平稳序列自相关函数正定的充要条件

本文导出了平稳序列的自相关函数Ｂ（τ）为正定的充分必要条件，并说明了ＡＲＭＡ（ｐ，ｑ）序列的Ｂ（τ）总是正定的     

Bergman空间A~p（ψ）中函数之零点

设Ｄ是Ｃ中的单位圆盘及为［０，１）上的正规函数。对于０＜Ｐ＜∞，这样的函数用于定义一个带权为￣ｐ（｜ｚ｜）／（１－｜ｚ｜￣２）的Ｂｅｒｇｍａｎ空间Ａ￣ｐ．本文刻画了Ａ￣ｐ中函数之零点集的结构．作为应用，又给出了Ａ￣ｐ中函数序列插值的条件。     

关于两指标AR（p）过程的偏相关函数

在文［１］、［２］的基础上，首次给出了两指标ＡＲ（ｐ）过程偏相关函数的定义，并建立了过程与其偏相关函数截尾性之间的关系。     

有界平均振动特征的随机幂级数

本文研究了随机幂级数Ｆω（ｚ）＝　ａｎωｎｚｎ，ａｎ≥０，其中（ωｎ）是概率空间（Ω，Ｐ）上的Ｓｔｅｉｎｈａｕｓ序列或Ｒａｄｅｍａｃｈｅｒ序列．我们分别给出了Ｆω几乎必然地属于Ｂ０和ＶＭＯＡ的条件，这些条件不仅包含了原有的结果，而且区分了Ｆω几乎必然地属于Ｂ０和ＶＭＯＡ这两个不同函数空间的条件，而原有的条件是不加区分的．     

逆自相关函数估计的渐近性质

逆自相关函数估计的渐近性质陈敏，常学将（山西大学数学系，太原０３０００６）ＴＨＥＡＳＹＭＰＴＯＴＩＣＰＲＯＰＥＲＴＩＥＳＯＦＴＨＥＥＳＴＩＭＡＴＩＯＮＯＦＴＨＥＩＮＶＥＲＳＥＣＯＲＲＥＬＡＴＩＯＮＦＵＮＣＴＩＯＮ￥ＣＨＥＮＭＩＮ；ＣＨＡＮＧＸＵＥＪＩ...     

带ARMA误差的曲线回归模型的估计

考虑广义回归模型ｙｉ＝ｇ（ｔｉ）＋εｉ,１,１≤ｉ≤ｎ,其中ｇ（．）为Ｒ上的未知函数,随机误差εｉ是ＡＲＭＡ（ｐ,ｑ）序列,本文利用线性小波光滑的方法,讨论未知函数ｇ（．）的小波光滑及ＡＲＭＡ（ｐ,ｑ）的参数估计。     

NA序列广义Jamison型加权和的几乎处处收敛性

本文从随机变量序列广义Ｊａｍｉｓｏｎ型加权和的一个系数指标函数自身性质出发，讨论了广义Ｊａｍｉｓｏｎ型加权和的强稳定性，避免了控制函数的引入， 进一步还得到了更一般的ＮＡ序列广义Ｊａｍｉｓｏｎ型加权和的几乎处处收敛的条件，并将前人的若干结论包含为特例．     

再论ARMA模型参数极大似然估计的收敛速度

本文给出了ＡＲＭＡ模型参数的极大似然估计和最小平方和估计的强收敛速度。     

环Z2l上广义Bent函数的稳定性

文献「４」为研究密钥流序列的线性复杂度稳定性和使一些流密码能抗ＢＡＡ（最佳仿射逼近）攻击,提出Ｂｅｎｔ函数稳定性概念,文献「７」研究了素域Ｚｐ上广义Ｂｅｎｔ函数的稳定性及其构造,并指出当ｍ是合数时,ｍ值广义Ｂｅｎｔ函数并不都有稳定性,本文进一步在环Ｚ２＾ｌ（ｌ〉１）上提出了广义Ｂｅｎｔ函数稳定性的概念,综合应用谱、概率和代数数论的方法考察了稳定的概率意义,给出了稳定函数的概率判别条件,提供了构造稳     

本原代换的非周期不动点的Hausdorff维数函数

设 Ａ＝｛０, １,…, Ｎ－１｝,ξ是 Ａ上的一个本原代换, ｕ是ξ的非周期不动点．记 Ｘ（ξ）＝Ｏｒｂ（ｕ） 本文证明了：Ｘ（ξ）的Ｈａｕｓｄｏｒｆｆ维数函数是ｈ（ｘ）＝－ｌｏｇＮ／ｌｏｇｘ     

非正交试验的平方和分解及其应用

在方差分析中,平方和分解占有很重要的地位.在正交试验里,可以将平方和分解为各效应平方和和误差平方和之和,且使各效应平方和相互独立,从而对各效应假设分别作F 检验.但在实际中,我们经常碰到的数据并不是正交的,此时用最小二乘法得到的估计,其总平方和不再等于各效应平方和与误差平方和之和,而且计算复杂,应用起来极不     

Matrices as sums of squares

How many squares are needed to represent elements in a matrix ring? A matrix over a field of characteristic two is a sum of two squares if and only if its trace is a square, otherwise it is not a sum of squares. Any proper matrix over a field of characteristic not two is always a sum of three squares. If the order of a matrix is even the matrix is a sum of two squares, but an odd order matrix which is q times the identity matrix is a sum of two squares if and only ifq is a sum of two squares in the field. Matrices of order 2,3 and 4 over the integers can always be written as the sum of three squares.     

