部分线性模型中估计的收敛速度

考虑回归模型（Ⅰ）：其中（ｘ＿ｉ，ｔ＿ｉ）是固定非随机设计点列，ｘ＿ｉ＝（ｘ＿（ｉｌ），…，ｘ＿（ｉｐ））＇β＝（β＿１，…，β＿ｐ）＇（ｐ＞１），ｇ是定义在［０，１］上的未知函数，β是未知待估参数，０＜ｔ＿ｉ＜１，ｅ＿ｉ是ｉ．ｉ．ｄ．随机误差，且Ｅｅ＿ｉ＝０，Ｅｅ＝σ￣２＜∞。基于ｇ的估计取一类非参数权估计（包括常见的核估计和近邻估计），我们讨论了β的最小二乘估计及ｇ的估计的最优强弱收敛速度。     

统计递归集的Hausdorff测度的上、下界

给出了由随机压缩算子生成的统计递归集的Ｈａｕｓｄｏｒｆ测度上、下界的估计．也就是说,在一些条件下,找出了Ｋ（ω）∩∞ｎ＝１∪ｉ∈Ｎｎ（ω）ｆ（ω）ｎ,ｉ（Ｅ）的α－维Ｈａｕｓｄｏｒｆ测度的上、下界,其中｛ｆｎ,ｉ,１≤ｉ,ｎ＜∞｝是一族随机压缩算子,｛Ｎｎ（ω）,ｎ≥１｝是一族可数的随机指标集．     

有阻尼Sine－Gordon方程的全局吸引子的维数

本文通过引入新范数，得到有阻尼Ｓｉｎｅ－Ｇｏｒｄｏｎ方程的Ｄｉｒｉｃｈｌｅｔ问题的全局吸引子的维数的一个估计．结果表明：当“阻尼”与“扩散”同时增大或正弦项系数减小时，吸引子的维数减小．特别地，得到了零维吸引子存在的参数条件．     

距离-边数拓扑指数: 饱和链烃类化合物的结构/性质相关性研究

本文提出一种新的拓扑指数——距离-边数拓扑指数S_q,并用于研究饱和链烃类化合物的理化性质,获得比较满意的结果.与其它已有的拓扑指数比较,该指数结构选择性和相关性好,并且计算更加简便.     

Distance—Stability of Nonlinear Discrete Systems

In this paper,the distance-sability of nonlinear discrete system is investigated by meansof the Gauss-Seidel iteration method.Some algebric criteria of the distance-stability are ob-tained.Construction of Lyapunov function is avoided.     

哈勃常数——一个难有确定值的重要参量

 何常同志的文章(《哈勃常数战和宇宙命运》,本刊1994年第4期11-14页)介绍了测定河外星系的几种方法、哈勃常数50与100之争,以及哈勃常数与宇宙命运的关系。本文旨在向读者介绍哈勃常数值演变的历史、近年来用不同方法测定的哈勃常数值以及对此问题的几点小结。     

Talagrand＇s T2-transportation Inequality w.r.t, a Uniform Metric for Diffusions

Using the method of Girsanov transformation, we establish the Talagrand‘s T2-inequality for diffusion on the path space C([0, N], R^d) with respect to a uniform metric, with the constant independent of N. This improves the known results for the L2-metric.     

On Weak Regular ^＊-semigroups

In this paper, a special kind of partial algebras called projective partial groupoids is defined.It is proved that the inverse image of all projections of a fundamental weak regular ^*-semigroup under the homomorphism induced by the maximum idempotent-separating congruence of a weak regular ^*-semigroup has a projective partial groupoid structure. Moreover, a weak regular ^*-product which connects a fundamental weak regular ^*-semigroup with corresponding projective partial groupoid is defined and characterized. It is finally proved that every weak regular ^*-product is in fact a weak regular ^*-semigroup and any weak regular ^*-semigroup is constructed in this way.     

Potential Analysis on Carnot Groups，Part II：Relationship between Hausdorff Measures and Capacities

Abstract In this paper, we establish the relationship between Hausdorff measures and Bessel capacities on any nilpotent stratified Lie group (i. e., Carnot group). In particular, as a special corollary of our much more general results, we have the following theorem (see Theorems A and E in Section 1): Let Q be the homogeneous dimension of . Given any set E ⊂ , B _α,p (E) = 0 implies ℋ ^{Q−αp+ ε}(E) = 0 for all ε > 0. On the other hand, ℋ ^Q−αp (E) < ∞ implies B _α,p (E) = 0. Consequently, given any set E ⊂ of Hausdorff dimension Q − d, where 0 < d < Q, B _α,p (E) = 0 holds if and only if αp ≤ d. A version of O. Frostman’s theorem concerning Hausdorff measures on any homogeneous space is also established using the dyadic decomposition on such a space (see Theorem 4.4 in Section 4). Research supported partly by the U. S. National Science Foundation Grant No. DMS99–70352     

MULTIFRACTAL FORMALISMS：BOXED VERSUS CENTERED INTERVALS

There are mainly two approaches to the multifractal analysis of measures. The first one, which is used in applications and in studying problems arising from dynamical systems, uses a hierarchy of boxes. The second one, which is more satisfactory from the viewpoint of geometric measure theory, uses more intrinsicconcepts. This article is an account of a work by J. Barral, F. Ben Nasr, and J. Peyriere [3] which pro-vides a bridge between these two theories.