equations

Equations are generally written with a two-bar equals sign.

等式通常用两道横的等号来表示。

To derive the transformation equations , we return to Fig. 14-1.

为了求出这个变换式, 我们回顾图14 - 1.

Einstein's equations showed the Universe to be expanding.

爱因斯坦的方程式表明宇宙正在膨胀。

After each reduction, the remaining equations remain symmetric and banded.

在每次约化后, 余下的方程是保持对称和带状的.

The characteristic equations of the two equations are identical.

两方程对应的特征方程是恒等的.

Einstein's equations showed the Universe to be expanding...

爱因斯坦的方程式表明宇宙正在膨胀。

Thus, enough equations are generated to make the problem determinate.

于是, 产生了足够的方程使问题为定解.

We propose a preconditioner based on the block diagonal matrices of SFVEM discretization system of2-D three temperature radiation heat conduction equations.

在三角形剖分下，针对二维三温辐射热传导方程组的SFVEM离散系统，设计了一类基于块对角逆的预条件，给出了条件数的理论估计式。

Anisotropic Tensor Force Finite Element Method of IFT Theory for Simplified Navier-Stokes Equations

简化Navier-Stokes方程的IFT理论的各向异性张力有限元法

This overall set of equations will now be determined.

现在将要确定这个总的方程组.

Lame-Maxwell equations of equilibrium have important applications in photoelasticity.

拉密 - 麦克斯韦平衡方程在光测弹性力学中具有重要的作用.

The situation can be handled conveniently by equations as follows.

这种情况可以用下面的公式很方便地表达.

Section 7.2 contains a resume of the fundamental equations.

第7.2节包括那些基本方程的摘要.

The overwhelming majority of nonlinear differential equations are not soluble analytically.

绝大多数非线性微分方程是不能用解析方法求解的.

Also derived in the paper are the Green-Lagrange strain tensor and the second Piola-Kirchhoff stress tensor in the Riemann space of the shell. Finally, on the basis of the virtual work, the non-linear equilibrium equations of thin-shell structures are developed.

其间，导出了其壳体黎曼空间中的Green－Lagrange应变张量和第二类Piola－Kirchhoff应力张量的表达形式，并通过虚功原理，建立了薄壳结构的非线性平衡关系。

These are equations of local conservation of mass and the jump condition.

这些就是局部质量守恒方程和跃变条件.

By the use of tensor calculus, basic aerothermodynamic equations in conservative form and characteristic theory in non-orthogonal curvilinear coordinates are derived. The boundary conditions in solving these problems are then discussed in detail. An improved version of MacCormack difference scheme is used in the numerical solution.

本文使用张量工具，导出非正交曲线坐标下弱守恒型基本方程组与特征理论，较全面地讨论了这类问题的边界条件；

Einstein's equations showed the Universe to be expanding

爱因斯坦的方程式表明宇宙正在膨胀。

Based on the Frenet-Serret formulas which are very important in the vector and tensor analysis theory, the force and moment equilibrium equations are established by the technique of apparent components system.

以在空间曲线理论中起重要作用的富列耐塞勒（Frenet Serret）公式为基础，把BHA所受的力及力矩表示为三维非正交坐标系中视分量的形式，建立了力和力矩平衡方程。

Governing Equations and Numerical Solutions of Tension Leg Platform With Finite Amplitude Motion

张力腿平台有限振幅运动的方程和数值解

They conclude their paper by showing how some partial differential equations and physical law can be expressed in tensor form.

他们在文章的末尾指出了如何把某些偏微分方程及物理规律表示成张量的形式。

Economic models often lead to the study of systems of equations.

经济模型经常导致对方程组的研究.

Even in this case the equations of motion cannot be integrated exactly.

即使是在这种情况下,运动方程也是不能精确积分的.

But when the Φ value is higher, as the Φ increases, τ is hardly altered. In the process of squeeze cast particles reinforced metal matrix composites, the temperature equilibrium equations of infiltration zone were established and solved.

但当Φ值很大时，Φ的升高使τ＊的减少不明显.建立了挤压铸造MMCs过程中液态金属浸渗区和未浸渗区的温度平衡方程，并求出了差分解。

The three-dimensional boundary layer equations with rotation terms are formulated in general tensor form.

本文对三维普遍张量形式的边界层方程进行了求解。

The Navier-Stokes equations are established for a nonorthogonal curvilinear cylindrical coordinate system based on tensor analysis.

本文根据张量理论，建立了非正交曲线柱坐标系中的N&S方程。

A Class of Coupled Nonlinear System of Hyperbolic Equations Analysis on Load-transfer Characters of Uplift Piles under Tensile Loading Based on Hyperbolic Model

基于双曲线模型的抗拔桩荷载传递分析方法研究

Based upon the equations of tension in continuous rolling, a steady state mathematical model is established, and the variation of thickness and tension with variations of roll gap, roll speed, slab thickness and hardness calculated with an electronic computer.

本文以连轧张力公式为基础建立了稳态数学模型，在电子计算机上计算了分别改变辊缝、轧辊速度、坯料厚度和坯料硬度时，厚度和张力的变化值，即影响系数。

Such steps mean the simultaneous solution of either two linear equations.

这样的步骤意味着同时求解两个线性方程.

These series satisfy all of the governing equations, crack surface boundary conditions term by term. Furthermore, some additional multi-valued terms in these series are introduced to satisfy the prescribed resultant conditions of forces and single-valued conditions of displacements around pin-holes.

该级数逐项满足弹性力学所有基本方程、裂纹表面边界条件与绕钉孔的合力平衡条件以及位移单值条件。