THE SCHWARZ ALTERNATING METHOD FOR A FOURTH-ORDER VARIATIONAL INEQUALITY

In this paper the Schwarz alternating method for a fourth-order elliptic variational inequality problem is considered by way of the equivalent form, and the geometric convergence is obtained on two subdomains.     

隐式曲面与参数曲面的G3过渡

通过几何过渡方法，结合重新标度连续概念，利用隐式曲面与参数曲面的各自等距曲面的交线，构成隐式曲面与参数曲面问的过渡面．用曲面的隐式与隐式、参数与参数形式，证明了所作的过渡面与给出的隐式曲面与参数曲面在连接线处是G^3连接的。     

求广义几何规划全局最优解的线性化方法

对广义几何规划问题(GGP)提出了一个确定型全局优化算法，这类优化问题能广泛应用于工程设计和非线性系统的鲁棒稳定性分析等实际问题中，使用指数变换及对目标函数和约束函数的线性下界估计，建立了GGP的松弛线性规划(RLP)，通过对RLP可行域的细分以及一系列RLP的求解过程，从理论上证明了算法能收敛到GGP的全局最优解，对一个化学工程设计问题应用本文算法，数值实验表明本文方法是可行的。     

两种群非自治Lotka-Volterra竞争扩散系统的概周期解

本文讨论两种群概周期竞争扩散系统，利用微分不等式，证明了系统概周期解的存在、唯一性及其在壳扰动下的稳定性．     

Necessary optimality conditions for abnormal problems with geometric constraints

The abnormal minimization problem with a finite-dimensional image and geometric constraints is examined. In particular, inequality constraints are included. Second-order necessary conditions for this problem are established that strengthen previously known results.     

Geometry of optimal value functions with applications to redundancy in linear programming

In 1967, Wets and Witzgall (Ref. 1) made, in passing, a connection between frames of polyhedral cones and redundancy in linear programming. The present work elaborates and formalizes the theoretical details needed to establish this relation. We study the properties of optimal value functions in order to derive the correspondence between problems in redundancy and the frame of a polyhedral cone. The insights obtained lead to schemes to improve the efficiency of procedures to detect redundancy in the areas of linear programming, stochastic programming, and computational geometry.The author is indebted to G. Dewan for his review and discussions.     

氏调制的几何布朗运动与布林带

在证券市场, 布林带作为流行的技术分析工具被广泛的运用\bd 到目前为止有许多模型被建立用来预测证券的价格, 因此研究这些模型是否具有布林带性质是一个重要的问题\bd Liu, Huang and Zheng (2006)和Liu and Zheng (2006)分别讨论了Black-Scholes模型和随机波动率模型作为真实的股票市场的布林带, 并且证明了相应的统计量的平稳性和大数定律成立\bd 本文我们将上述结果推广到马氏调制的几何布朗运动模型.     

Verified convex hull and distance computation for octree-encoded objects

This paper discusses algorithms for computing verified convex hull and distance enclosure for objects represented by axis-aligned or unaligned octrees. To find a convex enclosure of an octree, the concept of extreme vertices of boxes on its boundary has been used. The convex hull of all extreme vertices yields an enclosure of the object. Thus, distance algorithms for convex polyhedra to obtain lower bounds for the distance between two octrees can be applied. Since using convex hulls makes it possible to avoid the unwanted wrapping effect that results from repeated decompositions, it also opens a way to dynamic distance algorithms for moving objects.     

The proof of hermann''s conjecture

This note proves Thomas Hermann's conjecture on the comparison between twoboundaries of the derivatives of rational cubic Bezier curves. The result is valuable for computer aided geometric design.