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The functional relation between incident angle and refractive angle of energy flow is obtained. According to this relation, we can restructure the refractive angle as negative or positive readily by selecting suitable permittivity and permeability tensors.

导出了电磁波的入射角和能流折射角之间的函数关系,根据此关系可方便地选择合适的介电张量和磁导率张量,使特定入射角所对应的折射是正或是负。

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。

The definition of tensor product function was expounded, and its characteristic of convenient for probability integral was analyzed.

给出了张量积函数的定义,分析了张量积函数易于概率积分的特性。

Difference set is one kind of unbounded difference poset. The existenceof the tensor products of two cancellative difference sets are investigated. It isproved that the tensor product of a Boolean algebra and a cancellative differenceset always exists.

作为差分偏序集无界推广的差分集,我们研究了它的张量积问题,证明了任何消去差分集和布尔代数的张量积一定存在。

We calculate the energy-momentum pseudo-tensor of relic gravitational wave of both the polarized states by Riazuelo-Uzan expression of the energy-momentum pseudo tensor in the Cartesian coordinates, we can see that energy density and momentum densities of relic GWs are dependent on cosmic scale factor and square of the amplitudes,. At the same time, the energy density of relic GWs is positive definite, the momentum densities components have reasonable physical behavior,and their values are independent on the directions.

我们还用Riazuelo-Uzan表述在直角坐标系下对双极化态的遗迹引力波的能量动量赝张量进行计算,发现双极化态的遗迹引力波的能量张量密度与他们的振幅的平方和宇宙学尺度因子有关,他们的能量密度是正定的,大小跟传播方向无关,即遗迹引力波在宇宙学尺度上是各项均匀同性的。

Multiplication of a tensor by a scalar quantity yields a tensor of the same order.

张量和标量相乘仍为同阶张量

In contrast, in the linearized theory the deformation tensor is the sum of a rotation and a strain tensor and the order of their application is immaterial.

相反,在线性理论中,形变张量是旋转和平动张量的和,其值的数量级大小不重要。

We have described the stress tensor arising from equilibrium considerations and the strain tensor arising from kinematical considerations.

我们已经叙述了应力张量和应变张量的有关概念和某些特质,它们是分别从平衡的角度和运动的角度推导而得的。

Based on definition of strain energy function,increment formula of stationary potential energy of finite displacement theory were derived in terms of Kirchhoff stress tensor and Green strain tensor.

基于有限位移理论应变能密度函数的定义,利用Kirchhoff 应力张量和Green应变张量,推出了非线性分析中增量形式的势能驻值公式,并证明了由势能增量驻值原理得到的增量平衡方程形式与由虚位移原理所得的结果完全一致。

From the point of view of perfect interface, the stress tensor and the strain tensor are decomposed into two orthogonal complementary parts: in-plane components and out-of-plane components at interface, respectively.

从理想界面的观点出发,分别将应力张量和应变张量在界面坐标系下分解为面内分量和面外分量。

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