Jacobi Polynomial Estimates and Fourier-Laplace Convergence

ＪａｃｏｂｉＰｏｌｙｎｏｍｉａｌＥｓｔｉｍａｔｅｓａｎｄＦｏｕｒｉｅｒ－ＬａｐｌａｃｅＣｏｎｖｅｒｇｅｎｃｅＧａｖｉｎＢｒｏｗｎ（ＴｈｅＵｎｉｖｅｒｓｉｔｙｏｆＡｄｅｌａｉｄｅ，Ａｄｅｌａｉｄｅ）ＳｏｕｔｈＡｕｓｔｒａｌｉａ，５００５ＷａｎｇＫｕｎｙ...     

INSTRUCTIONS TO AUTHORS

ＩＮＳＴＲＵＣＴＩＯＮＳＴＯＡＵＴＨＯＲＳ１．ＴｈｅＣｈｉｎｅｓｅＡｎｎａｌｓｏｆＭａｔｈｅｍａｔｉｃｓ（ＣＡＭ）Ｓｅｒ．Ｂｉｓａｃｏｍｐｒｅｈｅｎｓｉｖｅｍａｔｈｅｍａｔｉｃａｌｊｏｕｒｎａｌｃａｒｙｉｎｇｏｒｉｇｉｎａｌｐａｐｅｒｓｏｎｐｕｒｅａ...     

INSTRUCTIONS TO AUTHORS

ＩＮＳＴＲＵＣＴＩＯＮＳＴＯＡＵＴＨＯＲＳ￥／／１．ＴｈｅＣｈｉｎｅｓｅＡｎｎａｌｓｏｆＭａｔｈｅｍａｔｉｃｓ（ＣＡＭ）Ｓｅｒ．Ｂｉｓａｃｏｍｐｒｅｈｅｎｓｉｖｅｍａｔｈｅｍａｔｉｃａｌｊｏｕｒｎａｌｃａｒｒｙｉｎｇｏｒｉｇｉｎａｌｐａｐｅｒｓｏｎｐ...     

INSTRUCTIONS TO AUTHORS

ＩＮＳＴＲＵＣＴＩＯＮＳＴＯＡＵＴＨＯＲＳ１．ＴｈｅＣｈｉｎｅｓｅＡｎｎａｌｓｏｆＭａｔｈｅｌｌｌａｔｉｃｓ（ＣＡＭ）Ｓｉｒ．Ｂｉｓａｃｏｍｐｒｅｈｅｎｓｉｖｅｍａｔｈｅｍａｔｉｃａｌｊｏｕｒｌｌａｌｃａｒｒｙｉｎｇｏｒｉｇｉｎａｌｐａｐｅｒｓｏｎｐ...     

INSTRUCTIONS TO AUTHORS

ＩＮＳＴＲＵＣＴＩＯＮＳＴＯＡＵＴＨＯＲＳ￥１．ＴｈｅＣｈｉｎｅｓｅＡｎｎａｌｓｏｆＭａｔｈｅｍａｔｉｃｓ（ＣＡＭ）Ｓｅｒ．Ｂｉｓａｃｏｍｐｒｅｈｅｎｓｉｖｅｍａｔｈｅｍａｔｉｃａｌｊｏｕｒｎａｌｃａｒｒｙｉｎｇｏｒｉｇｉｎａｌｐａｐｅｒｓｏｎｐｕｒ...     

The Spectral Pictures of Completely Irreducible Operators and Decomposition Theorem Of Hilbert Space Operators

ＴｈｅＳｐｅｃｔｒａｌＰｉｃｔｕｒｅｓｏｆＣｏｍｐｌｅｔｅｌｙＩｒｒｅｄｕｃｉｂｌｅＯｐｅｒａｔｏｒｓａｎｄＤｅｃｏｍｐｏｓｉｔｉｏｎＴｈｅｏｒｅｍｏｆＨｉｌｂｅｒｔＳｐａｃｅＯｐｅｒａｔｏｒｓ￥ＪｉａｎｇＣｈｕｎｌａｎ（蒋春澜）（Ｄｅｐａｒｔｍｅｎ...     

