基于零拍探测和压缩真空光输入增强Sagnac效应

利用量子技术增强Sagnac效应提高陀螺输出精度具有重要的研究意义, 是实现全自主导航的重要途径. 以相干态激光作为输入光源的光学陀螺因真空零点波动使其输出精度限制于散粒噪声极限而难以提高. 为减小真空波动的影响, 提出在激光输入的分束器的另一输入端输入压缩真空光并结合平衡零拍探测技术的方法增强Sagnac效应. 理论分析表明Sagnac效应性能得到有效提升: 干涉输出的灵敏度检测极限和动态范围均随着压缩程度的增加而呈指数级增长. 该方法只需对经典光学陀螺做少量改动就可实现, 是提高光学陀螺输出精度的一种新方法.     

轴对称流场干涉条纹折射率的模拟计算

提出一种获取流场干涉条纹折射率分布的新方法。该方法首先采用不等间隔的环带分割轴对称流场,使折射率变化大的地方获得的数据点密,然后通过对Abel变换进行离散数值计算来获取流场的折射率分布。通过模拟轴对称流场的实时全息干涉条纹证明了该方法不仅简单易行,而且所获取的折射率分布精度高。     

Stationary states of crystal growth in three dimensions

A new Markov process describing crystal growth in three dimensions is introduced. States of the process are configurations of the crystal surface, which has a terrace-edge-kink structure. The states are continuous along edges but discrete across edges, in accordance with the very different rates for the two types of captures of particles. Stationary distributions, describing steady crystal growth, are found in general. To our knowledge, these are the first examples of stationary distributions for layered crystal growth in three dimensions. The steady growth rate and other quantities are obtained explicitly for two interacting edges. For many interacting edges, growth behavior is determined (a) in various asymptotic regimes including thermodynamic limits, (b) via simulations, and (c) using series (cluster) expansions in the slope of the surface, the first three coefficients being computed. The theoretical growth rates show a marked dependence on surface dimensions. This may contribute to the size dependence and dispersion in the observed growth rate of small crystals.     

“保守系统平衡位置微振动”案例教学的探讨与实践

以“保守系统平衡位置微振动”为例,论述在理论力学中如何适当地整合知识点使之成为一个案例,使学生从具体的案例出发经过思考、分析、讨论,得到可能的解决方案,并进行评价、提炼理论.实践证明,把案例教学引入理论力学教学中,通过多个阶段的实践过程锻炼,有助于学生形成“主体性”和“实践性”的习惯,从而改善课堂教学关系,提高学生的独立学习和实践创新能力.     

美国NGSS科学与工程实践构架与化学教学案例——影响化学反应速率的因素

美国《新一代科学标准》（NGSS）强调科学实践的重要性并提出科学与工程实践的关键要素，不仅为科学实践的具体实施提供了方向而且使科学实践的评价标准更加明确。在介绍NGSS科学与工程实践的构架基础上，以“影响化学反应速率的因素”为例分析了科学与工程实践的关键要素在教学中的反映及实施特点，并基于案例分析提出对我国中学化学教学过程设计的借鉴与启示。     

次线性期望下的一般中心极限定理

受Peng-中心极限定理的启发,本文主要应用G-正态分布的概念,放宽Peng-中心极限定理的条件,在次线性期望下得到形式更为一般的中心极限定理.首先,将均值条件E[X_n]=ε[X_n]=0放宽为|E[X_n]|+|ε[X_n]|=O(1/n);其次,应用随机变量截断的方法,放宽随机变量的2阶矩与2+δ阶矩条件;最后,将该定理的Peng-独立性条件进行放宽,得到卷积独立随机变量的中心极限定理.     

Pb,Sr and Ba calix[6]arene hexacarboxylic acid octahedral complexation: a dramatic effect of dealkylation

Calix[6]arene hexacarboxylic acid binds instantly and with low symmetry to Pb, Sr and Ba. Later a highly symmetric up-down alternating conformation emerges. The solution structures are identical to their p-tert-butylcalix[6]arene hexacarboxylic acid counterparts. With either receptor, an octahedral cage is formed around the metal. The transformation from low to high symmetry however proceeds at significantly faster rates for the de-t-butylated host.     

A variational problem determined by probability measures

ABSTRACT

An optimization problem of maximizing an integral of a function over a family of probability measures is considered. The problem is a generalization of a well-studied variational problem in mathematical economics, concerning optimal allocations. The specific generalization that we examine arises also in the limit of singularly perturbed optimal control problems. We examine the mathematical problem and allude to the singular perturbation motivation.     

Quasistationary distributions for one-dimensional diffusions with singular boundary points

In the present work we characterize the existence of quasistationary distributions for diffusions on $(0,\infty )$ allowing singular behavior at 0 and $\infty$. If absorption at 0 is certain, we show that there exists a quasistationary distribution as soon as the spectrum of the generator is strictly positive. This complements results of Cattiaux et al. (2009) and Kolb and Steinsaltz (2012) for 0 being a regular boundary point and extends results by Cattiaux et al. (2009) on singular diffusions.