半相依非线性回归方程组中的近似得分函数和拟近似得分函数

本文定义了半相依非线性回归方程组中的近似得分函数和拟近似得分函数．这些函数利用了样本信息和附加信息，在均方误差准则下改进了独立得分函数和拟独立得分函数．     

On steepest descent curves for quasi convex families in Rn

A connected, linearly ordered subset $\gamma ?{\mathbb{R}}^n$ satisfying $$x_1,x_2,x_3\in \gamma ,\text{and}{x}_1?x_2?x_3\to |x_2?x_1|\le |x_3?x_1|$$ is shown to be a rectifiable curve; a priori bounds for its length are given; moreover, these curves are generalized steepest descent curves of suitable quasi convex functions. Properties of quasi convex families are considered; special curves related to quasi convex families are defined and studied; they are generalizations of steepest descent curves for quasi convex functions and satisfy the previous property. Existence, uniqueness, stability results and length bounds are proved for them.     

Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square

We prove lower bounds for the error of optimal cubature formulae for d‐variate functions from Besov spaces of mixed smoothness in the case , and , where is either the d‐dimensional torus or the d‐dimensional unit cube . In addition, we prove upper bounds for QMC integration on the Fibonacci‐lattice for bivariate periodic functions from in the case , and . A non‐periodic modification of this classical formula yields upper bounds for if . In combination these results yield the correct asymptotic error of optimal cubature formulae for functions from and indicate that a corresponding result is most likely also true in case . This is compared to the correct asymptotic of optimal cubature formulae on Smolyak grids which results in the observation that any cubature formula on Smolyak grids can never achieve the optimal worst‐case error.     

Weak and quasi approximation properties in Banach spaces

In this paper, we introduce weak versions (the weak approximation property, the bounded weak approximation property, and the quasi approximation property) of the approximation property and derive various characterizations of these properties. And we show that if the dual of a Banach space X has the weak approximation property (respectively the bounded weak approximation property), then X itself has the weak approximation property (respectively the bounded weak approximation property). Also we observe that the bounded weak approximation property is closely related to the quasi approximation property.     

Minimax Fractional Programming for <Emphasis Type="Italic">n</Emphasis>-Set Functions and Mixed-Type Duality under Generalized Invexity

We establish the sufficient optimality conditions for a minimax programming problem involving p fractional n-set functions under generalized invexity. Using incomplete Lagrange duality, we formulate a mixed-type dual problem which unifies the Wolfe type dual and Mond-Weir type dual in fractional n-set functions under generalized invexity. Furthermore, we establish three duality theorems: weak, strong, and strict converse duality theorem, and prove that the optimal values of the primal problem and the mixed-type dual problem have no duality gap under extra assumptions in the framework. This research was partly supported by the National Science Council, NSC 94-2115-M-033-003, Taiwan.     

Lagrange multipliers and infinite-dimensional equilibrium problems

We prove the existence of the Lagrange multipliers for a constrained optimization problem, being the constraint set given by the convex set which characterizes the most important equilibrium problems. In order to obtain our result, we’ll make use of the new concept of quasi relative interior.     

ON A LEMMA OF BOWEN

We are concerned with the sets of quasi generic points in finite symbolic space. We estimate the sizes of the sets by the Billingsley dimension defined by Gibbs measures. A dimension formula of such set is given, which generalizes Bowen＇s result. An application is given to the level sets of Birkhoff average.     

锰的准液膜富集及原子吸收法测定

本文利用准液膜法与火焰原子吸收法相结合测定锰，方法的精密度为１．９％，回收率为９８．９％，可富集测定ｎｇ／ｇ级的锰。本方法已用于人发，湖水和茶中锰的分析。     

闭曲面上的C^0流的几类局部结构

本文提出了闭曲面上的Ｃ＾０流的几类轨道（包括准吸引及准排斥的奇点及周期轨道，以及较广义的鞍点，等等）的定义，并讨论了这几类轨道的邻域的结构。     

基于四维表示的模糊数赋权排序及简便加减运算

引进模糊数的四维表示,并据此给出一种新的排序方法,简化了模糊数特别是e-型模糊数的加减运算。