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 o...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.展开更多
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 st...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.展开更多
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 Vo...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 ).展开更多
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...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.展开更多
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 prese...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.展开更多
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 close...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.展开更多
Bernstein-Kantorovich quasi-interpolants K^（2r-1）n（f, x） are considered and direct, inverse and equivalence theorems with Ditzian-Totik modulus of smoothness ω^2rφ（f, t）p （1 ≤ p ≤＋∞） are obtained.
In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechani...In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.展开更多
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...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。展开更多
目的为克服Lagrange插值多项式不能对任意连续函数都一致收敛的问题,构造了一类二元乘积型三角插值多项式算子使得该算子在全平面上能够一致收敛到每个以2π为周期的二元连续函数。方法通过对Lagrange插值三角多项式的平移与组合,在已...目的为克服Lagrange插值多项式不能对任意连续函数都一致收敛的问题,构造了一类二元乘积型三角插值多项式算子使得该算子在全平面上能够一致收敛到每个以2π为周期的二元连续函数。方法通过对Lagrange插值三角多项式的平移与组合,在已有成果的基础上做了推广,构造了一类形式较为广泛的二元乘积型三角插值多项式Tmn(f;x,y)=sum from κ=0 to 2m sum from l=0 to 2n f(xκ,yl)mακ(x)mβl(x),进而讨论了该算子的逼近性质。结果/结论证明了该算子在全平面上一致收敛到任意以2π为周期的二元连续函数,并且对C2sπ,r,2π(s≤α,r≤β)函数类的逼近均达到最佳收敛阶,即,当f(x,y)∈Cs2,πr,2π,s≤α,r≤β,成立|Tmn(f;x,y)-f(x,y)|=O{Em*n(f)+1/m^sω(~sf/x^s;1/m,0)+r/n^1ω(~rf/y^r;0,1/n)+1/m^s 1/n^rω(^(s+r)f/x^sy^r;1/m,1/n)}。展开更多
文摘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.
基金National Natural Science Foundation of China under Grant Nos.10775097 and 10874174
文摘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.
文摘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 ).
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11175113 and 11147009)the Natural Science Foundation of Shandong Province of China (Grant No. ZR2010AQ027)the Program of Higher Educational Science and Technology of Shandong Province,China (Grant No. J10LA15)
文摘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.
基金supported by the National Natural Science Foundation of China(Grant No.11175113)the Fundamental Research Funds for the Central Universities of China(Grant No.WK2060140013)the Natural Science Foundation of Jiangsu Higher Education Institution of China(Grant No.14KJD140001)
文摘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.
文摘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.
基金Supported by the National Natural Science Foundation of China (1057104010801043)+1 种基金Natural Science Foundation of Hebei Province (08M001)Foundation of Education Department of Hebei Province (2008126)
文摘Bernstein-Kantorovich quasi-interpolants K^（2r-1）n（f, x） are considered and direct, inverse and equivalence theorems with Ditzian-Totik modulus of smoothness ω^2rφ（f, t）p （1 ≤ p ≤＋∞） are obtained.
基金Project supported by the National Natural Science Foundation of China(Grant No.11775208)the Foundation for Young Talents at the College of Anhui Province,China(Grant Nos.gxyq2021210 and gxyq2019077)the Natural Science Foundation of the Anhui Higher Education Institutions of China(Grant Nos.KJ2020A0638 and 2022AH051586)。
文摘In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.
文摘目的为克服Lagrange插值多项式不能对任意连续函数都一致收敛的问题,构造了一类二元乘积型三角插值多项式算子使得该算子在全平面上能够一致收敛到每个以2π为周期的二元连续函数。方法通过对Lagrange插值三角多项式的平移与组合,在已有成果的基础上做了推广,构造了一类形式较为广泛的二元乘积型三角插值多项式Tmn(f;x,y)=sum from κ=0 to 2m sum from l=0 to 2n f(xκ,yl)mακ(x)mβl(x),进而讨论了该算子的逼近性质。结果/结论证明了该算子在全平面上一致收敛到任意以2π为周期的二元连续函数,并且对C2sπ,r,2π(s≤α,r≤β)函数类的逼近均达到最佳收敛阶,即,当f(x,y)∈Cs2,πr,2π,s≤α,r≤β,成立|Tmn(f;x,y)-f(x,y)|=O{Em*n(f)+1/m^sω(~sf/x^s;1/m,0)+r/n^1ω(~rf/y^r;0,1/n)+1/m^s 1/n^rω(^(s+r)f/x^sy^r;1/m,1/n)}。
