ON THE HYPER ORDER OF SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS＊＊

The author investigates the hyper order of Solutions of the higher order linear equation, and improves the results of M. Ozawa[15], G. Gundersen[6] and J. K. Langley[12].     

ON QUADRATURE OF HIGHLY OSCILLATORY FUNCTIONS

Some quadrature methods for integration of ∫a^bf（x）e^iwg（x）dx for rapidly oscillatory functions are presented. These methods, based on the lower order remainders of Taylor expansion and followed the thoughts of Stetter [9], Iserles and NФrsett [5], are suitable for all w and the decay of the error can be increased arbitrarily in case that g＇（x）≠0 for x∈[a, b], and easy to be implemented and extended to the improper integration and the general case I[f]=∫a^b f（x）e^ig（w,x）dx.     

ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATION

In this paper, a class of higher order linear differential equation is investigated. The order and the hyper-order of the solutions of the equation are exactly estimated under some certain conditions.     

A GENERAL PROPERTY OF THE QUADRATIC DIFFERENTIAL SYSTEMS

In this paper, it is proved that the quadratic differential systems with a weak saddle of order 2 or 3 have no closed or singular closed orbit. Then by the results of [3], it follows that the greatest order of the homoclinic loop bifurcation of a quadratic differential system is between 2 and 3 It means a homoclinic loop can be split into at most three limit cycles.     

ON THE ITERATED ORDER OF MEROMORPHIC SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.     

BOREL LINES OF RANDOM DIRICHLET SERIES

For random Diriclilet-haelnacher, Steillhaus and N series of order (R) infinite almostsurely (a.s.), it was proved that a.s. every horizontal line is a Borel line of order (R) illfi-uite and witli a possible exceptional value[6][n. In this paper f by generalized Paley-Zygmundlenru['], sonle sli11ple maPpillgs and Nevanlinlla tlieory[2], we prove that for more general ran-dom Dirichlet random Dirichlet series of order (R) infinite a.s. every horizontal line is a Borelline of order (R) infi…     

ON THE HYPER-ORDER OF MEROMORPHIC SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS

In this paper the order and the hyper-order of the solutions of higher-order homoge-neous linear differential equations is investigated.     

OPTIMAL ERROR ESTIMATES OF THE PARTITION OF UNITY METHOD WITH LOCAL POLYNOMIAL APPROXIMATION SPACES

In this paper, we provide a theoretical analysis of the partition of unity finite elementmethod (PUFEM), which belongs to the family of meshfree methods. The usual erroranalysis only shows the order of error estimate to the same as the local approximations[12].Using standard linear finite element base functions as partition of unity and polynomials aslocal approximation space, in 1-d case, we derive optimal order error estimates for PUFEMinterpolants. Our analysis show that the error estimate is of one order higher than thelocal approximations. The interpolation error estimates yield optimal error estimates forPUFEM solutions of elliptic boundary value problems.     

ON THE GROWTH OF THE SOLUTIONS FOR 1ST KIND OF HIGHER ORDER DIFFERENTIAL EQUATIONS IN THE UNIT DISC

In this paper, we study the growth of the solutions for 1st kind of differential equations of higher order in the unit disc. We give a sufficient condition for all solutions of second order linear differential equation to be inadmissible and a sufficient condition for all solutions of higher order linear differential equation to be of infinite order.     

BOUNDARY STABILIZATION OF HYPERBOLIC SYSTEM WITH NO DISSIPATIVE CONDITIONS

There has been much work (cf. [1], [4], [7]-[12]and references of [8]) on the stabilization of hyperbolic systems. Most of the papers, with the exception of [4] and[12], are concerned only with feedbacklaws such that the resulting systems are dissipative. As is pointed out at the beginning of [7], the dissipative property demands     

高阶非线性中立型方程正解的渐近性及存在性

本文利用非线性分析中半序方法和增算子不动点定理，对高阶非线性中立型方程正解的渐近性进行了详细分类，并且给出了各种类型正解存在的充要条件和具体例子．     

A ESTIMATE OF THE RATE OF ENTROPY DISSIPATION OF HIGH RESOLUTION MUSCL TYPE GODUNOV SCHEMES

1.IntroductionLetusconsidertheCauchyproblemsfornonlinearhyperbolicscalarconservationlaws:wheref:W~WisLipschitzcontinuousfunctions,andtheinitialdata"o(x)isagivenfunctioninLI(R)nLoo(R).Asitiswell--known,thisproblemingeneraldoesnotadmitsmoothsolution,so...     

高阶退化Bernoulli数和多项式

本文研究了高阶退化Berrioulli数和多项式的两个显明公式，得到了一个包含高阶Bemoulli数和Stirling数的恒等式，并推广了F．H．Howard，S．Shirai和K．I．Sato的结果。     

n阶中立型时滞方程衰减正解的存在性

研究了ｎ阶中立型方程（ｘ（ｔ）－ｃｘ（ｔ－τ）＾（ｎ）＋ｐ（ｔ）ｘ（ｇ（ｔ））＝０，ｔ≥ｔ０，ｎ≥１（＊）正解的存在性，在ｐ（ｔ）常号和变号的情况下，给出了（＊）存在衰减正解的充分条件，特别，这偏离 文「２」，「４－６」和「８－１２」的有关结果。     

Banach空间二阶非线性混合型脉冲微分-积分方程的解

本文在比张金清1999年的文章较弱的条件下,利用一个新的比较结果和Monch不动点定理,研究了Banach空间中二阶非线性混合型脉冲微分-积分方程初值问题解的存在性,改进和推广了郭大钧在1997年和张金清在1999年的论文中的主要结果.     

EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY

This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam's novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.     

ALGORITHMS FOR IMPLEMENTATION OF GENERAL LIMIT REPRESENTATIONS OF GENERALIZED INVERSES

1. Introduction and PreliminariesThe set of all m x n comPlex matrices of rank r is denoted by cy". By I we denote anappropriate ideniity matrix. Also, n(A) denotes the trace of a square matriX A. By n(A) andN(A) are denoted the range and the null space of A, respectively Finally ad(A) and det(A)denote the adoint of the matris A and the determinant of A, respectivelyFOr any matrix A E crxn consider the following equations in X:(1) AXA=A, (2) XAX=X, (3) (AX)*=AX, (4) (XA)*=XAand…     

混合序列加权和的强收敛性

本文给出混合序列加权和的强收敛性的一些充分条件，这些结论推广和改进了文［１］定理３，文［２］定理３；文［３］定理４．１５以及文［４］定理４．     

一般形式的一阶椭圆型偏微分方程组拟线性Riemann-Hilbert问题

在文［ｌ，２，３］中，Ｅ．Ｗｅｇｅｒｔ和Ｌ．Ｖ．Ｗｏｌｆｅｒｓｄｏｒｆ等人讨论了一类全纯函数的拟线性Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ 问题在 Ｈａｒｄｙ空间中的可解性，在文［４］中，讨论了广义解析函数的拟线性 Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ问题，同样得到该边值问题在Ｈ２类解空间中的可解性、本文在前面研究工作的基础上，对一般形式的一阶椭圆型偏微分方程组拟线性Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ问题作了更深入的讨论，在适当的假设条件下，应用积分算子理论，函数论方法及不动点原理，证明了该边值问题在相应的泛函空间中同样是可解的．