INSTRUCTIONS TO AUTHORS

ＩＮＳＴＲＵＣＴＩＯＮＳ ＴＯ ＡＵＴＨＯＲＳ￥／／１．ＴｈｅＣｈｉｎｅｓｅＡｌｌｎａｌｓｏｆＭａｔｈｅｍａｔｉｃｓ（ＣＡＭ）Ｓｅｒ．Ｂｉｓａｃｏｍｐｒｅｈｅｎｓｉｖｅｍａｔｈｅｍａｔｉｃａｌｊｏｕｒｌｌａｌｃａｒｒｙｉｎｇｏｒｉｇｉｎａｌｐａｐｅｒ...     

INSTRUCTIONS TO AUTHORS

ＩＮＳＴＲＵＣＴＩＯＮＳＴＯＡＵＴＨＯＲＳ￥／／１．ＴｈｅＣｈｉｎｅｓｅＡｎｎａｌｓｏｆＭａｔｈｅｍａｔｉｃｓ（ＣＡＭ）Ｓ．ｅｒ．Ｂｉｓａｃｏｍｐｒｅｈｅｎｓｉｖｅｍａｔｈ．ｅｍａｔｉｃａｌｊｏｕｒｎａｌｃａｒｒｙｉｎｇｏｒｉｇｉｎａｌｐａｐｅｒｓｏ...     

L~∞ESTIMATE FOR SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS IN R~N

Ｌ~∞ＥＳＴＩＭＡＴＥＦＯＲＳＯＬＵＴＩＯＮＳＯＦＮＯＮＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳＩＮＲ~ＮＬｉＧｏｎｇｂａｏ（李工宝）（Ｉｎｓｔ．ｏｆＭａｔｈ．Ｓｃｉ．，ＴｈｅＣｈｉｎｅｓｅＡｃａｃｌｅｍｙｏｆＳｃｉｅｎｃｅｓＳｉｎｉｃａ，ＰＯＢ...     

Boundary Value Problems for Nonlinear Differential Equations of Second Order inBanach Spaces

ＢａｎａｃｈＳｐａｃｅｓＢｏｕｎｄａｒｙＶａｌｕｅＰｒｏｂｌｅｍｓｆｏｒＮｏｎｌｉｎｅａｒＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓｏｆＳｅｃｏｎｄＯｒｄｅｒｉｎＢａｎａｃｈＳｐａｃｅｓＣｕｉＣｈａｎｇｊｕｎＬｉｕＹａｎｓｈｅｎｇ（Ｄｅｐｔ．ｏｆＭａ...     

Two Numerical Methods for Computing the Probability of Outcome of a Battle of Lanchester Type

Methods are developed for the computation of victory probabilities in the classical Lanchester ‘modern warfare’ model. The first method employs a bivariate normal approximation for state probabilities and a kind of steepest descents technique for the evaluation of the integral: the second proposes a truncated binomial approximation along certain diagonal lines. Both methods depend on moments. Computational performance is discussed.     

Quantitative estimations of bivariate summation‐integral–type operators

In this paper, we study the approximation properties of bivariate summation‐integral–type operators with two parameters . The present work deals within the polynomial weight space. The rate of convergence is obtained while the function belonging to the set of all continuous and bounded function defined on ([0],∞)(×[0],∞) and function belonging to the polynomial weight space with two parameters, also convergence properties, are studied. To know the asymptotic behavior of the proposed bivariate operators, we prove the Voronovskaya type theorem and show the graphical representation for the convergence of the bivariate operators, which is illustrated by graphics using Mathematica. Also with the help of Mathematica, we discuss the comparison by means of the convergence of the proposed bivariate summation‐integral–type operators and Szász‐Mirakjan‐Kantorovich operators for function of two variables with two parameters to the function. In the same direction, we compute the absolute numerical error for the bivariate operators by using Mathematica and is illustrated by tables and also the comparison takes place of the proposed bivariate operators with the bivariate Szász‐Mirakjan operators in the sense of absolute error, which is represented by table. At last, we study the simultaneous approximation for the first‐order partial derivative of the function.     

Some approximation properties by a class of bivariate operators

Starting with the well‐ known Bernstein operators, in the present paper, we give a new generalization of the bivariate type. The approximation properties of this new class of bivariate operators are studied. Also, the extension of the proposed operators, namely, the generalized Boolean sum (GBS) in the Bögel space of continuous functions is given. In order to underline the fact that in this particular case, GBS operator has better order of convergence than the original ones, some numerical examples are provided with the aid of Maple soft. Also, the error of approximation for the modified Bernstein operators and its GBS‐type operator are compared.     

