Two Ergodic Sample-Path Properties of the Poisson Process

For increasing sequences of real numbers we consider two types of asymptotic behavior that remind of the defining property of a (homogeneous) Poisson process according to which the numbers of points in disjoint intervals are independent and follow Poisson distributions with specified parameters. We prove that almost all paths of a Poisson process show this asymptotic behavior, and characterize the Poisson process by these properties. Further we discuss the connection to equidistribution notions.     

Gating processes in Na-channel of biological membrane from the standpoint of superionic phase transition

The method of condensed matter physics is applied to reason out the problem of Na transport through a biological membrane. A similiarity of gating process in Na ion channel to the superionic phase transition is discussed. A possible microscopic mechanism is suggested.     

韧性金属裂纹尖端损伤区内应变场测量——数字散斑相关法应用

本文用数字散斑相关方法测量了五种不同幂硬化指数韧性金属材料(铝和铜),双边裂纹尖端细观区域内应变场.对所得结果用韧性损伤模型进行了分析.在此法中以金属自然表面结构为散斑场,不同加载状态的散斑场进行比较,得到相对变形与应变.图象之间相关性 C 是变形参数或是位移及其导数的泛函.使其相关性 C 取最大值的试凑变形即为其真实变形场.这一方法在细观测量中应用得到满意的结果.     

Novel All Digital Scheme for Open Loop Fiber Optic Gyroscopes

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Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions

Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes.     

Size distribution of fractured areas in one-dimensional systems

We study a one-dimensional model for fracture, identifying fractured areas with intervals on which a stress field exceeds a threshold value. When is a diffusion process, the cumulative numberN(l) of fractured areas whose length is greater thanl obeys a power lawCl ^–p asl0 with probability one. The exponentp and the constantC are determined. The exponentp agrees with the Hausdorff dimension of the end points of fractured areas, i.e., ^–1(). Even if is self-similar with parameterH>0, i.e.,(cx)– is equivalent toc ^H {(x)–} for anyc>0, the exponentp does not depend solely onH;p=H, where(0, 1/H) is another parameter characterizing. Non-diffusion processes are given whereN(l) does not follow a power law.     

Front propagation in certain one-dimensional exclusion models

Recent results on two interacting particle systems on are summarized, the asymmetric simple exclusion process and the branching exclusion process.     

On the relationship betweenT 1 andT 2 for stochastic relaxation models

We consider the relaxation dynamics of two quantum levels coupled to a stochastic bath. We emphasize that even if the matrix elements of the fluctuating Hamiltonian are Gaussian, a second-order cumulant truncation is not exact. For various stochastic models, including the case of a spin-1/2 particle in a fluctuating magnetic field, we calculate 1/T ₁, the population relaxation rate, and 1/T ₂, the phase relaxation rate, up to fourth order in perturbation theory. We show that unlike the commonly accepted second-order result that 1/T ₂1/2T ₁, when fourth-order terms are included, in some instances 1/T ₂<1/2T ₁.     

On the Integration by Parts and Characterization of a Fractional Diffusion Process北大核心CSCD

本文研究分数扩散过程和其分部积分公式的关系.首先利用Bismut方法给出拉回公式,进而得到分数扩散过程的分部积分公式。反过来,证明了分数扩散过程可由其分部积分公式唯一刻画.     

The Discrete Approximation of Continuous-state Nonlinear Branching Processes in Lévy Random Environments北大核心CSCD

In this paper, we establish the discrete approximation of continuous-state nonlinear branching processes in Lévy random environments by using tightness and convergence sequence in infinite dimensional product space via stochastic differential equations. Taking α-stable branching as an example, the conditions which are given to discretize continuous-state nonlinear branching processes in Lévy random environments are verified. © 2022 Chinese Academy of Sciences. All rights reserved.