Geometric Characterizations for Subgroups of PU（1, n; C）

In this paper, we discuss non-elementary subgroups and discontinuous subgroups of PU(1,n; C), and give their geometric characterizations.     

一个改进的Hardy-Hilbert不等式

通过建立权系数的不等式,得到一个改进的Hardy-Hilbert不等式.     

一类It型非线性时滞关联随机大系统的分散鲁棒控制

在非线性项满足全局Lipschitz条件下,本文研究了一类It型非线性时滞关联随机大系统的分散鲁棒控制问题.系统的时滞是关于状态和控制输入的.基于Lyapunov泛函及线性矩阵不等式(LMI)的分析方法,得到了无记忆状态反馈控制器使整个时滞关联随机大系统可镇定的充分条件.     

相位差与q变形广义相干叠加态的压缩特性

对于q变形的非简谐振子广义相干态的叠加态β〉+eiφβeiδ〉,其量子涨落的可能高阶压缩阶数可以表示为k≠2πn/δ,这里n是整数.当δ=π时,压缩阶数不能是偶数即只能是奇数,这正是q变形非简谐振子广义奇偶相干态的结果.由此表明参数相位差δ对决定q变形的非简谐振子广义相干态叠加态的高阶压缩阶数起决定性作用.     

量子化电磁场中的非经典电子波包:电子与光子的纠缠

文中研究了量子化电磁场中非经典电子波包的运动。当初始光子态是Fock态时，随着电子和光子所组成系统的演化，初台可分离的电子态和光子态会互相纠缠，而且电子几率密度的时间演化呈非经典的分岔和汇合的现象。基到这些非经典特征，电子可以在光子场中被加速和减速，而系统保持能量守恒。     

Covariant Perturbation Theory of Non—Abelian Kinetic Theory

A “double perturbation” theory is presented in the framework of the kinetic theory of quark-gluon plasma.A solvable set of equations from the double perturbation are derived and proven to be gauge invariant.The Landau damping rate for the plasmon at zero momentum is shown to be a convergent series in correlators.     

随机环境中多物种分枝随机游动

引进了随机环境中多物种分枝随机游动的一般模型.在分枝过程非灭绝的情况下,讨论了系统的状态分类,得到了系统暂留及强常返的充要条件是存在k个定义在整数集上的函数分别满足某种性质.最后给出了系统强暂留的充分条件.     

Entangled States Based on Two Coherent States 3π/2 out of Phase

Entangled states based on two coherent states 3π/2 out of phase with each other, i.e. ｜α〉 and e^iФ｜-iα〉, as well as on a special state with a relative phase Ф = ｜α｜^2, are constructed. By analysing the amount of entanglement it is evident that entangled states based on this special state can be used as an excellent resource for quantum teleportation. It is also revealed that these entangled states possess some nonclassical features.     

Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.