关于集值Pramart的某些结果

本文引进了Boohner可积函数空间L~1[Ω;X]中子集的可分解包的概念,给出了集值随机变量族本性上确界的定义及基本性质。以此为基础,研究了集值Pramart的性质;用类似于实值Snell包的方法给出了集值superpramart的上鞅逼近,证明了集值superpramart在Kuratowski-Mosco意义下的收敛定理。     

集值L1极限鞅导出的集值测度

讨论集值L1极限鞅的一些性质,在此基础上,研究集值L1极限鞅导出的集值测度及其性质.     

集值拟鞅和集值一致渐近鞅

本文讨论了集值拟鞅和集值一致渐近鞅,证明了集值拟鞅与集值一致渐近鞅的选样定理,对于集值一致渐近鞅得到了一些收敛性结果,并由此刻化了空间的 Radon-Nikodym性质.     

集值Superpramart的上鞅逼近

文中讨论了可积随机集条件期望的若干性质,在此基础上给出了集值Ｓｕｐｅｒｐｒａｍａｒｔ的上鞅逼近,同时,证明了集值Ｓｕｐｅｒｐｒａｍａｒｔ 在Ｋｕｒａｔｏｗｓｋｉ－Ｍｏｓｃｏ意义下的收敛定理。     

集值增过程产生的集值测度

本文首先研究集值增函数在B(R+)上产生的集值测度,然后在其基础上研究集值增过程A(ω,t),(ω,t)∈Ω×R+,在乘积可测空间F×B(R+)上产生的集值测度,在一定条件下建立了两者之间的一一对应关系.     

集值映射与不动点

应用D关于β对应关系是正常的构架,引用子集法,通过取凸包与闭包,由单值映射构造集值映射,利用Kakutani不动点定理,讨论几种类型的集值映射的不动点.     

集值映象的某些重合定理

Browder[1]已得到了Schauder不动点定理的加强形式.许多作者从不同方向推广了Browder的结果.最近H.M.Ko;K.K.Tan[2]在放松紧性条件下得到了Browder定理的改进,K.K.Tan[3]将Browder定理推广到了集值映象对的重合定理,在本文中我们得到了集值映象对的某些重合定理,它们分别改进和推广了[1,2,3]中主要结果.     

集值测度的收敛性及其与Castaing向量表示中测度的收敛性之间的关系

本文研究了集值测度的收敛性. 利用极限理论的方法,在X有RNP,且M(∪)s-lim inf_(n→∞) M_n条件下,获得了集值测度的收敛性与其 Castaing表示中向量测度收敛性的关系,建立了集值测度列与集值测度选择列的收敛性,从而对进一步研究集值测度的一些件质提供了理论依据.     

集值局部平方可积鞅

介绍集值类（D）过程和集值局部鞅的概念和有关性质，进而讨论了集值局部平方可积鞅的概念和性质。     

实值非负函数关于集值序增函数的集值Riemann-Stieltjes积分

本文首先建立了实值非负函数关于集值序增函数的集值Riemann-Stieltjes积分,并讨论了集值Riemann-Stieltjes积分的性质,给出了集值Riemann-Stieltjes可积的充要条件,最后引入了集值Riemann-Stieltjes随机积分．     

Extremal Valued Fields

It is shown that every finite-dimensional skew field whose center is an extremal valued field is defect free. We construct an example of an algebraically complete valued field such that a finite-dimensional skew field over it has a non-trivial defect, that is, there exist algebraically complete valued fields that are not extremal.     

