它们在有关的计算和证明中应用非常多。
It has many applications to calculations and proof of geometry.
与一般的民事侵权行为相比，垄断行为造成的侵害有显著的特殊性，因此垄断损失的计算和证明多采用专家证言形式。
Since the notable particularities of antitrust violation compared with common tort behavior, the calculation and proof of the loss caused by an antitrust violation mostly rely on expert testimony.
科学家们称他们的计算证明了该制动系统的可靠性良好，能适用于飞机、火车和工厂的控制系统。
The scientists say their calculations have proved the brake system's reliability is so good it could be used to control systems in aircraft, trains and factories.
此外，Wolfram和MatthewCook还证明了110规则在计算上等同于一个一般性图灵机。
Moreover, Wolfram, and Matthew Cook have proven that rule 110 is computationally equivalent to a universal Turing machine.
但事实证明这些逻辑思考的例子要在计算机上实现其实并没有那么困难；所有它所需要的只是一些定义良好的规则和庞大的计算能力。
But it turned out that these examples of logical thinking are actually not so difficult for a computer to duplicate; all it takes is a few well-defined rules and a lot of computing power.
公司现在必须能够证明客户的计算机系统可以满足审计人员法规条例和遵从性的要求。
Companies must now be able to demonstrate that their computer systems meet the requirements of regulatory bodies and the compliance demands of auditors.
1986年，法马，惠普和考夫曼的计算机实验工作证明了这些观点。
These ideas have been shown to work in computer experiments in 1986, by Farmer, Packard and Kauffman.
它证明了云计算的强悍——可以从远距离的庞大数据中心而不是从电脑自身的硬盘驱动器准备好软件和信息。
It testifies to the power of cloud computing-the serving-up of software and information from big, distant data centers rather than from a computer's own hard drive.
一方面，云计算的提供商们比如amazon和Google已经证明云计算是运营it系统更有效率的方式。
For one, operators of computing clouds such as Amazon and Google have shown that this is a far more efficient way of running IT systems.
共同研究者Paul Kinsler博士研究证明了设计使用自定视觉纤维的理念，这将使研究人员能够将事件斗篷用在信号的处理和计算过程中。
Co-author Dr Paul Kinsler developed a proof of concept design using customised optical fibres, which would enable researchers to use the event cloak in signal processing and computing.
由两个测区的实测重力资料计算分析和对比，证明改正格值受温度影响后，重力资料的精度有所提高。
Through calculating, analysing and comparing the real data measured in two regions, indeed, it is proved that precision of gravity data after temperature correction increased somewhat.
通过对传统的仿形靠模设计和制造缺陷的分析，提出了用计算机辅助设计仿形靠模，实践证明，这是一种行之有效的方法。
Analyzing the traditional defects in the design and making of the profiling mould, this paper puts forward the computer aid mould design, a feasible method demonstrated by actual practice.
实验和计算结果证明激光能够干扰红外成像制导系统，并使其命中概率大幅度下降；
The experiments and calculation results prove that the laser weapons can disturb the IR imagining guided system and make the hitting probability decline greatly.
计算实例证明，利用波浪预报和切片理论相结合分析运输可行性的方法，可以得到满足工程需要的分析结果。
It is indicated by calculated example that the feasibility analysis method combining precise forecast of wave and wind with strip theory can give satisfactory results for engineering.
在介绍极化编码及相关检测原理的基础上，利用理想编码信号和实际数据进行了计算机仿真，仿真结果证明了此方法的有效性。
On the basis of the principle of polarization coding and correlative detection, computer simulation is done for the ideal coded signal and real data, the results prove the effectiveness of the method.
实验证明，该算法不但可以有效地克服标准遗传算法的缺陷，而且计算速度、精度和算法稳定性也得到了显著提高。
The research results show that the algorithm can not only overcome the shortcomings of SGA effectively, but also evidently improve the computing speed, computing precision and computing stability.
计算机模拟得到了很好的再现结果，证明了该方法的可行性和有效性。
The feasibility and validity of this method is demonstrated by computer simulation and the reconstructed image.
实验证明，该算法不但可以有效地克服标准遗传算法的缺陷，而且计算速度、精度和算法稳定性也得到了显著提高。
The research results show that the algorithm can not only overcome the short comings of SGA effectively, but also evidently improve the computing speed, computing precision and stability.
证明过程中主要应用了分析中的压缩映象原理和一些空间的性质，通过构造可计算函数，来把解从一个区间延拓到整个空间。
We mainly apply the contraction principle in analysis and properties of some Spaces. By the computable functions constructed, we extend the solution from the internal to the entire space.
计算的结果证明用狭义和广义等效辐射截面系数来计算立体金属目标的天线温度对比度是可行的。
The results proved that it was feasible to count the ATC of metal solid objects by using its special and general ERSC.
给出了应用该方法的具体步骤，通过模拟和实际数据计算证明了该方法的有效性。
Specific steps of the method are given, and the effectiveness is proved by simulation and actual data calculations.
通过模型试验的计算结果与实测值的比较，证明本文理论的合理性和有效性。
Through comparison between the calculated and measured results from model tests, the validity of present theory is verified.
通过计算机模拟实验，证明这种方法在移动障碍和移动目标的环境中能有效的实现机器人避碰和导航。
In the computer simulation experiment, this method can efficiently implement robot path searching in the dynamic environment with both moving obstacles and moving targets.
通过推导计算与实例证明，该驴头的行程、传动效率、线性度和寿命都满足设计要求。
By the derivation, calculation and illustration it is testified that the that of stroke, transmission efficiency, linearity and life time meet the design requirements.
通过推导计算与实例证明，该驴头的行程、传动效率、线性度和寿命都满足设计要求。
By the derivation, calculation and illustration it is testified that the that of stroke, transmission efficiency, linearity and life time meet the design requirements.
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