简化方程

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。

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。

A systematic study on computing the integral curvature line on NURBS surface is presented. Discrete normal is used to simplify calculation of the second fundamental form of the surface, resulting in accelerating the Euler iteration process in solving the differential equation of curvature line. Discrete points on the curvature line are then obtained and approximated by an explicitly presented B-spline curve on the NURBS surface using singular mixed interpolation and capable of controlling the error within a given tolerance.

对NURBS曲面的曲率线的积分进行了系统的公式推导，并利用NURBS曲面的离散法向量有效地简化了曲面第二基本量的计算，加速了Euler法迭代求解曲率线微分方程的过程；在求得曲率线上的离散点集以后，应用奇异混合插值技术，在可控精度内把曲率线用显式直接表示为位于NURBS曲面上的B样条曲线。

In this paper,a nonlinear ordinary differential equation system with periodic coefficients,an extended simplified Glycolysis model,was studied.

研究了一个以周期函数为系数的非线性常微分方程系统--一个推广的简化Glycolysis模型。

After simplification of the Jou model,a diffusion dynamic equation, which was characterized with hyperbolic type, was obtained, then simulative analysis for three combined dimensionless parameters was done to research various diffusion behavior resulted from the change of model parameters.

经过对Jou模型的简化处理，得到了双曲型的扩散动力学方程，通过对模型中3个组合参数的仿真分析，研究了参数的变化可能导致的不同的扩散行为。

Modeling method of multidimensional hyper-ellipsoid has been perfected in bionic pattern recognition, equation and discriminant function of multidimensional hyper-ellipsoid is educed. Considering the complexity of realization, small chain of hypersphere instead of hyper-ellipsoid can greatly simplify algorithm.

完善了仿生模式识别过程中高维超椭球建模的方法，推导出了高维超椭球的方程和判别函数，考虑到其实现的复杂性，用小超球链来代替超椭球，大大简化了算法。

A series of theoretical and experimental studies on the microstrip patch antennas with dielectric superstrates is carried out systematically. Firstly, a comprehensive survey of the microstrip antenna technology and its theories are presented. Then, two analysis techniques, named as the spectral domain Green's function method and the spectral domain integral equation method are developed. The SDGF method is a simplified analysis technique, which takes advantage of the spectral domain immittance approach to find the dyadic Green's function for the stratified media, and obtains the complete closed-form formulas for radiation patterns, directivity, efficiency, gain etc. Some interesting calculated results are presented. The SDIE method is capable of determining resonant frequency, radiation characteristics, input impedance etc, for the covered microstrip patch antennas. Comparing with other full-wave analyses it reduced computation and mathematical labour remarkably. The singularities near the pole location of the surface-wave modes and the difficulty of the integral computation over infinite range of oscillating integrands are dealt with actively and documented well. Results predicted by the SDIE method agree extremely well with our experimental results for resonant frequencies of various superstrates. The superstrate effects on impedance and radiation characteristics also have been investigated experimentally so that the gap due to lack of measured data and computed results for multi-layered superstrate has been filled to some degrees and two useful observations have been achieved for weakening the resonant frequency shift and optimizing the microstrip antenna gain. As a meaningful application, the design and analysis of a 4×4 patch array are introduced.

实用微带天线普遍加介质覆盖层来防护热，物理损伤和环境影响，也可能在飞行或严酷气候条件下自然形成覆盖层本论文对带介质覆盖层的微带贴片天线系统地作了一系列理论和实验研究首先，对微带天线技术和理论作了全面的综述然后，发展了两种分析方法，称为谱域格林函数法和谱域积分方程法SDGF法是一种简化的分析技术，它利用谱域导抗法来求得分层媒质的并矢格林函数，并得出方向图、方向性系数、增益等参数的完整的闭式公式，给出了一些令人感兴趣的计算结果SDIE法能确定介质覆盖微带天线的谐振频率、辐射特性和输入阻抗等与其它全波分析方法相比，它明显减小了计算量和数学工作量已有效地处理了表面波模极点附近的奇异性和对振荡的被积函数的无限区间积分计算的困难对于不同覆盖层情况下的谐振频率，由SDIE法所预示的结果与我们的实验结果吻合得很好对于覆盖层对阻抗和辐射特性的影响也已作了实验研究这在某种程度上填补了缺少实验数据和计算结果之间的间隙，并得出了缓解谐振频率偏移和优化天线增益的两点有用的结论作为有意义的应用，介绍了一个4×4元矩形贴片天线阵的设计和分析。

By using K-ε twoequation model to modify turbulent flow, the simulation results could coincide better with the real filling processes. Combined flow path analytical program which was used to revise the ingate velocity, it increased the accuracy effectively, and raised the calculating velocity.

该软件首次采用非均匀网格剖分技术，更为逼真地反映了铸件的几何形状；耦合计算过程中，采用简化耦合算法，避免了繁复的迭代过程，缩短了迭代时间，且计算精度能满足工程要求；采用K-ε双方程紊流模型对紊流流动进行修正，模拟结果更加符合实际充型过程；联合流路解析程序修正内浇口入流速度，有效地提高了计算精度，加快了计算速度。

In this paper, we present five sorts of methods for finding the particular solutions of the n-th-order inhomogeneous linear differential equation with constant coefficients.

本文给出了五种求n阶常系数线性非齐次微分方程待解的方法。这些方法只需计算特征函数A及其各阶导数在某点的值，方法简单，两种递推公式适合计算饥计算，本文还简化了文［1］中递推公式的证明

The computer simulation software was developed for figuring the path curves and instantaneous speed of the lapping process.

文中从运动学和几何学原理出发，建立了工件精密研磨过程的轨迹方程，通过将复杂的研磨运动简化为在中心距一定条件下夹具绕研磨盘中心轴的回转运动及夹具自身的回转运动，对工件上任意点相对于研磨盘的运动轨迹及瞬时速度进行了分析计算，并开发了相应的计算机仿真软件，对其运动轨迹曲线及瞬时速度进行了分析。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失