This paper analysis the local behavior of the bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin. It is shown that the bivariate quadratic Herm...This paper analysis the local behavior of the bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin. It is shown that the bivariate quadratic Hermite-Padé form always defines a bivariate quadratic function and that this function is analytic in a neighborhood of the origin.展开更多
In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to...In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.展开更多
In this work, a bridge density functional approximation （BDFA） （J. Chem. Phys. 112, 8079 （2000）） for a nonuniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa （HCRY） fluid. It is f...In this work, a bridge density functional approximation （BDFA） （J. Chem. Phys. 112, 8079 （2000）） for a nonuniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa （HCRY） fluid. It is found that the choice of a bulk bridge functional approximation is crucial for both a uniform HCRY fluid and a non-uniform HCRY fluid. A new bridge functional approximation is proposed, which can accurately predict the radial distribution function of the bulk HCRY fluid. With the new bridge functional approximation and its associated bulk second order direct correlation function as input, the BDFA can be used to well calculate the density profile of the HCRY fluid subjected to the influence of varying external fields, and the theoretical predictions are in good agreement with the corresponding simulation data. The calculated results indicate that the present BDFA captures quantitatively the phenomena such as the coexistence of solid-like high density phase and low density gas phase, and the adsorption properties of the HCRY fluid, which qualitatively differ from those of the fluids combining both hard-core repulsion and an attractive tail.展开更多
This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are ...This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are analysed and studied. This paper gives a certain theorem as a general rule to approximate any nonbounded continuous functions.展开更多
A new type of neural network is described, which is basing on Fourier series, and the activation transfer function in its neuron model is sinusoid, ft can approximate to any function, which is continuum in every segme...A new type of neural network is described, which is basing on Fourier series, and the activation transfer function in its neuron model is sinusoid, ft can approximate to any function, which is continuum in every segment, with any precision with by layers only. We also provide the computer approach emulation results of different kinds of static function.展开更多
By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of t...By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.展开更多
Hybrid density functional theory （DFT） calculations are performed to study MC2 （M= V, Cr, Fe and Co） clusters in the neutral and anionic charge states. We find that the equilibrium geometries of MC2 and their anio...Hybrid density functional theory （DFT） calculations are performed to study MC2 （M= V, Cr, Fe and Co） clusters in the neutral and anionic charge states. We find that the equilibrium geometries of MC2 and their anions are all cyclic structures with C2v symmetry, which agrees well with the previous theoretical studies. The Mulliken charge and spin populations of MC2 clusters and their anions are also calculated, and it is found that the electron charge transformations from anions to neutral molecules mainly take place on the M atoms. Time-dependent DFT is used to calculate the excited states, and a theoretical assignment for the features in the experimental photoelectron spectrum is given, which are in good agreement with the available experimental data.展开更多
Appealing to the Clifford analysis and matching pursuits, we study the adaptive decompositions of functions of several variables of finite energy under the dictionaries consisting of shifted Cauchy kernels. This is a ...Appealing to the Clifford analysis and matching pursuits, we study the adaptive decompositions of functions of several variables of finite energy under the dictionaries consisting of shifted Cauchy kernels. This is a realization of matching pursuits among shifted Cauchy kernels in higher-dimensional spaces. It offers a method to process signals in arbitrary dimensions.展开更多
The geometric structure,electronic structure,and optical properties of CdHg（SCN）4 crystal are calculated by using the density functional perturbation theory and Green function screening Coulomb interaction approxima...The geometric structure,electronic structure,and optical properties of CdHg（SCN）4 crystal are calculated by using the density functional perturbation theory and Green function screening Coulomb interaction approximation.The band gap of CdHg（SCN）4 crystal is calculated to be 3.198 eV,which is in good agreement with the experimental value 3.265 eV.The calculated second-order nonlinear optical coefficients are d14 = 1.2906 pm/V and d15 = 5.0928 pm/V,which are in agreement with the experimental results（d14=（1.4 ±0.6） pm/V and d15=（6.0 ±0.9） pm/V）.Moreover,it is found that the contribution to the valence band mainly comes from Cd-4d,Hg-5d states,and the contributions to the valence band top and the conduction band bottom predominantly come from C-2p,N-2p,and S-3p states.The second-order nonlinear optical effect of CdHg（SCN）_4 crystal results mainly from the internal electronic transition of（SCN）^-.展开更多
Fourier modal method incorporating staircase approximation is used to study tapered crossed subwavelength gratings in this paper. Three intuitive formulations of eigenvalue functions originating from the prototype are...Fourier modal method incorporating staircase approximation is used to study tapered crossed subwavelength gratings in this paper. Three intuitive formulations of eigenvalue functions originating from the prototype are presented, and their convergences are compared through numerical calculation. One of them is found to be suitable in modeling the diffraction efficiency of the circular tapered crossed subwavelength gratings without high absorption, and staircase approximation is further proven valid for non-highly-absorptive tapered gratings. This approach is used to simulate the ＂moth-eye＂ antireflection surface on silicon, and the numerical result agrees well with the experimental one.展开更多
基金Supported by the NNSF of China(10271022, 60373093)Supported by the Science and Technology Development Foundation of Education Department of Liaoning Province(2004C060)
文摘This paper analysis the local behavior of the bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin. It is shown that the bivariate quadratic Hermite-Padé form always defines a bivariate quadratic function and that this function is analytic in a neighborhood of the origin.
