曲面平滑的自适应几何扩散

1.引 言 本文的目的是用求解偏微分方程（PDE）的方法来消除离散三角形曲面的噪声,所使用的方程是热传导方程到曲面的推广.热传导方程应用于图像处理已有二十余年的历史,有关参考文献相当丰富（见[1,11,12,19]）.众所周知,对于给定的初始图像ρ0,热传导方程　　在τ时刻的解与用Gauss滤波器Gσ（x）=　（当标准差σ=2τ,时）和ρ0作卷积的结果相同.容易看出Gρ和ρ0的卷积运算相当于对ρ0做加权平均,当标准离差σ变大时,该加权平均在一个较大的范围实现,这解释了热传导方程的滤波作用.近来热传导方程已推广到空间曲面[4,5]以及高维空间中的二维流形（见[3]）,对     

线性分式规划最优解集的求法

本文使用多面集的表示定理，导出了线性分式规划最优解集的结构，并给出确定全部最优解的计算步骤。     

Using multi-exposure of color fringes to measure the beating motion of a moth

A multi-exposure of color fringes method has been developed to improve the capture speed of a conventional color CCD camera. In the method, four groups of projected fringe patterns encoded with different colors and different directions are stored in one CCD frame. Therefore the capture frequency of the conventional CCD can be improved to 200 Hz. It is available to measure the insect wings with low beating frequency, such as dragonfly, moth, or butterfly, whose beating frequency is about 30–40 Hz. We have used the method to measure the beating motion of a moth successfully.     

滚动实验的另一种演示

介绍了另一种滚动演示实验,并对演示结果进行了理论分析和解释     

股票价格遵循几何分式Brown运动的期权定价

讨论了股票价格过程遵循几何分式B row n运动的欧式期权定价.由于该过程存在套利机会使得传统的期权定价方法(如资本资产定价模型(CAPM),套利定价模型(APT),动态均衡定价理论(DEPT))不可能对该期权定价.利用保险精算定价法,在对市场无其它任何假设条件下,获得了欧式期权的定价公式.并讨论了在有效期内股票支付已知红利和红利率的推广公式.     

空气/水界面水分子的取向和运动

对四种不同的实验构型下空气／水界面自由O-H键在3700cm~(-1)的和频振动光谱的分析表明,水分子在空气／水界面的取向运动只可能是在平衡位置附近有限角度之内的受限转动。界面水分子的自由O-H键取向距界面法线约33°,而取向分布或运动的宽度不超过15°。这一图像显著地不同于Wei等人(Phys. Rev. Lett.86,4799(2001))只通过单一的SFG实验构型所得出结论,即：空气／水界面的水分子在超快的振动弛豫时间内在很大的角度范围内运动。     

第一类永动机幻梦的破灭

介绍了13~18世纪物理学史和科技史上曾名噪一时的第一类永动机的设计方案的破灭.第一类永动机幻梦破灭的历史引起了人们的反思与启示,有力地促进了19世纪中叶能量转化和守恒定律的确立.     

Development of a Simulation Model for Solid Objects Suspended in a Fluctuating Fluid

We introduce a new scheme for the future application of Real-coded Lattice Gas (RLG) to the numerical simulation of suspended solid objects in a fluctuating fluid environment. The reproduction of Brownian motion for a single solid object is verified through the Gaussian distribution of its displacements. The effectiveness of the solid–solid interaction model is also confirmed in an N-body simulation.     

Brownian surfaces with boundary and Deligne cohomology

We define differentiable random surfaces, which realize a kind of generalized parallel transport for line bundles over the loop space. This gives a realization of one of the axioms of Segal of conformal field theory.     

Statistical Inference with Fractional Brownian Motion

We give a test between two complex hypothesis; namely we test whether a fractional Brownian motion (fBm) has a linear trend against a certain non-linear trend. We study some related questions, like goodness-of-fit test and volatility estimation in these models.