Restrictions of Quadratic Forms to Lagrangian Planes,Quadratic Matrix Equations,and Gyroscopic Stabilization

We discuss the symplectic geometry of linear Hamiltonian systems with nondegenerate Hamiltonians. These systems can be reduced to linear second-order differential equations characteristic of linear oscillation theory. This reduction is related to the problem on the signatures of restrictions of quadratic forms to Lagrangian planes. We study vortex symplectic planes invariant with respect to linear Hamiltonian systems. These planes are determined by the solutions of quadratic matrix equations of a special form. New conditions for gyroscopic stabilization are found.     

Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

Estimation of integrated volatility in stochastic volatility models

In the framework of stochastic volatility models we examine estimators for the integrated volatility based on the pth power variation (i.e. the sum of pth absolute powers of the log‐returns). We derive consistency and distributional results for the estimators given high‐frequency data, especially taking into account what kind of process we may add to our model without affecting the estimate of the integrated volatility. This may on the one hand be interpreted as a possible flexibility in modelling, for example adding jumps or even leaving the framework of semimartingales by adding a fractional Brownian motion, or on the other hand as robustness against model misspecification. We will discuss possible choices of p under different model assumptions and irregularly spaced data. Copyright © 2005 John Wiley & Sons, Ltd.     

加权二次有理Bézier插值曲线

在本文中,给定一组有序空间数据点列及每个数据点的切矢向量,利用加权二次有理Bézier曲线对数据点作插值曲线,使该曲线具有C1连续性,并且权因子只是对相应顶点曲线附近产生影响,同调整两个相邻的权因子可以调整这两个相邻顶点之间的曲线和它的控制多边形.     

Index Heuristics for Multiclass M/G/1 Systems with Nonpreemptive Service and Convex Holding Costs

We consider the optimal service control of a multiclass M/G/1 queueing system in which customers are served nonpreemptively and the system cost rate is additive across classes and increasing convex in the numbers present in each class. Following Whittle's approach to a class of restless bandit problems, we develop a Langrangian relaxation of the service control problem which serves to motivate the development of a class of index heuristics. The index for a particular customer class is characterised as a fair charge for service of that class. The paper develops these indices and reports an extensive numerical investigation which exhibits strong performance of the index heuristics for both discounted and average costs.     

束晕-混沌的复杂性理论与控制方法及其应用前景

本文系统论述涉及强流加速器等强流离子束装置中产生的束晕-混沌的复杂性理论与控制方法及其应用前景。强流离子束在核材料生产与增殖、洁净核能、放射性废物嬗变、放射性药物生产、重离子聚变、高能物理、核科学与工程、国防与民用工业和医疗等许多方面都有极其重要的应用潜力和诱人的发展前景。尤其是，近年来强流加速器驱动的放射性洁净核能系统是国内外关注的热门课题，因为它比常规核电更安全、更干净、更便宜。但是，强流离子束形成的束晕-混沌的复杂性现象已引起了国内外广泛关注，需要加以抑制、控制和消除这类现象，解决这一难题已经成为强流离子束应用中的关键问题之一。目前不仅必须深入研究这类束晕-混沌的复杂特性及其产生的物理机制，而且需要研究如何实现对束晕-混沌的有效控制，并寻求和发展其新理论、新方法和新技术。这就向强流离子束物理和非线性-复杂性科学及其技术提出了一系列极富挑战性的新课题。本文结合国内外的研究概况，根据我们多年来的研究成果，特别是我们首创性地提出了一些束晕-混沌的有效控制方法，它们包括：非线性反馈控制法，小波反馈控制法，变结构控制法，延迟反馈控制法，参数自适应控制法等，进行重点的介绍。对上述课题当前的主要进展及相关问题进行系统的总结和比较全面综述的评论。最后，指出该领域今后的研究方向，以推动这个崭新领域的深入研究和应用发展。     

Optimal Control of Non-well-posed Heat Equations

This work is concerned with Pontryagin＇s maximum principle of optimal control problems governed by some non-well-posed semilinear heat equations. A type of approach to the non-well-posed optimal control problem is given.     

解线性最小二乘问题的一个新并行算法

讨论了求解无约束线性最小二乘问题的一种并行单纯形法以及对它的改进算法并行共轭梯度—单纯形法 .算法本身具有很强的并行机制 ,能够充分地发挥并行机快速省时的特点 .本文也对算法做了理论分析 ,对算法的收敛性给予了证明 (在二维情形下 ) .最后做了数值实验 (由于软硬件条件的限制 ,并行算法未能在并行计算机上实现 ,鉴于这种情况 ,我们所做的数值实验均是在串行机上完成的 )     

矩阵方程AXB=D的最小二乘Hermite解及其加权最佳逼近

本中,我们讨论了矩阵方程AXB=D的最小二乘Hermite解,通过运用广义奇异值分解(GSVD)，获得了解的通式。此外,对于给定矩阵F，也得到了它的加权最佳逼近表达式。     

光突发交换的交换控制策略和光缓存配置

光突发交换是面向下一代互联网的光交换模式.讨论了异步光突发交换系统的交换控制策略以及相应光缓存的优化配置策略.除了传统预约模式的交换策略,还研究了非预约和改进型预约模式,它们的性能评估由计算机仿真给出.结果表明:在条件相当情况下,改进型预约模式具有最低的丢包率.同时光缓存的配置对上述几类交换控制策略的性能都有很大影响,仿真结果指出:光缓存的粒度对系统性能具有重要影响,所讨论的几类交换模式都存在最佳时延粒度,研究结果对光交换矩阵的设计有指导意义.