文摘In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.
基金Project supported by the National Natural Science Foundation of China (Grant No 20673150)
文摘In this work, a bridge density functional approximation （BDFA） （J. Chem. Phys. 112, 8079 （2000）） for a nonuniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa （HCRY） fluid. It is found that the choice of a bulk bridge functional approximation is crucial for both a uniform HCRY fluid and a non-uniform HCRY fluid. A new bridge functional approximation is proposed, which can accurately predict the radial distribution function of the bulk HCRY fluid. With the new bridge functional approximation and its associated bulk second order direct correlation function as input, the BDFA can be used to well calculate the density profile of the HCRY fluid subjected to the influence of varying external fields, and the theoretical predictions are in good agreement with the corresponding simulation data. The calculated results indicate that the present BDFA captures quantitatively the phenomena such as the coexistence of solid-like high density phase and low density gas phase, and the adsorption properties of the HCRY fluid, which qualitatively differ from those of the fluids combining both hard-core repulsion and an attractive tail.
文摘This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are analysed and studied. This paper gives a certain theorem as a general rule to approximate any nonbounded continuous functions.
文摘A new type of neural network is described, which is basing on Fourier series, and the activation transfer function in its neuron model is sinusoid, ft can approximate to any function, which is continuum in every segment, with any precision with by layers only. We also provide the computer approach emulation results of different kinds of static function.
基金Project supported by the National Natural Science Foundation of China(Grant No.10671156)the Natural Science Foundation of Shaanxi Province of China(Grant No.SJ08A05)
文摘By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.
基金Supported by the National Natural Science Foundation of China under Grant No 10174039, the Natural Science Foundation of Jiangsu Province under Grant No BK2002099, and the Science Foundation of Nanjing University of Science and Technology under Grant No AB96129.
文摘Hybrid density functional theory （DFT） calculations are performed to study MC2 （M= V, Cr, Fe and Co） clusters in the neutral and anionic charge states. We find that the equilibrium geometries of MC2 and their anions are all cyclic structures with C2v symmetry, which agrees well with the previous theoretical studies. The Mulliken charge and spin populations of MC2 clusters and their anions are also calculated, and it is found that the electron charge transformations from anions to neutral molecules mainly take place on the M atoms. Time-dependent DFT is used to calculate the excited states, and a theoretical assignment for the features in the experimental photoelectron spectrum is given, which are in good agreement with the available experimental data.
基金supported by Macao FDCT(098/2012/A3)Research Grant of the University of Macao(UL017/08-Y4/MAT/QT01/FST)+1 种基金National Natural Science Funds for Young Scholars(10901166)Sun Yat-sen University Operating Costs of Basic ResearchProjects to Cultivate Young Teachers(11lgpy99)
文摘Appealing to the Clifford analysis and matching pursuits, we study the adaptive decompositions of functions of several variables of finite energy under the dictionaries consisting of shifted Cauchy kernels. This is a realization of matching pursuits among shifted Cauchy kernels in higher-dimensional spaces. It offers a method to process signals in arbitrary dimensions.
基金supported by the National Natural Science Foundation of China(Grant No.51372140)the Youth Scientist Fund of Shandong Province,China(Grant No.BS2011CL025)the Basic Discipline Research Fund of China University of Petroleum,Beijing,China(Grant No.01JB0169)
文摘The geometric structure,electronic structure,and optical properties of CdHg（SCN）4 crystal are calculated by using the density functional perturbation theory and Green function screening Coulomb interaction approximation.The band gap of CdHg（SCN）4 crystal is calculated to be 3.198 eV,which is in good agreement with the experimental value 3.265 eV.The calculated second-order nonlinear optical coefficients are d14 = 1.2906 pm/V and d15 = 5.0928 pm/V,which are in agreement with the experimental results（d14=（1.4 ±0.6） pm/V and d15=（6.0 ±0.9） pm/V）.Moreover,it is found that the contribution to the valence band mainly comes from Cd-4d,Hg-5d states,and the contributions to the valence band top and the conduction band bottom predominantly come from C-2p,N-2p,and S-3p states.The second-order nonlinear optical effect of CdHg（SCN）_4 crystal results mainly from the internal electronic transition of（SCN）^-.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60636030)
文摘Fourier modal method incorporating staircase approximation is used to study tapered crossed subwavelength gratings in this paper. Three intuitive formulations of eigenvalue functions originating from the prototype are presented, and their convergences are compared through numerical calculation. One of them is found to be suitable in modeling the diffraction efficiency of the circular tapered crossed subwavelength gratings without high absorption, and staircase approximation is further proven valid for non-highly-absorptive tapered gratings. This approach is used to simulate the ＂moth-eye＂ antireflection surface on silicon, and the numerical result agrees well with the experimental one.
