向量和

In this paper, using optimization theory and the maximum entropy formulism, a method for multi attribute group decision making based on the theory of grey fuzzy relation is established.

运用优化理论和熵极大化准则，建立了基于灰色模糊关系的多属性群体决策方法，分别对属性权重向量已知和未知两种情况给出了简便实用的算法，通过算例说明了算法的合理性。

The vector has the rich actual background and the widespread application function, it has the algebra and the geometry dual statuses, causes the algebra geometrization, the geometry algebra, has communicated the algebra, the geometry and the trigonometric function, has the good analysis method and the complete structure.

向量具有丰富的实际背景和广泛的应用功能，它具有代数和几何双重身份，使代数几何化、几何代数化，沟通了代数、几何与三角函数，具有良好的分析方法和完整的结构。

Boley and Golub used Gauss quadrature formula to solve the inverse problem, but I used other different methods and thoughts. I obtained a new decomposition form of orthogonal matrix consisted by the unit eigenvectors of Jacobi matrix and found the direct relations between the first row and the orther rows of this orthogonal matrix.

Boley和Golub的算法是用高斯求积公式，而本人另辟蹊径，推出了关于Jacobi矩阵单位特征向量组成的正交阵的一种分解形式，并找到此正交阵第一行和其它行的直接联系，由此避免了通过求特征多项式计算尾主子阵的特征值，得到了新的稳定解法。

He then starts with a discussion of linear equations, matrices and Gaussian elimination, and proceeds to discuss vector spaces, linear maps, scalar products, determinants, and eigenvalues.

然后，他开始与线性方程组，矩阵和高斯消去的讨论，并着手讨论向量空间，线性映射，标产品，决定因素和特征。

According to randomness and fuzziness of anonymity, a fuzzy pattern recognition model is presented based on entropy and least generalized weighted distance, which makes the membership vector of anonymity grades have a desirable dispersive property.

鉴于匿名的随机性和模糊性特点，提出了基于联合熵和最小加权广义距离的模糊模式识别方法，实现了系统匿名等级隶属度向量的离散化。

Yano about the harmonic and Killing vector fields in Compact orientable Riemannian spaces with boundary by means of Stokes' and Green's theorem.

Yano 关于具有边界的可定向黎曼流形上的调和和Killing向量场的结果加以推广，显然这个方法也可应用到调和张量场和Killing张量场的情形，这将在另文讨论。

For the ill conditioned load flow caused by the error produced in the transformation from electricity quantities to average power, direct current load flow and sensitivity vector are presented to find out the ill node, then by adjusting the load curve and generation curve in a certain principle, which is shown in detail with several flow charts, a new operation mode is reestablished to ensure the convergence of the calculation. Optimal multiplier method is proposed to work out the least square solution according to ill conditioned structural power network. The electricity quantities flow method enhances the reliability and accuracy of the calculation of the power transmission losses.

该方法可根据当前输电网中各个变电站24小时的电量记录，利用电量潮流计算对输电网总线损和各条线路损耗进行计算，使计算的精度满足降损措施分析和指标考核的要求；并且对于由负荷出力曲线转化成平均功率计算潮流时引入的误差，进而导致潮流计算不收敛的情况，采用直流潮流法，依据相角对有功功率的灵敏度向量判断出"网络异常点"，并且给出了解决此种情况的方法流程图；针对结构病态的电力系统潮流计算不收敛的情况，运用非线性约束优化方法中的最优乘子法求解潮流方程的最小二乘解，从而解决了电量潮流法计算理论线损时的收敛性问题，增强了该方法的适用性。

Enter your data as avector, mixed or improper fraction, any degree, radian or angle, sexadesimal and hexadecimal, decimal, octal and binary number to compute any scientific, logical, vectorial and statistical operationsincluding standard deviations and nonlinear regressions.

键入你的数据作为一个向量，混合/假分数，任何度数/弧度/角度，；六十进制数以及16进制/10进制/8进制/2进制数进行任何科学计算，逻辑运算，矢量运算和包括标准离差和非线性的回归的统计分析计算。

Because the genetic algorithms could search the optimization of objective function randomly, which via the evolution of groups, our work is based on the embedding/detecting way of "DWT-Based Audio Watermarking Using Support Vector Regression and Subsampling". And this method provides a preliminary discussion on the application of GA, which searching the individual with the highest fitness of attack-resistance in the aggregate of the optimal embedding strength. As an optimization solution of obtaining the optimal embedding strength, it could achieve an adaptive policy, and find a reasonable balance between the robustness and inaudibility of the watermark, just for the better robustness and inaudibility in the algorithm.

遗传算法是通过群体进化来随机搜索目标函数的最优化问题，对于前述基于支持向量回归机的小波域数字音频盲水印算法，进一步地探讨采用遗传算在嵌入强度集合中搜索对抗攻击能力适应度较高的个体，从而得到最佳嵌入强度的一个优化方案，以实现自适应策略，也使本算法能在水印的鲁棒性和不可感知性之间寻找到合理的平衡点，从而具有更良好透明性和鲁棒性。

There is considerable emphasis on linear algebra and vector integral calculus.

本课程是18.014的后续课程，它包括和课程18.02相同的材料，但程度更深，强调严谨的推理和对证明的理解，对线性代数和向量积分也有相当的强调。

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。