Contingent Solutions for the Bellman Equation in Infinite Dimensions

The present paper is concerned with the study of the Hamilton–Jacobi–Bellman equation for the time optimal control problem associated with infinite-dimensional linear control systems from the point of view of continuous contingent solutions.     

Scheduling orders on either dedicated or flexible machines in parallel to minimize total weighted completion time

We are interested in the problem of scheduling orders for different product types in a facility with a number of machines in parallel. Each order asks for certain amounts of various different product types which can be produced concurrently. Each product type can be produced on a subset of the machines. Two extreme cases of machine environments are of interest. In the first case, each product type can be produced on one and only one machine which is dedicated to that product type. In the second case, all machines are identical and flexible; each product type can be produced by any one of the machines. Moreover, when a machine in this case switches over from one product type to another, no setup is required. Each order has a release date and a weight. Preemptions are not allowed. The objective is minimizing the total weighted completion time of the orders. Even when all orders are available at time 0, both types of machine environments have been shown to be NP-hard for any fixed number (≥2) of machines. This paper focuses on the design and analysis of approximation algorithms for these two machine environments. We also present empirical comparisons of the various algorithms. The conclusions from the empirical analyses provide insights into the trade-offs with regard to solution quality, speed, and memory space. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users. This research is supported by the National Science Foundation through grants DMI-0300156 and DMI-0245603.     

使用MTV模型与Morkowitz证券组合选择模型的投资决策系统

利用期望和方差的秩系数法、MTV模型、Morkowitz证券组合选择模型构造了一实用的投资决策系统.     

二阶时标非线性中立型动力学方程的振动性

运用广义Riccati变换给出时标上二阶非线性中立型动力学方程振动的充分条件,进一步研究了具扰动项的动力学方程解的性态.所得结论推广和改进了已知文献的部分结果.     

Variations on a theme by Mark Kac

Mark Kac's theorem on the mean recurrence time in a stationary stochastic process in discrete time with discrete states is taken as the starting point for a series of variations, most of which are formulated in terms of 0–1 processes. Whereas the original theorem deals with the mean recurrence time of a given state under the condition that the state is realized at time 0, this condition is dropped in part of the variations; two others refer to the variance of the recurrence time and two to the Poincaré cycle of a dynamical system. Most variations consist in inequalities and formal identities for the mean first-arrival time and subsequent recurrence times for the given state.     

紧支撑三元正交小波滤波器的参数化

高维小波分析是分析和处理多维数字信号的有力工具．非张量积多元小波被广泛地应用在模式识别、纹理分析和边缘检测等领域．本文给出方体域上三元正交滤波器的一种参数化构造算法,三元小波滤波器的这种构造方法使我们能更方便地研究非张量积的三元正交小波．最后给出数值算例．     

Velocity variation of internal shock waves in gamma ray bursts: Observational properties

The work uses the data in the TTS mode of BATSE to analyze the time lags and pulse widths of GRB960113 and GRB960722 in high as well as low energy bands. The results show that their time lags increase monotonously. This phenomenon can reasonably be interpreted with the model of internal shock waves of γ-ray bursts (GRB). Perhaps we obtain the direct observational evidence for the fireball model of GRBs for the first time.     

Shear-wave speeds and elastic moduli for different liquids Part 3. Experiments-update

Tables of values of shear-wave speeds, shear moduli and relaxation times for 18 new liquids are presented, supplementing the tables for 51 liquids given in Part 2. A brief discussion of errors and analysis of the oscilloscope traces is presented. The relation of the effective moduli measured on the wave-speed meter to independent measurements using phase-modulated birefringence and delayed die swell is discussed. A method of measuring wave speeds and rigidities for sheared media is proposed.     

基于可控提前期和服务水平约束的(Q,r)库存问题

本文研究了存在顾客流失情况下，基于可控提前期和服务水平约束的连续盘点（Q，r）库存管理同题。当市场需求分布未知时采用MiniMax方法建立年总成本函数表达式，修正以往研究中对安全系数取值范围错误判断，推导出合理的安全系数取值范围，并给出最优解的计算方法。