查询词典 strain tensor

Finally, after defining an evaluation module of the corresponding Loop superalgebra (Section 4), two major results of the paper -Theorem 4.land Theorem 4.2 are proved: Theorem 4.1 reduces the irreducibility of the tensor product of finitely many evaluation modules to the irreducibility of the tensor product of finitely many irreducible modules of a nilpotent Lie superalgebra; Theorem 4.2 gives a criterion for the tensor product of such modules to be irreducible.

第4节在定义了相应的Loop超代数的赋值模之后，证明了本文的两个主要结论：定理4.1和定理4.2。定理4.1将有限多个赋值模其张量积的不可约性归结为一幂零李超代数的限多个不可约模其张量积的不可约性；定理4.2利用不可约指标给出了一幂零李超代数的限多个不可约模其张量积仍不可约的判别准则。

Complicated system ; space metric tensor ; natural base ; physical base ; non-Cartesian tensor ; Cartesian tensor ; helical-Cartesian coordinate system ; parabolic cylindrical coordinate system

复杂系统；空间度量张量；自然基物理基；笛卡儿张量；非笛卡儿；张量；螺旋线——笛卡儿坐标系；抛物柱面坐标系

With the help of the notation of the skew-symmetric tensor, the expression for the 1st order absolute and relative derivatives of a tensor was presented, and the expression for the 2nd order absolute and relative derivatives of a tensor was offered further.

由此，并借助于反对称张量，给出了张量的一阶绝对导数和相对导数之间的关系式，并又进一步给出了张量的二阶绝对导数和相对导数之间的关系。

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。

Then, the permeability tensor theory is utilized to calculate permeability tensor value of each measured chamber section in order to obtain crack medium three-dimension permeability tensor field.

针对裂隙岩体的非均质性、各向异性特点，本次毕业设计对紫坪铺水利枢纽工程地下洞室开挖后洞壁裂隙结构面进行了几何参数测量和分组，再利用渗透张量理论计算各测量洞段渗透张量值，获得裂隙介质三维渗透张量场。

First, a non-negative tensor factorization algorithm is improved by imposing sparseness constraints on it. Secondly, the bispectral images of mechanical signals are obtained and stacked to form a third-order tensor. Thirdly, the improved algorithm is used to extract features, which are represented by a series of basis images from this tensor. Finally, coefficients indicating these basis images' weights in constituting original bispectral images are calculated for fault classification.

首先，改进已有的非负张量分解算法，加入稀疏度控制策略；其次，将机械振动信号的双谱图像堆叠为一个三阶张量；然后利用改进后的分解算法对该张量进行二次故障特征提取，得到代表局部特征的"基图像"；最后，通过计算得出基图像在构成原双谱图像中所占的权重，并将得到的权重向量用于故障分类。

In this framework, image frame, audio and text are represented, which are the three modalities in video shots as data points by the 3rd-order tensor. Then a subspace embedding and dimension reduction method is proposed, which explicitly considers the manifold structure of the tensor space from temporal-sequenced associated co-occurring multimodal media data in video. It is called TensorShot approach. Transductive learning uses a large amount of unlabeled data together with the labeled data to build better classifiers. A transductive support tensor machines algorithm is proposed to train effective classifier. This algorithm preserves the intrinsic structure of the submanifold where tensorshots are sampled, and is also able to map out-of-sample data points directly. Moreover, the utilization of unlabeled data improves classification ability.

在此框架中，视频镜头首先被表示成由视频中所包含的文本、视觉和听觉等多模态数据构成的三阶张量；其次，基于此三阶张量表达及视频的时序关联共生特性设计了一种子空间嵌入降维方法，称为张量镜头；由于直推式学习从已知样本出发能对特定的未知样本进行学习和识别，最后在这个框架中提出了一种基于张量镜头的直推式支持张量机算法，它不仅保持了张量镜头所在的流形空间的本征结构，而且能够将训练集合外数据直接映射到流形子空间，同时充分利用未标记样本改善分类器的学习性能。

We first prove a formula to calculate the magnetic field in the internal region of magnetized objects on the viewpoint of magnetization, and then use the formula to define the point-function demagnetizing tensor and also prove some properties of the tensor. Finally we use this formula to construct a new method to predict the induced magnetic field of naval vessels in a nonuniform applied field, and we call it 'the Magnetization Method', in which the point-function demagnetizing tensor is used.

首先证明了一个基于磁化观点的铁磁物体内部磁场强度计算公式，随后通过该公式导出了点函数去磁张量的概并证明了它的一些性质，最后利用此公式构造了一个预测非均匀外场中舰船感应磁场的新方法——磁化强度法，且在该方法中用到了点函数去磁张量。

The osculating relation exists between rockfill fabric tensor and stress tensor, which have been proved theoretically in this paper. So creep mechanism and deformation law of rockfill can be gained from varying of fabric tensor. As a result creep mechanism of rockfill creep may be revealed from microcosmic view.

堆石体组构张量与应力张量和应变张量有密切的关系，从组构张量的变化可以导出堆石体的变形机理和规律，从而揭示堆石体材料流变变形的细观机理。

Results indicate that when the strain rate is 1200 s-1, the twin number of samples in different orientation increases with plastic strain increasing; when the strain rate increases to 2800 s-1, the σ-ε curves have no obvious charges as the angle is 0o and 45o, compared with that at 1200 s-1; however the σ-ε curves vary from concave to convex when the angle is 90o, because thermal softening has occurred with increasing plastic strain, which results in the number of twin decreasing, and smaller strain hardening

结果表明：当加载应变率为1200 s-1时，不同取样方向的样品中孪晶数量均随塑性变形应变量的增大而增多；当加载应变率增大到为2800 s-1时，取样方向为0°和45°、流变曲线形状较应变率为1200 s-1时没有明显变化，而取样方向为90°时曲线形状由应变率为1200 s-1时的凹形变为凸形，曲线形状变化的原因是由于应变量增大，热软化效应使得孪

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。