HYPER ORDER OF SOLUTIONS TO SOME LINEAR DIFFERENTIAL EQUATIONS IN THE UNIT DISC

In this paper, we investigate the growth of solutions to some linear diferential equations with analytic coefcients in the unit disc. When the coefcients of these equations have some special properties near a point on the boundary of the unit disc, the order and the hyper order of the solutions to these equations are estimated accurately. Especially, our conditions on the coefcients are more general and the results on the hyper order of the solutions are new to some extent.     

The Grouth of Laplace

On the analytic functions defined by exponential series convergent only in the right half plane, Yu Jiarong^[1,2] introduced the order (R) and the order (R-H) and studied some exponential series, Yu Jiuman^[3] introduced the proximate zero order (R) of the functions and obtained some results. For the study of the grouth of LaplaceStieltjes transform, we introduce the order (R) and get some results similar to the case of exponential series.     

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.     

$[p, q]$级整函数系数的二阶线性微分方程的复振荡

In this paper, the authors investigate the zeros and growth of solutions of second order linear differential equations with entire coefficients of [p, q]-order and obtain some results which improve and generalize some previous results.     

Euler数和高阶Euler数的推广

The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.     

Expression of meromorphic solutions of systems of algebraic differential equations with exponential coefficients

Using the Nevanlinna theory of the value distribution of meromorphic functions and theory of differential algebra, we investigate the problem of the forms of meromorphic solutions of some specific systems of generalized higher order algebraic differential equations with exponential coefficients and obtain some results.     

THE INVARIANCE OF SUBCLASSES OF BIHOLOMORPHIC MAPPINGS ON BERGMAN-HARTOGS DOMAINS

We mainly discuss the invariance of some subclasses of biholomorphic mappings under the generalized Roper-Suffridge operators on Bergman-Hartogs domains which are based on the unit ball Bn. Using the geometric properties and the distortion results of subclasses of biholomorphic mappings, we obtain the geometric characters of almost spirallike mappings of type β and order α, S_?~*(β, A, B), strong and almost spirallike mappings of type βand order α maintained under the generalized Roper-Suffridge operators on Bergman-Hartogs domains. Sequentially, we conclude that the generalized operators and the known operators preserve the same properties under some conditions. The conclusions generalize some known results.     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A CLASS OF HIGHER ORDER DIFFERENCE EQUATIONS

In this paper,we study the asymptotic behavior of solutions to a class of higher order difference equations.With the aid of the discrete inequality,we obtain some sufficient conditions which ensure that all the solutions to the equation are some high order of infinities,and also that some conditions which guarantee that every oscillatory solution to the equation has the property that the i order L operator of it tends to infinity when its independent variable tends to zero.     

ON THE GENERALIZED ORDER OF DIRICHLET SERIES

By the method of Knopp-Kojima, the generalized order of Dirichlet series is studied and some interesting relations on the maximum modulus, the maximum term and the coefficients of entire function defined by Dirichlet series of slow growth are obtained,which briefly extends some results of paper [1].     

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.     

关于随机阶的几个结果

在较弱条件下,对独立随机变量序列的极大值序列,给出了几个关于随机阶的结果.     

高阶亚线性Duffing方程的周期解

在本文中，二阶亚线性Ｄｕｆｆｉｎｇ方程周期解存在的结果被推广到高阶Ｄｕｆｆｉｎｇ方：ｘ＾（２ｎ）＋ｇ（ｘ）＝ｐ（ｔ）＝ｐ（ｔ＋２π）（ｎ≥１）和ｘ＾（２ｎ＋１）＋ｇ（ｘ）－ｐ（ｔ）＝ｐ（ｔ＋２π）。     

Classification of Krasner Hyperfields of Order 4

In this paper, first we introduce n-polygroups and characterize 2-polygroups of order 4 up to isomorphism. Then using 2-polygroups we introduce 2-Krasner hyperfields and we show that there exactly exists one 2-Krasner hyperfield of order 4. Moreover, we propose a hyperfield of order 4 which is not as a quotient hyperfield F/G. Finally, some programs written in MATLAB which are based on obtained results compute the number of polygroups, weak polygroups and Krasner hyperfields of order 4 up to isomorphism.     

全平面上零级Dirichlet级数的增长性

在较一般的指数条件下,研究了全平面上零级Dirichlet级数的增长性,得到了一些新的结果.     

一阶中立型时滞微分方程的振动定理

本文证明了常系数一阶中立型微分方程的一个新的振动定理,推广和改进了文献中的若干结果.     

带有最大值项的高阶中立型差分方程的振动性

对一类带有最大值项的高阶中立型差分方程的振动性进行了研究,得到一些方程振动的充分条件,推广和改进了已有的一些结果.     

广义Dirichlet级数的级和型

For an entire function represented by a generalized dirichlet series, we define its maximal term, maximal modulus, order and type. We use the classical methods to study the relation between order, type and coefficients, exponents, which improve and generalize some results of the dirichlet series with real exponents.     

二阶非线性中立型微分方程的振动准则

研究了一类二阶非线性中立型微分方程的振动性,得到了一些新的振动准则,推广、改进和统一了文献中的一些结果.     

一类三阶非线性微分方程的非振荡解

给出了一类三阶非线性微分方程存在非振荡解的充分条件，使得Parhi准则更加一般化。在一些特殊情况下，这些结论适合于更弱的条件。