Oscillation of a Second-order Impulsive Neutral Differential Equation

Oscillation theorems for a second-order impulsive neutral differential equation are established, which extend the main results developed by Li et alLi et al, Oscillation of second order self-coajugate differential equation with impuls[es. J Comput Appl Math 197（2006）： 78-88] to the considered equation. Two examples are also inserted to illustrate our main results.     

Comparison theorems for diffusion processes

We prove comparison theorems for diffusion processes onR ^d. From these theorems we derive lower and upper bounds for the transition probabilities of a diffusion process. In contrast to the known estimates for fundamental solutions of parabolic equations our bounds do not depend on the moduli of continuity of the coefficients of the differential operator.     

Recent developments in the stereological analysis of particles

Recent developments in the stereological analysis of particles are reviewed. The trend has been towards methods which are applicable without specific assumptions about particle shape. Geometric samples of a local 3-d character are used. Stereological estimators of particle intensity, particle size distribution and particle interaction are presented and discussed.An earlier version of this article was presented at the Symposium on the Analysis of Statistical Information held in the Institute of Statistical Mathematics, Tokyo during December 5–8, 1989.     

Second-order effects of the output resonance and frequency-locking in an electro-optic bistable system

Based on the dynamic equations of an electro-optic bistable system with delay in its feedback loop, we theoretically investigate second-order effects of the output resonance and frequency-locking of the system.     

An experiment to test the reality of de Broglie waves

A second-order interferometric experiment in which de Broglie waves pass through a set of beamsplitters and progressively lose intensity, leading to a decrease in the visibility, is presented. On the contrary, since the intensity reduction is the same in the two overlapping waves, quantum mechanics predicts a constant visibility.     

相空间中二阶线性非完整系统的形式不变性

研究相空间中二阶线性非完整系统的形式不变性.给出相空间中二阶线性非完整系统形式不变性的定义和判据，得到形式不变性的结构方程和守恒量的形式，并举例说明结果的应用. 关键词： 相空间 二阶线性非完整系统 形式不变性 守恒量     

A numerical study of flow over a confined backward-facing step

Numerical solutions using the SIMPLE algorithms for laminar flow over a backward-facing step are presented. Five differencing schemes were used: hybrid; quadratic upwind (QUICK); second-order upwind (SOUD); central-differencing and a novel scheme named second-order upwind biased (SOUBD). The SOUBD scheme is shown to be part of a family of schemes which include the central-differencing, SOUD and QUICK schemes for uniform grids. The results of the backward-facing step problem are presented and are compared with other numerical solutions and experimental data to evaluate the accuracy of the differencing schemes. The accuracy of the differencing schemes was ascertained by using uniform grids of various grid densities. The QUICK, SOUBD and SOUD schemes gave very similar accurate results. The hybrid scheme suffered from excessive diffusion except for the finest grids and the central-differencing scheme only converged for the finest grids.     

Parabolic Equations with Measurable Coefficients

We investigate the unique solvability of second order parabolic equations in non-divergence form in , p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables. The second author was partially supported by NSF Grant DMS-0140405.     

带非线性源项的Riesz回火分数阶扩散方程的预估校正方法

本文针对带非线性源项的Riesz回火分数阶扩散方程,利用预估校正方法离散时间偏导数,并用修正的二阶Lubich回火差分算子逼近Riesz空间回火的分数阶偏导数,构造出一类新的数值格式.给出了数值格式在一定条件下的稳定性与收敛性分析,且该格式的时间与空间收敛阶均为二阶.数值试验表明数值方法是有效的.