两两NQD列的Marcinkiewicz-Zygmund不等式及其应用

本文研究了两两NQD随机变量的Marcinkiewicz-Zygmund不等式及其应用的问题.利用截尾的方法,获得了两两NQD随机变量的p阶(1 ≤ p < 2) Marcinkiewicz-Zygmund不等式结果.作为应用,获得了两两NQD随机变量的两个L^r收敛性结果的简单证明,改进了陈平炎^[10]和Sung^[20]的相应工作.     

QK空间的插值序列

本文研究了Q_K空间的插值问题.利用复分析和调和分析的方法,获得了单位圆盘上的一个序列{z_n}是Q_K∩H^∞空间的插值序列的一个充分必要条件,推广了Q_p空间的部分结果.     

近切触流形的φ*-解析向量场

本文引入了近切触流形（M,ø,ξ,η,g）中φ^*-解析向量场的概念,并研究了其性质.利用近切触流形的性质,证明了切触度量流形中的φ^*-解析向量场v是Killing向量场且φv不是φ^*-解析的.特别地,如果近切触流形M是正规的,得到v与ξ平行且模长为常数.另外,证明了3维的切触度量流形不存在非零的φ^*-解析向量场.     

在险值与L~p-空间上的连续一致风险度量（英文）

本文研究了在险值和L~p-空间上的连续一致风险度量之间的关系.利用凸集分离定理和截尾逼近方法,获得了在险值可以用L~p-空间上的连续一致风险度量表示的结果,并且得到了L~p-空间上的表示定理的一种新的证明方法.它们分别是文献[2]的相关结论从L~∞-空间到L~p-空间上的推广和对Inoue~[4]做的一些补充证明.     

SL(2,R)上一类极大算子的(H∞,s1,L1)型

本文我们引入了函数类B_δ(G//K)={φ∈L¹(G//K)||φ(t)|≤Δ^-1(t)(1+t)^1-δ,δ>0),对f∈L^p(G//K),1≤p≤∞,和极大算子(?),证明了这类算子是(H_∞,s¹,L¹)型的.     

一类多线性齐性算子的Hardy空间估计 *

证明了一类带齐性核的奇异积分算子的多线性算子是乘积空间L^p1×L^p2 ×…×L^pK(Rⁿ)到Hardy空间H^r(Rⁿ)和弱Hardy空间H^{r ,∞}(Rⁿ)的有界算子 .作为应用 ,获得了一类带齐性核的奇异积分算子交换子的L^p(Rⁿ)有界性 .     

L0-线性函数的Hahn-Banach扩张定理的几何形式与随机赋范模中的Goldstine-Weston定理

本文给出了关于L⁰- 线性函数的Hahn-Banach 扩张定理的几何形式并证明这个几何形式等价于它的代数形式. 进一步, 我们利用这个几何形式给出了随机局部凸模中熟知的基本分离定理的一个新的且简单的证明. 最后, 利用这个分离定理, 我们同时在两种拓扑 —(ε, λ)- 拓扑和局部L⁰- 凸拓扑下证明了随机赋范模中的Goldstine-Weston 稠密性定理, 并举出一个反例说明在局部L⁰- 凸拓扑下如果随机赋范模不具有可数连接性质, 则Goldstine-Weston 稠密性定理不一定成立.     

(α,β)-γ开集与(α,β)-γ-Ti空间

本文首先给出(α,β)-γ开集定义,获得了(α,β)-γ开集性质;然后引入了(α,β)-γ-T_i空间和(α,β)-γ-T_i^*空间概念(i=0,1/2,1,2,5/2),并得到它们更广泛的拓扑性质.     

关于p-可除kG-模的一些结论

本文研究了p-可除kG-模,这是一类由群阶的素数因子来控制的模类.利用Heller算子,证明了n次Heller算子置换非投射不可分解p-可除kG-模的同类;利用模的诱导和限制方法,证明了若H是G的强p-嵌入子群,则Green对应建立了不可分解p-可除kG-模的同构类与不可分解p-可除kH-模的同构类之间的一一对应.推广了不可分解相对投射kG-模上的Green对应.     

可除阿贝尔p-群的自同构群

主要探讨了秩大于或者等于p-1的可除阿贝尔p-群的p-自同构群,并且得到这些p-自同构如何作用在该可除阿贝尔p-群上.这些结论有助于进一步理解 ?ernikov p-群的结构.     

直线上子集的H~s-拓扑及其应用

本文利用s-维Hausdorff测度给出了直线上一个子集E上的H~s拓扑和H~s-连通度的定义.讨论了它们的性质及其应用,解决了紧的s-集在欧氏拓扑下往往不连通的问题.     

