The occupation time of Brownian motion in a ball

LetW be a Wiener process of dimensiond3, starting from 0, and letX(t) be the total time spent byW in the ball centered at 0 with radiust. We give an affirmative answer to a conjecture of Taylor and Tricot⁽¹⁶⁾ on the tail distribution ofX(t). Lévy's lower functions ofX(t) are characterized by an integral test.     

On the inclusion of collisional correlations in quantum dynamics

We present a formalism to describe collisional correlations responsible for thermalization effects in finite quantum systems. The approach consists in a stochastic extension of time dependent mean field theory. Correlations are treated in time dependent perturbation theory and loss of coherence is assumed at some time intervals allowing a stochastic reduction of the correlated dynamics in terms of a stochastic ensemble of time dependent mean-fields. This theory was formulated long ago in terms of density matrices but never applied in practical cases because of its complexity. We propose here a reformulation of the theory in terms of wave functions and use a simplified 1D model of cluster and molecules allowing to test the theory in a schematic but realistic manner. We illustrate the performance in terms of several observables, in particular global moments of the density matrix and single particle entropy built on occupation numbers. The occupation numbers remain fixed in time dependent mean-field propagation and change when evaluating the correlations, then taking fractional values. They converge asymptotically towards Fermi distributions which is a clear indication of thermalization.     

从双层规划的角度看道德风险理论的一阶条件方法

本文首先对双层规划的一个特殊例子即道德风险模型中使用的一阶条件方法（FOA）做简要的梳理,然后提出一种更为一般的使FOA有效的原则与方法。新方法主要依赖于代理人对委托人设置的目标的最优反应映射是否存在不动点,这个性质不要求原问题与用一阶条件放松以后的问题之间的约束集等价,从而也不要求代理人的期望效用对行动具有全局凹性。在新方法下,可以用较为简单的方法证明FOA在以下两种情形之一有效,即如果分布函数是概率分布的凸组合或者分布函数来自某些特殊的指数族分布。     

电磁场与电磁波课程思政教学改革探索与实践

课程思政作为思想政治理论课程的有效补充，是落实立德树人根本任务的重要组成。《电磁场与电磁波》是物理、电类等专业的重要专业基础课程，深入挖掘其课程思政元素,能够发挥专业课程的隐性育人作用，实现知识传授、能力培养与价值引领的有机融合，对于理工科专业课进行课程思政改革具有现实指导作用。     

含弛豫项的广义光学Bloch方程的近似解

本文用叠代法求得了含弛豫项的广义光学Bloch方程的近似解。与计算机给出的数值积分解的比较表明,一阶叠代解具有足够好的精度。由此得出了上能级占有几率随时间变化的解析表达式及多光子吸收、Bloch-Siegert频移等有用结果。     

防范道德风险的博弈分析和契约设计

运用不完全信息动态博弈的理论，建立了一个防范道德风险的博弈模型．给出了该博弈的精炼贝叶斯纳什均衡．在此基础上给出了基于最优博弈策略的契约的具体形式。而这种基于博弈论的契约可以克服有成本的状态验证模型(CSV)及经典激励理论中承诺的可信性问题。     

Quantification of the push-pull character of azo dyes and a basis for their evaluation as potential nonlinear optical materials

The push-pull characters of a large series of donor-acceptor substituted azo dyes—71 structures in all—have been quantified by the NN double bond lengths, d_NN, the ¹⁵N NMR chemical shift differences, Δδ_15N, of the two nitrogen atoms and the quotient, π^∗/π, of the occupations of the antibonding π^∗, and bonding π orbitals of this partial NN double bond. The excellent correlation of the occupation quotients with the bond lengths strongly infers that both π^∗/π and d_NN are excellent parameters for quantifying charge alternation in the push-pull chromophore and the molecular hyperpolarizability, β₀, of these compounds. By this approach, selected compounds can be appropriately considered as viable candidates for nonlinear optical (NLO) applications.     

团队生产中的博弈模型与道德风险研究

首先根据团队生产在产出函数的特点,建立了由二人组成的团队生产模型;接着,在分析了团队生产的博弈过程后,求得团队成员努力投入的N ash均衡;最后,着重研究了两种证实团队生产中存在道德风险的方法.     

A probabilistic property of Katsuura's continuous nowhere differentiable function

Katsuura's example of a continuous nowhere differentiable function is based on a fixed-point method. In this paper we use probability theory to study the increments of Katsuura's function.     

风险企业的委托-代理模型

传统的委托—代理理论在解释风险企业家的行为时遇到了困难。通过对传统的委托—代理理论进行重新构造和拓展，本提出逆反努力法则，验证了隐藏行动的道德风险的存在，并通过Newton迭代法和图形学方法对风险企业家的长期努力水平进行计算，发现努力水平对努力效应指数n表现出协同效应。