Euler级数的收敛性与组合学技巧

通过优序列方法，建立了Ｅｕｌｅｒ级数，即反函数的幂级数的收敛性，而且，我们发现Ｅｕｌｅｒ级数的系数和具有ｎ个元素的Ｓｃｈｒｏｄｅｒ系的个数之间的联系，以及Ｅｕｌｅｒ级数收敛半径的确切下界可通过相应的指母函数的收敛半径得到 。     

矩阵方程AXB+CY D=E的三对角中心对称极小范数最小二乘解

本文研究了矩阵方程AXB+CY D=E的三对角中心对称极小范数最小二乘解问题.利用矩阵的Kronecker积和Moore-Penrose广义逆方法,得到了矩阵方程AXB+CY D=E的三对角中心对称极小范数最小二乘解的表达式.     

对称矩阵部分特征值之和的非光滑分析

本文研究n阶实对称矩阵A的前m项最大特征值之和fm（A）的非光滑分析问题．利用Ky－Fan的关于特征值之和的变分原理以及凸分析理论，得到了fm（A）的次梯度和方向导数的显式表达式．     

ON THE ACCURACY OF THE LEAST SQUARES AND THE TOTAL LEAST SQUARES METHODS

Consider solving an overdetermined system of linear algebraic equations by both the least squares method (LS) and the total least squares method (TLS). Extensive published computational evidence shows that when the original system is consistent. one often obtains more accurate solutions by using the TLS method rather than the LS method. These numerical observations contrast with existing analytic perturbation theories for the LS and TLS methods which show that the upper bounds for the LS solution are always smaller than the corresponding upper bounds for the TLS solutions. In this paper we derive a new upper bound for the TLS solution and indicate when the TLS method can be more accurate than the LS method.Many applied problems in signal processing lead to overdetermined systems of linear equations where the matrix and right hand side are determined by the experimental observations (usually in the form of a lime series). It often happens that as the number of columns of the matrix becomes larger, the ra     

Criteria for Unconstrained Global Optimization

We develop criteria for the existence and uniqueness of the global minima of a continuous bounded function on a noncompact set. Special attention is given to the problem of parameter estimation via minimization of the sum of squares in nonlinear regression and maximum likelihood. Definitions of local convexity and unimodality are given using the level set. A fundamental theorem of nonconvex optimization is formulated: If a function approaches the minimal limiting value at the boundary of the optimization domain from below and its Hessian matrix is positive definite at the point where the gradient vanishes, then the function has a unique minimum. It is shown that the local convexity level of the sum of squares is equal to the minimal squared radius of the regression curvature. A new multimodal function is introduced, the decomposition function, which can be represented as the composition of a convex function and a nonlinear function from the argument space to a space of larger dimension. Several general global criteria based on majorization and minorization functions are formulated.     

球面和射影平面上不可分地图的色和

给出了球面和射影平面上带根不可分地图的色和方程,从色和方程导出了球面和射影平面上带根一般不可分地图、二部地图的计数函数方程. 利用色和理论,研究不同类地图的计数问题,得到了一种研究计数问题的新方法. 此外,还得到了一些计数显示表达式.     

On the sum powers of matrices

A theorem of Lagrange says that every natural number is the sum of 4 squares. M. Newman proved that every integral n by n matrix is the sum of 8 (-1)ⁿ squares when n is at least 2. He asked to generalize this to the rings of integers of algebraic number fields. We show that an n by n matrix over a a commutative R with 1 is the sum of squares if and only if its trace reduced modulo 2Ris a square in the ring R/2R. It this is the case (and n is at least 2), then the matrix is the sum of 6 squares (5 squares would do when n is even). Moreover, we obtain a similar result for an arbitrary ring R with 1. Answering another question of M. Newman, we show that every integral n by n matrix is the sum of ten k-th powers for all sufficiently large n. (depending on k).     

关于正定厄米特矩阵的Schur补的迹和特征值的不等式

本文研究了正定厄米特矩阵Schur补的迹和特征值的性质,通过一个不等式的证明,得到了正定厄米特矩阵和的Schur补与正定厄米特矩阵Schur补的和的迹和特征值之间的不等式.