UNIQUENESS OF MEROMORPHIC OR ENTIRE FUNCTIONS AND THEIR DIFFERENTIAL POLYNOMIALS

This article studies the problem of uniqueness of two entire or meromorphic functions whose differential polynomials share a finite set. The results extend and improve on some theorems given in [3].

On the Growth and Polynomial Coefficients of Entire Series

In this paper we have generalized some results of Rahman [1] by considering the maximum of |f(z)| over a certain lemniscate instead of considering the maximum of|f(z)|, for |z|=r and obtain the analogous results for the entire function |f(z)|=Σpk(z) [q(z)]k-1 where q(z) is a polynomial of degree m and pk(z)is of degree m-1. Moreover, we have obtained some inequalities on the lover order, type and lower type in terms of polynomial coefficients.

A comparison of piecewise cubic Hermite interpolating polynomials,cubic splines and piecewise linear functions for the approximation of projectile aerodynamics

Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.

ON THE COEFFICIENTS OF DIFFERENTIATED EXPANSIONS AND DERIVATIVES OF CHEBYSHEV POLYNOMIALS OF THE THIRD AND FOURTH KINDS

Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds themselves are proved. Two other explicit formulae which express the third and fourth kinds Chebyshev expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of their original expansion coefficients are also given. Two new reduction formulae for summing some terminating hypergeometric functions of unit argument are deduced. As an application of how to use Chebyshev polynomials of the third and fourth kinds for solving high-order boundary value problems, two spectral Galerkin numerical solutions of a special linear twelfth-order boundary value problem are given.

Generalization of Uniqueness Theorems for Entire and Meromorphic Functions

In this paper, we deal with the uniqueness problems on entire and meromorphic functions con- cerning differential polynomials that share fixed-points. Moreover, we generalise and improve some results of Weichuan Lin, Hongxun Yi, Meng Chao, C. Y. Fang, M. L. Fang and Junfeng xu.

Uniqueness of Meromorphic Functions with Their Nonlinear Differential Polynomials Share a Small Function

In this paper we deal with the uniqueness of meromorphic functions when two nonlinear differential polynomials generated by two meromorphic functions share a small function. We consider the case for some general differential polynomials [fnP(f)f,] where P(f) is a polynomial which generalize some result due to Abhijit Banerjee and Sonali Mukherjee [1].

Entire functions sharing one small function

The uniqueness problem of entire functions sharing one small function was studied. By Picard＇s Theorem, we proved that for two transcendental entire functionsf（z） and g（z）, a positive integer n≥9, and a（z） （not identically eaqual to zero） being a common small function related to f（z） and g（z）, iffn（z）（f（z）-1）f＇（z） and gn（z）（g（z）-1）g＇（z） share a（z） ca, where CM is counting multiplicity, then g（z） ≡f（z）. This is an extended version of Fang and Hong＇s theorem [ Fang ML, Hong W, A unicity theorem for entire functions concerning differential polynomials, Journal of Indian Pure Applied Mathematics, 2001, 32 （9）： 1343-1348].

On a subclass of bi-univalent functions defined by convex combination of order α with the Faber polynomial expansion

In this paper,we define new subclasses of bi-univalent functions involving a differ-ential operator in the open unit disc△={z:z∈C and|z|<1}:Moreover,we use the Faber polynomial expansion to obtain the bounds of the coefficients for functions belong to the subclasses.

n 的多项式为系数的幂级数和函数注记

研究了以n的多项式为系数的幂级数的和函数的求解问题,给出了这类幂级数和函数的一种求解方法,并得到了其和函数的通用计算公式,通过实例验证了公式的正确性.文中还得到了两个关于组合数的等式.

On Miranda's Normal Criterion

In this paper, we study the normality of a family of analytic functions and prove the following theorem. Let F be a family of analytic functions in a domain D , k be a positive integer and a(z) , a 1(z) , a 2(z) , ... , a k(z) be analytic in D such that a(z)0 . If f(z)≠0 and the zeros of f (k) (z)+a 1(z)f (k-1) (z)+...+a k(z)f(z)-a(z) are of multiplicity at least 2 for each f∈F , then F is normal in D . This result improves Miranda s norm...

Generalization of Uniqueness of Meromorphic Functions Sharing Fixed Point

In this paper, we study the uniqueness problems of entire and meromorphic functions concerning differential polynomials sharing fixed point and obtain some results which generalize the results due to Subhas S. Bhoosnurmath and Veena L. Pujari [1].

