（0,1;0）-INTERPOLATION ON INFINITE INTERVAL （-∞, ＋∞）

In this paper, we study the explicit representation and convergence of （0, 1;0）-interpolation on infisite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values areprescribed at two set of points namely the zeros of Hn（x） and H′n （x） and the first derivatives at the zerosof H′n（x）.     

THEORY OF INTERPOLATION ON INFINITE INTERVAL—Ⅰ(UNIFORM CONVERGENCE OF STABLE INTERPOLATION PROCESSES)

§1. Preliminaries and Results Let us begin by defining a triangular matrix L whose n-th row consists of n distinct points x_(vn), v=1, n; n=1, 2, … such that 0相似文献   

ON A PROBLEM OF(O,2)-INTERPOLATION

The object in this paper is to consider the problem of existence,uniqueness,explicil representation of(0,2)-interpolation on the zeros of(1-x~2)P~_(n-1)(x)/x when n is odd,where P_(n-1)denotes Legendrepolynomial of degree n-1,and the problem of convergence of interpolatory polynomials.     

ON BIRKHOFF INTERPOLATION (0;2) CASE

P. Turan and his associates considered in detail the problem of (0.2) interpolation based on the zeros of πn(x). Motivated by these results and an earlier result of Szabados and Varma[9] here we consider the problem of existence, uniqueness and explicit representation of the interpolatory polynomial Rn (x) satisfying the function values at one set of nodes and the second derivative on the other set of nodes. It is important to note that this problem has a unique solution provided these two sets of nodes are chosen properly. We also promise to have an interesting convergence theorem in the second paper of this series, which will provide a solution to the related open problem of P. Turan.     

On Pal Type Weighted Lacunary (0 , 2 ; 0 )-Interpolation on Infinite Interval (?∞, +∞)

In this paper, we study the weighted (0, 2; 0)-interpolation on infinite interval, which means to determine a polynomial of degree 3n–1 when the function values are prescribed at two sets of points namely the zeros of H_n(x) and H_n(x) and the wieghted second derivative at the zeros of H_n(x).     

TWO POSITIVE PERIODIC SOLUTIONS OF NONLINEAR INTEGRAL EQUATION ON THE INFINITE INTERVAL MODELLING INFECTIOUS DISEASE

In this paper, by applying Avery-Henderson fixed point theorem in a cone, we establish some new existence results of two positive periodic solutions for a type of nonlinear integral equations with variant delay.     

A CLASS OF SINGULAR PERTURBATIONS FOR SECOND ORDER QUASI－LINEAR BOUNDARY VALUE PROBLEMS ON INFINITE INTERVAL

ＡＣＬＡＳＳＯＦＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＳＦＯＲＳＥＣＯＮＤＯＲＤＥＲＱＵＡＳＩ－ＬＩＮＥＡＲＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＯＮＩＮＦＩＮＩＴＥＩＮＴＥＲＶＡＬＺＨＡＯＷＥＩＬＩ（赵为礼）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈ...     

(0,1)-方阵的置换相抵

<正> 设A和B是n阶方阵,如果方阵A可经行的置换与列的置换化为方阵B,即存在n阶置换方阵P和Q,使得B=PAQ,则方阵A和B称为是置换相抵的.1974年,B.Gordan,T.S.Motzkin和L.Welch用图论的方法,证明了当permanent为1,2和3时n阶(0,1)-方阵置换相抵标准形的定理.由于方阵的置换相抵是方阵的一种等价关系,它自然应属于矩阵论的范畴,因此有必要从矩阵论的角度重新加以讨论.本文的目的是给出B.Gordan等人的结论的一个矩阵证明,方法是构造性的,且具有一般意义.作为一个说明,     

(0,1)-矩阵类(?)(R,S)

我们把元素全部是1或0的矩阵称为(0,1)-矩阵。设A是一个m×n阶(0,1)-矩阵,其第ⅰ行全部元素之和为r_i(1≤i≤m),第j列全部元素之和为s_j(1≤j≤n)。那么称向量R=(r_1,r_2,…,r_m)为A的行和向量;S=(s_1,s_2,…,s_n)为A的列和向量。所谓具有行和向量R,列和向量S的(0,1)-矩阵类(R,S)是指:     

论(0,1)-矩阵类的多项式表示

通过将(0,1)—矩阵类表示成多元多项式,可以简明地建立若干(0,1)—矩阵类的基数的母函数,并由此导出这些矩阵类的基数的递推公式。     

一类(0,1)-矩阵的最大积和式

本文给出了每条线恰有n-2个1的n阶(0.1)-矩阵的最大积和式的组合表达式.     

ON LAGRANGE INTERPOLATION FOR |X|~α (0 &lt; α &lt; 1)

We study the optimal order of approximation for |x|α (0 &lt; α &lt; 1) by Lagrange interpolation polynomials based on Chebyshev nodes of the first kind. It is proved that the Jackson order of approximation is attained.     

Stopped Doob inequality for p-th moment, 0 <p<∞, stochastic convolution integrals

We give stopped Doob inequalities for p-th moment, 0<p<∞, of stochastic convolution integrals ∫_(0,t] U(t,s)φ _{s ^?} dM _s in a Hilbert space, where M is a Hilbert space-valued cadlag square integrable martingale, φ is an operator-valued predictable process and U(t,s) is a contraction-type evolution operator. We also generalize the previous results and try to get smaller constants.

     

(0,1)-矩阵类u(R,S)的结构和基数

本文提出了两个保优向量间的极小保优对应段和分解列的概念,较详细地分析了全链的结构(见定理2),解决了u(R,S)中恒1与恒0的分布和计数问题(见定理1),讨论了u(R,S)的结构和基数(见定理3—5),并改进了魏万迪给出的|u(R,S)|的下界。最后,我们给出了两个命题和例子(本文基本结果曾于一九八二年四月在华中工学院数学系组合数学讨论班上报告过)。     

On Joint Realization of (0,1) -matrices

Let R=(r_1,…,r_m),S=(s_1,…,s_n),R’=(r_1',…,r_m') and S'=(S_1',…,S_m')be non-negative integral vectors.Denote by (R,S)the class of(0,1)-matrices withrow sum vector R and column sum vector S. The three classes (R,S), (R’,S’)and (R R’,S S’)are called jointly realizable if there exist a matrix A in (R,S)and a matrix B in (R’,S’)such that A B∈ (R R’,S S’). In 1980,R.A.Brualdi and R.P.Anstee posed the following conjecture inde-pendently(see [1]).     

(0,1)-矩阵类(?)(R,S)的结构和基数(英文)

本文提出了两个保优向量间的极小保优对应段和分解列的概念,较详细地分析了全链的结构(见定理2),解决了(R,S)中恒1与恒0的分布和计数问题(见定理1),讨论了(R,S)的结构和基数(见定理3—5),并改进了魏万迪给出的|(R,S)|的下界。最后,我们给出了两个命题和例子(本文基本结果曾于一九八二年四月在华中工学院数学系组合数学讨论班上报告过)。     

R_0-代数[0,1]的子代数与广义重言式

本文是对修正的Kleene系统中广义重言式理论的推广,讨论了R_0-代数[0,1]的各类无限子R_0-代数中的广义重言式,证明了在子R_0-代数E_2中,中存在着可数多个不同的广义重言式。