速度传感器的标定仪器,给出其原理、结构以及计算机处理过程.