高阶线性微分方程解的完全正规增长性

研究高阶线性微分方程完全正规增长性解的存在性,其中方程的控制系数为指数多项式.运用指数多项式的Nevanlinna特征,得到方程不存在完全正规增长性解的判定条件.同时,对具有指数多项式解的高阶线性微分方程,给出了方程解的表示形式与控制系数之间的关系.

Uniqueness of Entire Functions Related to Difference Polynomials

With the notion of weakly weighted sharing and relaxed weighted sharing,we investigate the uniqueness problems of certain type of difference polynomials sharing a small function.The results of the paper extend and generalize some recent results due to Meng(Math.Bohem.139:89-97,2014).

龙格现象难题破解之系数与阶次双确定方法

龙格现象指出,使用基于等距节点的高阶插值多项式逼近龙格函数时,插值多项式在逼近区间两端会产生明显的振荡现象。因此,传统认为,不适宜用基于等距节点的高阶多项式逼近龙格函数。针对龙格现象,展示一种新型的多项式系数与阶次双确定方法。该方法可快速构造出基于等距节点的不会振荡且有较高逼近精度的高阶多项式,良好地逼近龙格函数。计算机数值实验表明该方法是有效的,即运用基于等距节点的高阶多项式可以很好地消解龙格现象。

基于RGB色彩空间的彩色图像混合编码

在RGB色彩空间,利用彩色图像3个色彩分量之间存在的密切的相关性,建立它们之间的多项式相关函数。选择其中一个色彩分量用JPEG2000进行编码,依据该色彩分量与另两个色彩分量的差值分布均匀程度,用四叉树算法将图像分割成若干个不重叠的子块,用多项式相关函数计算出每个子块色彩分量之间的相关系数,由此对另两个色彩分量的编码就转变成对相关系数的编码。解码则是通过JPEG2000的逆变换得到一个重构的色彩分量,再由这个重构的色彩分量和重构的相关系数解得另两个色彩分量。实验结果表明,该方法不仅编解码速度快,而且信噪比、压缩比及视觉效果明显优于JPEG2000等算法的编码结果。

亚纯函数的微分多项式的唯一性

讨论亚纯函数的微分多项式分担一个有限集的唯一性问题,推广了已有的一些结果.

大规模柱面频率选择表面电磁特性分析

为了实现对大规模柱面频率选择表面(FSS)电磁特性的全波分析,该文对简化的子全域(SSED)基函数方法进行了修正,给出了一种分列提取基函数的SSED处理技术。通过经典矩量法求解单个单元面上的电流分布,并将其作为相应柱面阵列的基函数,同样采取矩量法模拟单元之间的耦合,进而求解整个阵列的透射系数和雷达散射截面。所给典型目标的电磁特性计算结果与商用软件仿真结果吻合良好,验证了该文修正技术的有效性。研究结果为工程应用中曲面FSS的设计提供了理论支持。

涉及微分多项式的亚纯函数的唯一性

设ｆ（ｚ）是非常数的整函数，ｎ是正整数，Ｆ（ｚ）＝ｆ￣（ｎ）（ｚ）＋ａ＿１（ｚ）ｆ￣（ｎ－１）（ｚ）＋…＋ａ＿ｎ（ｚ）ｆ（ｘ），其中ａ＿１（ｚ），ａ＿２（ｚ），…，ａ＿ｎ（ｚ）均是ｆ（ｚ）的小函数，本文证明了：若ｆ（ｚ）和Ｆ（ｚ）几乎ＣＭ分担两个不同的有穷复数ａ和ｂ，则ｆ（ｚ）≡Ｆ（ｚ）．

系数空间中多项式的鲁棒稳定性和有理函数的严格正实不变性

本文在多项式的系数空间中讨论离散时间意义下多项式的鲁棒稳定性和有理函数的严格正实不变性,证明了对于系数空间中的某种超矩形,其顶点多项式的稳定性就保证了全族无穷多个多项式的稳定性;对于有理函数的严格正实性,本文也得到了类似的结论。

数字图像相关中非迭代相关系数曲面拟合算法的研究

相关系数曲面拟合算法是数字图像相关中一种简单而有效的亚像素位移求解方法,具有计算效率高、实时性好等优点。在相关系数曲面拟合算法中,二元二次多项式曲面拟合算法和二元高斯曲面拟合算法可通过直接推导出的解析解获得亚像素位移量,无需迭代计算,且二元高斯曲面拟合算法无需对拟合后曲面函数求导获得极值点位置。因此对上述两种简单而非迭代的曲面拟合算法性能进行了研究。应用真实散斑图像从两种算法的计算精度与效率两方面进行了对比实验。实验结果表明,二元高斯曲面拟合算法具有较高的计算精度,且两种算法在相同的条件下的计算效率并无实质性的差异。