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The mixed boundary value problem is simplified to a pair dual integral equations using Laplace and Fourier integral transform method.

利用拉普拉斯和傅立叶变换将混合边界值问题简化为对偶积分方程，并得到裂纹尖端应力场的解析解答。

In the integral formula of Fourier transforms of option pricing formula,by using residues theorem two integrations were simplified into a single numerical integration which has a faster rate of decay.

在期权定价公式的傅立叶变换积分公式中，运用留数定理将公式中的两个积分式子化简成一个被积函数衰减较快的积分函数式，从理论上提高了计算效率，缩短了计算时间，为投资者快速计算期权价值节约了时间。

The frontogenesis process involves in the interactions among the systems of multiple scales. Since the hardness of the nonlinear problem, it is difficult to study frontogenesis analytically. The introduction of the effects of orography, friction and diabatic processes generally makes impossible the analytical resolution of the problem and leads to the use of numerical models. Primitive equations are numerical integrated together with a detailed description of physical processes. The circulation obtained is then used to diagnose and test theoretical mechanisms. It should be noted, however, that a fully description of frontogenesis in explicitly resolving the of large-, meso- and micro-scale flow in the same framework is not yet possible because of the excessive computer capacity and the time required. In order to deal with the problem, the action of large-scale background has been simplified and taken into consideration through the addition of the forcing into the nonhydrostatic cloud model.

大气锋生是一种多尺度相互作用的过程，理论研究遇到非线性的困难，在考虑地形、摩擦、非绝热等物理过程之后，解析研究更加棘手，通过数值模拟搞清其中的物理机制是重要的研究手段，但是把大、中、小尺度甚至微尺度的系统及其相互作用过程在一个模式里同时模拟好仍然受计算机速度和容量的限制，本论文在非静力云模式中通过强迫方式加入大尺度变形场的作用，在考虑到大尺度背景作用的同时，可以充分利用云模式所提供的丰富物理过程、非静力和高分辨率特点，开展一些过去较难进行的研究工作。

In addition,dynamical management of terrain dataset in view field was implemented effectively by visible detection based on the simplified view frustum and terrain data prediction strategy.

此外，简化视见体的可见性判断和数据预取策略，实现可见数据的动态管理。

This model was simplified to a single degree-of-freedom system by means of complex variable function. The stationary solution of system was solved by harmonic balance method, and the amplitude-frequency response was presented.

采用复变函数将系统的动力学方程简化，利用谐波平衡法分析了系统的稳态解，得到了系统的幅频响应。

The dynamic models were derived and simplified to be as a transfer function of the third order.

进行了闭环压力控制系统频率响应的实验，实验结果与计算结果十分接近。

GASKIN G J%MILLER J D Measurement of soil water content using a simplified impedance measuring technique 10.1006/jaer.1996.0017 Irriagric Engng Res , 1996,3

王一鸣%赵燕东基于驻波率原理的土壤水分测量方法研究北京：中国农业大学出版社， 1999，null

Firstly, from Gauss' equations and relative motion equations, the relation of control impulse and relative motion was expressed as analysis formulas and simplified based on the near circular condition. By deeply analyzing the mechanism of impulses in each directions (radial, in-track and cross-track directions) effect on relative motion respectively, two maneuvers to establish formation flying are provided: one is to utilize the impulses in radial and cross-track directions, the other is to utilize the impulses in along-track and cross-track directions. Both of the two methods can establish satellite formation flying of any configuration. The method with impulses irradial and cross-track directions needs only 3 impulses, while the method with impulses in along-back and cross-track directions needs 4 impulses. Lastly, by an example of establishing a space-circle formation flying, two maneuvers were compared with each other in the amount of impulses and fuel consuming estimation.

首先由高斯型拉格朗日轨道摄动运动方程得到轨道坐标系中控制冲量与轨道根数偏差的关系，基于近圆轨道的条件简化并带入相对运动方程，得到控制冲量与相对运动的关系表达式；通过深入分析各个方向（径向、沿迹向与轨道面法向）的控制冲量对相对运动的影响，给出了分别用径向与轨道面法向控制冲量组合和沿迹向与轨道面法向控制冲量组合实现编队捕获的两种控制策略；最后给出了一个空间圆编队捕获实例，并从燃料消耗、施加冲量次数及捕获时间等角度对比研究了两种控制策略的特点。

Though blocking computing matrix,it can decrease the calculation amount of matrix multiplication.Meanwhile,the different simplified formats are presented when computing Duhamel integration with Trapezium formula、Simpson formula、Cotes formula and Gauss formula.

通过分块计算矩阵，能够减小矩阵乘法的计算量，同时分别给出了利用梯形公式、Simpson公式、Cotes公式、高斯公式计算Duhamel积分时的不同简化格式。

By comparing with the real situation, the rationality of simplified Gauss model is proved.

通过简化模型与实际情况的比较，肯定了高斯近似简化模型在一定情况下的合理性。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。