那么我就能名正言顺地,用R上的某个函数的二重积分来替代通量的线积分。
Then I can actually -- --replace the line integral for flux by a double integral over R of some function.
除了这些，旋度还有一个用处，如果你还记得，我们讨论平面的时候,当把线积分转换成二重积分的时候。
But another place where this comes up, if you remember what we did in the plane, curl also came up when we tried to convert line integrals into double integrals.
但是你知道，它给了你一个例证，其中你可以，把复杂的线积分化成简单些的二重积分。
But, you know, it gives you an example where you can turn are really hard line integral into an easier double integral.
不管是线积分或是二重积分，也不管它们表示的是功还是通量，计算它们的方法实际上是一样的。
And whether these line integrals or double integrals are representing work, flux, integral of a curve, whatever, the way that we actually compute them is the same.
用格林公式计算…，只是计算…，让我们忘记…，应该是，算沿闭曲线的线积分值，可以通过二重积分来算。
To compute things, Green's theorem, let's just compute, well, let us forget, sorry, find the value of a line integral along the closed curve by reducing it to double integral.
不管哪种形式，都把线积分和二重积分联系在一起，来看看，能不能通过化简得到昨天的公式。
No matter which form it is, it relates a line integral to a double integral Let's just try to see if we can reduce it to the one we had yesterday.
我们已经学过，二重积分和线积分。
We've learned about double integrals, and we've learned about line integrals.
每两条线之间，有一个面团搅拌机，用于生产180公斤重的面团，分别倒入两侧生产线上。
For every two production lines, there was a dough mixer, which produced 180 kg lumps of dough that could be dumped to the left or the right.
我们对z=2重复这个过程，就得到另外的等高线，如此种种。
OK, and so we repeat the process with maybe z equals two, and we get another level curve, and so on.
上述两根管子最开始是接到水面“深水地平线”钻井平台的，而如今已经重新被专业人员用重质的管道连接到了附近一个叫做管汇（manifold）的金属架状结构上。
The two pipes, which originally went up to the Deepwater Horizon, have been reconnected with heavyweight hoses to a metal framework called a manifold that has been installed nearby.
船舶型线设计在船舶设计中居于十分重要的地位。
Ship lines design has been playing the important role in ship design.
梦境依旧会扮演一份十分重要的角色，作为我们依旧在清理的时间线，契约，协议和过去转世的问题。
Dreams are still playing a very important part as we are still clearing timelines, contracts, agreements and past lives.
图12。边界重色线的里维拉RI的板不适用，周围是北美太平洋PA的，和科科斯CO的车牌。
Figure 12. Boundaries (heavy colored lines) of the Rivera (ri) plate, surrounded by North America (NA), Pacific (PA), and Cocos (co) plates.
图17。边界重色线的爱琴海as和安纳托·利亚上板，这是包围的非洲自动对焦，沙特阿拉伯机铁，以及欧亚欧盟的车牌。
Figure 17. Boundaries (heavy colored lines) of the Aegean Sea (as) and Anatolia (at) plates, which are surrounded by the Africa (AF), Arabia (ar), and Eurasia (EU) plates.
超越重山和地平线。
生产线的柔性组合在这里起着十分重要的作用。
Production line flexible combination plays a key role in this process.
生产线控制系统是计算机集成制造的核心，其对于电子产品流水线生产企业而言，具有十分重要的作用。
Production line control system is the core of the Computer Integrated Manufacturing (CIM), an important system for the electronic line production enterprise to improve the productivity and quality.
中性线近地侧的等离子体团朝着地球运动，并合并于地球附近的重联区内。
The plasmoids on the earthward side of the neutral line move toward the earth and coalesce with the reconnection region near the earth.
便携式轴重仪主要组成部分为传感器，秤台台面、仪表、接线盒、数据线。
Portable axle load meter is mainly composed of sensor, weighing table, meter, junction box, data line.
结论重睑者重睑线与睑缘间有皮肤皱褶是一种常见的，并较易被人们接受的美学表现。
Conclusion the double eyelids person with skin fold between double eyelids line and palpebral edge is a common aesthetic phenomenon and accepted by the people.
图18。西部边界(重色线)的索马里(苏)由非洲板块，包围(自动对焦)，南极洲(安)，印度(中)和沙特阿拉伯(阿肯色州)。
Figure 18. Western boundaries (heavy colored lines) of the Somalia (SO) plate, surrounded by Africa (AF), Antarctica (an), India (in), and Arabia (ar).
焊管机组在线矫平机是焊管生产线的主要设备之一，为了确保高强度、大直径、厚壁焊管生产的顺利进行，矫平机的性能十分重要。
Online Flattener is main equipment of welded pipe unit, the property of Flattener is very important to ensure production of welded pipe with larger wall thickness going well.
方向彼此相反的磁场在此处重连，半数新生成的磁力线迅速向底部移动，堆叠在既有的磁环上面。
The oppositely directed magnetic fields reconnected there, and half of the newly formed field lines shifted rapidly downward, where they stacked up on existing magnetic loops.
介绍了大秦线车轮的服役表现，探讨了重载运输条件下车辆轴重增加对车轮钢种特性的要求。
The requirements on steel types and features of wheels with increase of axle load of heavy haul vehicles are discussed.
想了解磁力线重连事件中究竟发生了些什么事情，必须先对看不见的磁力环圈如何捕捉太阳大气里的热气有一些基本认识。
Following what exactly happens during a reconnection event requires, first off, a general understanding of how invisible magnetic loops can trap hot gas in the solar atmosphere.
这就是二重螺旋线的形状。
抛物线侦测在道路辨识应用中是个十分重要的议题。
Parabola detection is a fundamental problem in road recognition application.
根据工艺设计要求，对某加氢装置重沸炉转油线的设计特点进行了讨论，对应力计算的结果进行了汇总。
The article gives a chance to discuss some features in design of reboiler oil return pipeline with respect to process design and a summary of results of stress calculation is made.
图5。菲律宾造山带（孵化的黑色边框与交叉）环绕菲律宾海（注）-巽他（苏）会聚板块边界（重色线）。
Figure 5. The Philippines orogen (black outline with cross-hatching) surrounds the Philippine Sea (PS) - Sunda (SU) convergent plate boundary (heavy colored lines).
图5。菲律宾造山带（孵化的黑色边框与交叉）环绕菲律宾海（注）-巽他（苏）会聚板块边界（重色线）。
Figure 5. The Philippines orogen (black outline with cross-hatching) surrounds the Philippine Sea (PS) - Sunda (SU) convergent plate boundary (heavy colored lines).
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