查询词典 unitary invariant

In this thesis,on thebasis of this generalized invariant theory,the invariant-related unitary transformation methodis developed and used to investigate the problems as follows

本论文在推广了的不变量理论的基础上，进一步发展了与不变量有关的幺正变换方法，并应用这一方法对如下问题进行了深入的研究

By applying these two tools,we mainly discuss the problems as follows:1 Perturbation identities for the generalized polar decomposition:By applying singular value decomposition, we study the perturbation bounds of the generalized polar decomposition under unitary invariant norms when A is perturbed by addition or multiplication,respectively and give our bounds in identities.2 A class of new unitary invariant metrics: This paper generalized a class of new unitarily invariant metrics and give the upper-bounds and lower-bounds by C-S decomposition.

利用这两个强有力的工具，本文主要讨论了如下问题：1 矩阵广义极分解的扰动等式：利用奇异值分解，本文分别讨论了加法扰动和乘法扰动下矩阵广义极分解在任意酉不变范数下的扰动界，并首次以恒等式的形式给出了酉极因子和半正定因子的扰动界。2 一类新的酉不变度量：本文推广了文[22] 中的结论，定义了一类新的酉不变度量。

In other words, The Hermiticity of a matrix is invariant under unitary transformations.

换言之，矩阵的厄密性在幺正变换下保持不变。

An important property of quantum entanglement is that the entanglement of a quantum state remains invariant under local unitary transformations on the subsystems.

量子纠缠的一个重要性质是在局部幺正变换下是不变的。

Unlike the LSD,the SIC-LSD Hamiltonian is not invariant undera unitary transformation among the occupied orbitals,which must be determined self-consistentlyfrom minimizing the SIC-LSD total energy.

与LSD近似不同，SIC-LSD近似的哈密顿量没有占据态的幺正变换不变性，单粒子态由SIC-LSD近似下的总能量极小决定。

The main contents are as follows.1 For the state control problem in closed quantum systems, according to the distance between states, the error between states and the average value of an imaginary mechanical quantity, three Lyapunov functions are chosen, respectively. The corresponding control law designs and the convergence analyses are studied. Especially, for the Lyapunov function based on the distance between states, a class of control laws that can solve the problem that an initial state is orthogonal to a goal state is designed. The convergence of the system is analyzed via LaSalle\'s principle and one method to find the largest invariant set of the closed loop system is proposed by linearizing the unitary evolution operator at the corresponding instants.

在这一背景下，本论文在指出研究量子系统控制的必要性、回顾量子系统控制理论和方法的研究现状的基础上，从控制理论的角度研究Lyapunov理论和最优控制理论对于封闭量子系统的应用以及开放系统中的若干问题，主要内容包含以下几个方面。1针对封闭量子系统中的状态控制问题，根据状态间的距离、状态间的偏差、一个虚拟力学量的均值，分别选择三种Lyapunov函数进行相应的控制律设计和收敛性分析。

In this thesis, several problems of time-dependent systems in various branches of physics are investigated by making use of the generalized invariant theory and the invariant-related unitary transformation formulation. The problems are given as follows:(1) Spin model and geometric phase factor in the fiber We investigate the fiber experiment performed by Chiao-Tomita and the Chiao-Wu theory concerning the geometric phase factor in the optical fiber, and then show that the investigation of the propagation of photons inside the noncoplanar optical fiber can be regarded as that of a second-quantization spin model.

本论文用推广的不变量理论和与不变量有关的幺正变换方法研究了一些物理分支中的几个含时系统问题：(1)自旋模型与光纤中光子几何相因子问题重新考察了Chiao-Tomita光纤实验和Chiao-Wu关于光纤中光子几何相因子的理论，证明了在非共面弯曲光纤中传播的光子运动问题实际上可以化为二次量子化含时自旋模型研究。

Based on that, two particular indentities of unitarily invariant metrics are obtained.3 Perturbation analysis of the canonical subspaces: This paper gives the least perturbation bound of the unitary factor on the unitary decomposition.

并利用C-S分解，给出了这类新的酉不变度量的上下界。由此，得到两个特殊的酉不变度量的恒等表达式。3 标准子空间的扰动分析：本文给出了矩阵的酉分解中酉因子的最小扰动界。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。