数值函数

With the algebraic result in form of piecewise function expressions, the excitation and propagation processes of stress waves, including the longitudinal wave, the transverse wave, and Rayleigh-wave, are discussed in detail.

基于该分段函数形式的代数结果，纵波、横波、Rayleigh波等应力波成分在弹性表面的激发和传播过程得到详尽分析，其中很多结论是已有的解析积分结果或者数值计算结果不曾得到的。

Secondly, by applying inverse Fourier integral transform to the displacement, and uniting the constitutive and geometrical equations, the analytical expression of stress in Laplace domain were derived. Thirdly, by defining dislocation density functions, the Cauchy singular integral equations were obtained according to the boundary condition and interface connection conditions, and the problem was reduced to algebraic equations by Chebyshev orthogonal polynomial. Based the these, the unknown coefficient of the algebraic equations can be solved by Schmidt method. Finally, the time response of dynamic stress intensity factor and energy release rate are obtained by inverse Laplace transform.

首先，利用积分变换方法，推导出粘弹性层的控制方程组；其次，引入位错密度函数，并结合边界条件和界面连接条件，导出反映裂纹尖端奇异性的Cauchy型奇异积分方程组，然后，应用Chebyshev正交多项式化奇异积分方程组为代数方程组，并采用Schmidt方法对其数值求解，最后，经过Laplace逆变换，求得动态应力强度因子和能量释放率的时间响应。

By considering the trait of the artery and anabranch of the Three-Gorges reservoir and analyzing the environmental elements influencing the growth of the algae, we improved on thenutrition dynamic model of the algae"s growth, carried on computer numerical value simulating on the evolvement process of the eutrophication of the Wujiang River, the Hanjiang River and the Three Gorges reservoir by cell mapping algorithm and revealed the dynamics action and mutation forms in the process of the valleys" algae blooms and the relationship between the major elements influencing the algaes growth and the model surge function.

本文结合三峡水库干、支流水体环境特点，通过对影响流域水体藻类生长的环境因素进行分析，改进藻类生长营养动力学模型，并利用胞映射算法对乌江、汉江和库区流域富营养化演化性态进行了计算机数值模拟和仿真分析，揭示流域水华发生过程的动力学行为、混沌性态和流域水质中主要藻类生长控制因子与模型振荡函数间的关系。

A tapered incident wave is used to reduce the truncated error. The angular correlation function is calculated by Monte-Carlo generated rough surface, the enhancement on nonmemory line of the ACF can be used to detection a target placed over or under the rough surface.

在散射目标存在时，目标与粗糙面的复合多次散射场的角相关函数，在不满足记忆线条件下也有普遍较高的角相关函数值，即在非记忆线上的增强可以用于检测粗糙面上方、下方的散射目标。

Convert relationship of prototype robot joint angle and equivalent model joint angle is presented based on the method of kinematics inverse solution. The Jacobian algorithm of redundant robot for achieving effective joint excursion is studied, which is fit for digital calculating. The grads projection algorithm of redundant robot multi optimizing capability function's proportion factor is deduced. The issues of apery arm robot singularity and joint self-movement are researched. The simulation experiment result of apery arm joint self-movement and line movement is presented.

因为七自由度拟人手臂机器人的建模比较困难，采用了在等效模型下求解其运动学逆解的方法，给出了原机器人机构关节角与等效模型关节角之间的转换关系；提出了一种适于数值计算的有效的求解有关节偏置的冗余度机器人Jacobian的算法，并在此基础上推导了冗余度机器人多优化性能指标函数的均衡比例因子梯度投影算法；研究了拟人手臂机器人的奇异问题和关节自运动问题；给出了拟人手臂进行关节自运动和进行直线轨迹跟踪的仿真实验结果。

As substitute for fluorite lens, a double-layer DOE is used in a long focal-length apochromatic objective lens. The modulation transfer function of this hybrid optical system is suggested for evaluating diffraction efficiency of the multilayer DOE. The results show the diffraction efficiency has a wide and symmetrical distribution in the whole waveband.

利用双层衍射光学元件替代萤石透镜校正混合光学系统的二级光谱，设计并制作了一套长焦距物镜，并利用系统调制传递函数评价了多层衍射光学元件衍射效率，测试结果表明衍射效率在整个设计波段内以较高的数值平均分布。

A method for the generation of Weierstrass fractal surface is presented,based on Helmholtz equation,with the Kirchhoff approximation,the calculus formula of light scattered field on the 1-D Weierstrass fractal suface is deduced.

采用Weierstrass分形函数模拟实际粗糙表面，从简谐光波满足的亥姆荷兹方程出发，利用基尔霍夫近似推导出一维Weierstrass分形粗糙表面的光散射场的积分公式，考虑遮蔽效应后数值计算并分析了表面散射光强的角分布特性。

In the last part, we mainly introduce Prony approximation methods of exponential function.

第3部分："Z－变换的有理数值逼近"，主要介绍了Prony指数型函数逼近方法。

The value of the function f at argument x.

参数为x的正弦函数f的数值。

The value of the sine function at argument x.

参数为x的情形下正弦函数的数值。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。