具有绝对连续测度状态的超布朗运动

设X={Xt,Pμ}是d维超布朗运动,具有分支率函数A与一般分支机制ψ.讨论A满足什么条件时可以保证Xt具有绝对连续状态.特别当ψ（s,x,z）=z2时,Dawson与Fleischmann[2]讨论了类似问题.本文对他们的讨论进行了改进,将他们的结果推广到了ψ一般的情形,并且简化了他们对A所加的条件.     

Absolutely continuous spectrum of Schrödinger operators with potentials slowly decaying inside a cone

For a large class of multi-dimensional Schrödinger operators it is shown that the absolutely continuous spectrum is essentially supported by [0,∞). We require slow decay and mildly oscillatory behavior of the potential in a cone and can allow for arbitrary non-negative bounded potential outside the cone. In particular, we do not require the existence of wave operators. The result and method of proof extends previous work by Laptev, Naboko and Safronov.     

OSCILLATIONS OF SOLUTION FOR A CLASS OF HIGHER-ORDER NEUTRAL DIFFERENTIAL EQUATION

In this paper, the higher order neutral differential equation with continuous distributed delay is concerned and the oscillatory criteria are given.     

Hilbert空间中最终范数连续半群的特征条件

本文给出了Hilbert空间中当t>t0(t0≥0)时,按一致算子拓扑连续C0半 群T(t)的四个特征条件.     

阻滞增长模型支持下对益虫和害虫数量关系及农药影响的分析

研究了在自然状态和喷洒农药情况下益虫和害虫数量的发展趋势.基于logistic模型并加以改进建模,通过分析微分方程平衡点的稳定性,分别得出了自然状态下益虫和害虫的数量发展规律.在此基础上,进而建立了农药影响的模型并进行了计算机仿真,仿真结果证明了新模型的合理性和适用性,解决了Lotka—Volterra模型存在的问题.另外,该仿真程序本身可以作为应用程序用于实际的农田管理.     

CONTINUOUS DEPENDENCE ON THE TERMINAL CONDITION OF SOLUTIONS TO NONLINEAR REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper,we derive the continuous dependence on the terminal condition of solutions to nonlinear reflected backward stochastic differential equations involving the subdifferential operator of a lower semi-continuous,proper and convex function under non-Lipschitz condition by means of the corollary of Bihari inequality.     

差分方程解对初值连续性问题

本文讨论了差分方程的解对初值的连续性问题，对较一般的方程给出了保证解对初值连续的充分条件，对线性方程（组）利用系数矩阵的特征值给出其解对初值连续的条件．     

On sign-changing solutions for nonlinear operator equations

In this paper, the existence of sign-changing solutions for nonlinear operator equations is discussed by using the topological degree and fixed point index theory. The main theorems are some new three-solution theorems which are different from the famous Amann's and Leggett-Williams' three-solution theorems as well as the results in [F. Li, G. Han, Generalization for Amann's and Leggett-Williams' three-solution theorems and applications, J. Math. Anal. Appl. 298 (2004) 638-654]. These three solutions are all nonzero. One of them is positive, another is negative, and the third one is a sign-changing solution. Furthermore, the theoretical results are successfully applied to both integral and differential equations.     

Some properties of complete congruence lattices

For a complete lattice C, we consider the problem of establishing when the complete lattice of complete congruence relations on C is a complete sublattice of the complete lattices of join- or meet-complete congruence relations on C. We first argue that this problem is not trivial, and then we show that it admits an affirmative answer whenever C is continuous for the join case and, dually, co-continuous for the meet case. As a consequence, we prove that if C is continuous then each principal filter generated by a continuous complete congruence on C is pseudocomplemented. Received January 6, 1998; accepted in final form July 2, 1998.     

连续随机变量的随机独立性与回归独立性

回归独立性是指给定随机变量 X时 ,随机变量 Y的条件期望 E( Y|X)不依赖于 X.前人讨论了离散型随机变量回归独立性与随机独立性的关系 ,得到了二者等价的充分必要条件 .对连续型随机变量的情形加以讨论 ,获到了二者等价的几个充分必要条件 ,并说明在统计分析中的应用 .