The problem is not every vector field is a gradient.
问题是，不是所有向量场都是梯度。
Well, we've seen this criterion that if a curl of the vector field is zero and it's defined in the entire plane, then the vector field is conservative, and it's a gradient field.
我们已经知道了一个准则，如果向量场的旋度为零，而且它在整个平面上有定义，那么这个向量场是保守的，而且它是个梯度场。
If we have a vector field that cannot possibly be a gradient then we shouldn't try to look for a potential.
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。
So, if the gradient of a function is a vector, the divergence of a vector field is a function.
如果说函数的梯度是向量，那么向量场的散度就是函数。
Well, actually here it is not very hard to find a function whose gradient is this vector field.
实际上，找出一个函数，其梯度是这个向量场并不难。
OK, so, we've seen that if we have a vector field defined in a simply connected region, and its curl is zero, then it's a gradient field, and the line integral is path independent.
一个向量场,如果定义在单连通区域并且旋度为零，那么它就是一个梯度场，并且其上的线积分与路径无关。
One is to say that the vector field is a gradient in a certain region of a plane.
一个是向量场,在给定平面区域内是梯度场。
Ok, so just to reinforce my warning that not every field is a gradient field, let's look again at our favorite vector field from yesterday.
好的，为了强调，不是所有场都是梯度场，我们再来看看昨天那个向量场。
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.
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。
Say that f, our vector field is actually the gradient of some function.
也就是向量场f实际上是一个函数的梯度。
If you take the gradient of this, you should get again this vector field over there.
对这个函数取梯度，你应该又得到这个向量场。
And, of course, it is not a coincidence because this vector field is a gradient field.
当然这并非巧合，因为这个向量场是有势场。
In this paper, on the basis of Gradient Vector flow (GVF) snakes, a fully automatic image segmentation algorithm based on the analysis of flow field and the minimal path method is proposed.
人工干预使蛇模型只能用于半自动的图像分割，该文在梯度向量流(GVF)蛇模型的基础上提出一种基于流场节点与最小路径方法的全自动图像分割算法。
In this paper the transmission of paraxial light beams was analyzed based on the gradient vector potential of electromagnetic field.
本文运用电磁场的梯度矢势分析了一般情况下傍轴光束的衍射传输问题。
Based on prediction of searching starting-point and gradient diamond-shaped searching technique, the paper proposes a motion vector field self-adaptive searching algorithm (MVFSAS).
在基于搜索起点预测和梯度式菱形搜索方法的基础上，提出了一种运动矢量场自适应搜索算法(MVFSAS)。
According to features of edge gradient maps of face images, a new eye feature extraction algorithm based on gradient vector flow field was proposed.
根据人脸图像的边缘梯度图提出了一种新的基于梯度向量流场的眼睛特征提取方法。
Magnetic gradient tensor is that the three components of the magnetic field vector space rate of change, is able to do well for the dipole localization and tracking.
磁力梯度张量表示的是磁场矢量三个分量的空间变化率，能够很好地用于偶极子场源的定位跟踪。
This indicates that there is more profound physical meaning of the gradient vector potential of electromagnetic field.
因此，它表明电磁场的梯度矢势具有更明显的物理意义。
This indicates that there is more profound physical meaning of the gradient vector potential of electromagnetic field.
因此，它表明电磁场的梯度矢势具有更明显的物理意义。
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