AN APPLICATION OF BERNSTEIN-DURRMEYER OPERATORS

In the present paper, we find that the Bernstein-Durrmeyer operators, besides their better applications in approximation theory and some other fields, are good tools in constructing translation network. With the help of the de la Vallée properties of the Bernstein-Durrmeyer operators a sequence of translation network operators is constructed and its degree of approximation is dealt.

APPLICATIONS OF THE BERNSTEIN-DURRMEYER OPERATORS IN ESTIMATING THE NORM OF MERCER KERNEL MATRICES

The paper is related to the norm estimate of Mercer kernel matrices. The lower and upper bound estimates of Rayleigh entropy numbers for some Mercer kernel matrices on [0, 1] × [0, 1] based on the Bernstein-Durrmeyer operator kernel are obtained, with which and the approximation property of the Bernstein-Durrmeyer operator the lower and upper bounds of the Rayleigh entropy number and the l2 -norm for general Mercer kernel matrices on [0, 1] x [0, 1] are provided.

On Weighted L^p-Approximation by Weighted Bernstein-Durrmeyer Operators

In the present paper, we establish direct and converse theorems for weight-ed Bernstein-Durrmeyer operators under weighted L^p-norm with Jacobi weight w（x）=x^a（1-x）β.All the results involved have no restriction a,β〈1-1/p,which indicates that the weighted Bemstein-Durrmeyer operators have some better approxi- mation properties than the usual Bernstein-Durrmeyer operators.

APPLICATIONS OF BERNSTEIN-DURRMEYER OPERATORS IN ESTIMATING THE COVERING NUMBER

The paper deals with estimates of the covering number for some Mercer kernel Hilbert space with Bernstein-Durrmeyer operators. We first give estimates of l2- norm of Mercer kernel matrices reproducing by the kernelsK（α,β）（x,y）：=∑∞k=0 Ck（α,β）（x）Qk（α,β）（y）,where Qk（α,β） （x） are the Jacobi polynomials of order k on （0, 1 ）, Ck（α,β） 〉 0 are real numbers, and from which give the lower and upper bounds of the covering number for some particular reproducing kernel Hilbert space reproduced by Kα,β （x, y）.

GLOBAL SMOOTHNESS PRESERVATION BY BIVARIATE INTERPOLATION OPERATORS

Extending the results of [4] in the univariate case, in this paper we prove that the bivariate interpolation polynomials of Hermite-Fejér based on the Chebyshev nodes of the first kind, those of Lagrange based on the Chebyshev nodes of second kind and ±1, and those of bivariate Shepard operators, have the property of partial preservation of global smoothness, with respect to various bivariate moduli of continuity.

SOME APPROXIMATION THEOREMS FOR MODIFIED BERNSTEIN-DURRMEYER OPERATORS

The modified Bernstein-Durrmeyer operators discussed in this paper are given by M_nf≡M_n(f,x)=(n+2)P_(n,k)∫_0~1p_n+1.k(t)f(t)dt, where We will show,for 0<α<1 and 1≤p≤∞ M,f-f_p=O(n^-a)ω_Φ~2(f,t)_p=O(t^(2a)), |M_n f-f(x)|≤M(x(1-x)/n+1/_n2)~a/2ω(f,t)=O(t^a), where otherwise.

Approximation Theorems of Bernstein-Durrmeyer Operators in L_M^（Ba） Spaces

With the weighted modulus of smoothness as a metric,we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in LBa M spaces. Especially an approximation equivalent theorem of the operators is also obtained.

APPROXIMATION BY A CLASS OF AIODIFIED BERNSTEIN-DURRMEYER OPERATORS

We modify Bernstein-Durrmeyer operators by means of digonal matarix which overeome a difficulty in extending a Berens-Lorentz result to the Bernstein-Durrmeyer operators for second order of smoothness. The direct and converse theorems for these operators in L_p are also presented by Ditzian-Totik, modulus of smoothness.

