Some counterexamples to a generalized Saari's conjecture

For the Newtonian -body problem, Saari's conjecture states that the only solutions with a constant moment of inertia are relative equilibria, solutions rigidly rotating about their center of mass. We consider the same conjecture applied to Hamiltonian systems with power-law potential functions. A family of counterexamples is given in the five-body problem (including the Newtonian case) where one of the masses is taken to be negative. The conjecture is also shown to be false in the case of the inverse square potential and two kinds of counterexamples are presented. One type includes solutions with collisions, derived analytically, while the other consists of periodic solutions shown to exist using standard variational methods.

     

LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES

Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.     

奇异线性模型参数估计的相对效率

提出了奇异线性模型中参数β的最佳线性无偏估计(BLUE)相对于最小二乘估计(LSE)的一种新的相对效率,并给出了该相对效率的下界,最后讨论了该相对效率与广义相关系数的关系.     

一种有偏估计与最小二乘估计的两种新的相对效率

考察了线性回归模型的回归系数的一类有偏估计,在均方误差矩阵准则下将其与最小二乘估计(LSE)进行比较,导出了这类有偏估计相对于LSE的两种新的相对效率的上、下界.     

Relative n-widths of periodic convolution classes with NCVD-kernel and B-kernel

In this paper,we consider the relative n-widths of two kinds of periodic convolution classes,Kp(K) and Bp(G),whose convolution kernels are NCVD-kernel K and B-kernel G. The asymptotic estimations of Kn(Kp(K),Kp(K))q and Kn(Bp(G),Bp(G))q are obtained for p=1 and ∞,1≤ q≤∞.     

Lattice Boltzmann simulations of high-order statistics in isotropic turbulent flows

The lattice Boltzmann method (LBM) is coupled with the multiple-relaxation-time (MRT) collision model and the three-dimensional 19-discrete-velocity (D3Q19) model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high-order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investigated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity (ESS) method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This validation provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.     

基于绿色化学的基础化学实验改进——以“二氧化碳相对分子质量的测定”为例

以“二氧化碳相对分子质量的测定”为例,分析了传统实验中存在的试剂用量大、“三废”排放多等问题,以绿色化学为突破口,采用氢氧化钠-酚酞溶液替代火柴进行验纯,使用注射器代替碘量瓶集气,通过上述方法对实验进行优化设计,达到了绿色化、准零排放的要求,可以增强学生的环保意识。     

Entropic Kullback-Leibler type distance measures for quantum distributions

Entropic distance measures for quantum mechanical probability distributions, which are characterized by nodal structure and symmetry holes, are considered. We illustrate how the Kullback-Leibler (KL) distance is not well defined in some instances and propose instead the use of the cumulative residual Kullback-Leibler (CRKL) distance. The KL and CRKL measures are compared and contrasted for some representative quantum mechanical systems: The particle in an infinite well, the harmonic oscillator, and hydrogenic systems. We present cases where CRKL can be used to obtain distances whereas KL cannot be used, and also highlight examples where the KL and CRKL measures yield different behaviors and interpretations. An extension of the CRKL definition is obtained for application to harmonic oscillator systems defined over [−∞, ∞]. Distance measures for two-variable (particle) distributions are also considered to address generalizations of the mutual information correlation measure. The use of CRKL in measuring distances between orbitals is also discussed.     

与XY双自旋链耦合的双量子比特系统的关联性与相干性

研究了双量子比特系统中在具有Dzyaloshinsky-Moriya相互作用的独立XY自旋链环境下的相干性与关联性动力学.推导出相干性与关联性的演化规律.发现在自旋链的临界点附近,当tt_0时,系统相干性的演化与经典关联完全相同;而在tt_0时,则与量子关联完全相同;在t_0时刻,量子关联突变为经典关联.     

基于瞬态光栅频率分辨光学开关装置的阿秒延时相位控制

操控多路激光脉冲之间的相对延时（相对相位）对于亚周期相干合成技术意义重大.当周期量级脉冲之间的相对延时接近数十飞秒时,常见的飞秒脉冲测量手段已无法满足脉冲之间相对相位的精确调控需求.本文基于瞬态光栅频率分辨光学开关装置,精确反演出脉冲之间的相对相位.此方案不仅有助于直接产生亚周期（亚飞秒）脉冲,还可应用于时间隐身学和二维相干光谱学等相关领域.