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(r,k)-catching code

chinese Science Bulletin 1998年第10期43卷 812-815页

作者： LI Anping institute of applied mathematics, chinese academy of sciences, beijing 100080, china institute of applied mathematics Chinese Academy of Sciences Beijing China

A collection of r_words on an alphabet of n letters is called (r,k)_catching code if for every r_word w there is one selected member v such that v coincides with w in at least k places. How large is the smallest size of the (r,k)_catching code and how to find the minimal (r,k)_\%catching code? Some methods are advanced to construct such codes.

关键词： catching code.

How big are the Csorgo-Revesz increments of two-parameter Wiener processes?

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Science china mathematics 2004年第6期47卷 894-907页

作者： WANG WenshengDepartment of mathematics, Hangzhou Teacher’s College, Hangzhou 310012, china institute of applied mathematics, chinese academy of sciences, beijing 100080, china Dept. of Math. Hangzhou Teacher's Coll. Hangzhou 310012 China Inst. of Appl. Math. Chinese Acad. of Sci. Beijing 100080 China

In this paper, we prove a theorem on the set of limit points of the increments of a two-parameter Wiener process via establishing a large deviation principle on the increments of the two-parameter Wiener process.

关键词： two-parameter Wiener process increment functional law of the iterated logarithm large deviation.

The Multifractal Analysis of the Occupation Measure of a Lévy Process

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Wuhan University Journal of Natural sciences 2000年第3期5卷 253-256页

作者： Hu Xiao\|yu institute of applied mathematics, chinese academy of sciences, beijing 100080, china institute of applied mathematics Chinese Academy of Sciences Beijing 100080 China

We introduce the results on the multifractal structure of the occupation measures of a Brownian Motion, a stable process, a general subordinator and a stochastic process derived from random reordering of the Cantor se... 详细信息

关键词： occupation measure Levy process Brownian motion stable process subordinator

GLIVENKO-CANTELLI TYPE THEOREMS ANDTHEIR APPLICATIONS

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Acta Mathematica Scientia 1997年第3期17卷 309-318页

作者：朱力行 Probability Laboratory Institute of Applied Mathematics Chinese Academy of Sciences Bcijing 100080 China

In this paper, we present a sufficient condition for uniform convergence of means to their expectations over the classes of real functions. Our proof is very simple via connecting this convergence to uniform convergence over the class of indicator functions. Furthermore, we obtain a convergent result concerning a non=VC class with an application to variable transformation for fitting regression model.

关键词： uniform convergence non-VC class of functions variable transformation method

On some tests-based projection pursuit for elliptical symmetry of a high-dimensional distribution

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chinese Science Bulletin 1998年第6期43卷 450-458页

作者： JING Ping 1 and ZHU Lixing 2 1. mathematics Lab, china University of Mining & Technology, beijing 100083, china 2. Probability Lab, institute of applied mathematics, chinese academy of sciences, beijing 100080, china mathematics Lab China University of Mining & Technology Beijing China Probability Lab Institute of Applied Mathematics Chinese Academy of Sciences Beijing China

Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. The asymptotic properties of bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on the number theoretic method, is suggested.

关键词： bootstrap approximation projection pursuit type statistic elliptical symmetry.

(a, b, k )-critical graphs

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chinese Science Bulletin 1997年第17期42卷 1492-1493页

作者： LIU Guizhen and WANG Jianfang Department of mathematics, Shandong University, Jinan 250100, china institute of applied mathematics, chinese academy of sciences, beijing 100080, china Department of mathematics Shandong University Jinan China institute of applied mathematics Chinese Academy of Sciences Beijing China

THE graphs considered in this letter will be finite and undirected simple graphs. Let G be a graph with vertex set V(G) and edge set E(G) . The minimum degree of G is denoted by δ(G) . Notation and definition not given in this letter can be found in reference [1]. For S V(G) the induced subgraph of G by S is denoted by G[S] . For any vertex

关键词： Math critical graphs

Two-dimensional Riemann problems of simplified Euler equation

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chinese Science Bulletin 1998年第6期43卷 441-444页

作者： YANG Xiaozhou 1,2 and HUANG Feimin+1 1. institute of applied mathematics, chinese academy of sciences, beijing 100080, china 2. Department of mathematics, Shantou University, Guangdong 515063, china institute of applied mathematics Chinese Academy of Sciences Beijing China Department of mathematics Shantou University Guangdong China

The two-dimensional Riemann problem of simplifed Euler equation is discussed, in which initial value contains two different constant states that are separated by a smooth curve. This problem is a natural description of realistic phenomena, but it is hard to study by conventional idea. So a new approach is proposed. Some new properties about two-dimensional rarefaction wave, shock wave and intermediate state of solutions are disclosed.

关键词： D Riemann problem implicit functions cylindrical surface pencil of cylindrical surface.

A matrix version of the Wielandt inequality and its application to statistics

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chinese Science Bulletin 1999年第2期44卷 118-121页

作者： WANG Songgui Wai-Cheung IpDepartment of applied mathematics, beijing Polytechnic University, beijing 100022, china institute of applied mathematics, chinese academy of sciences, beijing 100080, china Department of applied mathematics, Hong Kong Polytechnic University, Hong Kong, china Department of applied mathematics Beijing Polytechntc University Beijing China institute of applied mathematics Chinese Academy of Sciences Beijing China Department of applied mathematics Hong Kong Polytechnic University Hong Kong China

Suppose that A is an n×n positive definite Hemitain matrix. Let X and Y ben×p and n×q matrices（p+q≤n）, such that X*Y=O. The following inequality is provedX*AY（YAY）-Y*AX≤（（λ1-λn）/（λ1+λn）2）X*AX,where λ1 and λn are respectively the largest and smallest eigenvalues of A, and M- stands for a generalized inverse of M. This inequality is an extension of the well-known Wielandt inequality in which both X and Y are vectors. The inequality is utilized to obtain some interesting inequalities about covariance matrix and various correlation coefficients including the canonical correlation, multiple and simple correlation.

关键词： Wielandt inequality Cauchy-Schwarz inequality Wishart matrix.

The proof of FFD(L)≤11/9OPT(L) +7/9

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chinese Science Bulletin 1997年第15期42卷 1262-1265页

作者： LI Rongheng, YUE Minyi1. Department of mathematics, Hunan Normal University, Changsha 410081, china 2. institute of applied mathematics, chinese academy of sciences, beijing 100080, china Department of mathematics Hunan Normal University Changsha 410081 China institute of applied mathematics Chinese Academy of Sciences Beijing 100080 China

THE one-dimensional bin-packing problem is defined as follows: for a given list L={p1, p2,…, Pn}, where 0i≤1 denotes the item and its size as well, we are to pack all the items in-to bins, each of which has a capacity 1, and the goal is to minimize the number of bins *** first-fit-decreasing （FFD） algorithm is a famous approximate algorithm for the bin-pack-ing problem. The FFD algorithm first sorts all the list into non-increasing order and then pro-cesses the pieces in that order by placing each item into the first bin into which it fits.

关键词： bin-packing minimal counter-example weigtht-function FFD-algorithm.