关于4阶极小渐近基的一个结果

设h≥2,若h阶渐近基A的任一真子集均不是h阶渐近基,则称集合A是自然数集N的h阶极小渐近基.为进一步刻画渐近基与极小渐近基之间的关系,本文综合运用自然数的b进制表示理论及分类讨论的方法,证明了存在一个集合是4阶渐近基且其任何子集均不是4阶极小渐近基.     

关于三阶渐近基和极小渐近基

设N是自然数集,N=W0∪W∪W2是自然数集的分拆,其中集合Wi(i=0,1,2)是无限集.本文中,在W1,W2,W3中有一个仅包含两个连续整数,另外两个不包含连续整数的条件下,我们构造了三阶渐近基和极小渐近基.这个成果将进一步丰富渐近基相关领域的研究.     

随机删失下极大似然估计的局部渐近正态与渐近极小极大有效

研究观察数据被随机右删失时 ,参数分布族的局部渐近正态与渐近极小极大有效 .建立局部渐近正态成立的充分条件 ,给出渐近极小极大风险的下界以及达到该下界的充分必要条件 ,并证明随机删失下参数极大似然估计的渐近极小极大有效.     

高维空间中一类Ginzburg-Landau型泛函的极小元的渐近分析

在空间H1,pg(Ω,Rn)中讨论如下一类变系数Ginzburg-Landau型泛函Eε(Ω)=∫Ωa(x)p|Δu|p+14εpb(x)(|u|2-β2(x))2dx的极小元列的渐近性质.这里2≤p0,m≤a(x),b(x),β(x)≤M,且a(x),b(x),β(x)是光滑函数.研究了当ε→0时极小元的渐近性态,证明了极小元列在H1,pg(Ω,Rn)中强收敛于某个元素,且得到了该元素所满足的微分方程边值问题.     

一类Ginzburg-Landau型泛函的径向极小元的渐近性

The behavior of radial minimizers for a Ginzburg-Landau type functional is considered. The weak convergence of minimizers in W1,n is improved to the strong convergence in W1,n. Some estimates of the rate of the convergence for the module of minimizers are presented.     

二阶滞后型差分方程解的渐近性质

本文研究非线性差分方程 △~2x_n+q_nx_(n+1)=a_nφ(x_n+m)(x_n+k)+bn的解的渐近表示,设对应的齐次方程非振动,建立条件使方程的任意解可表成(z_n+y_n+z_no(1))的形式,其中z_n和y_n分别是对应齐次方程的主解和非主解。     

线性泛函微分方程解的渐近表示

本文利用一类特殊方程的一致稳定性与收敛性定理研究Ｒ^ｎ中线性泛函微分方程解的渐近表示，在较弱的条件下得到了与文［１］同样的渐近积分公式．文中还讨论了一些特殊解的存在性、零解的吸引性等等     

一类四阶非线性微分方程解的渐近性态

本文利用Liapunov函数方法，研究了一类四阶非线性微分方程解的渐近稳定性及有界性。     

线性泛函数微分方程解的渐近表示

本文利用一类特殊方程的一致稳定性与收敛性定理研究Ｒ中线性泛函数分方程解的渐近表示，在较弱的条件下得到了与文「１」同样的渐近积分公式。文中还讨论了一些特殊解的存在性，零解的吸引性等等。     

On the Restricted Order of Asymptotic Bases of Order Two

The restricted order of an asymptotic basis A is the least integer h, if it exists, such that every sufficiently large integer is the sum of h or fewer distinct elements of A. We show that any asymptotic basis of order 2 has a restricted order at most equal to 4. We also provide an example of an additive basis of order 2 whose restricted order is 4.To Jean-Louis Nicolas2000 Mathematics Subject Classification: Primary—11B13     

整数集的加权表示的渐进基

Let k1, k2 be nonzero integers with(k1, k2) = 1 and k1k2≠-1. Let Rk1,k2(A, n)be the number of solutions of n = k1a1 + k2a2, where a1, a2 ∈ A. Recently, Xiong proved that there is a set A  Z such that Rk1,k2(A, n) = 1 for all n ∈ Z. Let f : Z-→ N0∪ {∞} be a function such that f-1(0) is finite. In this paper, we generalize Xiong's result and prove that there exist uncountably many sets A  Z such that Rk1,k2(A, n) = f(n) for all n ∈ Z.     

某些二阶微分方程解的渐近性

Two criteria for asymptotic behavior of certain second order differential equations are obtained. The results extend and improve Feng‘s theorem.     

Minimal Representations of Cuntz Algebras

Suppose that O_n(2 ≤ n ≤∞) is a Cuntz algebra. There exists a number 1 ≤ k(π, Ω) ≤∞such that if the cyclic representations(H, π, Ω) and(H, π, Ω) of the Cuntz algebra O_n are unitary equivalent, k(π, Ω) = k(π, Ω). Applying the number, one can define a minimal representation of O_n and give a sufficient condition of the minimality for a representation of O_n. Moreover, the relations between minimal states and minimal representations of Cuntz algebras and the relations between the minimality and the irreducibility of the representation of O_n are investigated, respectively.     

球面上径向基函数最小范数插值逼近的误差估计

研究了球面径向基插值对球面函数的逼近问题,给出了一致逼近的上界估计式．文中结果说明,球面径向基插值的逼近阶会随函数光滑性的提高而增加．     

Inapplicability of Asymptotic Results on the Minimal Spanning Tree in Statistical Testing

Penrose has given asymptotic results for the distribution of the longest edge of the minimal spanning tree and nearest neighbour graph for sets of multivariate uniformly or normally distributed points. We investigate the applicability of these results to samples of up to 100 points, in up to 10 dimensions. We conclude that the asymptotic results provide an acceptable approximation only in the uniform case. Their inaccuracy for the multivariate normal case means that they cannot be applied to improve Rohlf's gap test for an outlier in a set of multivariate data points, which depends on the longest edge of the minimal spanning tree of the set.     

极小非PNN-群

有限群G称作PNN-群,如果G的每一个极小子群X要么正规于G,要么是自正规化的.本文将讨论PNN-群的性质,并给出极小非PNN-群,也就是本身不是PNN-群,每个真子群都是PNN-群的有限群的完全分类.     

循环图圈空间的最小基

For most of circular graph the length of the minimum cycle basis is given.For the others a bound of the length of the minimum cycle basis is given and the given bound is reached.     

Minimal and maximal unconditional bases with respect to framings

This paper studies framings in Banach spaces, a concept raised by Casazza, Han and Larson, which is a natural generalization of traditional frames in Hilbert spaces and unconditional bases in Banach spaces. The minimal unconditional bases and the maximal unconditional bases with respect to framings are introduced. Our main result states that, if （xi, fi） is a framing of a Banach space X, and （eimin） and （eimax） are the minimal unconditional basis and the maximal unconditional basis with respect to （xi, fi）, respectively, then for any unconditional basis （ei） associated with （xi, fi）, there are A,B 〉 0 such that A｜｜i=1∑∞aieimin｜｜≤｜｜i=1∑∞aiei｜｜≤B｜｜i=1∑∞aieimax｜｜ for all （ai） ∈ c00.
It means that for any framing, the corresponding associated unconditional bases have common upper and lower bounds.