Say that it is a gradient field.
如果F是梯度场。
为什么要说F是一个梯度场？
Now it should be a gradient field.
那么它应该就是一个梯度场。
也就是梯度场。
So, indeed, this is not a gradient field.
因此这不是一个梯度场。
It is a gradient field. We need three conditions.
这是一个有势场，我们需要三个条件。
We have said if we have a gradient field then we have this.
如果有一个梯度场，那就能得到这个。
If you have a gradient field then it should have this property.
如果给定一个梯度场，那么它就应该满足这个性质。
And that means also it's a gradient field. It's the same thing.
这意味着，F是个梯度场，这是一样的。
So, if you have a gradient field, it's what's called conservative.
如果有一个梯度场，它也是一个保守场。
So, in particular, only if you have a conservative field, a gradient field.
特别地，仅当是保守场，即有势场时才可以使用。
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。
An enhanced image is finally reconstructed from the target gradient field by least square fitting.
最后采用最小二乘拟合从目标梯度场重建出增强后的图像。
It changes things quite a bit, however, when it comes to testing whether a field is a gradient field.
然而，当考虑到一个场是否是一个有势场时，它有极大的影响。
If you fail this test then you know for sure that you are not gradient field so you might as well do that.
如果通不过检验，那么可以肯定，它不是梯度场，你可能也会那样做。
In this study, a new magnetic resonance (MR) fast imaging method in the invariant gradient field is presented.
本研究提出了恒定梯度场下磁共振快速成像的方法。
And it is a gradient field in that part of the plane and conservative and so on. The answer for now is, in general, no.
在那部分平面上，梯度场，是保守的，目前来说结论一般是不对的。
Well, if we know that it's a gradient field, that we've seen that we get these properties out of the fundamental theorem.
如果我们知道它是一个梯度场，就可以由基本定理，得到上面那些性质。
And, basically, we say that these properties are equivalent being a gradient field or being path independent or being conservative.
根本上说，以下性质是等价的，一个向量场是梯度场，等价于积分与路径无关，也等价于向量场是保守的。
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。
The size of current path, resistivity, power density are main factors that effect the temperature field and temperature gradient field at crack tip.
试件的通流尺寸、电阻率、导入电流密度是影响裂纹尖端温度场和温度梯度场的主要因素。
Points are moved onto the iso-surface by an iterative clustering along gradient field, where the noise and outliers are removed and defective data are repaired.
原始点云经梯度方向迭代移动后，过滤噪音和剔除离群点，并修补点云缺失数据。
The test that we saw last time saying, well, to check if something is a gradient field if it's conservative, 0 we just have to compute the curl and check whether it's zero.
由上次的测试可知，如果一个东西是保守的，要确定是不是梯度，我们只需要计算旋度，查看它是否是。
The invention is used for measuring the distribution of the space charges in the high-voltage direct current power equipment insulation in the temperature gradient field.
本发明用以测量温度梯度场下高压直流电力设备绝缘中的空间电荷的分布。
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。
Well, if I have a gradient field, then if I try to compute this line integral, I know it will be the value of the function at the end point minus the value at the starting point.
如果有一个梯度场，然后想计算线积分，我知道积分值是,起点的函数值减去终点的函数值。
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。
For the natural convection in enclosure under permanent magnetic gradient field, the way to generate different magnetic accelerations by different magnetic field arrangements is developed.
针对永磁梯度磁场作用下封闭腔内的自然对流换热，提出通过不同磁场布置产生不同磁加速度的方法。
The problem is not every vector field is a gradient.
问题是，不是所有向量场都是梯度。
The problem is not every vector field is a gradient.
问题是，不是所有向量场都是梯度。
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