向量值Nevanlinna理论初探

本文主要讨论定义在复平面取值为无穷维希尔伯特空间上的向量值亚纯函数的Ｎｅｖａｎｌｉｎｎａ理论．给出了推广的Ｐｏｉｓｓｏｎ－Ｊｅｎｓｅｎ－Ｎｅｖａｎｌｉｎｎａ公式以及推广的第一基本定理的证明，并对向量值特征函数的性质予以讨论     

Stable valued fields

We are concerned with a class of valued fields, called stable. We propound an extension of a notion in the monograph by S. Bosch, U. Güntzer, and R. Remmert (Non-Archimedean Analysis. A Systematic Approach to Rigid Analytic Geometry, Springer, Berlin (1984)), namely, that of a (ultrametric) norm on groups, rings, algebras, and vector spaces, to the case where the value of the norm is taken from an arbitrary (not necessarily Archimedean) linearly ordered Abelian group (using — as in the general theory of valuations — the version of a logarithmic norm). Our main result extends Proposition 6 in the cited monograph to the general case, thereby making it possible to use the technique of Cartesian spaces to deliver further results on stable valued fields. Supported by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools via project NSh-4787.2006.1 and by RFBR grant No. 05-01-00481. __________ Translated from Algebra i Logika, Vol. 46, No. 6, pp. 707–728, November–December, 2007.     

有限值l-群与特殊值l-群等价的一个充要条件

G是l-群，本文主要证明：G是有限值的当且仅当G是特殊值的且C（G）＝K（G），作为应用，我们证明了G是有基的l-群，则两者之间是等价的。     

Imprecise set and fuzzy valued probability

Set valued probability and fuzzy valued probability theory is used for analyzing and modeling highly uncertain probability systems. In this paper the set valued probability and fuzzy valued probability are defined over the measurable space. They are derived from a set and fuzzy valued measure using restricted arithmetics. The range of set valued probability is the set of subsets of the unit interval and the range of fuzzy valued probability is the set of fuzzy sets of the unit interval. The expectation with respect to set valued and fuzzy valued probability is defined and some properties are discussed. Also, the fuzzy model is applied to binomial model for the price of a risky security.     

Givens' Transformation Applied to Quaternion Valued Vectors

Givens' transformation (1954) was originally applied to real matrices. We shall give an extension to quaternion valued matrices. The complex case will be treated in the introduction. We observe that the classical Givens' rotation in the real and in the complex case is itself a quaternion using an isomorphism between certain (2×2) matrices and R ⁴ equipped with the quaternion multiplication. In the real and complex case Givens' (2×2) matrix is determined uniquely up to an arbitrary (real or complex) factor with ||=1. However, because of the noncommutativity of quaternions, we shall show that in the quaternion case such a factor must obey certain additional restrictions. There are two numerical examples including a MATLAB program and some hints for implementation. Matrices with quaternion entries arise, e.g., in quantum mechanics.This revised version was published online in October 2005 with corrections to the Cover Date.     

Boolean Valued and Stone Algebra Valued Measure Theories

In conventional generalization of the main results of classical measure theory to Stone algebra valued measures, the values that measures and functions can take are Booleanized, while the classical notion of a σ-field is retained. The main purpose of this paper is to show by abundace of illustrations that if we agree to Booleanize the notion of a σ-field as well, then all the glorious legacy of classical measure theory is preserved completely. Mathematics Subject Classification: 03C90, 28B15.     

Two theorems on defect-freeness for cyclic extensions

The article contains the proofs of two theorems. Under quite special assumptions, we prove that the p-cyclic extensions of Henselian valued fields are defect-free. However, the well-known results by Epp and Kuhlmann are easy consequences of these theorems.     

向量值Nevanlinna第二基本定理的余项S(r)的估计

首先通过建立并证明推广的对数导数基本引理,讨论了１２π∫２π０ｌｏｇ＋‖ｆ′（ｒｅｉθ）‖‖ｆ（ｒｅｉθ）‖ｄθ的增长问题,进而对向量值Ｎｅｖａｎｌｉｎｎａ第二基本定理的余项进行了估计     

B-值函数Riemann-Stieltjes积分

引入数值函数关于B-值函数的R-S积分,研究了此类积分的性质及向量值R-S积分存在的几个充分条件,并给出了积分的收敛定理.