Polynomial Asymptotics of Entire Functions of Finite Order

We obtain new asymptotic relations for entire functions of finite order with zeros on a ray under the condition of regular growth for the counting function of their zeros. These relations improve the well-known results of Valiron.     

A Quasi-Interpolation Satisfying Quadratic Polynomial Reproduction with Radial Basis Functions

In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by making convolution integral with a constructed spline and a given radial basis function.In particular,for twicely differ- entiable function the proposed method provides better approximation and also takes care of derivatives approximation.     

关于多项式函数的计数

Polynomial functions （in particular, permutation polynomials） play an important role in the design of modern cryptosystem. In this note the problem of counting the number of polynomial functions over finite commutative rings is discussed. Let A be a general finite commutative local ring. Under a certain condition, the counting formula of the number of polynomial functions over A is obtained. Before this paper, some results over special finite commutative rings were obtained by many authors.     

On the Convergence of Polynomial Approximation of Rational Functions

This paper investigates the convergence condition for the polynomial approximation of rational functions and rational curves. The main result, based on a hybrid expression of rational functions (or curves), is that two-point Hermite interpolation converges if all eigenvalue moduli of a certainr×rmatrix are less than 2, whereris the degree of the rational function (or curve), and where the elements of the matrix are expressions involving only the denominator polynomial coefficients (weights) of the rational function (or curve). As a corollary for the special case ofr=1, a necessary and sufficient condition for convergence is also obtained which only involves the roots of the denominator of the rational function and which is shown to be superior to the condition obtained by the traditional remainder theory for polynomial interpolation. For the low degree cases (r=1, 2, and 3), concrete conditions are derived. Application to rational Bernstein–Bézier curves is discussed.     

On Polynomial Functions over Finite Commutative Rings

Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditions for a function to be a polynomial function over some special finite commutative local rings were obtained.     

Polynomial Reproduction in Subdivision

We study conditions on the matrix mask of a vector subdivision scheme ensuring that certain polynomial input vectors yield polynomial output again. The conditions are in terms of a recurrence formula for the vectors which determine the structure of polynomial input with this property. From this recurrence, we obtain an algorithm to determine polynomial input of maximal degree. The algorithm can be used in the design of masks to achieve a high order of polynomial reproduction.     

On the Order of Strongly Starlikeness of Convex Functions of Order Alpha

In this work the order of strongly starlikeness of convex functions of order alpha is discussed.     

On the Pseudo-Primeness of Meromorphic Functions of Infinite Order

In this paper the pseudo -primeness of meromorphic functions of infinite order is dissoussed in detail and quite a few result are obtained, which are improvments of that of Ozawa.     

On Some Problems of Polynomial Approximation of Entire Transcendental Functions

For entire transcendental functions of finite generalized order, we obtain limit relations between the growth characteristic indicated above and sequences of their best polynomial approximations in certain Banach spaces (Hardy spaces, Bergman spaces, and spaces ).     

亚纯函数及其导数多项式的值分布

本文主要得到亚纯函数及其导数的多项式的零点的定量估计，推广并改进了Ｗ．Ｋ．Ｈａｙｍａｎ及敖海龙等人的有关结果．     

On Bers Generating Functions for First Order Systems of Mathematical Physics

Considering one of the fundamental notions of Bers’ theory of pseudoanalytic functions the generating pair via an intertwining relation we introduce its generalization for biquaternionic equations corresponding to different first-order systems of mathematical physics with variable coefficients. We show that the knowledge of a generating set of solutions of a system allows one to obtain its different form analogous to the complex equation describing pseudoanalytic functions of the second kind and opens the way for new results and applications of pseudoanalytic function theory. As one of the examples the Maxwell system for an inhomogeneous medium is considered, and as one of the consequences of the introduced approach we find a relation between the time-dependent one-dimensional Maxwell system and hyperbolic pseudoanalytic functions and obtain an infinite system of solutions of the Maxwell system. Other considered examples are the system describing force-free magnetic fields and the Dirac system from relativistic quantum mechanics.     

Optimization of Polynomial Fractional Functions

A new approach is proposed for optimizing a polynomial fractional function under polynomial constraints, or more generally, a synomial fractional function under synomial constraints. The approach is based on reformulating the problem as the optimization of an increasing function under monotonic constraints.     

Some Polynomial Expansions for Functions of Several Variables

In the present paper three new expansion formulae are givenfor a function of several variables, which is defined by a multiplepower series with arbitrary terms. It is also indicated howthese general results can be applied to derive various knownor new multiplication theorems for certain hypergeometric functionsof one and more variables.     

矩阵函数计算的插值多项式方法

矩阵函数是数学专业课程中的重要内容之一,也是部分非数学类专业课程中的内容.关于矩阵函数符号计算的传统教学方法,是借助矩阵的Jordan标准形,这种方法需要求出矩阵到Jordan标准形的过渡矩阵,运算相对复杂.利用插值多项式计算矩阵函数的方法,可以避开计算过渡矩阵,节省教学时间,并能起到很好的教学效果.     

On the Distribution of Alternation Points in Uniform Polynomial Approximation of Entire Functions

We consider the distribution of alternation points in best real polynomial approximation of a functionf∈C[−1, 1]. For entire functionsfwe look for structural properties of f that will imply asymptotic equidistribution of the corresponding alternation points.     

关于α阶星像函数类的一个子类

设f(z)=z+…在单位圆|z|<1内解析.给定λ(0≤λ<1),我们定义线性算子Ω^λ Ω^λf=Γ(2-λ)z^λD_z^λf(z);和Ω^n+λf=Ωⁿ(Ω^λf),n∈N∪{0}.其中D_z^λf(z)表示f(z)的分数阶导数且Ω¹ f(z)=zf′(z).用A_{n相似文献}   

$\alpha$阶星象亚纯函数

令$S(p)$表示单位圆盘$\mathbb{D}$上在$p\in(0,1)$处有一个简单极点的单叶亚纯函数全体.令$\alpha\in[0,1)$,我们用$\Sigma^{*}(p,\omega_{0},\alpha)$表示$f\in S(p)$使得$\hat{\mathbb{C}}\setminus f(\mathbb{D})$是关于不动点$\omega_{0}\neq0$, $\infty$星象的$\alphga$阶区域的函数全体.在本文中,$f\in\Sigma^{*}(p,\omega_{0},\alpha)$的一些解析刻画条件和系数估计被考虑.