Lenglart不等式与特殊半鞅的收敛集

本文讨论局部鞅和特殊半鞅的收敛集。我们给出Ｌｅｎｇｌａｒｔ不等式的一个推广形式，利用这一不等式对一些定理给出了简单证明，对一些结果作了改进和推广。     

特殊半鞅的一个局部性质

本文讨论特殊半鞅的一个局部性质,将局部（平方可积）鞅的结果推广到了一类特殊半鞅的情形。     

非同分布随机元和的收敛速度

本文在弱于［１］的矩条件下,对,ｒ＞１讨论了ｐ（１＜ｐ≤２）型空间中非同分布随机元和的收敛速度,同时获得了ｐ型巴拿哈空间的刻划,作为应用,我们给出了随机元随机指标部分和的收敛速度．     

特殊半鞅的收敛集

本文讨论特殊半鞅的收敛集，利用随机过程的控制关系和停时技巧，给出了特殊半鞅的收敛集的一般定理，推广和改进了已有的部分结果．     

一个鞅不等式及其在独立和中的应用

建立了一个鞅不等式,将这一不等式应用于独立随机变量和,对一个矩不等式的系数的增长阶给出了精确估计。     

独立增量过程的一个强逼近定理

该文给出了独立增量过程的一种强逼近定理,由此得到相应的ｓｔｒａｓｓｅｎ重对数律．     

局部平方可积鞅的比值不等式

本对局部平方可积鞅建立了几个比值不等式，推广了连续鞅的相应结果．     

A COMPREHENSIVE PROOF OF THE GREENBERGER-HORNE-ZEILINGER THEOREM FOR THE FOUR-QUBIT SYSTEM

Greenberger-Horne-Zeilinger(GHZ)theorem asserts that there is a set of mutually commuting nonlocal observables with a common eigenstate on which those ob- servables assume values that refute the attempt to assign values only required to have them by the local realism of Einstein,Podolsky,and Rosen(EPR).It is known that for a three-qubit system.there is only one form of the GHZ-Mermin-like argument with equiva- lence up to a local unitary transformation,which is exactly Mermin's version of the GHZ theorem.This article for a four-qubit system,which was originally studied by GHZ,the authors show that there are nine distinct forms of the GHZ-Mermin-like argument.The proof is obtained using certain geometric invariants to characterize the sets of mutually commuting nonlocal spin observables on the four-qubit system.It is proved that there are at most nine elements(except for a different sign)in a set of mutually commuting nonlocal spin observables in the four-qubit system,and each GHZ-Mermin-like argument involves a set of at least five mutually commuting four-qubit nonlocal spin observables with a GHZ state as a common eigenstate in GHZ's theorem.Therefore,we present a complete construction of the GHZ theorem for the four-qubit system.     

THE VALUE DISTRIBUTION OF RANDOM DIRICHLET SERIES ON THE RIGHT HALF PLANE(Ⅱ)

Kahane has studiedthe value distribution ofthe Gauss-Taylor series∑anXnzn,∞where{Xn}is a complex Gauss sequence and∑|an|2=∞.Inthis paper,by trans forming the right half plane into the unit disc and setting up some important inequalities,the value distribution of the Dirichlet series∑Xne- nS is studied where{Xn}is a sequence of some non-degenerate independent random variable satisfying conditions:EXn=0;∞E|Xn|2=+∞;An∈N,Xn or ReXn or ImXn of bounded density.There exists α＞0 such that An:α2E|Xn|2≤E2|Xn|＜+∞(the classic Gauss and Steinhaus random variables are special cases of such random variables).The important results are obtainedthat every point on the line Res=0 is a Picard point of the series withoutfinite exceptional value a.s..     

Banach空间的型与B值随机元和的完全收敛性

本文讨论了Ｂ值随机元非随机足标与随机足标和的完全收敛性．当０＜ｔ＜１时，得到了任意随机元完全收敛性的一般性结论；当１≤ｔ＜ｐ≤２时，揭示了独立零均值随机元的完全收敛性与Ｂａｎａｃｈ空间ｐ型性质的关系．推广并加强了许多熟知的结果