Limit theorems in financial market models

Invariance principle states that a scaled simple random walk converges to the standard Brownian motion.In this article, we present a discrete time stochastic process, which reflects a microstructure of market dynamics, and prove a convergence to a scaling limit process with a drift term and a jump term. These terms are derived from a macroscopic condition on volumes traded in some time intervals. The mathematical tools for obtaining our results are Dobrushin-Hryniv theory and the method of cluster expansion developed in mathematical studies of statistical mechanics.     

紫细菌捕光天线LH2中的超快光物理研究

采用飞秒泵浦探测技术研究了紫细菌外周捕光天线LH2中的超快光动力学过程.从B800蓝侧的激发态动力学中观察到B800到B850的能量传递时间,实验结果与理论计算结果的差别说明激发B800时可能引起B850上激子带的直接激发,或存在由B800到B850上激子态的能量传递通道.在B800红侧激发的动力学过程中,漂白信号前端存在的一个快速光吸收信号主要来源于B850上激子带的直接激发.在天然RS601和突变体GM309的LH2中,800 nm激发时的动力学过程都表现为一个类似的光漂白过程,动力学曲线的衰减时间常量在天然LH2中明显快于突变体中,说明在GM309中B800到B850的激发能传递速率有所降低.而在845 nm激发下两个样品中的快过程类似,但慢过程在GM309中有所增快,激发态中的能量重新分布包括逆向的能量传递也受到类胡萝卜素微结构的影响.     

Planar Line Processes for Void and Density Statistics in Thin Stochastic Fibre Networks

Using results for the distribution of perimeters of random polygons arising from random lines in a plane, we obtain new analytic approximations to the distributions of areas and local line densities for random polygons and compute various limiting properties of random polygons. Using simulation, we show that the lengths of adjacent sides of polygons generated by random line processes in the plane are correlated with ρ=0.616±0.001.     

Monitoring of Paint Drying Process by Digital Speckle Correlation

The state of drying paint is monitored from the dynamic behaviors of the speckle pattern arising from laser illumination of the region inspected. Temporal variation of the peak height of the cross-correlation function between successive frames taken with a fixed interval is plotted until the peak maintains a stationary maximum value. We used a speckle pattern in the diffraction field for monitoring of a single region and that in the image field for simultaneous monitoring of various regions. Both the normal and the phase-only algorithms were compared for cross-correlation computation. The former showed more distinct variation of peak height.     

Calculation of the photoelectron spectra under the scaling transform

By solving time-dependent Schrödinger equation, the dependence of photoelectron energy spectra on the binding energy of targets, wavelength and intensity of laser pulse is exhibited and a scaling law of kinetic energy spectra of both the direct and the rescattered photoelectrons is concluded. The scaling law provides a convenient tool to determine the equivalent photoionization process of various atoms or molecules in various laser fields. The verification of the scaling law by independent methods provides an incontestable support to the validity of the scaling law.     

Modelling non-equilibrium self-assembly from dissipation

Non-equilibrium self-assembly is ubiquitous in physico-chemical and biological systems, and manifests itself at different scales, ranging from the molecular to the cosmological. The formation of microtubules, gels, cells and living beings among many others takes place through self-assembly under nonequilibrium conditions. We propose a general thermodynamic non-equilibrium model to understand the formation of assembled structures such as gels and Liesegang patterns and at the same time able to describe the kinetics and the energetics of the structure formation process. The model is supported for a global mechanism to obtain self-assembled structures from building blocks via activation, deactivation, assembly, and disassembly processes. It is proposed that the resulting structures can be characterised by a structural parameter. Our model may contribute to a better understanding of non-equilibrium self-assembly processes and give deeper insight as to how to obtain a specific structural architecture to materials, such as hydrogels which are of great importance in the design of advanced devices and novel materials.     

La(Ⅲ)、Gd(Ⅲ)、Tb(Ⅲ)8-羟基喹啉固体配合物的光声光谱与弛豫过程

本文合成Ｌａ（Ⅲ）、Ｇｄ（Ⅲ）、Ｔｂ（Ⅲ）８－羟基喹啉固体配合物，通过对其光声光谱的分析，研究了８－羟基喹啉稀土配合物的荧光性质和弛豫过程     

高次非球面的工艺技术研究

 高次非球面在光学系统应用中意义重大,但是一直以来缺乏一套快速、有效的工艺方法。利用VC6.0编制了一款面型计算软件以辅助加工,并提出了一种新的高次非球面补偿检验方法。针对一块巡天光谱仪中口径Φ244 mm的一面平面另一面为高次非球面的改正镜开展工艺方法的设计与研究,从铣磨成形开始,根据高次非球面的特点提出了几种新型磨削工艺,建立相应的数学模型。由于高次非球面的特殊性,试验了数控铣磨直接成型法,很大程度上降低后继工艺难度,在细磨和抛光阶段采用数控小工具和整工具研磨相结合,能够很好地克服面型不平滑等技术难题。总结出了一套高效率、低成本、高精度的高次非球面工艺方法。     

Study of domain structure and magnetization reversal after thermal treatments in Fe40Co38Mo4B18 microwires

We have studied the effect of thermal treatment on the magnetic domain structure and magnetic reversal process of amorphous and nanocrystalline Fe₄₀Co₃₈Mo₄B₁₈ microwires. The domain structure and the magnetization reversal of amorphous FeCoMoB microwires reflect the complex stress distribution introduced by the glass coating. Hence, the thickness of radial domain structure decreases with temperature and the temperature dependence of the switching field presents a discontinuous behavior. After nanocrystallization, the domain structure of FeCoMoB microwire is almost constant within the temperature range 10-400 K and the switching field decreases almost linearly with temperature mostly because of the decrease of saturation magnetization.     

Phase and shape controlling of MnS nanocrystals in the solvothermal process

MnS nanocrystals with different phases and shapes were prepared through solvothermal synthesis. The products were characterized by X-ray diffraction (XRD), transmission electron microscope (TEM), UV–vis absorption and photoluminescence (PL) spectra. The solvent and reaction time played an important role in controlling the phase and shape of MnS nanocrystals. The possible mechanism of the shape evolution was investigated, which revealed that the crystal growth along the unique c axis of γ-MnS resulted in the rod-like MnS at the primary period, and the tetrahedral crystal seed of β-MnS with zincblende structure resulted in the interlinking of MnS rods, so the zigzag and three-branched and palm-like MnS appeared; with increasing reactive time the thermodynamically stable spherical α-MnS was favored through the Ostwald ripening process. The PL results showed that the intensity of γ-MnS was much weaker than that of α-MnS, and the trap state emissions of γ-MnS at 470 and 482 nm, respectively, disappeared, which might be ascribed to the difference of the shapes between the sphere and the rod or branch.