目标是一样的，就是找出势函数。
我想找出这个向量场的势函数。
那它还是个势函数。
你可能会得到，一个没有明确定义的势函数。
引入随机正则函数和随机位势函数的概念。
The concepts of random regular function and random potential function are introduced.
这是来自于势函数的。
这意味着，沿一条闭合曲线，势函数的变化量是。
That means when you go along a closed curve, 0 well, the change of value of a potential should be zero.
那么我们只需要知道，线积分正是势函数值的变化。
Then, we just have to, well, the line integral is just the change in value of a potential.
我们要做的就是关于x积分，然后得到势函数和一个积分常数。
What we do is integrate with respect to x, and we will get our potential function up to an integration constant.
这取决于你想找出一个势函数，还是找出所有的势函数。
Well, it depends whether you are just trying to find one potential or if you are trying to find all the possible potentials.
如果问题，只要求找出一个势函数，你就不必用这个常数。
If a problem just says find a potential then you don't have to use the constant.
用该位移势函数表示的应变及应力分量，其解答简捷适用。
A simple and useful representation of the stress and strain components are obtained by displacement function.
因为我们不知道，势函数是否明确定义，在洞上是否取值相同。
Because what you don't know is whether your potential is actually well-defined and takes the same value when you move all around the hole.
如果一个向量场不可能是梯度场，那我们就不应该尝试去找势函数。
If we have a vector field that cannot possibly be a gradient then we shouldn't try to look for a potential.
首先给出反平面弹性情况下，无限大域中多裂纹问题的复势函数。
Firstly, complex potential of multiple cracks problem of infinite region in antiplane elasticity was given.
通过引入“对势函数的有效核电荷”，讨论了氩原子场的物理特征。
By introducing "the effective nucleus charge number for the potential", the physical features of argon atom field have been discussed.
我们有这个积分常数，但是除去它，我们应该从这里能得到一个势函数。
We have this integration constant, but apart from that we know that we should be able to get a potential from this.
经过验证，塑性势函数等于屈服函数，流动规律为相适应的流动法则。
It has been verified that plastic potential function is equal to yield function and flow law is the associated flow rule.
本文运用赝势函数变分有限元方法数值模拟了绕翼型的跨音速有旋流动。
The variation finite element method (FEM) using the pseudo-potential function was presented for the simulation of transonic rotational flows.
引入两个势函数，在频域中得到了应力、位移和超孔隙水压力响应解答。
The analytical solutions of stresses, displacement and pore pressure amplitude are derived in frequency domain by introducing two scalar potential functions.
根据广义塑性公设，证明了塑性余位势函数在应变空间塑性区的存在性。
The plastic complementary potential function was proved to exist in the plastic region of strain space by virtue of the new plastic postulation.
推导了边界内电场势函数和力函数的解析表达式，以及非线性场表达式；
The paper reports analytic expressions on the electric potential and field lines, and the non linear field expressions derived from the potential function.
在起点取势函数的值，抱歉，在终点取势函数的值，减去起点的势函数值。
OK, so we take the value of a potential at the starting point, sorry, we take value potential at the endpoint minus the value at the starting point.
周二我们就知道，怎样确定一个场是不是梯度，如果确实是梯度的话，怎样算出势函数。
So, actually on Tuesday we'll see how to decide whether a vector field is a gradient or not, and if it is a gradient, how to find the potential function.
通过定义接触面滑动屈服函数和流动势函数，得出了热接触边界的互补方程。
Through defining slide yield function and floating potential function of thermo-contact surface, the complementary equation of thermo-contact boundary was got.
将障碍物的运动信息引入到排斥势函数中，使传统的静态势场变为动态势场。
Combining the motion information into the repulsive force function, which transform the static artificial field function to the dynamic artificial field function.
过了周末，周二我们就知道,怎样确定这些性质成立与否，以及怎样找出势函数。
OK, so after the weekend, on Tuesday we will actually figure out how to decide whether these things hold or not, and how to find the potential.
心脏运动的势函数模型是以收缩末和舒张末为节点的尖点突变的形式来表示的。
The heart beating model is described as cusp catastrophe with end node of systole and diastole.
应用变量代换的方法，导出了中心力场中势函数不同的薛定谔方程解的对应关系。
By using a method of changing variables, a relationship of solutions between Schrodinger equations for different potential functions in central field is obtained.
在第二个问题中，我们给出了在离散的情形下，指数族势函数严凸的充分必要条件。
In the second we give the necessary and sufficient conditions for strict convexity of power function of exponential family in the discrete case.
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