Stochastic coupling for von Neumann algebras

We consider even and odd stochastic transitions of von Neumann algebras when dual mappings intertwine (couple) modular groups of the corresponding states (with the occurrence of a sign exchange for the odd case). We show that one can define modular objects and cones associated to linear combinations of von Neumann algebras, which generalize objects and cones in the standard modular theory. In the odd case, we find sufficient conditions for the intertwining property and consider several applications to noncommutative Markov processes. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 760–774, May, 1999.     

基态中性原子(Z=2-54)径向距离的期望值

原子的径向距离r是原子、分子结构的重要信息．Fraga”’和Slater’‘’等人指出：＜r－’＞正比于电子亲和势和电子势能,＜r－’＞与元素的电负性有关,＜r－’＞与电场梯度、磁偶极子相互作用、轨一旅耦合相关,＜＞与屏蔽常数有关,＜严＞与抗磁化率有关,＜尸＞近似等于球形对称原子的极化率,＜／＞与晶体场分裂能相关．由此可见,·精确求解原子及其轨道的径向期望值对原子、分子相关性质的研究具有重要意义．ShustCk、Pekeris、Weiss、Baker和Wakim等人”－’‘分别研究了某些原子特定态的电子结构及其径向期望值,但其成果比较…     

Convergences of Random Variables Under Sublinear Expectations

In this note, the authors survey the existing convergence results for random variables under sublinear expectations, and prove some new results. Concretely, under the assumption that the sublinear expectation has the monotone continuity property, the authors prove that convergence in capacity is stronger than convergence in distribution, and give some equivalent characterizations of convergence in distribution. In addition, they give a dominated convergence theorem under sublinear expectations, which may have its own interest.     

浅谈三年"拔尖计划"经历的收获与期望

This article briefly discusses the harvest and impression of Top Talent Training Program in terms of mechanism of student recruitment and training, individualized course selection, specialized scientific research training, and foreign exchange, from the point view of top talented students of Sun Yat-Sen University. This article also puts forward some expectations and considerations for the 2.0 plan of Top Talent Training Program.     

具有Rao简单结构的多元t-模型的MLE的数字特征

本文在文[7]已求得未知参数MLEs的基础上，利用条件期望方法，研究了具有Rao简单结构多元t-模型的极大似然估计的数字特征．     

次线性算子在齐型空间的弱Herz-Morrey空间上的有界性

作者在齐型空间上定义了Herz-Morrey空间。并研究了某些次线性算子在弱HHerz-Morrey空间上的有界性．     

概率方法在证明不等式中的应用

本文针对不同的问题，通过构造适当的离散型随机变量，用概率方法推出了一系列不等式，证明方法简洁独特。     

Characterization and statistical test using truncated expectations for a class of skew distributions

The expectation of left truncated Waring and Pareto distributions is a linear function of the point of truncation. Based on this property, a characterization theorem and statistical tests can be constructed.     

Completely positive projections on a Hilbert space

The purpose of this paper is to prove that a completely positive projection on a Hilbert space associated with a standard form of a von Neumann algebra induces the existence of a conditional expectation of the von Neumann algebra with respect to a normal state, and we consider the application to a standard form of an injective von Neumann algebra.

     

Some properties of record values coming from the geometric distribution

The independence between spacings of record values and of individual record values is well known when the records come from a geometric distribution. Here we examine the form a function of two record values must have if we require independence from a lower record value. Also similar questions are examined in relation to conditional expectation and conditional variance.