双基地MIMO雷达多目标定位及互耦参数估计

针对MIMO雷达收发阵元间存在互耦会严重影响目标定位算法性能的情况,提出一种双基地MIMO雷达多目标定位及互耦参数估计的算法.利用均匀线阵互耦矩阵的特点和MIMO雷达的特性获得满足ESPRIT算法的信号子空间,在不需要任何互耦矩阵信息情况下采用ESPRIT算法实现了目标角度估计,且估计出的角度参数自动配对.根据所估计的目标方位角度,利用信号子空间和联合导向矩阵之间的关系,将MIMO雷达的互耦参数估计转化为线性约束二次最小化问题,估计出互耦系数矩阵,实现了MIMO雷达的自校正.该方法的优点是避免了多维空间谱搜索带来的庞大计算量和迭代中的全局收敛性问题,同时得到了收、发阵列互耦参数估计的闭式解.仿真结果表明算法估计性能接近于互耦已知时二维MUSIC算法.     

完整力学系统运动方程的形式不变性

研究一种新的不变性,即一般完整力学系统运动微分方程的形式不变性,给出形式不变性的定义和判据;研究形式不变性与Noether对称性以及Lie对称性之间的关系.证明了在一定的条件下,形式不变性可以导致守恒量,并举例说明结果的应用.     

重对数律与局部鞅渐近性的一个注记

给中续中鞅关于重对数律的不变原理，并得到随机微分方程的一个渐近定理。     

单调集射动力系统及其稳定性

提出单调集射动力系统及其相关概念,研究了一些极限集的不变性,讨论了吸引性、稳定性及其之间的关系.     

Minkowski spacetime and Lorentz invariance: The cart and the horse or two sides of a single coin?

Michel Janssen and Harvey Brown have driven a prominent recent debate concerning the direction of an alleged arrow of explanation between Minkowski spacetime and Lorentz invariance of dynamical laws in special relativity. In this article, I critically assess this controversy with the aim of clarifying the explanatory foundations of the theory. First, I show that two assumptions shared by the parties—that the dispute is independent of issues concerning spacetime ontology, and that there is an urgent need for a constructive interpretation of special relativity—are problematic and negatively affect the debate. Second, I argue that the whole discussion relies on a misleading conception of the link between Minkowski spacetime structure and Lorentz invariance, a misconception that in turn sheds more shadows than light on our understanding of the explanatory nature and power of Einstein׳s theory. I state that the arrow connecting Lorentz invariance and Minkowski spacetime is not explanatory and unidirectional, but analytic and bidirectional, and that this analytic arrow grounds the chronogeometric explanations of physical phenomena that special relativity offers.     

Three principles for canonical quantum gravity

We outline three principles that should guide us in the construction of a theory of canonical quantum gravity: (1) diffeomorphism invariance, (2) implementing the proper dynamics and related constraint algebra, (3) local Lorentz invariance. We illustrate each of them with its role in model calculations in loop quantum gravity.     

具有细胞内时滞的耦合传染病模型

考虑一类具有Logistic增长的时滞耦合模型. 首先, 利用特征方程和Lyapunov-LaSalle不变性原理, 证明当R₀≤1时, 无感染平衡点的全局渐近稳定性; 当R₀>1时, 病毒感染平衡点Hopf分岔的存在性. 其次, 得到了Logistic增长与时滞会影响系统稳定性的结果. 最后通过数值模拟验证理论结果的正确性.     

约束Birkhoff方程的形式不变性与Lie对称性

研究约束Birkhoff方程的形式不变性和Lie对称性及其关系.给出了形式不变性和Lie对称性的定义和判据;然后导出形式不变性与Lie对称性的关系,指出形式不变性与Lie对称性的结构方程和守恒量有相同的形式;最后,给出一个说明性的例子.