平稳序列中的一些结果

平稳过程预报方法相继在气象、水文、黑子预报、地震……上有一定应用,都需用资料估计相关函数,估计出的相关函数不一定是正定的,因此有时计算出奇怪的结果,预报误差为负数,或预报出的数值数量级过大,这才引起我们研究本文的问题。 R_0 R_1 … R_m R_1 R_0 … R_(m-1) …………………………设R_0,R_1,…,R_m为一串实数,称 R_m R_(m-1) … R_0 为实对称的平稳矩阵。本文的问题是设R_0,R_1,…,R_(n-1)对应的平稳矩阵为正定的,问R_n满足什么条件,使R_0,R_1,…,R_(n-1),R_n对应的平稳矩阵为非负定的,得到的结果是:R_n必须在闭区间[q_(n-1)-V_(n-1),q_(n-1)+V_(n-1)]中,q_(n-1),V_(n-1)是实常数,有清楚的概率论意义,V_(n-1)是熟知的子报误差,q_(n-1)的引入可能是新的,还把这基本结果应用于宽平稳N重马尔柯夫过程,退化时,R_N,R_(N+1),…均取上述可取值之闭区间之边点。非退化时,均取其可取值之闭区间之中点。     

B值混合序列的一些收敛性结果

本文获得了B值ρ混合随机元序列的均值收敛性,Kolmogorov强大数定律以及正则和极大值矩的存在性问题,推广和改进了已有的结果.     

关于带宽极值问题的一些结果

本文研究的问题是确定f(p,B）的值，也就是给定顶点数p和带宽B，求满足最大度不超过B的连通图的最小边数，本文给出了一些f(p,B）的值及相应极图。     

关于遗传代数的一些结果

In this paper,the Alprin‘s conjecture is verified for △- tilt algebras,where △ is not a wild quiver;and a necessary and sufficient condition for F(X)being resolving is also given,where X is an exceptional sequence over a hereditary algebra.     

关于微分多项式的一些结果

设ｆ是平面内超越亚纯函数，满足Ｎ（ｒ，ｆ）＝Ｓ（ｒ，ｆ）．Ｐ［ｆ］是ｆ的多项式，Ｑ［ｆ］是ｆ的微分多项式。本文考虑了形如Ｐ［ｆ］ｆ＇＋Ｑ［ｆ］（特殊情形为ｆ￣ｎｆ＇＋Ｑ［ｆ］及Ｐ［ｆ］ｆ＇－Ｃ，Ｃ为常数）的微分多项式的值分布，推广并改进了Ｗ．Ｋ．Ｈａｙｍａｎ，Ｊ．Ｃｌｕｎｉｅ，Ｅ．Ｍｕｅｓ等人关于整函数的一些结果。     

关于λ性质的一些结果

In this paper we have proved a open problen of [1].     

算子稳定随机向量序列的一些极限结果

对于独立同分布的没有Gauss分量的指数为可逆线性算子A的算子稳定的R~d值随机向量序列,本文通过积分检验讨论了其部分和及加权和(包括一些经典的加权和,如Cesàro加权和,后置和方式,Euler可和方式,Borel可和方式,几何加权和等)的极限结果.由此得到了部分和及加权和在相对于A的谱分解下的Chover型重对数律,这是与A的特征值的实部有关的结果.     

关于稳定调和映照的一些结果

设M是复射影空间CP~n或四元数射影空间QP~n的紧致子流形。本文研究了从M到任意Riemann流形或从任意紧致Riemann流形到M的稳定调和映照,得到了一些不存在性定理。     

关于张量最小长度的一些结果

本文根据不同重数张量空间之间的关系,采用对张量空间分划的方法,得到了张量空间中张量达到最小长度的一个充分条件和一个必要条件.此外,本文还讨论了最小长度的上界K_max,得到了如下估计:对n维向量空间上的m阶张量空间,n^[m/2]≤K_max≤n^m-1。     

Some results on the proportional reversed hazards model

The proportional reversed hazards model consists in describing random failure times by a family {[F(x)]^θ, θ>0} of distribution functions, where F(x) is a baseline distribution function. We show various results on this model related to some topics in reliability theory, including ageing notions of random lifetimes, comparisons based on stochastic orders, and relative ageing of distributions.     

Some special results on convergent sequences of radon measures

Two problems will be considered. In Part I we consider a class of subsets of a topological space X and a Radon measure on X; if it is known that, for sufficiently many , the restrictions of the sets in constitutes a uniformity class in T w.r.t. the restriction of the given measure, then we ask if it follows that is a uniformity class in X.Part II, which can be read independently of Part I, is concerned with the question whether, to a given convergent sequence of Radon measures, say _n, there always exist sufficiently many compact sets K such that _n(K)(K).     

Some negative results on multiplier sequences of the first kind

It is proved that the composition of a polynomial with a multiplier sequence of the first kind may lead to a diminishing of the number of real roots of this polynomial and that the reciprocals of the moments of a nonnegative function on [0, 1] need not form a multiplier sequence of the first kind. On the basis of these facts one establishes the inaccuracy of the solution, obtained by T. Craven and G. Csordas, to S. Karlin's problem on the characterization of linear transformations that do not increase the number of zeros and also the incorrectness of M. Kostova's certain results, given in L. Iliev's monograph Laguerre entire functions (Sofia, 1987).Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 305–309, March, 1992.     

Some results about the cross-correlation function between two maximal linear sequences

Let {a₁} and {a_d1} be two maximal linear sequences of period pⁿ ? 1. The cross-correlation function is defined by C_d(t) =

for t = 0, t…pⁿ ? 2, where $\text{ζ = exp(2π}\text{1}\text{p}\text{)}$. We find some new general results about C_d(t). We also determine the values and the number of occurences of each value of C_d(t) for several new values of d.     

Some conditional results for conditionally strong mixing sequences of random variables

The relation between strong mixing and conditionally strong mixing is answered by examples, that is, the strong mixing property of random variables does not imply the conditionally strong mixing property, and the opposite implication is also not true. Some equivalent definitions and basic properties of conditional strong mixing random variables are derived, and several conditional covariance inequalities are obtained. By means of these properties and conditional covariance inequalities, a conditional central limit theorem stated in terms of conditional characteristic functions is established, which is a conditional version of the earlier result under non-conditional case.     

Convergence theorems for adapted sequences of random sets

We consider random sets with values in a separable Banach space. We study set-valued amarts, L¹-amarts, uniform amarts and submartingales. For all these classes of random sets, we prove convergence theorems in all main modes of set convergence (weak, Wijsman, Mosco, and Hausdorff). We also prove new convergence theorems for vector-valued subpramarts and pramarts.     

Some remarks on indiscernible sequences

We prove a property of generic homogeneity of tuples starting an infinite indiscernible sequence in a simple theory and we use it to give a shorter proof of the Independence Theorem for Lascar strong types. We also characterize the relation of starting an infinite indiscernible sequence in terms of coheirs.     

关于B值随机元序列的强收敛性

利用截尾方法构造几乎处处收敛的指数鞅，用鞅方法与分析方法相结合，研究了B值适应可积随机元序列的局部收敛性及其强大数定理．