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In this part, a new method, using tensor algebra, is developed to yield any order approximate analytical solution of a universal nonlinear dynamic system equation, which is abstracted from a large class of nonlinear dynamic systems in many different disciplines.

该篇采用张量代数，首次用严格的分析方法获得了适合不同学科的、普遍的非线性动力系统方程任意阶近似解析解。

Briefly covered vector and tensor notation, vector and tensor algebra, wave kinematics, eigenvectors/values, dimensional analysis, and scale analysis.

简要的介绍向量和张量符号，向量和张量代数，波的运动，特徵向量／值，向量分析，以及尺度分析。

This method is based on tensor and tensor algebra. To utilize the multidimensional data of the remote sensing image, the vector-based learning machine is generalized to the tensor-based learning machine which accepts tensors as input, then the convex optimization theory and the alternating projection procedure are used to get the solution of the TLM.

该方法基于张量数据模型和张量代数运算，针对遥感影像数据多维或高维的特点，将基于向量的监督法学习机扩展为基于张量的监督法学习机，然后利用凸函数最优化理论和交互投影迭代法求得张量学习机的最优解。

Tensor algebra is tied to coordinates.

张量代数则离不开坐标系。

The research about the subject largely developed and extended the classical results about homological algebra.The theory of relative homological dimensions of modules and rings are the main research field in the subject.

关于这门学科的理论研究，极大的丰富和发展了同调代数的经典结果，而环与模的相对同调维数理论是相对同调代数这一门学科的重要研究领域。

To obtain the RCS of dipole-array antennas, the system of electric field integral equations is turned into a linear algebra system whose coefficient matrix is a symmetric block Toeplitz complex matrix by using Calerkin method with pulse basis functions.

为计算线天线阵列的雷达散射截面，用脉冲函数为基函数的Galerkin法将线天线阵列的电场积分方程组转化为一个线性方程组，其系数矩阵是一个对称的二重复Toeplitz矩阵。

The purpose of studing LPP is to discuss and so as to solve topological algebra's problems by linear methods, and to get information of classifying operator algebras from a new direction.

线性保持问题研究的目的是利用线性手段探讨和解决拓扑代数的问题，从新的角度提供算子代数的整体结构和对算子代数分类的信息。

The theory of graphs and relations between the spectra and fixed variate (e.g. chromatic number, degree sequence, diameter and connectivity) of graphs by means of the well-developed theory and technique of algebra, topological structure properties of graph, combination and matrix theories so as to establish firm essential relation between the algebraic properties and topological properties of graphs and networks.

图谱理论的研究主要是利用成熟的代数理论和技巧，并结合图的拓扑结构性质和组合数学的理论、矩阵理论来研究图谱及其与图的结构性质、图的其它不变量(如色数，度序列，直径，连通度等)之间的关系，将图与网络的代数性质与图的拓扑性质紧密地联系在—起。

With computer algebra system Maple, the instant plots of the refracted wave of the total internal reflection is showed and the effect on the physics teaching is discussed.

介绍了借助计算机代数系统Maple实现全反射现象折射波瞬时行为动态展示的做法，讨论它在基础物理教学中的作用。

People had always considered the problem of selecting dynamically threshold as a problem about measure of fuzziness of fuzzy sets, but they did not notice that it is essentially comparison of elements in an algebra structure, and thereby regarded mistakenly order homorphism (partial ordered set to totally ordered set) as order isomorphism.

本文从模糊系统理论和代数理论的相关思想出发，在序结构的观点下从理论上对模糊度的不一致性进行了详细的分析，提出了模糊度计算公式选用的统一标准，进而结束了随意选用模糊度计算公式的混乱状态。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。