Evaluation of the three-dimensional elastic Green's function in anisotropic cubic media

By using the Fourier transforms method, the three-dimensional Green's function solution for a unit force applied in an infinite cubic material is evaluated in this paper. Although the elastic behavior of a cubic material can be characterized by only three elastic constants, the explicit solutions of Green's function for a cubic material are not available in the literatures. The central problem for explicitly solving the elastic Green's function of anisotropic materials depends upon the roots of a sextic algebraic equation, which results from the inverse Fourier transforms and is composed of the material constants and position vector parameters. The close form expression of Green's function is presented here in terms of roots of the sextic equation. The sextic equation for an anisotropic cubic material is discussed thoroughly and specific results are given for possible explicit solutions.     

用直射线穿透CT技术反演介质的速度分布

本文简述了以射线理论为基础的井间CT的基本原理、数学方法和重构技术.用直射线穿透CT技术对地震波在地层中传播时速度场的变化进行了数值模拟和实测数据处理.结果表明,对速度梯度变化不大的地质结构,利用直射线穿透CT 技术反演介质的速度分布是可行的.     

Time integration for spherical acoustic finite–infinite element models

In this paper, we analyse the numerical time integration of models of exterior acoustics. The major challenge lies in the instabilities that may arise from the infinite elements. In this paper we consider the special case of spherical infinite elements formulations, which have shown their relevance for industrial applications. We propose a method that combines Crank–Nicholson's method with a filtering step by the backward Euler method. The paper is illustrated with an example relevant to industry. Copyright © 2005 John Wiley & Sons, Ltd.     

A Fusion Development Facility Based on the Spherical Torus

The Fusion community could soon have available an opportunity to significantly advance fusion development, an opportunity afforded by the potential of the spherical torus as a plasma confinement system. That opportunity is, in a single device at an affordable price and at a suitable site, to move sequentially through the major fusion objectives of advanced confinement physics, burning plasma and DT physics, blanket and other fusion nuclear technology development, tritium self-sufficiency, and, perhaps at the end with an upside performance outcome, a chance at net electric breakeven. Meeting this set of objectives would dramatically advance the development of fusion.     

Algebraically rectifiable parametric curves

Sufficient and necessary conditions for the arc length of a polynomial parametric curve to be an algebraic function of the parameter are formulated. It is shown that if the arc length is algebraic, it is no more complicated than the square root of a polynomial. Polynomial curves that have this property encompass the Pythagorean-hodograph curves—for which the arc length is just a polynomial in the parameter—as a proper subset. The algebraically rectifiable cubics, other than Pythagorean-hodograph curves, constitute a single-parameter family of cuspidal curves. The implications of the general algebraic rectifiability criterion are also completely enumerated in the case of quartics, in terms of their cusps and intrinsic shape freedoms. Finally, the characterization and construction of algebraically rectifiable quintics is briefly sketched. These forms offer a rich repertoire of curvilinear profiles, whose lengths are readily determined without numerical quadrature, for practical design problems.     

Parametrization of all minimal square spectral factors

Two different parametrizations of minimal square spectral factors are given. These parametrizations extend recent results by Picci and Pinzoni since they characterize spectral factors without specification on the zero or pole structure.     

Stability analysis and control of a class of differential‐algebraic nonlinear systems

A new methodology based on the linear matrix inequality (LMI) framework is presented for the computation of polynomial Lyapunov functions for differential–algebraic nonlinear systems. The method is applied for estimating the domain of attraction of equilibria and also as a control design tool to increase the damping of the system. Numerical examples are used to demonstrate the approach. The results show the potential of the proposed approach as a tool for analysis and control design. Copyright © 2004 John Wiley & Sons, Ltd.     

Algebraic multigrid methods for solving generalized eigenvalue problems

Three algebraic multigrid (AMG) methods for solving generalized eigenvalue problems are presented. The first method combines modern AMG techniques with a non‐linear multigrid approach and nested iteration strategy. The second method is a preconditioned inverse iteration with linear AMG preconditioner. The third method is an enhancement of the previous one, namely the locally optimal block preconditioned conjugate gradient. Efficiency and accuracy of solutions computed by these AMG eigensolvers are validated on standard benchmarks where part of the spectrum is known. In particular, the problem of isospectral drums is addressed. Copyright © 2005 John Wiley & Sons, Ltd.     

What Level of Mathematical Reasoning can Computer Science Demand of a Software Implementer?: Auf Deutsch: Welche Art mathematischer Argumentation darf die Informatikwissenschaft einem Softwareimplementierer auf jeden Fall zumuten?

The article starts out from the observation that software engineering splits in two large activity areas: Software specification with its verification and software implementation with its verification. To find answers to the question in the title the article studies a practical systems software engineering area where theory is better developed than compared to other areas: Compiler construction. Our answer is a conclusion from work in the DFG-project Verifix, U.Karlsruhe, U.Kiel, U.Ulm, 1995-2003. One very complex cooperational task has been construction of a so called initial correct compiler for a realistic high level programming (and compiler writing) language correctly implemented and executed on a real life host processor. The interface between compiling specification and compiler implementation is given by algebraic-style, conditional formula transformation or program term rewriting rules which the specifier figures out and must prove correct w. r. t. source program and target processor semantics and data and states representations.Intensive cooperation of compiling specifiers and compiler implementers has revealed that the implementer's mathematical reasoning is algebraic reasoning of moderate depth. The specifier overtakes semantical issues and does induction proofs, a field of much more intricate mathematical reasoning.     

性能好的布尔函数的研究

对n(n=3,4,5)个变量的布尔函数进行了研究,得出了满足平衡性、相关免疫性、SAC和高的代数式次数的布尔函数的精确数目,利用它们可以构造出满足上述特性的任意n(n>5)个变量的布尔函数。