Some uniform convergence results for kernel estimators

This paper derives some uniform convergence rates for kernel regression of some index functions that may depend on infinite dimensional parameter. The rates of convergence are computed for independent, strongly mixing and weakly dependent data respectively. These results extend the existing literature and are useful for the derivation of large sample properties of the estimators in some semiparametric and nonparametric models.     

GLOBAL EXISTENCE AND POINTWISE ESTIMATES OF SOLUTIONS TO GENERALIZED KURAMOTO-SIVASHINSKY SYSTEM IN MULTI-DIMENSIONS

The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L~p convergence rate of the solution is obtained.     

ON THE CONVERGENCE OF PADE-TYPE APPROXIMANTS IN TWO VARIABLES

In [1], C. Brezinski raised three unsolved questions in studing multivariable Pade-iype approximation, and the convergence of multivariable Pade-iype approximants under the general conditions is one of them. We have only seen in [2] that the convergence of the mullivariable Fade-type approximants is discussed for a kind of functions defined by Stieltjes integrations under some special conditions. However, the general convergence theorem has not been seen so far. In this paper, some error formulae of bivariate Fade-type approximants in in-legral form are given. By virtue of them, a number of convergence theorems of bivariate Pade-iype approximants are proved under general conditions.     

ON LACUNARY STATISTICAL CONVERGENCE OF ORDER α

In this article, we introduce the concept of lacunary statistical convergence of order α of real number sequences and give some inclusion relations between the sets of lacunary statistical convergence of order α and strong Nαθ(p)-summability. Furthermore, some relations between the spaces Nαθ(p) and Sαθare examined.     

λ-STATISTICAL CONVERGENCE OF ORDER α

In this paper,we introduce the concept of λ-statistical convergence of order α.Also some relations between the λ-statistical convergence of order α and strong(V,λ)-summability of order α are given.     

解线性方程组的预条件迭代方法

In this paper,we study the preconditioning iterative methods for the solution of the linear system and provide a convergence theorem of this method,it improves some recent results,We prove that if all parameters are in [0,1],the convergence rates for the MGS (Modified Gauss-Seidel)type methods are better than those of the corresponding SOR type methods.     

Complete Convergence and Complete Moment Convergence for Maximal Weighted Sums of Extended Negatively Dependent Random Variables

In this paper,the complete convergence and complete moment convergence for maximal weighted sums of extended negatively dependent random variables are investigated.Some sufficient conditions for the convergence are provided.In addition,the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of extended negatively dependent random variables is obtained.The results obtained in the article extend the corresponding ones for independent random variables and some dependent random variables.     

CONVERGENCE OF NEWTON＇S METHOD FOR SYSTEMS OF EQUATIONS WITH CONSTANT RANK DERIVATIVES

The convergence properties of Newton＇s method for systems of equations with constant rank derivatives are studied under the hypothesis that the derivatives satisfy some weak Lipschitz conditions. The unified convergence results, which include Kantorovich type theorems and Smale＇s point estimate theorems as special cases, are obtained.     

Convergence of the Cesàro mean for rational orthonormal bases

This paper deals with the convergence of the Cesaro mean for the rational orthonormal bases. Provided the set of zeroes of rational orthonormal bases is formed by a periodic repetition of the same finite sequence, the explicit expression of so-called block-Fejer kernel is available, and some properties of the block-Fejer kernel are discussed. Based on the convergence of the block-Cesaro mean, the convergence of Cesaro mean is also provided.     

Some remarks on holomorphic functions and taylor series in C

Some previous results on convergence of Taylor series in C^n [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy-Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in C^n are constructed and the Taylor series expansion is deduced.     

Lacunary equi-statistical convergence of positive linear operators

In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin type approximation theorem via lacunary equi-statistical convergence is proved. Moreover it is shown that our Korovkin type approximation theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. Finally the rates of lacunary equi-statistical convergence by the help of modulus of continuity of positive linear operators are studied.      

广义函数Denjoy积分的收敛性问题

本文讨论广义函数De njoy积分的收敛性问题.首先给出了广义Denjoy可积函数空间中强收敛、弱收敛、弱~*收敛和广义函数Denjoy积分收敛的关系;证明拟一致收敛是广义函数Denjoy积分收敛的一个充分必要条件;最后指出了Denjoy可积广义函数列弱~*收敛与强收敛等价当且仅当原函数等度连续.     

关于拟概率测度的收敛理论

本文研究了拟概率空间上收敛概念之间的关系这一问题.利用类比的方法,在拟概率空间上提出了一些新的关于拟-随机变量的收敛概念并讨论了这些收敛概念之间的关系,获得了模糊测度下的收敛理论,推广了关于经典测度的收敛概念.     

Complete Moment Convergence for Arrays of Rowwise Widely Orthant Dependent Random Variables

In this paper, complete moment convergence for widely orthant dependent random variables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results extend recent results on complete convergence to complete moment convergence. These results on complete moment convergence are shown to yield new results on complete integral convergence.     

Complete moment convergence for arrays of rowwise NSD random variables

In this paper, the complete convergence and complete moment convergence for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables are investigated. Some sufficient conditions to prove the complete convergence and the complete moment convergence are presented. The results obtained in the paper generalize and improve some corresponding ones for independent random variables and negatively associated random variables.     

关于不等式约束的信赖域算法

对于具有不等式约束的非线性优化问题，本文给出一个依赖域算法，由于算法中依赖区域约束采用向量的∞范数约束的形式，从而使子问题变二次规划，同时使算法变得更实用。在通常假设条件下，证明了算法的整体收敛性和超线性收敛性。     

THE CONVERGENCE OF BROYDEN ALGORITHMS FOR LC GRADIENT FUNCTION

1. IntroductionWe know that the variable metric algorithms, such as the Broyden algorithms, are veryefficient methods for solving the nonlinear programming problem:With exact line search, [11 proved that all the Broyden algorithms produce the same iterations for general functions. [21 proved that the rate of convergellce of these algorithms isone-step superlinear for the uniformly convex object function, and [3] proved that if thepoints given by these algorithms are convergent they are globall…     

拓扑半群上概率测度的条件组合收敛与SHIFT组合收敛

本文用部分群化的方法,研究拓扑半群上概率测度的条件组合收敛性与SHIFT组合收敛性,得到了一些充分条件,并推广了一些组合收敛性结果.     

Some Properties of Methods of Centers

Huard's method of centers is a method that solves constrained convex problems by means of unconstrained problems. In this paper we give some properties of this method, we analyse its convergence and rate of convergence and suggest some other variants and techniques to improve the speed of convergence.     

R~n上扩散过程的代数式收敛

本文研究n维欧氏空间上的扩散过程在L2意义下的代数式收敛的情况,给出了判定代数式收敛的方法,并对两种特殊情形扩散算子进行了讨论.将所得判敛法应用于两个例子可得到精确的结果.