Banach空间非扩张映像不动点强收敛定理

设E是具弱序列连续对偶映像自反Banach空间, C是E中闭凸集, T:C→ C是具非空不动点集F(T)的非扩张映像.给定u∈ C,对任意初值x0∈ C,实数列{αn}n∞=0,{βn}∞n=0∈ (0,1),满足如下条件:(i)sum from n=α to ∞α_n=∞, α_n→0;(ii)β_n∈[0,α) for some α∈(0,1);(iii)sun for n=α to ∞|α_(n-1) α_n|<∞,sum from n=α|β_(n-1)-β_n|<∞设{x_n}_(n_1)~∞是由下式定义的迭代序列:{y_n=β_nx_n (1-β_n)Tx_n x_(n 1)=α_nu (1-α_n)y_n Then {x_n}_(n=1)~∞则{x_n}_(n=1)~∞强收敛于T的某不动点.     

截断和随机乘积的渐近性质

对一列独立同分布平方可积的随机变量序列{Xn,n≥1},当随机变量的分布具有中尾分布时,讨论了其截断和Tn(a)的随机乘积的渐近正态性质,其中Tn(a)=Sn-Sn(a),n=1,2,…,Sn(a)=n∑ j=1 XjI{Mn-a＜Xj≤Mn},a为某一大于零的常数'Mn=max 1≤k≤n{Xk}.     

关于群中乘积元素的阶

讨论群中两个元素a,b的阶不相等时其乘积ab的阶的一类计算问题.设ㄧaㄧ=m,ㄧ bㄧ=n,若(m,n)=1,且存在k∈N使a=bk,则有ㄧabㄧ=mn/d1d2,其中d1=(m,k+1),d2=(n,k+1).若m≠n,ab=ba,且(m,n)ㄧm/(m,n),或(m,n)ㄧn/(m,n),则有ㄧabㄧ=[m,n].     

立方幂补数除数函数的均值

设 n是正整数 ,S(n)是 n的立方幂补数 ,τ(n)表示 n的除数函数 .本文的主要目的是探讨∑n xτ(S(n) )n 和 ∑n xτ(S(n) ) 的渐近性质 ,得到了两个渐近公式 ,进一步解决 F.Smarandache教授提出的第2 8个问题 .     

具有四个素因子的奇亏完全数

设n为自然数,σ(n)表示n的所有正因子和函数.令d是n的真因子,若n满足σ(n)=2n-d,则称n为亏因子为d的亏完全数.本文给出了具有四个素因子的奇亏完全数的一些性质的刻画.     

A General Comparison Result for Higher Order Nonlinear Difference Equations With Deviating Arguments

The authors consider m -th order nonlinear difference equations of the form D m p x n + i h j ( n , x s j ( n ) )=0, j =1,2,( E j ) where m S 1, n ] N 0 ={0,1,2,…}, D 0 p x n = x n , D i p x n = p n i j ( D i m 1 p x n ), i =1,2,…, m , j x n = x n +1 m x n , { p n 1 },…,{ p n m } are real sequences, p n i >0, and p n m L 1. In Eq. ( E 1 ) , p = a and p n i = a n i , and in Eq. ( E 2 ) , p = A and p n i = A n i , i =1,2,…, m . Here, { s j ( n )} are sequences of nonnegative integers with s j ( n ) M X as n M X , and h j : N 0 2 R M R is continuous with uh j ( n , u )>0 for u p 0. They prove a comparison result on the oscillation of solutions and the asymptotic behavior of nonoscillatory solutions of Eq. ( E j ) for j =1,2. Examples illustrating the results are also included.     

相伴于随机自相似分形的随机测度的强测度的收敛性

构造了随机自相似分形及其上的记忆函数,并得出了有关结论,在此基础上,我们可以定义一个随机概率测度dΦn(τ)=Kn(τ)dτ,Φn(τ)弱收敛于Φ,进一步可得到强测度序列Ψn(·)=EΦn(·),则{Ψn}弱收敛于Ψ=EΦ.     

Asymptotic Behavior of Solutions of Some Linear Difference Equations with Oscillatory Decreasing Coefficients

We investigate the asymptotic behavior of solutions of the system x ( n +1)=[ A + B ( n ) V ( n )+ R ( n )] x ( n ), n S n 0 , where A is an invertible m 2 m matrix with real eigenvalues, B ( n )= ~ j =1 r B j e i u j n , u j are real and u j p ~ (1+2 M ) for any M ] Z , B j are constant m 2 m matrices, the matrix V ( n ) satisfies V ( n ) M 0 as n M X , ~ n =0 X Á V ( n +1) m V ( n ) Á < X , ~ n =0 X Á V ( n ) Á 2 < X , and ~ n =0 X Á R ( n ) Á < X . If AV ( n )= V ( n ) A , then we show that the original system is asymptotically equivalent to a system x ( n +1)=[ A + B 0 V ( n )+ R 1 ( n )] x ( n ), where B 0 is a constant matrix and ~ n =0 X Á R 1 ( n ) Á < X . From this, it is possible to deduce the asymptotic behavior of solutions as n M X . We illustrate our method by investigating the asymptotic behavior of solutions of x 1 ( n +2) m 2(cos f 1 ) x 1 ( n +1)+ x 1 ( n )+ a sin n f n g x 2 ( n )=0 x 2 ( n +2) m 2(cos f 2 ) x 2 ( n +1)+ x 2 ( n )+ b sin n f n g x 1 ( n )=0 , where 0< f 1 , f 2 < ~ , 1/2< g h 1, f 1 p f 2 , and 0< f <2 ~ .     

