The exact classical limits for the coefficient of variation c for the normal distribution are derived. The hand-calculating approximated classical limits for c having high accuracy are given to meet practical engineer...The exact classical limits for the coefficient of variation c for the normal distribution are derived. The hand-calculating approximated classical limits for c having high accuracy are given to meet practical engineering needs. Using Odeh and Owen's computational method and Brent's algorithm, the tables for the r-upper exact classical limits of coefficient of variation for normal distribution are calculated for the different confidence coefficient y, the sample size n=1(1)30,40,60,120, the sample coefficient of variation c=0.01(0.01)0.20. It is shown that if n<8,c<0.20, then the V -upper exact classical limits cu for c are slightly higher than the exact fiducial limits cu,F for c if. n>8, c<0.02,then cu-cu,f<5x10-6展开更多
A technique for coherent imaging based on spatial frequency heterodyning is described. Three images corresponding to three physical measurements are recorded. For the first measurement, a scene is simply illuminated w...A technique for coherent imaging based on spatial frequency heterodyning is described. Three images corresponding to three physical measurements are recorded. For the first measurement, a scene is simply illuminated with a coherent beam and for measurements 2 and 3, the scene is projected with cosine and sine fringes, respectively. Due to spatial frequency heterodyning, upper and lower side hand information falls in the pass band of the imager. These bands are separated and correct phases and positions are assigned to these bands in the spatial frequency domain. An extension of bandwidth is achieved in the frequency domain and the inverse frequency domain data then give a high resolution coherent image.展开更多
We investigate the global classical solutions of the non-relativistic Vlasov-D arwin system with generalized variables(VDG)in three dimensions.We first prove the global existence and uniqueness for small initial data ...We investigate the global classical solutions of the non-relativistic Vlasov-D arwin system with generalized variables(VDG)in three dimensions.We first prove the global existence and uniqueness for small initial data and derive the decay estimates of the Darwin potentials.Then,we show in this framework that the solutions converge in a pointwise sense to solutions of the classical Vlasov-Poisson system(VP)at the asymptotic rate of 1/c2 as the speed of light c tends to infinity for all time.Moreover,we obtain rigorously an asymptotic estimate of the difference between the two systems.展开更多
We prove a concentration result of a Bloch eigenstate in a periodic channel under a constant gauge, In the semi-classical limit h → 0 these eigenstates concentrate near a maximizer of the scalar potential of the asso...We prove a concentration result of a Bloch eigenstate in a periodic channel under a constant gauge, In the semi-classical limit h → 0 these eigenstates concentrate near a maximizer of the scalar potential of the associated Schr6dinger operator, provided the constant gauge converges to a critical value from above. This is in contrast with the ground states which concentrate for any gauge in this limit near a minimizer of the scalar potential.展开更多
Quantum dispersions of various sets of dynamical variables of an open Bose-Hubbard system in a classical limit are studied. To this end, an open system is described in terms of stochastic evolution of its quantum pure...Quantum dispersions of various sets of dynamical variables of an open Bose-Hubbard system in a classical limit are studied. To this end, an open system is described in terms of stochastic evolution of its quantum pure states. It is shown that the class of variables that display classical behaviour crucially depends on the type of noise. This is relevant in the mean-field approximation of open Bose-Hubbard dynamics.展开更多
We review the semiclassical method proposed in [1], a generalization of this method for n-dimensional system is presented. Using the cited method, we present an analytical method of obtain the semiclassical Husimi Fun...We review the semiclassical method proposed in [1], a generalization of this method for n-dimensional system is presented. Using the cited method, we present an analytical method of obtain the semiclassical Husimi Function. The validity of the method is tested using Harmonic Oscillator, Morse Potential and Dikie’s Model as example, we found a good accuracy in the classical limit.展开更多
By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechan...By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.展开更多
This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces.The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in...This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces.The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in the pth-mean(p≥2).As an application,a classical limit theorem on the dependence of such equations on a parameter is obtained.The novelty of this paper is that the combination of this approximating system and such equations has not been considered before.展开更多
文摘The exact classical limits for the coefficient of variation c for the normal distribution are derived. The hand-calculating approximated classical limits for c having high accuracy are given to meet practical engineering needs. Using Odeh and Owen's computational method and Brent's algorithm, the tables for the r-upper exact classical limits of coefficient of variation for normal distribution are calculated for the different confidence coefficient y, the sample size n=1(1)30,40,60,120, the sample coefficient of variation c=0.01(0.01)0.20. It is shown that if n<8,c<0.20, then the V -upper exact classical limits cu for c are slightly higher than the exact fiducial limits cu,F for c if. n>8, c<0.02,then cu-cu,f<5x10-6
文摘A technique for coherent imaging based on spatial frequency heterodyning is described. Three images corresponding to three physical measurements are recorded. For the first measurement, a scene is simply illuminated with a coherent beam and for measurements 2 and 3, the scene is projected with cosine and sine fringes, respectively. Due to spatial frequency heterodyning, upper and lower side hand information falls in the pass band of the imager. These bands are separated and correct phases and positions are assigned to these bands in the spatial frequency domain. An extension of bandwidth is achieved in the frequency domain and the inverse frequency domain data then give a high resolution coherent image.
基金supported by the National Natural ScienceFoundation of China(11871024)the Fundamental Research Program of Shanxi Province(202103021223182)。
文摘We investigate the global classical solutions of the non-relativistic Vlasov-D arwin system with generalized variables(VDG)in three dimensions.We first prove the global existence and uniqueness for small initial data and derive the decay estimates of the Darwin potentials.Then,we show in this framework that the solutions converge in a pointwise sense to solutions of the classical Vlasov-Poisson system(VP)at the asymptotic rate of 1/c2 as the speed of light c tends to infinity for all time.Moreover,we obtain rigorously an asymptotic estimate of the difference between the two systems.
文摘We prove a concentration result of a Bloch eigenstate in a periodic channel under a constant gauge, In the semi-classical limit h → 0 these eigenstates concentrate near a maximizer of the scalar potential of the associated Schr6dinger operator, provided the constant gauge converges to a critical value from above. This is in contrast with the ground states which concentrate for any gauge in this limit near a minimizer of the scalar potential.
基金supported in part by the Ministry of Education and Science of the Republic of Serbia (Grant No. ON171017)
文摘Quantum dispersions of various sets of dynamical variables of an open Bose-Hubbard system in a classical limit are studied. To this end, an open system is described in terms of stochastic evolution of its quantum pure states. It is shown that the class of variables that display classical behaviour crucially depends on the type of noise. This is relevant in the mean-field approximation of open Bose-Hubbard dynamics.
文摘We review the semiclassical method proposed in [1], a generalization of this method for n-dimensional system is presented. Using the cited method, we present an analytical method of obtain the semiclassical Husimi Function. The validity of the method is tested using Harmonic Oscillator, Morse Potential and Dikie’s Model as example, we found a good accuracy in the classical limit.
文摘By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.
基金Supported by the National Natural Science Foundation of China(Grant No.12171361)the Humanity and Social Science Youth foundation of Ministry of Education(Grant No.20YJC790174)。
文摘This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces.The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in the pth-mean(p≥2).As an application,a classical limit theorem on the dependence of such equations on a parameter is obtained.The novelty of this paper is that the combination of this approximating system and such equations has not been considered before.
