A novel method for automated grid generation of ice shapes for local‐flow analysis

Modelling a complex geometry, such as ice roughness, plays a key role for the computational flow analysis over rough surfaces. This paper presents two enhancement ideas in modelling roughness geometry for local flow analysis over an aerodynamic surface. The first enhancement is use of the leading‐edge region of an airfoil as a perturbation to the parabola surface. The reasons for using a parabola as the base geometry are: it resembles the airfoil leading edge in the vicinity of its apex and it allows the use of a lower apparent Reynolds number. The second enhancement makes use of the Fourier analysis for modelling complex ice roughness on the leading edge of airfoils. This method of modelling provides an analytical expression, which describes the roughness geometry and the corresponding derivatives. The factors affecting the performance of the Fourier analysis were also investigated. It was shown that the number of sine–cosine terms and the number of control points are of importance. Finally, these enhancements are incorporated into an automated grid generation method over the airfoil ice accretion surface. The validations for both enhancements demonstrate that they can improve the current capability of grid generation and computational flow field analysis around airfoils with ice roughness. Copyright © 2004 John Wiley & Sons, Ltd.     

Structure of Regular Solutions of the Three-Body Schrödinger Equation near the Pair Impact Point

We investigate the six-dimensional Schrödinger equation for a three-body system with central pair interactions of a more general form than Coulomb interactions. Regular general and special physical solutions of this equation are represented by infinite asymptotic series in integer powers of the distance between two particles and in the sought functions of the other three-body coordinates. Constructing such functions in angular bases composed of spherical and bispherical harmonics or symmetrized Wigner D-functions is reduced to solving simple recursive algebraic equations. For projections of physical solutions on the angular bases functions, we derive boundary conditions at the pair impact point.     

Almost strongly regular matrices and a core theorem for double sequences

The idea of almost convergence for double sequences was introduced by Moricz and Rhoades [Math. Proc. Cambridge Philos. Soc. 104 (1988) 283-294] and they also characterized the four dimensional strong regular matrices. In this paper we define and characterize the almost strongly regular matrices for double sequences and apply these matrices to establish a core theorem.     

Elliptic fibers over non-perfect residue fields

Kodaira and Néron classified and described the geometry of the special fibers of the Néron model of an elliptic curve defined over a discrete valuation ring with a perfect residue field. Tate described an algorithm to determine the special fiber type by manipulating the Weierstrass equation. In the case of non-perfect residue fields, we discover new fiber types which are not on the Kodaira-Néron list. We describe these new types and extend Tate's algorithm to deal with all discrete valuation rings. Specifically, we show how to translate a Weierstrass equation into a form where the reduction type may be easily determined. Having determined the special fiber type, we construct the regular model of the curve with explicit blow-up calculations. We also provide tables that serve as a simple reference for the algorithm and which succinctly summarize the results.     

A fourth‐order compact finite difference scheme for the steady stream function–vorticity formulation of the Navier–Stokes/Boussinesq equations

A fourth‐order compact finite difference scheme on the nine‐point 2D stencil is formulated for solving the steady‐state Navier–Stokes/Boussinesq equations for two‐dimensional, incompressible fluid flow and heat transfer using the stream function–vorticity formulation. The main feature of the new fourth‐order compact scheme is that it allows point‐successive overrelaxation (SOR) or point‐successive underrelaxation iteration for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature. Copyright © 2003 John Wiley & Sons, Ltd.     

Q-正则Loewner空间中的拟对称映射

本文在Q-正则Loewner空间中用环模不等式刻划了拟对称映射.另外,在 Q-维Ahlfors-David正则空间中建立了拟对称映射作用下的Grotzsch-Teichmuller型 模不等式,它是通过伸张系数的积分平均来表示.     

MPEG-2解码器中视频、音频同步的实现

本文分析了理想的MPEG－2信源解码器中视频、音频同步实现的关键，给出了实际的解码器中实现视频、音频同步会遇到的问题和解决的方法。实践证明，这些方法是有效的，已用于我们的MPEG-2信源解码器中。     

Constructing two-weight codes with prescribed groups of automorphisms

We construct new linear two-weight codes over the finite field with q elements. To do so we solve the equivalent problem of finding point sets in the projective geometry with certain intersection properties. These point sets are in bijection to solutions of a Diophantine linear system of equations. To reduce the size of the system of equations we restrict the search for solutions to solutions with special symmetries.Two-weight codes can be used to define strongly regular graphs. We give tables of the two-weight codes and the corresponding strongly regular graphs. In some cases we find new distance-optimal two-weight codes and also new strongly regular graphs.     

The Choquet-Deny convolution equation μ=μ*σ for probability measures on Abelian semigroups

In this note, we characterize the regular probability measures satisfying the Choquet-Deny convolution equation =* on Abelian topological semigroups for a given probability measure .     

曝光数据流优化问题的蒙特卡罗算法

集成工艺中控制图形发生器产生掩模图形的数据流文件的数据排列顺序优化,是一个其结点数可达数千个之多的大规模旅行商问题(从镜头架的位置,即每个矩形的矩心为结点),常规算法早已不适用。本文采用多阶段蒙特卡罗算法并加以改进,补充了“分层优化模式”,邻接结点的预合并和在各个阶段末提取共同子路径并删去相关结点等一系列逐步缩小问题规模的措施,形成了一个实用的优化算法。相应的软件已成功地应用于薄膜磁头的数据流文件的优化。