关于非负随机变量的几个矩不等式

设X是非负随机变量且0相似文献   

原子偶极压缩的相干控制和Cauchy-Schwarz不等式的破坏

通过研究孤立二能级原子与双模纠缠相干光场的相互作用,分析了体系中原子偶极压缩量子效应的时间演化规律.体系中作用场模的性质决定了原子偶极压缩程度;同时定义了体系的Cauchy-Schwarz不等式破坏参数ΔV,研究了不同条件下参数ΔV的时间演化特性,Cauchy-Schwarz不等式破坏程度和体系中所具有的非经典特性是一致的;即可以通过调控相干场参数来远程控制体系中的非经典特性. 关键词： 量子光学 双模纠缠相干态 偶极压缩效应 Cauchy-Schwarz 不等式     

一个非负矩阵的不等式

把 Horst A lzer在 L inear A lgebra and its Application上发表的文章中得到关于指数为 2的非负矩阵的不等式推广到指数为 2 k的一般情况 .并给出了不等式中等号成立的充要条件 .     

Operator versions of the Kantorovich inequality

The Operator Kantorovich Inequality

holds for a wide class of operators on a Hilbert space and all operators for which is a partial isometry, being the range projection of

     

一个概率不等式的三种证明与应用

将给出概率论中Cauchy-Schwarz不等式的三个证明,并借助随机变量的分布,应用这个不等式导出与代数、积分有关的一些重要不等式,谨供教学参考.     

A Cauchy-Khinchin matrix inequality

We derive a matrix inequality, which generalizes the Cauchy-Schwarz inequality for vectors, and Khinchin's inequality for zero–one matrices. Furthermore, we pose a related problem on the maximum irregularity of a directed graph with prescribed number of vertices and arcs, and make some remarks on this problem.     

A Cauchy-Schwarz type inequality for bilinear integrals on positive measures

If is Borel measurable, define for -finite positive Borel measures on the bilinear integral expression

We give conditions on such that there is a constant , independent of and , with

Our results apply to a much larger class of functions than known before.

     

On upper bounds for the variance of functions of random variables

The upper bounds for the variance of a function g of a random variable X obtained in Cacoullos (1982) (for short CP) are improved in the case μ = E(X) ≠ 0. A main feature of these bounds is that they involve the second moment of the derivative or the difference of g. A multivariate extension for functions of independent random variables is also given.     

关于正定矩阵一不等式的简单证明

设A=(aij)是一n阶正定实对称矩阵,本文用代数方法证明了|A|≤a11a22…ann,当且仅当A是对角矩阵时等号成立.且证法简单.