向量

The existence theorem of generalized weak efficient solutions with respect to variable, cone for a linear G〓teaux differentiable mapping is proved with set valued mapping fixed-point theorem and the relation between a vector optimization and a variational inequality problem. The existence of weak efficient solutions for multi-objective convex vector optimization is characterized.

建立映射在线性G〓teaux可微条件下关于可变锥的广义弱有效解的存在性及多目标凸向量优化问题在G〓teaux可微条件下弱有效解的特征，利用集值映射不动点定理及向量优化与变分不等式的关系证明线性G〓teaux可微锥凸映射关于可变锥的广义弱有效解的存在性定理。

A sidelight here is that if you look at the mathematical representations of a PM signal versus an FM signal, the difference is that the modulation component in a PM signal is the mathematical derivative of the modulating signal in the FM signal.

如果你看调相PM信号和调频FM信号的数字表达式的对比，它们的不同点是调相PM信号调制向量是调频FM信号调制向量的数学派生。

Sine law of spherical trigonometry spherical trigonometry Vector Proof of sine law of the vector method of proof.

球面三角学正弦定律的向量证明方法球面三角学正弦定律的向量证明方法。

By using the exist- ence result of VF- ICP and VF - IVIP with single - valued mappings and the continuous selection theorem due to Ding,Kim and Tan, solution existence for GVF- ICP and GVF- IVIP is derived under suitable assumptions.

通过具单值映象的向量F-隐补问题和向量F-隐变分不等式问题解的存在性的研究和使用Ding，Kim和Tan的连续选择定理，在适当假设下证明了CVF-ICP和GVF-IVIP解的存在性，推广了其他人的结果。

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。

Latent semantic index LSIis a new algebraic model for information retrieval, which maps documents and queries vectors into a lower dimensional space by singular value decomposition, so that the inherent vagueness associated with a retrieval process based on keyword sets is considerably reduced and semantic association among the documents is highlighted consequently.

隐含语义索引是一种新型的信息检索模型，它通过奇异值分解，将词向量和文档向量投影到一个低雏空间，消减了词和文档之间的语义模糊度，使得文档之间的语义关系更为明晰。

The image matrix is transformed into vector by singular value decomposition. The angle between singular vectors of the original image and the distorted image is used to measure the image quality.

考虑原始图像和畸变图像尺寸不一致的情况，提出了用奇异值分解把图像矩阵转为向量，用奇异值向量之间的夹角作为图像的质量评价指标。

The algebraic and geometric invariance of singular value vector is firstly given,and then singular value vector compressed is extracted as the image feature,then RBF neural network is used to training and recognition.

首先说明了彩色图像的奇异值向量具有代数和几何不变性，再将降维的奇异值向量作为图像的特征，然后应用RBF神经网络进行训练和识别。

The conditional nonlinear optimal perturbation is a new theoretical method proposed by Mu,et al in 2003, which is an extension of the linear singular vector to nonlinear regimes. It has become a powerful tool to study some issues of nonlinear systems like predictability, sensitivity and so on, because it overcomes the defect of LSV for not representing the fastest developing perturbation of a nonlinear system.

条件非线性最优扰动是Mu等2003年提出的一个新的理论方法，它是线性奇异向量在非线性情形的推广，克服了线性奇异向量不能代表非线性系统最快发展扰动的缺陷，成为非线性系统可预报性和敏感性等研究新的有效工具。

The conditional nonlinear optimal perturbation is a new theoretical method proposed by Mu , et al in 2003, which is an extension of the linear singular vector to nonlinear regimes. It has become a powerful tool to study some issues of nonlinear systems like predictability, sensitivity and so on, because it overcomes the defect of LSV for not representing the fastest developing perturbation of a nonlinear system.

摘要条件非线性最优扰动是 Mu 等2003年提出的一个新的理论方法，它是线性奇异向量在非线性情形的推广，克服了线性奇异向量不能代表非线性系统最快发展扰动的缺陷，成为非线性系统可预报性和敏感性等研究新的有效工具。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。