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设{Xn}为i.i.d.r.v.s.,EX1=0,EX1~2=1,S_n=sum from i=1 to n(Xi),H(x)>0 (x≥0)为非降连续函数,对某γ>0和x0>0,当x≥x0时,x-2-γH(x)非降,x-1logH(x)非增,且x-1logH(x)→0(x→∞),则有一标准Wiener过程{W(t),t≥0},使得 Sn-W(n)=O(invH(n))a.s.(n→∞)的充分必要条件是:对任何t>0有EH(t|X1|)<∞. 相似文献
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设A是B(H)中的极大交换*-子代数, G是离散群,在不要求G自由地作用在A的情况下,得到了交叉积A×αG是因子的充分且必要条件. 相似文献
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在本文中,我们推广了[2]中相关对的概念,从而导出强稠密语言的概念,利用强稠密语言作为桥梁,我们给出了[1]中一个公开问题——G.R.T.-问题的一个等价陈述,同时也部分地回答了该问题. 相似文献
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D. V. Goryashin 《Moscow University Mathematics Bulletin》2011,66(3):125-128
For the number N(x) of solutions to the equation aq − bc = 1 in positive integers a, b, c and square-free numbers q satisfying the condition aq ≤ x the asymptotic formula
$N\left( x \right) = \sum\limits_{n \leqslant x} {2^{\omega \left( n \right)} \tau \left( {n - 1} \right) = \xi _0 x\ln ^2 x + \xi _1 x\ln x + \xi _2 x + O\left( {x^{{5 \mathord{\left/
{\vphantom {5 {6 + \varepsilon }}} \right.
\kern-\nulldelimiterspace} {6 + \varepsilon }}} } \right)}$N\left( x \right) = \sum\limits_{n \leqslant x} {2^{\omega \left( n \right)} \tau \left( {n - 1} \right) = \xi _0 x\ln ^2 x + \xi _1 x\ln x + \xi _2 x + O\left( {x^{{5 \mathord{\left/
{\vphantom {5 {6 + \varepsilon }}} \right.
\kern-\nulldelimiterspace} {6 + \varepsilon }}} } \right)} 相似文献
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Yanxun Chang 《数学学报(英文版)》2000,16(1):103-112
Abstract
Given any positive integers k≥ 3 and λ, let c(k, λ) denote the smallest integer such that v∈B(k, λ) for every integer v≥c(k, λ) that satisfies the congruences λv(v− 1) ≡ 0(mod k(k− 1)) and λ(v− 1) ≡ 0(mod k− 1). In this article we make an improvement on the bound of c(k, λ) provided by Chang in [4] and prove that
. In particular,
.
Supported by NSFC Grant No. 19701002 and Huo Yingdong Foundation 相似文献
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Huan-song Zhou Hong-bo Zhu 《应用数学学报(英文版)》2007,23(4):685-696
In this paper,we consider the following ODE problem(P)where f ∈ C((0, ∞)×R,R),f(r,s)goes to p(r)and q(r)uniformly in r>0 as s→0 and s→ ∞,respectively,0≤p(r)≤q(r)∈ L~∞(0,∞).Moreover,for r>0,f(r,s)is nondecreasing in s≥0.Some existenceand non-existence of positive solutions to problem(P)are proved without assuming that p(r)≡0 and q(r)hasa limit at infinity.Based on these results,we get the existence of positive solutions for an elliptic problem. 相似文献
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Abstract
The singular second-order m-point boundary value problem
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Let 0 < c < s be fixed real numbers such that
, and let f : E2 → E
d
for d ≥ 2 be a function such that for every p, q ∈ E
2 if |p − q| = c, then |f(p) − f(q)| ≤ c, and if |p − q| = s, then |f(p) − f(q)| ≥ s. Then f is a congruence. This result depends on and expands a result of Rádo et. al. [9], where a similar result holds, but for
replacing
. We also present a further extensions where E2 is replaced by E
n
for n > 2 and where the range of c/s is enlarged.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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Let n ≥ 2 be a fixed integer, let q and c be two integers with q > n and (n, q) = (c, q) = 1. For every positive integer a which is coprime with q we denote by [`(a)]c{\overline{a}_{c}} the unique integer satisfying 1 £ [`(a)]c £ q{1\leq\overline{a}_{c} \leq{q}} and a[`(a)]c o c(mod q){a\overline{a}_{c} \equiv{c}({\rm mod}\, q)}. Put
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