“矩阵有理插值及其误差公式”一文的注

本文对文[1]中所给出的错误的误差公式做了修订,并给出了相应的证明。     

基于小波分形理论的股价指数信息量测度研究

本把小波分析和分形理论引入到股价指数时间序列的分析中，给出了股价指数波动复杂性的信息量测度方法——信息熵和分形维方法。通过对上证综指和深证成指1994年1月3日至2002年3月4日期间的数据进行的实证分析显示，两种方法均能刻画股价指数波动的复杂程度，这对初步了解我国股市场的波动规律有一定的实际意义。     

平面运动学位似运动Steiner公式的推广

对单参数闭平面复意义位似运动，给出了Muller提出的Steiner公式和混合面公式的表达式。利用推广的Steiner公式得到了位似运动的Holditch定理．作为特例，给出了Muller位似比h≡1时的结果。     

非退化扩散过程的极性与相交性

本文讨论非退化扩散过程的极性，得到了几个较好的充分条件，它可看作[1]的进一步深化，此外，我们将这些结果用来研究两个独立的非退化扩散过程的相交性，得到了一些有意思的结果。     

Proper actions on cohomology manifolds

Essential results about actions of compact Lie groups on connected manifolds are generalized to proper actions of arbitrary groups on connected cohomology manifolds. Slices are replaced by certain fiber bundle structures on orbit neighborhoods. The group dimension is shown to be effectively finite. The orbits of maximal dimension form a dense open connected subset. If some orbit has codimension at most , then the group is effectively a Lie group.

     

DIMENSIONS FORRANDOM SELF——CONFORMAL SETS

A set is called regular if its Hausdorff dimension and upper box-counting dimension coincide. In this paper, we prove that the random self-con formal set is regular almost surely. Also we determine the dimen-sions for a class of random self-con formal sets.     

Almost automorphic solutions for abstract functional differential equations

For abstract linear functional differential equations with an almost automorphic forcing term, we establish a result on the existence of almost automorphic solutions, which extends the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations.     

Convolution semigroups and central limit theorem associated with a dual convolution structure

We consider hypergroups associated with Jacobi functions ⁽⁾ (x), (–1/2). We prove the existence of a dual convolution structure on [0,+[i(]0,s ₀]{{) =++1,s ₀=min(,–+1). Next we establish a Lévy-Khintchine type formula which permits to characterize the semigroup and the infinitely divisible probabilities associated with this dual convolution, finally we prove a central limit theorem.     

Rate conservation laws: A survey

We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=G, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=G can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.     

Cord-slope form of Taylor's expansion in univariate global optimization

Interval arithmetic and Taylor's formula can be used to bound the slope of the cord of a univariate function at a given point. This leads in turn to bounding the values of the function itself. Computing such bounds for the function, its first and second derviatives, allows the determination of intervals in which this function cannot have a global minimum. Exploiting this information together with a simple branching rule yields an efficient algorithm for global minimization of univariate functions. Computational experience is reported.The first and second authors have been supported by FCAR (Fonds pour la Formation de Chercheurs et l'Aide à la Recherche) Grant 92EQ1048 and AFOSR Grant 90-0008 to Rutgers University. The first author has also been supported by NSERC (Natural Sciences and Engineering Research Council of Canada) Grant to HEC and NSERC Grant GP0105574. The second author has been supported by NSERC Grant GP0036426, FCAR Grant 90NC0305, and a NSF Visiting Professorship for Women in Science at Princeton University. Work of the third author was done in part while he was a graduate student at the Department of Mathematics, Rutgers University, New Brunswick, New Jersey, USA and during a visit to GERAD, June–August 1991.