拓扑线性空间中的Drop定理和Phelps引理以及Ekeland变分原理

将Phelps引理, Ekeland变分原理, Pareto有效性定理推广到拓扑线性空间,同时证明了这三个定理与郑喜印证明的拓扑线性空间中的Drop定理彼此等价．     

The Choquet-Deny convolution equation μ=μ*σ for probability measures on Abelian semigroups

In this note, we characterize the regular probability measures satisfying the Choquet-Deny convolution equation =* on Abelian topological semigroups for a given probability measure .     

Metastability and exponential approach to equilibrium for low-temperature stochastic Ising models

We present a proof of the exponential convergence to equilibrium of single-spin-flip stochastic dynamics for the two-dimensional Ising ferromagnet in the low-temperature case with not too small external magnetic fieldh uniformly in the volume and in the boundary conditions.     

Stochastic modeling of a billiard in a gravitational field: Power law behavior of Lyapunov exponents

We consider the motion of a point particle (billiard) in a uniform gravitational field constrained to move in a symmetric wedge-shaped region. The billiard is reflected at the wedge boundary. The phase space of the system naturally divides itself into two regions in which the tangent maps are respectively parabolic and hyperbolic. It is known that the system is integrable for two values of the wedge half-angle ₁ and ₂ and chaotic for ₁<< ₂. We study the system at three levels of approximation: first, where the deterministic dynamics is replaced by a random evolution; second, where, in addition, the tangent map in each region is, replaced by its average; and third, where the tangent map is replaced by a single global average. We show that at all three levels the Lyapunov exponent exhibits power law behavior near ₁ and ₂ with exponents 1/2 and 1, respectively. We indicate the origin of the exponent 1, which has not been observed in unaccelerated billiards.     

Dynamics of the current-driven Josephson junction

The irreversible macroscopic dynamics of the Josephson junction coupled to external wires acting as a current source is derived rigorously from the underlying microscopic Hamiltonian quantum mechanics. The external systems are treated in the singular coupling limit. The use of this limit is explicitly justified via an interpretation of the singular coupling limit in terms of the relative magnitudes of system, reservoir, and coupling energies. The qualitative behavior of the macroscopic dynamical equations is shown to depend sensitively and crucially on the interaction between the wires and the superconductors and on the size of the wires: the dc Josephson effect only happens when one lets Cooper pairs be driven into the junction by collective (i.e., small) reservoirs.     

Ar—Kr溶液扩散系数的分子动力学模拟及其与温度的关系

用分子动力学模拟方法研究确定Ａｒ－Ｋｒ溶液的自扩散系数Ｄ１、Ｄ２和互扩散系数Ｄ１２以及它们随温度变化的规律。结果表明，分别用Ｇｒｅｅｎ－Ｋｕｂｏ法和Ｅｉｎｓｔｅｉｎ法得到的扩散系数在数值上一致；该溶液的３种扩散系数均满足Ｄ＝Ｄ０ｅ＾Ｅ／ＲＴ关系。     

液体和非晶态Ni64B36合金结构的从头算分子动力学模拟

运用从头算分子动力学模拟了液体以及猝冷后形成的非晶态Ni₆₄B₃₆合金体系, 得到了它们的对相关函数、结构因子、键对分析方面的结构信息, 与实验结果相当一致; 结果表明, 猝冷得到的合金性质与液体合金性质相似, 为非晶态结构. B原子多数以B—B双原子成键形式分散于Ni原子构成的骨架中. 电子态密度分析表明, Ni 3d电子最活泼, 因此在合金中Ni为活性位. 轨道电荷分析从电子结构角度揭示了在NiB 催化剂中B作为修饰剂的机理.     

Local elevation: A method for improving the searching properties of molecular dynamics simulation

Summary The concept of memory has been introduced into a molecular dynamics algorithm. This was done so as to persuade a molecular system to visit new areas of conformational space rather than be confined to a small number of low-energy regions. The method is demonstrated on a simple model system and the 11-residue cyclic peptide cyclosporin A. For comparison, calculations were also performed using simulated temperature annealing and a potential energy annealing scheme. Although the method can only be applied to systems with a small number of degrees of freedom, it offers the chance to generate a multitude of different low-energy structures, where other methods only give a single one or few. This is clearly important in problems such as drug design, where one is interested in the conformational spread of a system.     

拓扑指数法研究显色剂结构与反应性能关系

本文讨论了２９个不对称色酸双偶氮膦酸型显色剂的分子联接性指数，并将其与结构选择性因子相结合，用于偶氮类剂结构与铈显色反应灵敏度的相关性研究，讨论了显色剂结构对显色反应灵敏度的影响。     

Structure-activity relationships of pyrethroid insecticides. Part 2. The use of molecular dynamics for conformation searching and average parameter calculation

Summary Molecular dynamics simulations have been performed on a number of conformationally flexible pyrethroid insecticides. The results indicate that molecular dynamics is a suitable tool for conformational searching of small molecules given suitable simulation parameters. The structures derived from the simulations are compared with the static conformation used in a previous study. Various physicochemical parameters have been calculated for a set of conformations selected from the simulations using multivariate analysis. The averaged values of the parameters over the selected set (and the factors derived from them) are compared with the single conformation values used in the previous study.