Optimal Lp-Lq-estimates for parabolic boundary value problems with inhomogeneous data

In this paper we investigate vector-valued parabolic initial boundary value problems , subject to general boundary conditions in domains G in with compact C ^2m -boundary. The top-order coefficients of are assumed to be continuous. We characterize optimal L ^p -L ^q -regularity for the solution of such problems in terms of the data. We also prove that the normal ellipticity condition on and the Lopatinskii–Shapiro condition on are necessary for these L ^p -L ^q -estimates. As a byproduct of the techniques being introduced we obtain new trace and extension results for Sobolev spaces of mixed order and a characterization of Triebel-Lizorkin spaces by boundary data.      

Consecutive customer losses in oscillating GIX/M//n systems with state dependent services rates

We address the probability that k or more Consecutive Customer Losses take place during a busy period of a queue, the so-called k-CCL probability, for oscillating GI ^X /M//n systems with state dependent services rates, also denoted as GI ^X /M(m)−M(m)//n systems, in which the service rates oscillate between two forms according to the evolution of the number of customers in the system. We derive an efficient algorithm to compute k-CCL probabilities in these systems starting with an arbitrary number of customers in the system that involves solving a linear system of equations. The results derived are illustrated for specific sets of parameters.     

A Polynomial Factorization Approach for the Discrete Time GIX/>G/1/K Queue

This paper proposes a polynomial factorization approach for queue length distribution of discrete time GI ^X /G/1 and GI _X /G/1/K queues. They are analyzed by using a two-component state model at the arrival and departure instants of customers. The equilibrium state-transition equations of state probabilities are solved by a polynomial factorization method. Finally, the queue length distributions are then obtained as linear combinations of geometric series, whose parameters are evaluated from roots of a characteristic polynomial.     

A new look at KK-theory

We describe the Kasparov group KK(A, B) as the set of homotopy classes of homomorphisms from an algebra qA associated with A into K B. The algebra qA consists of K-theory differential forms over A. Its construction is dual to that of M ₂(A). The analysis of qA and of its interplay with M ₂(A) gives the basic results of KK-theory.Partially supported by NSF.     

On the k-sample Behrens-Fisher problem for high-dimensional data

For several decades, much attention has been paid to the two-sample Behrens-Fisher (BF) problem which tests the equality of the means or mean vectors of two normal populations with unequal variance/covariance structures. Little work, however, has been done for the k-sample BF problem for high dimensional data which tests the equality of the mean vectors of several high-dimensional normal populations with unequal covariance structures. In this paper we study this challenging problem via extending the famous Scheffe’s transformation method, which reduces the k-sample BF problem to a one-sample problem. The induced one-sample problem can be easily tested by the classical Hotelling’s T ² test when the size of the resulting sample is very large relative to its dimensionality. For high dimensional data, however, the dimensionality of the resulting sample is often very large, and even much larger than its sample size, which makes the classical Hotelling’s T ² test not powerful or not even well defined. To overcome this difficulty, we propose and study an L ²-norm based test. The asymptotic powers of the proposed L ²-norm based test and Hotelling’s T ² test are derived and theoretically compared. Methods for implementing the L ²-norm based test are described. Simulation studies are conducted to compare the L ²-norm based test and Hotelling’s T ² test when the latter can be well defined, and to compare the proposed implementation methods for the L ²-norm based test otherwise. The methodologies are motivated and illustrated by a real data example. The work was supported by the National University of Singapore Academic Research Grant (Grant No. R-155-000-085-112)     

K-theory of reduced C*-algebras and rapidly decreasing functions on groups

We associate to any length function L on a group a space of rapidly decreasing functions on (in the l ² sense), denoted by H _L (). When H _L () is contained in the reduced C*-algebra C _r ^* () of (), then it is a dense *-subalgebra of C _r ^* () and we prove a theorem of A. Connes which asserts that under this hypothesis H _L () has the same K-theory as C _r ^* (). We introduce another space of rapidly decreasing functions on (in the l ¹ sense), denoted by H _L ^1, (), which is always a dense *-subalgebra of the Banach algebra l ¹(), and we show that H _L ^1, () has the same K-theory as l ¹().     

Relative K-homology and K-homology of an ideal

We provide a straightforward proof of one of the main results of the Baum-Douglas K-homology theory: If A is a separable nuclear C ^*-algebra and I an ideal of A, then the natural restriction map K ⁰(A, I) K ⁰(I) is an isomorphism of Abelian groups.     

K-theory for rickart C*-algebras

We give an explicit index map for any properly infinite closed ideal of a Rickart C ^*-algebra. This generalizes Olsen's work on von Neumann algebras. We use our results to compute the topological and the algebraic K ₁-groups of any quotient algebra of a Rickart C ^*-algebra.