Stechkin-Marchaud Type Inequalities in Lp for Linear Combination of Bernstein-Durrmeyer Operators

In this paper, we use the equivalence relation between K-functional and modulus of smoothness, and give the Stechkin-Marchaud-type inequalities for linear combination of Bernstein-Durrmeyer operators . Moreover, we obtain the inverse result of approximation for linear combination of Bernstein-Durrmeyer operators with . Meanwhile we unify and extend some previous results.

L^p APPROXIMATION BY GENERAL BERNSTEIN-DURRMEYER OPERATOR DEFINED ON SIMPLEX

As a generalization of the Bernstein-Durrmeyer operatora defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong direct theorem and an inverse theorem of weak type for these operators by using a decom-position way. From the theorems the characterization of Lp approximation behavior is derived.

Generalized Wigner Operator and Bivariate Normal Distribution in p-q Phase Space

We introduce a kind of generalized Wigner operator,whose normally ordered form can lead to the bivariatenormal distribution in p-q phase space.While this bivariate normal distribution corresponds to the pure vacuum state inthe generalized Wigner function phase space,it corresponds to a mixed state in the usual Wigner function phase space.

A BIVARIATE EXTENSION OF BLEIMANN-BUTZER-HAHN OPERATOR

Let C(R_+~2) be a class of continuous functions f on R+2. A bivariate extension Ln(f,x,y) of Bleimann-Butzer-Hahn operator is defined and its standard convergence properties are given. Moreover, a local analogue of Voronovskaja theorem is also given for a subclass of C(R+2 ).

二元Bernstein-Durrmeyer算子在Orlicz空间中的逼近定理

研究了二元Bernstein-Durrmeyer算子在Orlicz空间中的逼近性质,应用Jensen不等式和Höder不等式,以及定义在Orlicz空间中的K-泛函,推出了其在Orlicz空间中逼近正定理和逆定理.

A generalized Weyl-Wigner quantization scheme unifying P-Q and Q-P ordering and Weyl ordering of operators

By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral （dyduexp [iu（q-Q）＋iy（p-P）＋is/2yu]） from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented.

Generating function of product of bivariate Hermite polynomials and their applications in studying quantum optical states

By virtue of the operator-Hermite-polynomial method, we derive some new generating function formulas of the product of two bivariate Hermite polynomials. Their applications in studying quantum optical states are presented.

Maximum Entropy Empirical Likelihood Methods Based on Bivariate Laplace Transforms and Moment Generating Functions

Maximum Entropy Empirical Likelihood (MEEL) methods are extended to bivariate distributions with closed form expressions for their bivariate Laplace transforms (BLT) or moment generating functions (BMGF) without closed form expressions for their bivariate density functions which make the implementation of the likelihood methods difficult. These distributions are often encountered in joint modeling in actuarial science and finance. Moment conditions to implement MEEL methods are given and a bivariate Laplace transform power mixture (BLTPM) is also introduced, the new operator generalizes the existing univariate one in the literature. Many new bivariate distributions including infinitely divisible(ID) distributions with closed form expressions for their BLT can be created using this operator and MEEL methods can also be applied to these bivariate distributions.

Simultaneous Approximation by Modified Bernstein-Durrmeyer Operators *

The aim of the present paper is to prove direct and converse results for simultaneous approximation by modified Bernstein-Durrmeyer operators. A point-wise equivalence characterization of simultaneous approximation is obtained.

二元Baskakov算子的一致逼近

Baskakov算子也是一类很重要的正线性算子 ,在其它领域 (如概率及其它学科 )都应用很广 。

二元Bernstein型算子的Lipschitz性质

本文定义了二元Bernstein型算子,研究了其一个重要性质:函数与算子属于同一Lipschitz类。

应用Open Meta-Analysis软件实现诊断准确性试验的Meta分析

Open Meta-Analysis软件是用于二分类数据、连续型数据以及诊断数据Meta分析的开放软件,该软件提供了四种模型来执行诊断准确性试验的Meta分析,即诊断随机效应模型、倒方差混合效应模型、双变量模型和分层综合受试者工作特征曲线法,其中前两者为单变量模型,只能执行单个指标合并,而后两者为双变量模型,能够对灵敏度和特异度之间的负相关性进行综合分析。本文以实例就Open Meta-Analysis软件实现诊断准确性试验Meta分析做相关简述。