Bolzano's Theorems for Holomorphic Mappings

The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple way from Cauchy's theorem for holomorphic functions.A more complicated proof,using Cauchy's argument principle,provides uniqueness of the zero,when the sign conditions on the boundary are strict.Applications are given to corresponding Brouwer fixed point theorems for holomorphic functions.Extensions to holomorphic mappings from Cn to Cn are obtained using Brouwer degree.     

Option Pricing and Hedging under a Markov Switching Lévy Process Model

In this paper,we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to option pricing and hedging.In this model,the market interest rate,the volatility of the underlying risky assets and the N-state compensator,depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process.We use the MEMM(minimal entropy martingale measure) as the equivalent martingale measure.The option price using this model is obtained by the Fourier transform method.We obtain a closed-form solution for the hedge ratio by applying the local risk minimizing hedging.     

SMALE HORSESHOES AND CHAOS IN DISCRETIZED PERTURBED NLS SYSTEMS(Ⅰ)-POINCAR(E) MAP

The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger(NLS) equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized perturbed NLS system is shown to possess an invariant set Λ on which the dynamics is topologically conjugate to a shift on four symbols.     

L~p空间中的Fejér和Hermite-Hadamard型不等式

给出了二阶导数属于Lp空间时Fejér和Hermite-Hadamard型不等式的推广,得到两个新结果.     

由Lévy过程驱动的BSDE定义的一般非线性期望

本文研究了平凡可积随机变量的一类非线性期望f-期望.利用陈增敬推广g-期望的方法,扩张了f-期望的定义空间.     

有限元插值误差的下界估计

基于一维区域上的拟一致剖分,证明了线性元插值误差的最优下界估计.基于此并利用超收敛理论,我们得到了有限元离散误差的上、下界.     

重分数布朗运动的列维连续模

重分数布朗运动是布朗运动的一种推广，有较强的实用背景.该过程的增量既不是独立的，也不是平稳的. 本文研究了它的列维连续模.     

空间扫描型光纤法布里珀罗传感解调系统中CCD的光照度数学模型研究

针对空间扫描型光纤法布里珀罗（F-P）传感解调系统中CCD的光照度分布建立了数学模型,研究了不同帧扫描频率下CCD输出信号和信噪比。利用已设计的解调模块进行了CCD光照度分布的实验,实验结果表明,当帧扫描频率不同时,CCD各个像素输出信号电压的实验值与计算值的相对误差均小于2.5%,同一像素输出信号电压的实验值与计算值的相对误差变化数值均小于0.005,随实验所用CCD帧扫描频率变化,信噪比以184 Hz为分界点以两种变化斜率改变,验证了数学分析模型的有效性。     

金属网栅法布里珀罗干涉仪测量太赫兹波波长

设计并制作了用于测量波长大于150 μm(频率低于2 THz)的太赫兹波波长的金属网栅法布里珀罗干涉仪(FPI)。采用光电子微纳制造工艺制作了五组周期不大于40 μm,线宽不大于10 μm的有衬底方形金属网栅,利用太赫兹时域光谱技术测量了金属网栅的太赫兹波段光电特性,得到了各组金属网栅在感兴趣频段的反射率和金属网栅FPI的反射精细度,结果表明所制作的金属网栅FPI均可用于测量波长大于150 μm的太赫兹波。实验搭建金属网栅FPI扫描测量了212 μm的太赫兹波波长,与理论结果吻合。研究了金属网栅FPI对太赫兹波偏振方向的依赖性以及对FPI腔镜平行度的要求,结果表明,方形金属网栅FPI对正入射太赫兹波偏振方向不敏感,而对FPI腔镜平行度很敏感。     

介质球掺杂导致的无序效应对光子晶体光学性能的影响

采用自组装法制备了聚苯乙烯(PS)微球三维光子晶体结构,通过在PS微球悬浮液中掺入不同浓度的二氧化硅大球,实现了光子晶体结构从有序向无序过程的转变。通过对这些样品的透射、反射进行测量和分析,发现无序效应对光子晶体的光子响应特性具有极大的影响,随着无序程度的增加,高频波段的透射率急剧下降,低频波段的法布里-珀罗振荡消失,光子带隙蓝移且逐渐消失;而在掺杂浓度为0.02%(质量分数)时,光子晶体带隙中心的最低透射率从10%下降到1%,且反射单峰随着探测角度的增大而分裂为双峰。这有助于基于介质球三维光子晶体沿Γ-L方向透射消光,促进其在新型光学器件领域的应用发展。