Martingale property of empirical processes

It is shown that for a large collection of independent martingales, the martingale property is preserved on the empirical processes. Under the assumptions of independence and identical finite-dimensional distributions, it is proved that a large collection of stochastic processes are martingales essentially if and only if the empirical processes are also martingales. These two results have implications on the testability of the martingale property in scientific modeling. Extensions to submartingales and supermartingales are given.

     

Conservation Laws of K(m, n) and mK(m, n) Equations

Based on the rank analysis method, algorithmization idea, and symbolic computation, in this paper we have presented a method to construct the conservation laws for nonlinear evolution equations. The polynomial conservation laws for K (n 2, n) equations and mnK(m, n) equations are found by using of this approach and some new results have been obtained.     

Potential-dependent structure of the interfacial water on the gold electrode

Doubly tunable sum frequency generation (SFG) spectra demonstrate that the water molecules at gold/electrolyte interface change their orientation with applied potential. At negative potentials, water molecules in the double layer align with their oxygen atom pointing to the solution. As potential became positive to be close to the potential of zero charge (PZC), the SFG signal decreased, suggesting the OH groups of the water molecule are either in random orientation or parallel to the electrode. As potential became more positive than the PZC, the SFG signal increased again with the oxygen-up orientation as same as in the negative potential region, indicating that water molecules interact with the adsorbed sulfate anions. The peak position of the SFG spectra indicates a relatively disordered state of water molecules at the gold electrode surface, in contrast to the previously observed ice-like structure of water at electrolyte/oxide interfaces.     

A Glivenko-Cantelli Theorem and Strong Laws for L-Statistics

We prove a weighted Glivenko-Cantelli theorem and apply it to study the rate of convergence in the strong law for L-statistics.     

IR-poled second-harmonic generation in glass

Infrared (IR)-induced second-harmonic generation in the chalcogenide glasses is observed. A phenomenological approach of IR picosecond non-linear optical (NLO) response in glass is developed for the middle IR spectral range (5–15 μm). The observed effect is explained within the framework of fifth-order NLO susceptibilities. A model that reproduces the basic characteristics of the experimental data, in which the optical non-linearities caused by photoinduced electron–phonon anharmonic interactions, is proposed. The role of the IR-induced phase matching conditions in the observed phenomenon is discussed.     

球面空间中的一类几何不等式

本文首先给出n维球面空间的正弦定理,其次得到了一类几何不等式及其应用(即文中的推论)。     

表面垂直裂痕诱发瑞利波散射的数值分析

激光激发的声表面波为材料表面缺陷的检测提供了有力的工具.针对含缺陷材料在模型边界上的复杂性,建立了基于平面应变的有限元模型并选取了相同厚度但含有不同深度的表面裂痕的单层铝板进行了对比计算,得到了声表面波经过不同深度的表面裂痕时产生的反射及透射信号波形的时域特征.进而引入了基于Wigner-Ville分布理论的时-频分析方法计算裂痕前、后散射的瞬态表面波的能量在时间-频率平面内分布的情形.结果显示：声表面波接近中心频率的某一频率成分在经过深度小于其中心波长的表面缺陷时,随着裂痕深度的增加,对应于该频率的反射系数呈现单调递增的趋势;而透射系数呈现递减的特征,这一结果可以为激光超声检测表面缺陷提供一种定量的表征手段.     

STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Some strong laws of large numbers for the frequcncies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields(NSMC)on Cayley trees are studied.In the proof,a new technique for the study of strong liinit theorems of Markov chains is extended to the case of Markov chain fields.The asymptotic equiparti- tion properties with almost everywhere(a.e.)convergence for NSMC on Cayley trees are obtained.     

带松弛项的单个守恒律方程解的时态渐近性质

本文研究一维空间中带松弛项的单个守恒律方程解的大时间状态估计.在松弛项满足耗散条件下通过对线性化方程Green函数的逐点估计得到方程解在时间充分大时的衰减估计,并由此反映出“弱”惠更斯原理.     

Combinational simulations of free energy of polymer solution

It is conceptually proposed that the total entropy of polymer solution is contributed from two distinct parts: the positional and the oomformational. The former can be represented analytically, while the latter can be simulated with the random self-avoiding walk model on the simple cubic lattice for multichain systems. The obtained results indicated that both the conformational entropy and the mixing heat are consistent with the scaling laws wry well.