Dynamic programming in cricket: optimizing batting order for a sticky wicket

In cricket, a rain-affected pitch can make batting more difficult than normal. Several other conditions such as poor light or an initially lively pitch, may also result in difficulties for the batsmen. In this note, we refer to all of them as ‘sticky wickets’. On sticky wickets, lower order batsmen are often sent into ‘hold the fort’ until conditions improve. In this paper, a stochastic dynamic programming model is used to examine the appropriateness of this policy. The model suggests that the tactic is often optimal when the sticky wicket persists until the end of the day's play, but not often when the sticky wicket is transitory. In some circumstances, it is worthwhile, on a normal wicket near the end of the day, to send in a lower order batsman to hold the fort (a night watchman): when the wicket is sticky, this tactic is even more worthwhile.     

毛细管电色谱中进样时间对柱效的影响

毛细管电色谱是近年发展起来的一种新型微分离技术，它结合了高效液相色谱和毛细管电泳的物点，具有高效、快速，高选择性，其有关理论研究和应用越来越深入，本文从色谱动力学角度讨论了毛细管电色谱中进样时间对柱的影响。     

Effect of end groups on complexation kinetics between cyclodextrins and guest polymers

α‐Cyclodextrin (α‐CD) has been complexed with various poly(ethylene glycol) (PEG) derivatives in aqueous solution. It has been found that the end groups of PEG derivatives affect the complexation kinetics greatly, but have only a little influence on the thermodynamic behavior. By increasing the hydrophobicity of end groups, the complexation speeds up rapidly. On the other hand, the bulky end groups slow down the threading of polymeric guests into the cavity of CD. By changing the hydrophobicity and the size of end groups, the complexation rate can be adjusted in the range of several orders of magnitudes, which should be quite useful in the design of new supramolecular systems. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2050–2057, 2006     

CP violation and extra dimensions

It is shown that new sources of CP violation can be generated in models with more than one extra dimension. In the supersymmetric models on the space-time , where the radius moduli have auxiliary vacuum expectation values and the supersymmetry breaking is mediated by the Kaluza–Klein states of the gauge supermultiplets, we analyze the gaugino masses and trilinear couplings for two scenarios and obtain the result that there exist relative CP violating phases among the gaugino masses and trilinear couplings. Received: 10 October 2001 / Published online: 20 December 2001     

Controlling global stochasticity of Hamiltonian systems by nonlinear perturbation

A method of controlling global stochasticity in Hamiltonian systems by applying nonlinear perturbation is proposed. With the well-known standard map we demonstrate that this control method can convert global stochasticity into regular motion in a wide chaotic region for arbitrary initial condition, in which the control signal remains very weak after a few kicks. The system in which chaos has been controlled approximates to the original Hamiltonian system, and this approach appears robust against small external noise. The mechanism underlying this high control efficiency is intuitively explained. Received 15 January 2002 Published online 6 June 2002     

Improving the Fundamental Theorem of Algebra

Theorems 2 and 3 establish the minimum algebraic conditions necessary for a field to be algebraically closed, and they can therefore be said to “optimize” the Fundamental Theorem of Algebra. But each specific“degree implication” is a first-order consequence of the axioms for fields, and could have been discovered two centuries ago; the existence of these finitary relationships appears to have been unsuspected by practically everyone, with one important exception.     

A TVD Type Wavelet-Galerkin Method for Hamilton-Jacobi Equations

In this paper,we use Daubechies scaling functions as test functions for the Galerkin method,and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations.It can be proved that the schemesare TVD schemes.Numerical tests indicate that the schemes are suitable for the Hamilton-Jacobi equations.Furthermore,they have high-order accuracy in smooth regions and good resolution of singularities.     

感性与理性的和谐统一--构建和谐课堂的点滴体会

1感性认识与理性认识的和谐统一 在教育理念不断更新发展的今天，有一个新的课堂环境和课堂教学理念，是每一个教育工作者自身发展的一项重要任务．特别是在高中物理学科的课堂教学中，构建人与自然的和谐统一，就要从身边的自然环境出发，立足于感性认识为本，再升华为理性认识，把二者有机结合起来，才能让学生获得一个情感与理论上的和谐统一，提高学生对物理学科的浓厚兴趣．