I.I.D. STATISTICAL CONTRACTION OPERATORS AND STATISTICALLY SELF－SIMILAR SETS

I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.     

指标在T_θ~d上变动的B-值I.I.D.R.V.’S的叠对数律

记B是可分Banach空间,X是B-值随机变量,N~d={■=n_1,…,n_d);n_i=1,2,…,i=1,…,d},T_θ~d={■∈=(n_1,…,n_d),θn_i≤n_y≤θ~(-1)n_4,i≠j,i,j=1,…,d},其中d≥2,0<1。本文研究指标在T_θ~d上变动的B-值i. i. d. r. v. ’s的四种类型的叠对数律(即BLIL~(θ,α)_1,BLIL~(θ,d)_2CLIL~(θ.D)_1和GLIL~(θ,d)_2,获得了X∈BLIL~(θ,α)_1、X∈BLIL~(θ,d)_2、X∈GLIL~(θ,d)_1和X∈GLIL~(θ,d)_2的充要条件。     

I.J.Matrix定理的进一步推广

文献 [1]— [5 ]连续讨论了 I.J.Matrix定理的一些推广及应用 ,特别是文 [5 ]利用高阶微分的知识简明地给出了一个推广 ,本文给出其进一步的推广 .设 a0 ,a1 ,… ,an 是 n 1个互不相同且不为零的数 ,f ( x)是次数为 m的多项式 ,文 [5 ]讨论的是m相似文献   

ON THE EXPECTATION AND VARIANCE OF HAMMING DISTANCE BETWEEN TWO I.I.D RANDOM VECTORS

1.IntroductionLetFZn={0,1}"beann-dimensionalvectorspaceoverthebinaryfieldFZ={0,1}.TheHammingdistancebetweentwovectorsx=(xl,'tx.)andy=(yi,'ty.)isthenumberofcoordinateswheretheydiffer,andisdenotedbydH(x,y),dH(X,y)=ZIXi~ail.i=1TheHammingweightofxisthenumberofnon-zerocoordinates,andisdenotedbyWH(x).ObviouslyAH(x)=dH(x,0),where0isthezerovector.Thescalarproductofxandyis(x,y)=xlyl ' xestinF2.ForasetAgFZn,IAIdenotesthecardinalityofA.TheaveragedistanceinAisdefinedby*Thisresearchissupp…     

Solution to a Problem of J.P.Hutchinson and P.B.Trow

Use of the Pigeonhole Principle to solve the following problem was discussed in several books, for example [1,2]. Suppose a player (e. g., tennis or chess) practices on d consecutive days, playing at least one game a day and a total of no more than b games where d相似文献   

有限典型空间的对偶极图的次成分I

设Fq是一个含有q个元素的有限域.用T表示Fq上2v维辛空间的对偶极图.对于Г的任何顶点Р,Г的所有次成分Гi(Р)(1≤i≤v)的结构被研究,并且以下结果被证明Ti(P)同构于[vi]q·Sym(i,q),其中Sym(i,q)是Fq上i×i对称矩阵图.进一步,Fq上2v+δ维伪辛空间的对偶极图△δ的相应问题也被解决.     

评V.I.Arnold问题

一、一个共同存在的问题 1976年V.I.Arnold提出:向量场是由固定次数带有有理系数多项式来给定,是否能给出—个稳定性的判定准则? 王联、王慕秋在文[2]中解决了当n=2情况下的V.I.Arnold问题,杨世藩同志在文[3]中对n=3的情况进行了研究。并得到很好的结果,但在对于系统:     

一类二阶微分算子属于L.S.或L.S.∩L.C.的判定

本文在半直线a≤t<∞上研究二阶微分算子L=d/dt(p(t)d/dt)-q(t),建立了三个定理,利用这些定理,可以判定算子 L属于 L.S.或 L.S.∩L.C.即 定理1 假设 i)p(t)>0,q(t)?0 当 t∈[a,∞)、ii)∫_a~∞|q(t)|dt<∞ 则算子L属于L.S.的充要条件是 ∫_a~∞ dt/p(t)t<∞。 定理2 假设 i) p(t)>0,当t∈[a,∞)时;ii)?a,1≤a≤∞使∫_a~∞|b(t)|~a dt<∞(当a=∞时,应设|b(t)}=O(1));(iii)算子 L属于 L.C.∩L.S.,则算子 L~*=d/dt(p(t)d/dt)-[q(t)+b(t)]也属于L.C.∩L.S.。 定理3 假设 i)p(t)>0,q(t)?0;ii)算子L属于L.C.∩L.S.,则当1≤a≤∞时, ‖|q(t)|-q(t)‖_(L~2[a,∞)=∞。     

i.i.d情况下非参数回归模型的误差密度估计的收敛性质

本文研究了i．i．d情况下非参数回归的误差密度估计的一致收敛和均方收敛，给出了一定条件下误差密度的估计量f^n(x)的一致收敛速度和均方收敛速度。     

A Comment on a Necessary and Sufficient Condition for Transitive Permutation Group by P.J.Cameron

P.J. Cameron had mentioned that "It can be shown that a permutation group is transitive if and only if its centralizer in the symmetric group is semiregular, and vice versa (Wielandt, page 9)."[1] The latter is true, i.e. G≤S_Ω is semiregular(?)Cs_Ω(G) is transitive. [cf. 2] But in the former statement fails, i.e. Cs_Ω(G) is semiregular(?)G≤S_Ω is transitive. In this note we give a series of the     

I.I.D.随机变量序列矩完全收敛的精确渐近性

{X,Xn;n≥1}为独立同分布的随机变量序列, EX=0,01 p/2满足E|X|r<∞,且E|X|3<∞,那么其中Z服从均值为0,方差为σ2的正态分布.     