F.Smarandache的一个问题

设 n是正整数 ,a( n)表示 n的三次方幂补数 .本文的主要目的是研究 a( n)和 a( n)n 的 k次均值性质 ,解决 F.Smarandache教授提出的第 2 8个问题 ,并用解析方法给出两个有趣的渐近公式     

Purely tetrahedral quadruple systems

An oriented tetrahedron is a set of four vertices and four cyclic triples with the property that any ordered pair of vertices is contained in exactly one of the cyclic triples. A tetrahedral quadruple system of order n (briefly TQS(n)) is a pair (X,B), where X is an nelement set and B is a set of oriented tetrahedra such that every cyclic triple on X is contained in a unique member of B. A TQS(n) (X,B) is pure if there do not exist two oriented tetrahedra with the same vertex set. In this paper, we show that there is a pure TQS(n) if and only if n = 2,4 (mod 6), n > 4, or n = 1,5 (mod 12). One corollary is that there is a simple two-fold quadruple system of order n if and only if n = 2,4 (mod 6) and n > 4, or n = 1,5 (mod 12). Another corollary is that there is an overlarge set of pure Mendelsohn triple systems of order n for n=1,3 (mod 6), n > 3, or n =0,4 (mod 12).     

二次剩余问题的一个新定理

研究了二次剩余问题,利用整数分类的办法,给出了|Jn|和|Qn|的公式(这里n是奇合数,Jn是Zn*中有Jacobi符号为1的所有元素的集合,Qn是模n的所有二次剩余的集合) .基于这些结果,可以得出当a对模n的Jacobi符号等于1时,正确猜测a为模n的二次剩余的可能性,从而推广了[1]p .74中的结果.     

Asymptotic normality of the nearest neighbor hazard estimates

1.IntroductionSupposethatXI)')Xu,'beani.i.d.sequenceofrandomvariableswithdistributionfunctionF(x)anddensityfunctionf(x).TOestimatethedensityfunctionatxbasedonthefirstnobservations,thekerneltypeestimategiveswhereK')isakernelfunction,R.(x)isabandwidthsequenceandFi')isanestimateofF,usuallytakentobetheempiricaldistributionfunction.Formoredetails,see[21.Inmedicalapplications,itisoftenmoreimportanttoestimatethehazardfunctiondefinedbyA(x)~f(x)/(1--F(x)).IfXrepresentsalife-time,thenA(x)repre…     

不完整区间上整数及其逆的差

设实数λ, δ 满足0 < λ, δ ≤ 1, n > 2 为整数. 本文研究了不完整区间[1,[λn]] 上整数与其模n逆的差. 定义S(n, λ, δ) = #{a : 1 ≤ a ≤ λn, (a, n) = 1, |a - a| < δn}, 本文给出了有关S(n, λ, δ) 的一些渐近公式.     

关于Hardy不等式的加强改进

对 Hardy不等式 ,建立如下结构的加强不等式 :∑∞n=11n∑nk=1akp 1 ,an≥ 0 (n∈ N) ,0 <∑∞n=1apn<∞ ,Cp=1 -(1 -p- 1) p- 1,p≥ 2 ;1 -p- 1,1 相似文献   

完全二部多重图的K2,3-因子分解

如果完全二部多重图λK<,m,n>的边集可以划分为λK<,m,n>的K<,p,q>-因子,则称λK<,m,n>存在K<,p,q>-因子分解.当p=1和q=2时,λK<,m,n>的K<,1,2>-因子分解的存在性问题已被完全解决.最近我们得到了当λ=1时,K<,m,n>存在K<,2,3>-因子分解的充分必要条件.对于任意...     

典型域的调和函数论(Ⅲ)——斜对称方阵双曲空间的调和函数

<正> 3.1.斜对称方阵双曲空间的调和函数 命 Z 代表 n×n 斜对称方阵(?)(?)个复变数 z_(12),z_(13),…z_(1n),z_(23),…,(?)…,z_(n-1,n)空间的域我们引进运算子     

交换环上严格上三角矩阵的广义李三导子(英文)

本文研究了交换环R上所有n×n严格上三角矩阵构成的李代数N(n,R)(n≥5)上广义李三导子.利用矩阵技巧,证明了N(n,R)(n≥5)上任意广义李三导子为一李三导子与一位似映射的和.对于N(n,R)(n≥3)上广义李导子,得出类似结果.     

THE EXISTENCE OF OVERLARGE SETS OF IDEMPOTENT QUASIGROUPS

A idempotent quasigroup (Q, o) of order n is equivalent to an n(n-1)×3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n+1)-set. Denote by T(n+1) the set of (n+1)n(n-1) ordered triples of X with the property that the 3 coordinates of each ordered triple are distinct. An overlarge set of idempotent quasigroups of order n is a partition of T(n+1) into n+1 n(n-1)×3 partial orthogonal arrays A_x, x∈X based on X\{x}. This article gives an almost complete solution of overlarge sets of idempotent quasigroups.     

Smarandache函数在两数列上的下界估计

设S(n)是Smarandache函数,其中n是一正整数.讨论Smarandache函数S(n)在数列F((2k),1)=F(n,1)=n2n+1(n=2k)与数列G(2n,1)=(2n)2n+1上的下界估计.基于初等方法证明了:当偶数n≥6时,有S(F((2k),1))=S(F(n,1))≥6×2n+1;当n≥4时,有S(G(2n,1))≥6×2n+1.     

关于两个群元素乘积的阶的研究

本文主要讨论满足交换性的两个元素乘积的阶的问题。设G是一个群,a,b∈G,ab=ba,a的阶为n1,b的阶为n2。一般情况下ab的阶不等于n1与n2的最小公倍数。例如当a=b,n1=n2=4时,ab=a2,ο(ab)=2≠[n1,n2]。本文获得了ab的阶等于n1与n2的最小公倍数的几个充分条件。