查询词典 contraction of tensor

In multilinear algebra one deals with the 'several variables' problem of mappings linear in each of a number of different variables, inevitably leading to the tensor concept.

在实践中与非线性问题的差异是很重要的。用线性观点看待问题，并用线性代数的语言描述它，解决它的方法。

Some important applications of structure matrix in the tensor product multilinear mapping are given. Compared with the method of matrix algebra knowledge, the proposed method enjoys obvious advantages.

给出了结构矩阵在解决张量积多重线性映射问题时的一些重要应用，经过与用矩阵代数知识解决此问题相比较对照，更显示出用结构矩阵解决问题的优越性。

Moreover, their intrinsic connection, advantages and disadvantages were analyzed from the view of multilinear projections, essential differences and their own superiorities between tensor and vector patterns were clarified, and the problems to be solved and future research were discussed.

对现有张量型学习算法进行总结：针对向量模式表示存在的问题，讨论了设计张量型学习算法的必要性和重要意义；从特征提取和分类器设计2个层面，对现有张量型学习算法进行分类和汇总，并着重从多线性投影方式出发，讨论了其内在联系及优缺点；分析了张量模式与向量模式表示间的本质关系及各自优势；探讨了张量型学习算法有待解决的问题及可能的研究趋势。

It is not easy to solve the problem of tensor product multilinear mapping if only matrix algebra knowledge is used. The introduction of structure matrix will make this problem much easier to be solved and more acceptable among people.

在解决张量积多重线性映射问题时，只用矩阵代数知识解决问题有些繁琐，而引入结构矩阵来解决张量积多重线性映射问题，不仅能使问题变得更加简单而且更加容易理解接受。

This is based on the definition of tensor product over R〓= R〓 R〓, where R is a noncommutative ring.

这是建立在〓上的张量积，其中R是非交换环。

In case of high input dimension system model, taking norm of input vector as the input of wavelet network instead of using tensor product method to construct wavelet network ,which could solve the problems of high computation and curse of dimensionality.

在模型结构方面，对于多维输入输出系统建模，本文放弃选用传统的标量积确定小波基函数的方法，将输入矢量的范数作为小波网络基函数的输入变量，从而避免了高维输入所带来的可用小波基数量巨大和计算复杂的缺点。

It is shown that the elements of the probability damage tensor matrix obey the normal distribution.

结果表明，眼前山铁矿南帮岩体概率损伤张量矩阵的元素均服从正态分布。

The key idea is that the proposed numerical scheme involves the operator splitting technique, balance tensor diffusivity, Runge-Kutta time-stepping method, and a conjugate gradient iterative solver.

此法最主要的概念是使用一种分离的离散式、数值平衡扩散式、时间前进法及共轭梯度法来求解。

According to thermal conduction theories of anisotropic materials that are irradiated with continuously modulated laser, a photothermal measuring method about the thermal conductivity tensor and the orientation of the principal axis of the conductivity of arbitrarily opaquely anisotropic materials is given based on the theories of So(3) group rotation.

以在连续调制光辐照下的各向异性介质的热传导理论为基础，通过So(3)群转动理论，导出不透明各向异性介质的热导张量和热导主轴方向的光热测量方法。

By introducing reasonable fundamental assumptions and the Green strain in orthogonal curvilinear coordinates,geometric equations expressed by the Green strain tensor for solving thin shells with large deformation are derived in this paper.

将正交曲线坐标下的格林应变张量引入到薄壳大变形分析，通过建立恰当的基本假设，直接导出了用格林应变张量表示的壳体变形几何方程，将该方程代入到本构方程，由能量原理得到了小应变非线性变形平衡方程、内力方程和边界条件，在此基础上提出了大应变变形的简化分析方法。

I want to be a big fish in a small pond.

我要做一条在小池塘里的大鱼。

While the software functioned well, we did not feel the same about their customer support!

虽然该软件运行良好，我们没有同样的感觉他们的客户支持！