每一个Cappable度都有ω个两两组成最小对的r.e.度与之组成最小对

本文证明了,对任意Cappable度α-deg(W_i),b=deg(W_i)可以一致地找到r.e.度c=deg(W_(f(i,f)))使得a∩ c=b∩c=0这里f(x,y)是一个递归函数.进而,本文证明了,对任意Cappable度a=deg(W_e),ω个r.e.度b_i=deg(W_(f(e,t)))可以一致地找到,使得a∩b_i=0,i∈ω.这里f(x,y)也是递归函数.在证明中用到了Lachlan提出的树形构造和gap-cogap方法.要确定真路径f,需要0的外部信息源.     

Q过程的不变分布(I)

设E为一可数集,Q=（qij；i，j∈E）为E×E上的矩阵,满足qij≥0（i≠j），     

CHINESE ANNALS OF MATHEMATICS Vol.8 Ser.A No.4(1987) CONTENTS AND ABSTRACTS

The Proof of the班orse一Smale Theore皿L俪Sh“l落”(刘书麟) Int五i,paper,tho au七hor proves rigorously and cons七ra毗ively Moroe Smale theorem indi任eren饭able toPology·on the Termination of the伪nstruetion of the兀ower Radioal Clas吕for a Clas吕of人ssooiative RingsG肠。(郭晋云) In 1966,Sulinski Anderoon and Divinsky studied the eons七ru晚ion of the lower radieal ela日日for assoeia七ive and alterna七i7e ringo.They lef七an in七eresting problem of且nding a ela,。K of ring,sueh tha七K汾.…     

三维非线性抛物型积分-微分方程的A.D.I.Galerkin方法及其分析

研究三维非线性抛物型积分-微分方程的A.D.I.Galerkin方法.通过交替方向,化三维为一维,简化计算;通过Galerkin法,保持高精度.成功处理了Volterra项的影响;对所提Galerkin及A.D.I.Galerkin格式给出稳定性和收敛性分析,得到最佳H1和L2模估计.     

ON ONE CONJECTURE OF R. S. SINGH

In 1979 R. S. Singh(Ann. Statist, 1979, p. 890) made a conjecture concerning the convergence rate of EB estimates of the parameter θ in an one-dimensional continuous exponential distribution family, under the square loss function, the prior distribution family being confined to a bounded interval. The conjecture asserts that the rate cannot reach o(1/n) or even O(1/n). In this article, the weaker part of this conjecture(i. e. the o(1/n) part) is shown to be correct.     

本刊英文版Vol.28(2012),No.5论文摘要

<正>On Tame Operators betWeen Non-Archimedean PoWer Series Spaces Wiestaw SLIWA Agnieszka ZIEMKOWSKA Abstract Let P∈{1,∞).We show that any continuous linear operator T from A1(a)to Ap(b)is tame,i.e.,there exists a positive integer C such that supx‖Tx‖k/|x|ck〈∞for every k∈N.Next we prove that a similar result holds for operators from A∞(a)to Ap(b)if and only if the set M_(b,a) of all finite limit points of the double sequence(bi/aj)i,jeN is bounded.Finally we show that the range of every tame operator from A∞(a)to Ao∞(b)has a Schauder basis.     

本刊英文版Vol.25(2009),No.12论文摘要

<正>Pfaffians and Representations of the Symmetric Group Alain LASCOUX Pfaffians of matrices with entries z[i,j]/(x_i+x_j),or determinants of matrices with entries z[i,j]/(x_i-x_j),where the antisymmetrical indeterminates z[i,j]satisfy the Pl_(u|¨)cker relations,can be identified with a trace in an irreducible representation of a product of two     

D.C.隶属函数模糊集及其应用(I)--D.C.隶属函数模糊集基本概念与性质

本文是D.C.隶属函数模糊集及其应用系列研究的第一部分.建立了D.C.隶属函数模糊集的基本概念.探讨了D.C.隶属函数模糊集的基本性质和D.C.隶属函数模糊集对一些常见的重要t模、余模和伪补的封闭性.并以此建立了丰富的模糊数学应用模型.     

关于I. Laine和杨重骏的一个问题

本文主要研究线性差分方程 $A_n(z)f(z+n)+\cdots+A_1(z)f(z+1)+A_0(z)f(z)=0$亚纯解的增长级.当上述方程的系数中没有起控制作用的系数时,我们给出了一些约束条件,得到了一些结果,所得结果部分回答了I. Laine和杨重骏的一个问题.