Letter: Cerenkov Radiation from a Charged Particle in a Weyl–Dirac Theory

A thin shell can separate an interior region of Riemannian geometry from an exterior spherically symmetric Weyl space. We explore the possibility that a charged particle propagating in the gravitational field outside this thin shell could emit Cerenkov radiation. Some astrophysical scenarios in which such effect could arise are discussed.     

Polarizable-Vacuum (PV) Approach to General Relativity

Standard pedagogy treats topics in general relativity (GR) in terms of tensor formulations in curved space-time. An alternative approach based on treating the vacuum as a polarizable medium is presented here. The polarizable vacuum (PV) approach to GR, derived from a model by Dicke and related to the TH formalism used in comparative studies of gravitational theories, provides additional insight into what is meant by a curved metric. While reproducing the results predicted by GR for standard (weak-field) astrophysical conditions, for strong fields a divergence of predictions in the two formalisms (GR vs. PV) provides fertile ground for both laboratory and astrophysical tests to compare the two approaches.     

开普勒二体系统的修正和统一的Runge-Lenz矢量

基于平方反比有心力系统的特性,并在二体运动系统等效的单体描述基础上,给出了开普勒二体系统的Runge-Lenz矢量的修正和统一的表达形式,尤其是通过恒等变换推导出该矢量的一种等效的张量积表达形式.研究表明,开普勒二体系统的RungeLenz矢量是由两质点相对于质心系的能动张量与相对位矢构成;给出了其守恒性的统一的数学证明;罗列并证明了该矢量的一些性质,并基于该守恒矢量讨论了质点作各类开普勒运动的判据.     

旋转式重力梯度测量系统试验及数据处理

旋转式重力梯度测量系统采用旋转调制方式求取重力梯度信息。首先,从旋转加速度计的基本原理出发,给出了重力梯度测量系统的主要工作模式;其次,构建了旋转加速度计重力梯度测量系统组成和主要功能模块,提出了采用引力产生装置开展实验室引力梯度测量的试验方案;最后,给出了旋转加速度计重力梯度测量系统的静态梯度试验验证基本条件、试验设备,并开展了重力梯度测量试验。试验结果表明,旋转式重力梯度测量系统在实验室条件下完成引力梯度试验,该系统可以检测优于200 Eu(1 Eu=10~(-9)/s~2)的引力梯度,该系统开展的试验验证为动态重力梯度仪的研制奠定了基础。     

Comparative analysis of the electrogravitational Kepler problem in GRT and RTG

In the framework of Einstein's General Relativity Theory and of the Relativistic Theory of Gravitation, the equations governing the trajectories of charged particles in the field created by a charged mass point are given. An analysis of the shape of the trajectories in both theories is presented. The first and the second order approximate solutions of the electrogravitational Kepler problem are found in the two theories and the results are compared with each other. I have pointed out the differences between the predictions in the two theories.     

基于共面特征点的单目视觉位姿测量误差分析

为了克服单目视觉测量中景深信息缺失的问题,运用改进的两段式迭代算法,对刚体位姿测量解算模型进行了优化.给出了特征标靶最优化布局,理论分析了标靶尺寸大小、标靶基线长度及特征圆点大小和解算准确度的关系.实验结果表明,优化的特征标靶布局、较大的特征标靶基线长度及较小的特征圆点靶标能够提高测量解算准确度.该研究对提高实际测量系统解算准确度具有一定的理论指导意义.     

牛顿是如何站在巨人肩膀上的?

将以现今的微积分学符号,对开普勒(Kepler)行星运行定律进行三步简单的数理分析,推出著名的牛顿(Newton)万有引力定律,以此显示微积分学的巨大威力.在微积分学的教学中,不仅可以让学生知道微积分有用,而且可以让学生知道如何应用.对现代数学建模的教学与学习也具有一定的启发意义.     

Synthesis and Structure of One Novel Polyoxometalate Compound Connected via Cerium(Ⅲ) Cation with Three-dimensional Framework H2{[K(H2O)2]2[Ce(H2O)5]2(H2Mo1.16W10.84O42)}·8H2O

One novel polyoxometalate compound connected via trivalent cerium cation as bridge H2{[K(H2O)2]2[Ce(H2O)5]2(H2Mo1.16W10.84O42)}·8H2O 1 was designed and synthesized in aqueous solution. X-ray diffraction analysis reveals that the structure of 1 is a three-dimensional framework assembled from the arrangement of H2Mo1.16W10.84O42 (named paradodecmetalate-B) and Ce(H2O)53 containing two planes, which are constructed through the unification of H2Mo1.16W10.84O4210- and Ce(H2O)53 along the [100] and [001] directions. Crystal data: H96Ce4K4Mo2.32O128W21.68, Mr = 7074.89, monoclinic, P21/n, a = 12.5037(17), b = 17.002(2), c = 12.7473(17) (A), β = 105.966(2)°, V = 2605.4(6) (A)3, Z = 1, Dc = 4.509 g/cm3, F(000) = 3132, μ = 26.098 mm(1, R = 0.0377 and wR = 0.0789 (I ＞ 2σ(I)).     

具有引力场的气体中激波传播的近似理论

本文在三维不定常流体力学特征理论的基础上,运用CCW方法,获得了激波速度的变化和激波阵面曲率、引力的大小和方向之间的解析关系,讨论了引力场对激波的加强和减弱的影响以及超新星爆炸中反弹激波的问题。利用得到的激波面积变化公式,给出了二、三维激波在引力场作用下传播问题的模拟处理方法。作为简单的例子,具体地研究了引力场变密度气体中强激波传播问题。