一个非协调膜元的高精度分析

本文讨论一个四自由度三角形非协调膜元的整体超收敛性，外推和亏量校正。     

A parallel version of the preconditioned conjugate gradient method for boundary element equations

The parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two-dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems.     

Sparse-grid finite-volume multigrid for 3D-problems

We introduce a multigrid algorithm for the solution of a second order elliptic equation in three dimensions. For the approximation of the solution we use a partially ordered hierarchy of finite-volume discretisations. We show that there is a relation with semicoarsening and approximation by more-dimensional Haar wavelets. By taking a proper subset of all possible meshes in the hierarchy, a sparse grid finite-volume discretisation can be constructed.The multigrid algorithm consists of a simple damped point-Jacobi relaxation as the smoothing procedure, while the coarse grid correction is made by interpolation from several coarser grid levels.The combination of sparse grids and multigrid with semi-coarsening leads to a relatively small number of degrees of freedom,N, to obtain an accurate approximation, together with anO(N) method for the solution. The algorithm is symmetric with respect to the three coordinate directions and it is fit for combination with adaptive techniques.To analyse the convergence of the multigrid algorithm we develop the necessary Fourier analysis tools. All techniques, designed for 3D-problems, can also be applied for the 2D case, and — for simplicity — we apply the tools to study the convergence behaviour for the anisotropic Poisson equation for this 2D case.     

产生特殊聚焦图形的二元光学元件

通过面积编码将伽博（Gabor)波带片的透过率函数的余弦分布等效为二元分布，研制了能产生各种特殊聚焦图形的二元光学元件。根据透镜聚焦的物理原理制作的二元振幅型波带片可以方便地产生多种聚焦线，给出了相应的实验结果，并讨论了改善聚焦效果的优化条件。     

Mixed methods on quadrilaterals and hexahedra

We describe a new family of discrete spaces suitable for use with mixed methods on certain quadrilateral and hexahedral meshes. The new spaces are natural in the sense of differential geometry, so all the usual mixed method theory, including the hybrid formulation, carries over to these new elements with proofs unchanged. Because transforming general quadrilaterals into squares introduces nonlinearity and because mixed methods involve the divergence operator, the new spaces are more complicated than either the corresponding Raviart-Thomas spaces for rectangles or corresponding finite element spaces for quadrilaterals. The new spaces are also limited to meshes obtained from a rectangular mesh through the application of a single global bilinear transformation. Despite this limitation, the new elements may be useful in certain topologically regular problems, where initially rectangular grids are deformed to match features of the physical region. They also illustrate the difficulties introduced into the theory of mixed methods by nonlinear transformations.     

电子直线加速器磁控管频率稳定的自适应线性神经元方法

 电子直线加速器电子束能量的稳定与否取决于功率源工作频率的稳定性,磁控管在短时间内的散谱和轻微跳谱造成稳频系统的控制精度下降,最后电子束的扫描均匀度下降。引入自适应线性神经元方法(ADALINE)和噪声对消技术以消除对工作频率长期稳定性的影响,从而保证了电子束的扫描均匀度。     

塑料光学元件的清洗、镀膜和胶合

各种塑料光学元件在光学系统中的应用越来越广泛。作为光学元件,必然涉及清洗、镀膜和胶合等工艺技术问题。本文就塑料光学元件的这三个技术作一介绍。     

Discrete duality finite volume schemes for Leray−Lions−type elliptic problems on general 2D meshes

Discrete duality finite volume schemes on general meshes, introduced by Hermeline and Domelevo and Omnès for the Laplace equation, are proposed for nonlinear diffusion problems in 2D with nonhomogeneous Dirichlet boundary condition. This approach allows the discretization of non linear fluxes in such a way that the discrete operator inherits the key properties of the continuous one. Furthermore, it is well adapted to very general meshes including the case of nonconformal locally refined meshes. We show that the approximate solution exists and is unique, which is not obvious since the scheme is nonlinear. We prove that, for general W^?1,p′(Ω) source term and W^1‐(1/p),p(?Ω) boundary data, the approximate solution and its discrete gradient converge strongly towards the exact solution and its gradient, respectively, in appropriate Lebesgue spaces. Finally, error estimates are given in the case where the solution is assumed to be in W^2,p(Ω). Numerical examples are given, including those on locally refined meshes. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Pure quantitative characterization of finite simple groups

Let G be a finite group, and let π _e (G) be the set of all element orders of G. In this short paper we prove that π _e (B _n (q)) ≠ π _e (C _n (q)) for all odd q.      

环的根性质

研究的对象是不含单位元分次环 R,首先证明了有关 Jacobson根的重要性质 J( R) =J( S)∩ R,其中 S =R× Z.然后利用它得到了一些好的性质