A hybrid vortex method for the simulation of three‐dimensional flows

This paper presents an integral vorticity method for solving three‐dimensional Navier–Stokes equations. A finite volume scheme is implemented to solve the vorticity transport equation, which is discretized on a structured hexahedral mesh. A vortex sheet algorithm is used to enforce the no‐slip boundary condition through a vorticity flux at the boundary. The Biot–Savart integral is evaluated to compute the velocity field, in conjunction with a fast algorithm based on multipole expansion. This method is applied to the simulation of uniform flow past a sphere. Copyright © 2007 John Wiley & Sons, Ltd.     

关于3阶Carmichael数

朱文余和孙琦（见《数学进展》，2004，33（4）：505-507）提出了关于3阶Carmichael数的三个问题，我们（见《四川大学学报（自然科学版）》，2006，43（6）：1197-1201）肯定地回答了问题1．本文模仿Howe的寻找严格2阶Carmichael数（见Mathematics of Computation，2000，69（232）：1711—1719）的方法，提出寻找满足某种条件的3阶Carmichael数的方法，并用这种方法确实找到了几百个这样的数，因而完全肯定地回答了问题2．     

负离子源引出系统束光学的数值模拟

根据在表面-等离子体型负离子源中,负离子主要由转换电极表面产生这一特点,参考正离子源引出系统数值计算程序,建立了负离子源引出系统的数值计算模型和计算程序;对表面-等离子体型桶式负离子源引出系统束光学的性质进行了数值模拟。对计算结果的检验和分析表明,这个计算模型和程序反映了负离子源引出系统束光学的基本特性。     

A partial differential equation connected to option pricing with stochastic volatility: Regularity results and discretization

This paper completes a previous work on a Black and Scholes equation with stochastic volatility. This is a degenerate parabolic equation, which gives the price of a European option as a function of the time, of the price of the underlying asset, and of the volatility, when the volatility is a function of a mean reverting Orstein-Uhlenbeck process, possibly correlated with the underlying asset. The analysis involves weighted Sobolev spaces. We give a characterization of the domain of the operator, which permits us to use results from the theory of semigroups. We then study a related model elliptic problem and propose a finite element method with a regular mesh with respect to the intrinsic metric associated with the degenerate operator. For the error estimate, we need to prove an approximation result.

     

热传导型半导体瞬态问题的特征有限体积方法及分析

在这篇文章中,将特征线方法与有限体积方法相结合,构造了热传导型半导体瞬态问题的全离散特征有限体积方法(CFVM).在一般的条件下进行理论分析,得到了次优阶L2误差估计结果.     

Wave reflection in slightly compressible, finitely deformed elastic media

Summary  In this paper, the reflection of a plane wave at an incrementally traction-free boundary of a half-space composed of nearly incompressible elastic material is considered. It is shown that two distinct cases exist, these being dependent on the underlying primary deformation. In the first case, the appropriate slowness sections are each approximately elliptical, and the corresponding reflection phenomena closely mirrors that associated with the corresponding linear isotropic theory. Specifically, an angular range of direction of incident wave exists, for which both a quasi-longitudinal and quasi-shear wave are reflected, the former being replaced by a surface wave outside this angular range. In the second case, the outer slowness section is re-enrant and, in addition to the scenarios previously mentioned, it is possible for two quasi-shear waves to be reflected. Numerical illustrations of reflection coefficients are presented in respect of a modified Varga material and the case of increasing bulk modulus is investigated. Received 17 January 2000; accepted for publication 22 February 2000     

非紧超凸度量空间中的一个新的极大元定理及其对抽象经济的应用

在非紧超凸度量空间中建立了一个新的极大元定理.作为应用，获得了连续选择及其不动点定理和一个Browder-Fan不动点定理.最后，新建了非紧超凸度量空间中的定性对策和抽象经济的平衡点存在定理.     

A SET OF SYMMETRIC QUADRATURE RULES ON TRIANGLES AND TETRAHEDRA

We present a program for computing symmetric quadrature rules on triangles and tetrahedra. A set of rules are obtained by using this program. Quadrature rules up to order 21 on triangles and up to order 14 on tetrahedra have been obtained which are useful for use in finite element computations. All rules presented here have positive weights with points lying within the integration domain.     

Numerical approximations of one-dimensional linear conservation equations with discontinuous coefficients

Conservative linear equations arise in many areas of application, including continuum mechanics or high-frequency geometrical optics approximations. This kind of equation admits most of the time solutions which are only bounded measures in the space variable known as duality solutions. In this paper, we study the convergence of a class of finite-difference numerical schemes and introduce an appropriate concept of consistency with the continuous problem. Some basic examples including computational results are also supplied.