Large deviations for martingales with some applications

Let(X _i ) be a martingale difference sequence. LetY be a standard normal random variable. We investigate the rate of uniform convergence

天竺葵绒毡层发育的细胞学及其与花粉发育的关系

本文应用细胞化学和光镜及电子显微镜技术对天竺葵绒毡层发育的全过程进行了系统研究．发现天竺葵变形绒毡层的发育具有如下特点：（１）绒毡层侵入药室的时间在小孢子大液泡时期;（２）侵入后要经历一个细胞质重建过程,并在较长的一段时间内保持生理活跃状态,合成大量的脂类物质;（３）绒毡层合成的营养物质及自身降解的产物均被花粉吸收利用,物质的吸收通过萌发孔进行．     

Generalized solutions of a stochastic partial differential equation

We discuss the Cauchy problem of a certain stochastic parabolic partial differential equation arising in the nonlinear filtering theory, where the initial data and the nonhomogeneous noise term of the equation are given by Schwartz distributions. The generalized (distributional) solution is represented by a partial (conditional) generalized expectation ofT(t)° _0,t ^–1 , whereT(t) is a stochastic process with values in distributions and _s,t is a stochastic flow generated by a certain stochastic differential equation. The representation is used for getting estimates of the solution with respect to Sobolev norms.Further, by applying the partial Malliavin calculus of Kusuoka-Stroock, we show that any generalized solution is aC -function under a condition similar to Hörmander's hypoellipticity condition.     

Essential spectrum and -solutions of one-dimensional Schrödinger operators

In 1949, Hartman and Wintner showed that if the eigenvalue equations of a one-dimensional Schrödinger operator possess square integrable solutions, then the essential spectrum is nowhere dense. Furthermore, they conjectured that this statement could be improved and that under this condition the essential spectrum might always be void. This is shown to be false. It is proved that, on the contrary, every closed, nowhere dense set does occur as the essential spectrum of Schrödinger operators which satisfy the condition of existence of -solutions. The proof of this theorem is based on inverse spectral theory.

     

高阶微分中值定理及其应用

利用向量形式的微分中值定理,把一阶微分中值定理推广到全新的高阶微分中值定理,并研究了它的应用．     

特勒根定理的验证及其应用

本文对特勒根定理的内容,特别是其适用的普通性进行了验证．并运用该定理对网络的灵敏度进行了分析．最后对一个具体电路的灵敏度进行了计算,进一步验证了文中所述方法的正确性．     

稳定非线性动力系统周期的计算机分析

提出采用后继函数法来确定非线性动力系统的周期,并编制计算机程序对Ｖａｎ ｄｅｒ Ｐｏｌ方程实例计算周期和绘制相图,结果表明,该方法计算结果准确且实用性强,本方法不但适合于求解保守系统和具 周期解非线性动力系统的周期,也适合于耗散系统和不稳定系统的分析。     

批量制造业模糊交货期准时化生产计划方法

通过建立批量制造业模糊交货期下的准时化生产计划模型,将隶属度函数引入到生产计划问题中,从而拓宽了准时化生产计划问题的研究范围,并为实际生产计划的编制提供了一种有效途径。     

一些基本图的〔强〕自同态摹群

确定了一些基本图的〔强〕自同态摹群的基数,并在证明过程中实际上确定了这些摹群的全部元素,同时发现确定一些极其简单的图之自同态摹群却是极其困难的事情,有时甚至导致一些一般的组合难题．