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.     

A novel design of membrane mirror with small deformation and imaging performance analysis in infrared system

A method of diminishing the shape error of membrane mirror is proposed in this paper. The inner inflating pressure is considerably decreased by adopting the pre-shaped membrane. Small deformation of the membrane mirror with greatly reduced shape error is sequentially achieved. Primarily a finite element model of the above pre-shaped membrane is built on the basis of its mechanical properties. Then accurate shape data under different pressures can be acquired by iteratively calculating the node displacements of the model. Shape data are applicable to build up deformed reflecting surfaces for the simulative analysis in ZEMAX. Finally, ground-based imaging experiments of 4-bar targets and nature scene are conducted. Experiment results indicate that the MTF of the infrared system can reach to 0.3 at a high spatial resolution of 10l p/mm, and texture details of the nature scene are well-presented. The method can provide theoretical basis and technical support for the applications in lightweight optical components with ultra-large apertures.     

A Novel Fabrication for Method Long Period Fiber Grating

A new method of fabricating all-fiber broadband-rejection filter based on long period fiber grating (LPFG) is proposed. The principle in the method is to make periodic asymmetrical deformation in the core of fiber without microbends by electrode discharging so as to induce periodic refractive index changes. Two kinds of filters whose rejection peak wavelength at 1550 nm and 1310 nm are obtained. The insertion loss is less than 0.6 dB and 1.4 dB respectively. The 20 dB bandwidth ranges from 10 nm to 39 nm. The backward reflection loss is extremely small (less than -70 dB). Such devices can be used as isolation filters in 1310/1550 nm WDM system and other fields.     

Convergent Star Product Algebras on ‘ax+b’

We define nontempered (exponential growth) function spaces on the Lie group ax+b which are stable under some left-invariant (convergent) star product. The techniques used to achieved the latter come from symmetric spaces geometry and star representation theory.     

温度对潜望式激光通信终端SiC反射镜性能影响

分析了温度梯度和均匀温度对潜望式激光通信终端反射镜形变的影响,利用椭圆域上的Zernike多项式对椭圆反射镜的波前进行拟合,计算由于热形变导致的波前畸变误差,给出了星间激光通信终端反射镜均方根值、发射光束瞄准误差、接收端光强随温度梯度和均匀温度的变化关系。结果表明:温度梯度对反射镜的影响只是引起峰值光强的漂移和少许下降,当温度梯度为14 ℃/m时瞄准误差达2.1 μrad。均匀温度会引起接收端的光强分布变化,从而导致很大的瞄准误差和光强衰减,当均匀温度与参考温度的差值小于0.6 ℃时,由波前畸变误差引起的瞄准误差小于1 μrad,当差值大于0.6 ℃时,瞄准误差突然增大到几μrad,接收端光强分布发生变化,此时反射镜热形变引起的像散项对光强分布起重要作用。     

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.