n元等比级数

定义了n元等比数列、n元等比级数,给出了它们的通项公式及前n项和.并解决了多元等比级数的敛散性问题,求出了多元等比级数的和.指出了多元等比数列及多元等比级数在特殊情况下与一元等比数列及一元等比级数的一致性.     

广义调和级数的推广

将广义调和级数sum from n=1 to ∞ 1/n~x推广为一类指数项级数sum from n=1 to ∞ a_nd_n~x,并证明了这类指数项级数有结构简单的收敛域,其和函数的性质与幂级数的相似.     

The Polynomial Caratheodory--Fejer Approximation Method for Jordan Regions

We propose a method for the approximation of analytic functionson Jordan regions that is based on a Carathéodory—Fejértype of economization of the Faber series. The method turnsout to be very effective if the boundary of the region is analytic.It often still works when the region degenerates to a Jordanarc. We also derive related lower and upper bounds for the errorof the best approximation. ^*Research carried out while this author was at ETH Zurich partiallysupported by a Royal Society European Visiting Fellowship.     

有限级Dirchlet级数及随机Dirchlet级数

本文研究了全平面上有限级Dirichlet级数的增长性和正规增长性,得到了两个充要条 件;证明了有限级随机Dirichlet级数的增长性几乎必然与其在每条水平直线上的增长性相同．     

Flat Power Series over a Finite Field

We define and describe a class of algebraic continued fractions for power series over a finite field. These continued fraction expansions, for which all the partial quotients are polynomials of degree one, have a regular pattern induced by the Frobenius homomorphism.This is an extension, in the case of positive characteristic, of purely periodic expansions corresponding to quadratic power series.     

一类牛顿插值级数的推广

Theorem 1 Let ψ(r) be a really continuous and differentiable function on [0,∞) to satisfy that.     

Rigid and Finite Type Geometric Structures

Rigid geometric structures on manifolds, introduced by Gromov, are characterized by the fact that their infinitesimal automorphisms are determined by their jets of a fixed order. Important examples of such structures are those given by an H-reduction of the first order frame bundle of a manifold, where the Lie algebra of H is of finite type; in fact, for structures given by reductions to closed subgroups of first order frame bundles, finite type implies rigidity. The goal of this paper is to generalize this to geometric structures defined by reductions of frame bundles of arbitrary order, and to give an algebraic characterization of the property of being rigid in terms of a suitable notion of finite type.     

The Finite Subsets of Z2 Having the Extension Property

The paper considers finite subsets Z^d which possess the extensionproperty, namely that every collection {c_k}_k– of complexnumbers which is positive definite with respect to is the restrictionof the Fourier coefficients of some positive measure on T^d.All finite subsets of Z² which possess the extension propertyare described.     

Analysis of Data from a Series of Events by a Geometric Process Model

Geometric process was first introduced by Lam.A stochastic process {X_i,i=1,2,...} iscalled a geometric process (GP) if,for some a>0,{a~(i-1)X_i,i=1,2,...} forms a renewal process.In thispaper,the GP is used to analyze the data from a series of events.A nonparametric method is introduced forthe estimation of the three parameters in the GP.The limiting distributions of the three estimators are studied.Through the analysis of some real data sets,the GP model is compared with other three homogeneous andnonhomogeneous Poisson models.It seems that on average the GP model is the best model among these fourmodels in analyzing the data from a series of events.     

Notes on Two Geometric Inequalities for a Finite Set of Points

Two geometric inequalities for a finite set of points were established in Geom. Dedicata 62 (1996), 157--160. In this paper, we point out a computational mistake in that paper, and give corrections to two geometric inequalities.     

Immersions of Finite Geometric Type in Euclidean Spaces

In this paper, we introduce the class of hypersurfaces of finitegeometric type. They are defined as the ones that share the basicdifferential topological properties of minimal surfaces of finite totalcurvature. We extend to surfaces in this class the classical theorem ofOsserman on the number of omitted points of the Gauss mapping ofcomplete minimal surfaces of finite total curvature. We give aclassification of the even-dimensional catenoids as the only even-dimensional minimal hypersurfaces of R ⁿ of finite geometric type.     

有限域乘法群结构定理及其拓广

有限域乘法群结构定理在理论研究及工程应用上均具有重要意义.主要介绍了有限域乘法群结构定理的三种证明方法,并做了一些拓广.     

The Loewy Series of the Steinberg-Pim of Finite General Linear Groups

In this paper we calculate the Loewy series of the projectiveindecomposable module of the unipotent block contained in theGelfand–Graev module of the finite general linear groupin the case of non-describing characteristic and Abelian defectgroup. 2000 Mathematics Subject Classification 20C33.     

Algebraic and Badly Approximable Power Series over a Finite Field

We will exhibit certain continued fraction expansions for power series over a finite field, with all the partial quotients of degree one, which are non-quadratic algebraic elements over the field of rational functions.     

有限级Dirichlet级数及随机Dirichlet级数

本文研究了全平面上有限级Dirichlet级数的增长性和正规增长性,得到了两个充要条件;证明了有限级随机Dirichlet级数的增长性几乎必然与其在每条水平直线上的增长性相同.     

边缘分布条件分布的几何意义及推广

从几何的角度,揭示边缘分布条件分布的几何意义,浅显易懂,帮助学生深入正确理解定义所隐含的内容,同时,进一步推广了边缘分布和条件分布.     

稳定随机变量序列几何加权和的Chover重对数律

设｛Ｘｎ,ｎ≥ ０｝是独立同分布的随机变量序列,其分布函数是一个对称的指数为 ａ（０＜ ａ＜ ２）的稳定分布·本文证明了依概率 １有 ｌｉｍ ｓｕｐβ－ｌ－｜（ ｌ－βα）１／α∑∞ ｎ＝０βｎＸｎ＝ｅｘｐ（１／α）·