一个二元矩阵插值连分式的展开式

本文借助于文[1]定义的一种实用的矩阵广义逆,构造了一个二元Stieltjes型矩阵值插值连分式的展开式,它的截断分式可以定义二元矩阵值插值函数.     

二元Jackson插值多项式及其在Orlicz空间中的逼近阶

本文引进了Ｋａｎｔｏｒｏｖｉｔｃｈ算子型的二元修正Ｊａｃｋｓｏｎ三角插值多项式，给出了其在Ｏｒｌｉｃｚ空间中的收敛阶，作了推论，给出了二元修正Ｈｅｒｍｉｔｅ－Ｆｅｊｅｒ插值算子在带Ｏｒｌｉｃｚ空间中的逼近的量化估计。     

Kantorovich variant of a new kind of q‐Bernstein–Schurer operators

Ren and Zeng (2013) introduced a new kind of q‐Bernstein–Schurer operators and studied some approximation properties. Acu et al. (2016) defined the Durrmeyer modification of these operators and studied the rate of convergence and statistical approximation. The purpose of this paper is to introduce a Kantorovich modification of these operators by using q‐Riemann integral and investigate the rate of convergence by means of the Lipschitz class and the Peetre's K‐functional. Next, we introduce the bivariate case of q‐Bernstein–Schurer–Kantorovich operators and study the degree of approximation with the aid of the partial modulus continuity, Lipschitz space, and the Peetre's K‐functional. Finally, we define the generalized Boolean sum operators of the q‐Bernstein–Schurer–Kantorovich type and investigate the approximation of the Bögel continuous and Bögel differentiable functions by using the mixed modulus of smoothness. Furthermore, we illustrate the convergence of the operators considered in the paper for the univariate case and the associated generalized Boolean sum operators to certain functions by means of graphics using Maple algorithms. Copyright © 2017 John Wiley & Sons, Ltd.     

SINGULAR INTEGRAL OPERATORS AND SINGULAR QUADRATURE OPERATORS ASSOCIATED WITH SINGULAR INTEGRAL EQUATIONS OF THE FIRST KIND AND THEIR APPLICATIONS

ＳＩＮＧＵＬＡＲＩＮＴＥＧＲＡＬＯＰＥＲＡＴＯＲＳＡＮＤＳＩＮＧＵＬＡＲＱＵＡＤＲＡＴＵＲＥＯＰＥＲＡＴＯＲＳＡＳＳＯＣＩＡＴＥＤＷＩＴＨＳＩＮＧＵＬＡＲＩＮＴＥＧＲＡＬＥＱＵＡＴＩＯＮＳＯＦＴＨＥＦＩＲＳＴＫＩＮＤＡＮＤＴＨＥＩＲＡＰＰＬＩＣＡＴＩ...     

一种四次有理插值样条及其逼近性质

1引言有理样条函数是多项式样条函数的一种自然推广,但由于有理样条空间的复杂性,所以有关它的研究成果不象多项式样条那样完美,许多问题还值得进一步的研究．近几十年来,有理插值样条,特别是有理三次有理插值样条,由于它们在曲线曲面设计中的应用,已有许多学者进行了深入研究,取得了一系列的成果(见[1]-[7])．但四次有理插值样条由于其构造所花费的计算量太大以及在使用上很不方便而让人们忽视了其重要的应用价值,因此很少有人研究他们．实际上,在某些情况下四次有理插值样条有其独特的应用效果,如文[8]建立的一种具有局部插值性质的分母为二次的四次有理样条,即一个剖分     

GLOBAL SMOOTHNESS PRESERVATION BY BIVARIATE INTERPOLATION OPERATORS

1　IntroductionIn the case when Pn(f,x) represents the univariate interpolation polynomial of Her-mite-Fejér based on Chebyshev nodesof the firstkind or the univariate interpolation polyno-mials of Lagrange based on Chebyshev nodes of the second kind and± 1 ,or the univariaterational Shepard operators,the following result of partial preservation of global smoothnessis proved in[4] :If f∈Lip M(α;[-1 ,1 ] ) ,0 <α≤ 1 ,then there existsβ=β(α) <α and M′>such thatω(Pn(f ) ;h)≤ M′h…     

Adaptive Bivariate Chebyshev Approximation

We propose an adaptive algorithm which extends Chebyshev series approximation to bivariate functions, on domains which are smooth transformations of a square. The method is tested on functions with different degrees of regularity and on domains with various geometries. We show also an application to the fast evaluation of linear and nonlinear bivariate integral transforms.