查询词典 unitary

We alsostudy the Lie skew multiplicative bijective maps on B that is, the maps satisfyingΦ(AB- BA~*=ΦΦ-ΦΦ~*, and show that these maps must be of theformΦ=UAU~*, where U is a unitary or a conjugate unitary operator.

刻画了B(H是复Hilbert空间)上的Lie-skew可乘双射即满足Φ(AB-BA~*=ΦΦ-ΦΦ~*的双射，结果表明这样的映射一定是UAU~*的形式，其中U是酉算子或共轭酉算子。

This paper queries the main viewpoint and the argument support of the unitary training theory, from the perspective of the text structure, the talent theory citing, the antinomy of the two criterion, certain less convincing argumentation, false of science and the backer's restrictive thinking, accelerate introspectiveness, development and transcendence of the unitary training theory and brings forward a consummate image for this system.

以一元训练理论文本方式解构、天才理论的借鉴、"二律背反"例证的出现、部分论据引证效度问题、科学证伪角度、支持者思维定势的影响6个框架内容，质疑一元训练理论主流观点及论据支撑方面的若干问题，旨在促进一元训练理论自省、发展、超越的过程，最后就理论体系完善方向提出设想。

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。

It has deep connections with the theory of projective space and justifies the use of unitary and anti-unitary group representations in physics.

鉴于Wigner定理的重要意义，本文对Wigner定理的提出、论证、在不同背景条件下的推广和发展做了简要的总结。

In quantum mechanics,the evolution of a quantum state is a unitary evolution ,the evolution process can be described by an action of a unitary operator on the quantum state and the process is time reversible.

在量子力学中，态的演化是一个幺正演化过程，态的演化过程可以用演化算子对态的作用来表示，幺正演化过程是时间可逆的。

And the sufficient and necessary conditions are obtained and the uniqueness of T is discussed and an algorithm for solving the inverse problem is provided. The other kind of structure inverse eigenvalue problem is for unitary Hessenberg matrices with positive subdiagonal elements. That is, a unitary Hessenberg matrices with positive sub-diagonal elements can be constructed when its eigenvalues and the eigenvalues of H_(11) and H_(22) are known. Here H_(11) and H_(22) are rank-one modifications of k × k leading principal submatrix of H and of its × remain submatrix respectively. In the end, the uniqueness of H and an algorithm is obtained.

文中首先讨论了这三组特征值之间的交错关系，接着确定了该逆问题有解的充要条件，并论证了其解的唯一性问题，最后给出了相应的数值算法；本文第二个问题解决的是一类不可约的酉Hessenberg阵的逆特征值问题：即一个不可约的酉Hessenberg阵可以由它的特征值、它的前k阶秩一修正的顺序主子阵的特征值以及它的后n—k阶余子阵的秩一修正阵的特征值来确定，文中最后讨论了唯一性和相应的算法。

It is also pointed out that an n-mode boson coupled quadratic Hamiltonian can be diagonalized by a "negative unitary" matrix which is an element of complex symplectic group SP(2n,c),and an n-mode fermion coupled quadratic Hamiltonian can be diagonalized by a unitary matrix which is an element of complex fermion group F(2n,c).

并且指出，对于n模玻色子耦合二次型哈密顿量，通过一个负幺正矩阵它是复辛群SP(2n，c的元素可以把它对角化；对n模费米子耦合二次型哈密顿量，通过一个幺正矩阵它是复费米群F(2n，c的元素可以把它对角化。

Next, we construct a group of unitary basis on, and form the unitary basis on by tensor product.

我们构造M_2上的酉基，并用张量积方法构造M_(2~n)上的酉基。

In Chapter Ⅲ, we introduce some special case of Unitary groups, and give out the normality of the elementary group of hyperbolic Unitary group.

在第三章中，本文介绍了几类特殊的酉群和双曲空间上酉群U_(2n)的基本子群的正规性定理。

Owing to Wei-Norman decomposition＇s application being confined in a little time area, in order to obtain the Unitary evolution matrix at any time, a small division of time is proposed in this paper, and Wei-Norman decomposition is used in every small division to obtain the unitary evolution.

由于Wei-Norman分解适用的范围是小时间变化的邻域，为了求出量子系统在任意时刻的幺正演化矩阵，根据量子系统的特性，提出了对量子系统的控制时间进行分段，利用Wei—Norman分解来获得每段小时间的幺正演化矩阵。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失