加权Lebesgue空间的对偶和嵌入

本文建立了加权Lebesgue空间的对偶空间，并且给出了在这些空间之间嵌入的必要条件。     

Function Spaces with Exponential Weights I

In this paper we define weighted function spaces of type B^s_pq(u) and F^s_pq(u) on the Euclidean space IRⁿ, where u is a weight function of at most exponential growth. In particular, u(x) = exp(±|χ|) is an admissible weight. We prove some basic properties of these spaces, such as completeness and density of the smooth functions.     

Trapezoidal approximations of fuzzy numbers preserving the expected interval — Algorithms and properties

Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is discussed. Algorithms for calculating the proper approximations are proposed and some properties of the approximation operators are discussed. It is shown that an adequate approximation operator might be chosen through the comparisons of some characteristics of the fuzzy number, like its ambiguity, width, its value and weighted expected value.     

New tools: Uncertainty-based data evaluation

 The principles of uncertainty-based data evaluation are explained. Based on a brief review of recent publications on the topic, examples for application to standard procedures in analytical chemistry – calibration, method validation, standard addition etc., – are given. The performance and the advantages of uncertainty-based data evaluation are discussed. Received: 4 July 1998 · Accepted: 6 July 1998     

Some weighted estimates for Littlewood-Paley functions and radial multipliers

We prove some weighted estimates for certain Littlewood-Paley operators on the weighted Hardy spaces H_w^p (0<p?1) and on the weighted L^p spaces. We also prove some weighted estimates for the Bochner-Riesz operators and the spherical means.     

加权总体最小二乘问题的解集和性质

本文讨论了加权总体最小二乘问题的等价解集，分析了加权总体最小二乘解与加权最小二乘问题的解之间的关系。推广了Ｇｏｌｕｂ和Ｖａｎ Ｌｏａｎ，Ｖａｎ Ｈｕｆｆｅｌ和Ｖａｎｄｅｗａｌｌｅ，及Ｗｅｉ的相应结果。     

Additive Schwarz algorithm for the nonlinear complementarity problem with M-function

In this paper, an additive Schwarz algorithm is considered for solving the finite-dimensional nonlinear complementarity problem with M-function. The monotone convergence of the algorithm is obtained with special choices of initial values. Moreover, the weighted max-norm bound is obtained for the iterative errors.     

Controlled Markov processes on the infinite planning horizon: Weighted and overtaking cost criteria

Stochastic control problems for controlled Markov processes models with an infinite planning horizon are considered, under some non-standard cost criteria. The classical discounted and average cost criteria can be viewed as complementary, in the sense that the former captures the short-time and the latter the long-time performance of the system. Thus, we study a cost criterion obtained as weighted combinations of these criteria, extending to a general state and control space framework several recent results by Feinberg and Shwartz, and by Krass et al. In addition, a functional characterization is given for overtaking optimal policies, for problems with countable state spaces and compact control spaces; our approach is based on qualitative properties of the optimality equation for problems with an average cost criterion.Research partially supported by the Engineering Foundation under grant RI-A-93-10, in part by the National Science Foundation under grant NSF-INT 9201430, and in part by a grant from the AT&T Foundation.Research partially supported by the Air Force Office of Scientific Research under Grant F49620-92-J-0045, and in part by the National Science Foundation under Grant CDR-8803012.     

Rank equalities related to outer inverses of matrices and applications

A matrix X is called an outer inverse for a matrix A if XAX=X. In this paper, we present some basic rank equalities for difference and sum of outer inverses of a matrix, and apply them to characterize various equalities related to outer inverses, Moore-Penrose inverses, group inverses, Drazin inverses and weighted Moore-Penrose inverses of matrices.     

On Vertex Connectivity and Absolute Algebraic Connectivity for Graphs

Let G be a graph on n vertices with vertex connectivity v with 1 ≤ v ≤ n -2. We produce an attainable upper bound on the absolute algebraic connectivity of G in terms of n and v .