查询词典 unitary invariant

Based on definition of orthogonal counterbalance, authors definite the unitary counterbalance of matrix and prove the unitary counterbalance properties of unitary symmetric matrix and it s mother matrix, obtain some results as the Moore-Penrose inverses of unitary symmetric matrices are unitary counterbalance if unitary symmetric matrices are unitary counterbalance .

从矩阵正交相抵的概念出发，给出了矩阵酉相抵的概念，证明了酉对称矩阵与母矩阵之间的酉相抵性，得到了酉相抵矩阵的Moore Penrose逆等一些新的结论。

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。

Unitary linear regression is done between w~e、 w~ρ、 e~ρ、w_L~w_P. For α_v 、 C_ c between w、ρ、 e、 w_P in eastern China, unitary linear regression is done to silty clay as well as multivariant regression with coefficient iteration method and least-squares procedure are done to all kinds of soil, and the two results are compared. Unitary linear regression and multivariant regression are done to c_q、φ、 c_d、φ_d between e and I_P. Unitary linear regression and multivariant linear regression are done to napierian logarithm of q_u between e 、 I_L、 w_P and w_L, then the equations of regression are checked with other parameters.

对物理指标含水量～孔隙比、含水量～湿密度、孔隙比～湿密度、液限～塑限作了一元线性回归；对华东地区粉质粘土的压缩系数、压缩指数和含水量、湿密度、孔隙比及塑性指数作了一元线性回归；对华东地区所有土类的压缩系数、压缩指数和物理性质参数用系数迭代法和最小二乘法作了多元线性和非线性回归，并对两种方法得到的回归结果作了比较；作了快剪强度指标和固结快剪强度指标关于孔隙比和塑性指数的一元线性回归和多元线性及非线性回归；对无侧限抗压强度的自然对数值和孔隙比、液性指数、液限及塑限作了一元和多元线性回归，并用其它工程的参数对回归方程进行了检验。

Based on the summarizing of the exiting algorithms of the texture mapping and antialiasing, this paper goes deeply into the basic theory and processing of texture mapping. The texture compress algorithm which can satisfy the need of the memory and time is given for the stochastic sampling in the inverse texture mapping; the geometry transformation in the texture mapping are discussed and the concepts of the unitary parametrization and the patch parametrization is proposed, some kinds of the unitary parametrization methods of parametric surfaces and the geometry transformation in the patch parametrization are also presented; in order to solve the aliasing in the parametrization of intermediate surface-sphere in two-part texture mapping, an area-preserving transformation is presented also; to improve the quality of the graph the aliasing in the texture mapping is analyzed from the aspect of signal process, and the modified summed-area tables algorithms is proposed; the distortion of the scanline conversion algorithms under perspective transformation is analyzed and the proper interpolation algorithm is presented so the aliasing problem of the polyhedral object after the unitary parametrization is efficiently solved.

本文在总结现有的纹理映射和反走样算法的基础上，深入研究了纹理映射的基本原理与过程，根据反向纹理映射对纹理随机采样的特殊要求，提出了一种可满足存储空间和寻址时间的纹理压缩存储算法；通过对纹理映射中几何变换理论的进一步深入探讨，提出了整体参数化和面片参数化的概念，并给出了参数化曲面的各种整体参数化方法和面片参数化的几何变换形式；针对现有的两步映射算法所存在的中间曲面—球面的参数化问题，提出一种等积映射方法，较好地实现了由非参数化面片拼接而成的多面体表面的纹理映射；从信号采样的角度深入分析了纹理映射中走样产生的原因，提出了改进的区域求和表算法，使图形生成的效果有所提高；还分析了一般的扫描线算法在透视变换中所存在的问题，提出了一种正确的插值算法，从而解决了整体参数化后多面体表面纹理映射的几何变形问题。

This paper is divided into two parts: The first part, mainly discussed the properties of unitary equivalence and the relation between unitary equivalence and similarity, introduced a unitary equivalent of the necessary and sufficient condition: Specht theorem; The second part of a major demonstration of the 11 normal matrix's necessary and sufficient conditions, given some important properties of normal matrix such as simultaneous diagonalization.

本文主要分为两部分：第一部分，主要讨论了酉等价的性质及酉等价与相似的关系，介绍了酉等价的充分必要条件Specht定理；第二部分，主要论证了正规矩阵的11条充分必要条件，给出了正规矩阵的一些重要性质

This chapter clarifies the nested relationship between the matrix family of unitary, orthogonal, Givens, Householder, permutation, and row or column symmetric matrices. A precise correspondence of the singular values and singular vectors between the unitary-symmetric matrix and its mother matrix is derived and proved (hence a fast algorithm of singular value decomposition for unitary-symmetric matrix is straightforwardly obtained), and the corresponding perturbation bound is provided.

该章揭示了酉对称矩阵、正交对称矩阵、 Givens 对称矩阵、 Householder 对称矩阵、置换对称矩阵和行对称矩阵之间的逐级包含关系；推导并证明了，酉对称矩阵的奇异值和奇异向量与母矩阵的奇异值和奇异向量之间的定量关系，据此可得酉对称矩阵奇异值分解的快速算法；给出并证明了摄动矩阵的摄动界。

According to the problems and shortages exited in the first national judicial cxalnination,author suggests that the system sheRid be perfected in the following three aspects:first,on the basis of lower condition for the entrance of the examination and lower matriculating score,We should keep the balance of right and obligation;second,we could deepen the judicial officials and personal system at the turning point of establishing the national judicial examination system;third,We should perfect the existing judicial unitary examination system through the combination of unitary examination and unitary study so that the purpose of practicing the national judicial examination system can be fulfilled much better.

针对首届国家统一司法考试存在的问题及不足，笔者建议从三处着手进行完善：首先，在放宽报名条件和降低录取分数线上应讲求&权义平衡&；其次，以国家司法统一考试制度为契机深化司法官人事制度改革；最后，以&统一考试+统一研修&的结合来完善现行的司法统一考试制度，使国家实行司法统一考试制度的目的能更好地实现。

Essentially, it is concerned with the improvement of national structure so in pushing forward the constitutionality, we should avoid the following theoretical misunderstandings: our national structure is unitary; federal system advocates the principle of "double sovereignties"; compared with federal system, unitary system has the more authoritative central; we should stick to the unitary system to improve our national structure.

中央与地方关系的法治化问题在实质上就是国家结构形式的完善问题，在推进中央与地方关系法治化的过程中，应当注意走出国家结构形式的几个理论误区：我国的国家结构形式是单一制；联邦制奉行的是&双重主权&原则；单一制与联邦制相比，中央更具权威；完善国家结构形式，我们必须坚持单一制。

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。

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

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。