重力场与静电场特点的比较

“场”是一种客观存在的物质，但由于“场”具有不易直接感受的特殊存在形态，同学们对“场”的物质性的理解不够深刻，解决“场”的相关问题时也感到棘手．笔者就高中阶段最典型的两种场——“重力场”和“静电场”的力学性质与能量特点进行比较，使同学们对“场”的概念有更深刻的认识．     

冲击载荷下剪切断裂研究

利用Hopkinson压杆技术对单边平行双裂纹试样倒向加载，在较大的加载率范围，对Ti6Al4V钛合金和40CrNiMoA两种材料的动态剪切断裂行为进行了研究．实验结果表明：存在两类韧性剪切断裂模式，即常规的韧性剪切型断裂和绝热剪切断裂．常规剪切型断裂模式的断裂韧性KⅡd随加载率的提高而增大，而绝热剪切型的断裂韧性KⅡd则随加载率的提高而减小，并且，当加载率增大至某一临界值时，常规的韧性剪切断裂模式将转变为绝热剪切断裂破坏模式．     

Dynamics of Random One-Dimensional ±J Systems

Finite chains of a two-state random Potts spin model with periodic boundary conditions are studied within Glauber dynamics. The spin exchange is assumed random with frustration between ferro and antiferromagnetic values (±J). Time-dependent fluctuations are induced by periodic temperature oscillations. Master type differential equations for spin correlation functions are solved within linear response theory. The spectrum of relaxation times are calculated at different temperatures. The ±J Potts glass chains undergo a zero temperature phase transition. The barriers against inversion of the spin chain take only two values; 0 and 2|J|. The temperature behaviour of specific heat is characterized by rounded peaks. The frequency dependence displays two plateaus for the real part of specific heat and two corresponding peaks for the imaginary part. The dynamic specific heat is not affected by the longest relaxing mode like susceptibility. The time separation of the modes is demonstrated by the Cole-Cole plots.     

Subgame Consistent Cooperative Solutions in Stochastic Differential Games

Subgame consistency is a fundamental element in the solution of cooperative stochastic differential games. In particular, it ensures that: (i) the extension of the solution policy to a later starting time and to any possible state brought about by the prior optimal behavior of the players would remain optimal; (ii) all players do not have incentive to deviate from the initial plan. In this paper, we develop a mechanism for the derivation of the payoff distribution procedures of subgame consistent solutions in stochastic differential games with transferable payoffs. The payoff distribution procedure of the subgame consistent solution can be identified analytically under different optimality principles. Demonstration of the use of the technique for specific optimality principles is shown with an explicitly solvable game. For the first time, analytically tractable solutions of cooperative stochastic differential games with subgame consistency are derived.     

动态规划在教学管理中的应用

本将动态规划理论应用于高校教学管理当中，得出了教学管理中重要的环一排课的最优策略。     

Analysis of a Duopoly Supply Chain and its Application in Electricity Spot Markets

This paper studies a supply chain consisting of two suppliers and one retailer in a spot market, where the retailer uses the newsvendor solution as its purchase policy, and suppliers compete for the retailer’s purchase. Since each supplier’s bidding strategy affects the other’s profit, a game theory approach is used to identify optimal bidding strategies. We prove the existence and uniqueness of a Nash solution. It is also shown that the competition between the supplier leads to a lower market clearing price, and as a result, the retailer benefits from it. Finally, we demonstrate the applicability of the obtained results by deriving optimal bidding strategies for power generator plants in the deregulated California energy market. Supported in part by RGC (Hong Kong) Competitive Earmarked Research Grants (CUHK4167/04E and CUHK4239/03E), a Distinguished Young Investigator Grant from the National Natural Sciences Foundation of China, and a grant from Hundred Talents Program of the Chinese Academy of Sciences.     

Qualitative Theory and Identification of Dynamic System with One Degree of Freedom

Dynamic systems described by nonlinear differential equations of the second order are studied. It is assumed that certain preliminary information on the dissipative or elastic characteristics of systems is known. A new approach is demonstrated to obtaining full information on unknown or partially known characteristics of a system from measurements of not only displacements but also velocities and accelerations __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 139–143, June 2005.     

Existence results for second order boundary value problem of impulsive dynamic equations on time scales

In this paper, Schaefer's fixed point theorem and nonlinear alternative of Leray-Schauder type are used to investigate the existence of solutions for second order boundary value problem for impulsive dynamic equations on time scales.     

On the tribological characteristics of dynamically loaded journal bearing with micropolar fluids

The addition of the additives to the lubricant oil to enhance the characteristics of the lubricant will influence the performance of the bearings. Based on the theory of micropolar fluids, the tribological characteristics of a dynamically-loaded journal bearing are numerically studied. Comparisons are made between the Newtonian fluids and the micropolar fluids. It is shown that for a dynamically-loaded journal bearing, the micropolar fluids yield an increase not only in the friction force, but also in the friction coefficient. In addition, the oil film pressure and the oil film thickness are obviously higher than that of Newtonian fluids.     

Hg1-xCdxTe/Cd1-zZnzTe的X射线反射率及半峰全宽的动力学研究

X射线衍射摇摆曲线的计算机模拟是一种获得材料晶体质量参量的有效方法，其中材料本征摇摆曲线的计算是计算机模拟的基础。用X射线动力学理论计算了Hg1-xCdxTe和Cd1-zZnzTe本征反射率曲线，并研究了组分、膜厚分别对本征反射率和半峰全宽的影响。结果表明Hg1-xCdxTe和Cd1-zZnzTe的本征反射率和半峰全宽与材料组分和厚度有明显的依赖关系，且该依赖关系取决于X射线在材料中的散射和吸收的相对强弱。薄膜的厚度也是直接影响本征摇摆曲线峰形、半峰全宽和反射率的重要因素，当薄膜厚度小于穿透深度时，表征本征反射率曲线的各个参量均与薄膜厚度有直接的关系。对于(333)衍射面，碲镉汞材料厚度大于7μm后，本征反射率和半峰全宽将不再发生明显变化。