Applications of interval arithmetic in solving polynomial equations by Wu''''s elimination method

Wu's elimination method is an important method for solving multivariate poly- nomial equations.In this paper,we apply interval arithmetic to Wu's method and convert the problem of solving polynomial equations into that of solving interval polynomial equa- tions.Parallel results such as zero-decomposition theorem are obtained for interval poly- nomial equations.The advantages of the new approach are two-folds:First,the problem of the numerical instability arisen from floating-point arithmetic is largely overcome.Second, the low efficiency of the algorithm caused by large intermediate coefficients introduced by exact compaction is dramatically improved.Some examples are provided to illustrate the effectiveness of the proposed algorithm.     

A Comparative Study on Dynamic and Static Sparsity Patterns in Parallel Sparse Approximate Inverse Preconditioning

Sparse approximate inverse (SAI) techniques have recently emerged as a new class of parallel preconditioning techniques for solving large sparse linear systems on high performance computers. The choice of the sparsity pattern of the SAI matrix is probably the most important step in constructing an SAI preconditioner. Both dynamic and static sparsity pattern selection approaches have been proposed by researchers. Through a few numerical experiments, we conduct a comparable study on the properties and performance of the SAI preconditioners using the different sparsity patterns for solving some sparse linear systems. This revised version was published online in July 2006 with corrections to the Cover Date.     

A projection method for solving incompressible viscous flows on domains with moving boundaries

In this paper, a projection method is presented for solving the flow problems in domains with moving boundaries. In order to track the movement of the domain boundaries, arbitrary‐Lagrangian–Eulerian (ALE) co‐ordinates are used. The unsteady incompressible Navier–Stokes equations on the ALE co‐ordinates are solved by using a projection method developed in this paper. This projection method is based on the Bell's Godunov‐projection method. However, substantial changes are made so that this algorithm is capable of solving the ALE form of incompressible Navier–Stokes equations. Multi‐block structured grids are used to discretize the flow domains. The grid velocity is not explicitly computed; instead the volume change is used to account for the effect of grid movement. A new method is also proposed to compute the freestream capturing metrics so that the geometric conservation law (GCL) can be satisfied exactly in this algorithm. This projection method is also parallelized so that the state of the art high performance computers can be used to match the computation cost associated with the moving grid calculations. Several test cases are solved to verify the performance of this moving‐grid projection method. Copyright © 2004 John Wiley Sons, Ltd.     

Phase Measurement Algorithm in Wavelength Scanned Fizeau Interferometer

Wavelength scanned interferometry allows the simultaneous measurement of top surface shape and optical thickness variation of a transparent object consisting of several parallel surfaces. Interference signals from these surfaces can be separated in frequency space, and their phases are detected by discrete Fourier analysis. However, these signal frequencies are shifted from the detection frequency by the refractive index dispersion of the object and a nonlinearity of the wavelength scanning. The Fourier analysis is sensitive to the detuning of the signal frequency and suffers from the multiple-beam interference noise. Conventional error-compensating algorithms cannot be applied to an object consisting of more than three reflecting surfaces. We derive a new 2N-1 sample error-compensating algorithm, which allows the phase detection of any order of harmonic frequency among the interference signals. The new algorithm suppresses the effect of signal frequency detuning as well as the multiple-beam interference noise and can be applied to the measurement of complex objects consisting of more than three reflecting surfaces.     

旋转带电体磁矩计算的若干法则与算例

本文在文献 [1]、[2 ]等的基础上给出关于旋转带电体的磁矩计算的若干法则 ,均以定理形式表达 ,并列表枚举其相关算例     

Ring resonators with N × M couplers

Multiple-zero multiple-pole optical filter transfer functions may be implemented more efficiently in an integrated optics architecture if higher order N × M optical couplers are utilized. For example, a coherent ring resonator made from two 3×3 couplers offers some advantages over the three mirror Fabry-Perot etalon, which is its analog. To this end we develop the formalism for obtaining the transfer functions and scattering matrices of ring resonators made from two N × M couplers. We then present a methodology for analyzing serial and parallel systems of N × M optical coupler ring resonators.     

A Relationship Among Gentzen's Proof-Reduction,Kirby-Paris' Hydra Game and Buchholz's Hydra Game

We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game (Section 1 and Appendix). Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game (which is two-dimensional but without labels), by a simple and natural interpretation (Section 2). Jervell proposed another type of a combinatorial game, by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show (Section 3) that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φ_ω (0) (while that of PA or of Kirby-Paris' Game is φ₁ (0) = ?₀) in the Veblen hierarchy of ordinals.     

光盘阵列系统的一种性能优化方法

提出了一种用低性能驱动器组建高性能光盘阵列系统性能的优化方法。针对传统的低性能光盘驱动器(驱动器内部数据传输率及接口速率均较低),提出了一种新型的数据传输模式。采用此优化方法可以使光盘阵列系统的整体性能得到较大地提高。同时还可以提高系统整体的性价比。