Normalization and the detection of integrability: The generalized Van Der Waals potential

Deprit and Miller have conjectured that normalization of integrable Hamiltonians may produce normal forms exhibiting degenerate equilibria to very high order. Several examples in the class of coupled elliptic oscillators are known. In order to test the utility of normalization as a detector of integrability we normalize, to high order, a perturbed Keplerian system known to have several integrable limits; the generalized van der Waals Hamiltonian for a hydrogen atom. While the separable limits give rise to high order degeneracy we find a non-separable, integrable limit for which the normal form does not exhibit degeneracy. We conclude that normalization may, in certain cases, indicate integrability but is not guaranteed to uncover all integrable limits.     

基于均值漂移的粒子滤波算法设计及其在导航数据处理中的应用

针对标准粒子滤波算法中存在的计算量大和粒子的权值退化的缺陷,将均值漂移算法和PF算法进行融合,设计基于均值漂移搜索算法的粒子滤波新算法。该算法仍遵从粒子滤波算法的计算框架,基本原理是利用MS算法对粒子的聚类作用,将均值漂移思想融合到粒子滤波算法的重要性采样过程中,对粒子集进行确定性搜索,使每个粒子收敛于局部最优值,这样粒子的状态表示更接近真实的状态分布,因此只需较少的粒子数便可达到未嵌入MS的使用大量粒子数的粒子滤波状态估计的性能,从而在缓解粒子的权值退化的同时提高粒子滤波算法的实时性。大量的数值试验和对GPS/DR组合导航数据处理的结果验证了该方法的有效性。     

基于MKLD准则的PSOPF算法设计及其应用

针对标准粒子滤波算法中存在的粒子权值退化和计算量大的缺陷,提出了基于MKLD准则的粒子群优化粒子滤波算法。该方法将粒子群优化算法嵌入到粒子滤波算法的重要性采样过程中,对采样过程进行了优化,提高了粒子集的优良性的同时保证了粒子滤波状态估计的性能。同时,为了降低计算量,算法设计时基于MKLD准则自适应地选择粒子群优化算法所...     

Some properties of an intrinsically degenerate Hamiltonian system

Using theoretical arguments we study some properties of a time independent, two-dimensional Hamiltonian system in the 1:1 resonance case. In particular we find the frequency of the oscillation near the elliptic points, the ratio of the semiaxes of the ellipses surrounding them and the inclination angle of the asymptotes of the hyperbolic orbits in the original variablesx–p _x. The results are in satisfactory agreement with those given by numerical integration of the equations of motion. Some possible applications for the motion of stars in elliptical galaxies are also discussed.     

应用高斯粒子群优化的无迹粒子滤波

针对粒子滤波算法中存在的粒子退化与粒子匮乏的缺陷,提出了利用高斯粒子群优化无迹粒子滤波的新算法。算法使用无迹粒子滤波进行重要性采样,并将高斯粒子群优化算法融入重采样过程中。该算法选取的概率密度更加接近系统真实状态,有效增加了粒子的多样性,提高了抽样效率,降低了粒子退化程度,缓解了粒子匮乏现象。试验结果表明,该算法的滤波精度明显优于粒子滤波与无迹粒子滤波算法所得到的滤波精度。     

Invariants of Spectral Moments and their Degeneracy for a Gaussian Surface

The transformation and symmetry properties of surface derivatives and spectral moments under rotation of the coordinate axes are examined. It is shown that the moments as well as the derivatives are generally represented in terms of their rotational invariants. For a Gaussian surface, which is characterized by additional symmetry of correlation matrices, the even moments higher than the second order are degenerate; i.e., only three of them are independent, and only two invariants are nonzero. Specific properties of spectrum symmetry and the joint statistical distribution of the mean and differential curvatures are found in this case. As an application of these results to observation of the sea surface, a simple optical method is suggested for simultaneous remote-sensing measurement of the second- and fourth-order moments. This method is based on the count of reversely reflected light impulses, arising from sea-surface scanning by the continuous laser radiation.     

拟线性退化椭圆型方程的边值问题

运用逼近理论来讨论在Ｘ轴上退化的拟线性偏微分方程的混合边值问题,提出并证明了解的存在性。     

一类退化椭圆型方程的边值问题解的存在性及唯一性

运用逼近理论及矩阵理论证明 :如果一类退化椭圆型方程在非退化边界上满足第三边界条件 ,在退化边界上满足给定微商值 ,那么它的解是存在且唯一的。