好滴，目前这里，在有定义的区域里，减掉原点，即移去原点，就不是单连通的。
OK, so for this guy, domain of definition, which is plane minus the origin with the origin removed is not simply connected.
我们来看中间的那个点，在原点上，那就是一个鞍点，在这点做一个切平面,你可以看到这个切平面,是在原点上水平的。
See the point in the middle, at the origin, is a saddle point. If you look at the tangent plane to this graph, you will see that it is actually horizontal at the origin.
力场由一个指向原点的向量场给出，并且此向量场的大小，与其到原点的距离的平方成反比。
That would be given by a vector field that points toward the origin and whose magnitude is inversely proportional to the square of a distance from the origin.
也就是，这个向量场等价于,从原点指向给定位置的向量，所以它是以原点为心向外辐射的。
Well, , see, that is a vector field that is equal to the vector from the origin to the point where I am, so it is pointing radially away from the origin.
举个例子，取一个圆心为原点的圆盘，重心应该在原点。
For example, take a disk center at the origin, well, the center of mass should be at the origin.
类似的，对于任何不经过原点的环路，都能找到一个以之为界的曲面，该曲面不经过原点。
So, and similarly, if I take any other loop that avoids the origin, I can find, actually, a surface bounded by it that does not pass through the origin.
清单4 所示代码实现不是将现有对象以中心为原点进行旋转，而是以其左上角为原点进行旋转。
The code in Listing 4 didn't actually rotate the object in place around its center, but around its upper-left corner.
于是先写上，因为是从原点指向定点的向量，从而它也是从原点向外辐射，现在出现个小问题。
Maybe I should start by writing because that is the vector that goes from the origin to my point so it points radially away from the origin Now there is a small problem with that.
算出这个积分，我们要做的是-，把原点固定，然后绕着原点旋转。
When you integrate this, - the motion that we try to do — we keep this fixed and then we just rotate around the origin.
那么在我画的这幅图中,充满了方向指向原点的向量场,离原点越远，它就越小。
The picture, if I really wanted to draw a picture, would be everywhere it is a field that points towards the origin. And if I am further away then it gets smaller.
如果该曲面过原点，只需稍微摆动一下，就能保证它不再经过原点。
Well, if that surface passes through the origin, just wiggle it a little bit, you can make sure it doesn't pass through the origin anymore.
在原点右边的细胞为正数，原点左边的细胞为负数。
Cells to the right of the origin are numbered positively, and cells to the left of the origin are numbered negatively.
特别地，取原点,让物体以一定的角速度，围绕原点旋转。
Instead of just somewhere,maybe I will have the origin,and I am trying to make it go around the origin in a circle at a certain angular velocity.
无论函数是什么，如果你的函数除了原点处处为，在原点是其他的值，那积分还是0的。
no matter what value you put for a function, 0 if you have a function that's zero everywhere except at the origin, and some other value at the origin, the integral is still zero.
为了描述一条直线的方向，我们把位于原点一侧的直线叫正，而把位于原点另一侧的直线叫负。
To get a description of direction along the line we shall call the line on one side of the origin positive, on the other side negative.
同时还研究了一类五次系统原点的中心条件及在同步扰动下原点与无穷远点的极限环分支问题。
At the same time, the center conditions and bifurcation of limit cycles at the origin of the quintic polynomial system are also investigated.
通过对工件原点的剖析，提出了一种在数控机床或加工中心上，通过人工快速、准确地找到工件原点的方法。该方法在实际工作中有一定的推广应用价值。
Through analysis of part origin, Lodge a method pass artificially quick accurate search out part origin at CNC machine tool. The have surely extend apply value at practical work.
该方法不但能保证闭环系统稳定，而且可使跟踪误差收敛于原点或原点的一个小邻域内。
It is proved that the proposed method can not only guarantee the stability of the closed-loop system, but also make the tracking error converge to the origin or its small neighborhood.
基于纯压缩原点竖向刚度和偏压原点刚度理论，提出了预测橡胶座压缩变形量的计算理论。
Based on the basic concept and calculating theory suggested newly, the deformation calculating theory related to pure compression state and shear compression state of isolating bearing is established.
如果两个节点的距离比原点和离原点最远节点之间距离的0.01%大，则认为两个节点具有非一致性。
The two nodes in the spring are considered non-coincident if the distance between them is more than 0.01 percent of the distance between the origin and the node farthest from the origin.
数控加工中有许多“点”，如机床原点、机床参考点与工件原点等，理解和掌握这些“点”是正确进行数控加工的基础，因此，本文对数控加工中这些关键的“点”进行了分析和比较。
To correctly implement NC machining, it is necessary to grasp the meaning of these points. Therefore, these key points are analyzed and compared with each other in this paper.
同样，旋转以原点为中心的对象与旋转已离开原点的对象所得到的结果也不同。
Similarly, rotating an object that is centered at the origin produces a different result than rotating an object that has been moved away from the origin.
获取原点宽度，即页面左边缘到成像区域左上角(也称为成像区域的“原点”)的距离。
Gets the origin height, which is the distance from the upper-left corner of the imageable area (also called the "origin" of the imageable area) to the nearest point on the top edge of the page.
缩放以原点为中心的对象与缩放已离开原点的对象所得到的结果不同。
Scaling an object that is centered at the origin produces a different result than scaling an object that has been moved away from the origin.
缩放以原点为中心的对象与缩放已离开原点的对象所得到的结果不同。
Scaling an object that is centered at the origin produces a different result than scaling an object that has been moved away from the origin.
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