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 .     

一类Lyness方程的一些性质

本文主要研究下列Lyness方程的性质Xn+1=Xn\(a+b0Xn+b1Xn-1+…+bkXn-k)Xn-k-1,n=0,1,2,…,其中a,b0,b,…,bk∈[0,∞),a+k∑i=0bi＞0,k∈{0,1,2,…}.文中给出了方程(*)严格振动的充分条件,以及环长和环上极值的位置.另外,还得到了方程(*)在特殊情况下分别具有4,5,6周期的必要充分条件.本文的结果改进并推广了一些已知结果.     

On a Statistical Framework for Estimation from Random Set Observations

Using the theory of random closed sets, we extend the statistical framework introduced by Schreiber⁽¹¹⁾ for inference based on set-valued observations from the case of finite sample spaces to compact metric spaces with continuous distributions.     

Rank-<Emphasis Type="Italic">k</Emphasis> solutions of hydrodynamic-type systems

We present a variant of the conditional symmetry method for obtaining rank-k solutions in terms of Riemann invariants for first-order quasilinear hyperbolic systems of PDEs in many dimensions and discuss examples of applying the proposed approach to fluid dynamics equations in n+1 dimensions in detail. We obtain several new types of algebraic, rational, and soliton-like solutions (including kinks, bumps, and multiple-wave solutions). __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 83–100, July, 2007.     

Variable Separation and Derivative-Dependent Functional Separable Solutions to Generalized KdV Equations

Using the generalized conditional symmetry approach, a complete list of canonicalforms for the Kortewegde-Vries type equations with which possessing derivative-dependent functional separable solutions (DDFSSs) is obtained.The exact DDFSSs of the resulting equations are explicitly exhibited.     

数值积分公式中间点的渐近性质及其应用

主要研究了三类数值积分公式的中间点的渐近性质,得到了更一般性的结果.基于中间点的渐近性质,获得了数值积分的校正公式及其条件误差估计.数值例子显示了校正公式的精度明显高于对应的计算公式.     

Models for Stationary Max-Stable Random Fields

Models for stationary max-stable random fields are revisited and illustrated by two-dimensional simulations. We introduce a new class of models, which are based on stationary Gaussian random fields, and whose realizations are not necessarily semi-continuous functions. The bivariate marginal distributions of these random fields can be calculated, and they form a new class of bivariate extreme value distributions.     

Chernoff's Theorem and Discrete Time Approximations of Brownian Motion on Manifolds

Let be a one-parameter family of positive integral operators on a locally compact space . For a possibly non-uniform partition of define a finite measure on the path space by using a) for the transition between any two consecutive partition times of distance and b) a suitable continuous interpolation scheme (e.g. Brownian bridges or geodesics). If necessary normalize the result to get a probability measure. We prove a version of Chernoff's theorem of semigroup theory and tightness results which yield convergence in law of such measures as the partition gets finer. In particular let be a closed smooth submanifold of a manifold . We prove convergence of Brownian motion on , conditioned to visit at all partition times, to a process on whose law has a density with respect to Brownian motion on which contains scalar, mean and sectional curvatures terms. Various approximation schemes for Brownian motion on are also given.      

油溶性二正辛基二硫代氨基甲酸铈的合成及其摩擦化学特性研究

以二正辛胺、Ｃｅ２Ｏ３和ＣＳ２为原料合成出一种新型油溶性润滑油极压抗磨添加剂二正辛基二硫代氨基甲酸铈（Ⅲ），并在环－块式摩擦磨损试验机和四球试验机上，测定了它的减摩性能、承载能力和抗磨性能等，同时还就其添加量对这些性能的影响进行了考察；利用俄歇电子能谱仪和Ｘ射线光电子能谱仪，对边界润滑状态下形成的摩擦表面膜的元素组成和化学状态进行了分析．结果表明：在给定的试验条件下，这种添加剂可以使ＩＳＯＶＧ３２石蜡基矿物油的摩擦系数明显降低，能够使这种油的初始卡咬负荷和烧结负荷分别提高２．２倍和４．７倍，可见其减摩和抗磨性能良好；在这种添加剂作用下形成的表面层内含有有机物膜、氧化物膜、化学反应膜和Ｃｅ３＋渗透层等，这是摩擦化学作用的产物     

一些磷－氮型极压抗磨添加剂性能的研究

合成了一些磷－氮型极压抗磨添加剂烷基亚磷酸酯胺盐和氮杂环胺盐，并对其油溶性和润滑性等进行了试验研究。结果表明，磷－氮型极压抗磨添加剂的化学结构对其油溶性和极压抗磨性都有较大的影响：烷基链增长有助于油溶性的改善，氮杂环胺盐的油溶性更好；伯胺盐的抗磨性比仲胺盐和叔胺盐的都好，氮杂环胺盐的抗磨性更好；磷－氮型极压抗磨添加剂的减摩性明显比硫化烯烃、烷基亚磷酸酯和苯三唑十八胺的都好，有的在２５０℃时的摩擦系数仅约为０．０４．Ｘ射线光电子能谱和俄歇电子能谱分析发现，磷－氮型极压抗磨添加剂在摩擦表面形成了一种含氮富磷的化学反应膜。其中，元素磷是以磷酸铁的化合态形式存在，而元素氮则是以其原有的价态形式存在，这表明氮参与了整个摩擦过程。在试验研究和分析讨论的基础上，通过综合归纳还提出了磷－氮型极压抗磨添加剂的作用机理模式图。