余弦公式

To reduce the evil influence of the window effect to discrete Fourier transform spectrum analysis, interpolation equations of generalized cosine window function with different K are derived.

为了减少加窗效应对基于离散傅里叶变换频谱分析的测频算法产生的不良影响，推导了不同K值下，广义余弦类窗函数的频谱及幅度比值法插值校正公式。

In chapter 3, combining the traditional augmented Lagrange function and the hyperbolic cosine function, we construct a new hyperbolic penalty function multiplier method for the equality constrained optimization and deduced the iterative formulas, and proved the convergence under some conditions.

在第三章中，我们把传统的增广Lagrange函数和双曲余弦函数结合，构造了一类新的在等式约束下的双曲罚函数乘子法，推导出了双曲乘子迭代公式。

According to the Source attenuation model, Lambert′s cosine law of diffuse reflection and Phong specular reflection model, 2 equations used to calculate the opacity and intensity of every voxel in the volume data were obtained.

方法由源衰减模型、朗伯漫反射余弦定律和Phong镜面反射模型，推导出计算数据场中每一点的不透明度和明暗度的计算公式，通过旋转光源和视点，来自不同观察方向的感兴趣结构的体绘图被满意地生成。

By adjusting the weight, different component in the volume can be filtered out. According to the Source-attenuation model, Lambert's cosine law of diffuse reflection and Phong specular-reflection model, two equations used to calculate the intensity of every voxel in the volume data are obtained.

由源-衰减模型，朗伯漫反射余弦定律和Phong镜面反射模型，推导出了计算数据场中每一点明暗度的计算公式，通过旋转光源和视点，来自不同观察方向的感兴趣结构的体绘图能被满意地生成，从而避免了对内存中整个体数据的旋转。

Via the stochastic averaging method, the four-dimensional system is reduced to a two-dimensional one. Through the logarithmic polar transformation , and then Girsanov theorem and Feynmann-Kac formula, the backword differential operator is then obtained. By expanding the eigenfunctions as a Fourier cosine series, the approximate analytic expansion of the moment Lyapunov exponent is then obtained.

首先在经典二元机翼颤振方程加入随机激励，通过随机平均法，Girsanov定理和Feynmann-Kac公式得到关于矩Lyapunov指数的特征值问题，其次采用Fourier余弦级数对特征函数进行正交展开得到系统矩Lyapunov指数的近似解析式。

The forward kinematics is analyzed by choosing one of the mechanisms which have one, two,three or zero angle constraint.Wherein,3-CCC is a new parallel mechanism which has three angle constraints and three distance constraints, Calay\'s formular and direction cosine matrix are used to describe the rotation matrix respectively.By setting Dixon\'s and Sylvester\'s resultant with the three angle constraint equations respectively and using parameters replacement to deal with the distance constraint equations,the 64 order input-output equation of the forward kinematics is obtained under both of the methods.Numerical example confirms these theretical results and the motion simulation is shown in VC++ by integrating OpenGL.

3对高小山提出的广义并联机构进行了研究，以其中具有角度约束的并联机构进行了分析，选取具有一个、两个、三个和零个角度约束类型中各一个机构进行了运动学正解求解，其中3-CCC是一种全部由圆柱副构成的具有三个线线角度和三个距离约束的新型并联机构，文中分别用Calay公式和方向余弦两种旋转矩阵建模方法对其位置正解进行了分析，通过对三个角度约束方程分别构造Dixon结式和Sylvester结式，以及对三个距离约束方程进行变量代换分别导出了位置正解输入输(来源：4040ABC论文网www.abclunwen.com)出方程，得出64组位置正解，并使用数值算例验证了其全部根。

By the procedure, we first use the cosine values of the angle between view vector and normal vector on each vertex as the texture coordinates, through calculation of the dot product of the two vectors. The derivative of radial curvature on the model surface is used as the second pass texture mapping coordinates, by a calculation using Euler formula.

该方法首先通过模型顶点的视线向量和法线向量的点乘积计算其夹角的余弦值，作为第一步的纹理坐标进行映射；再通过欧拉公式计算径向曲率及其方向导数值，作为第二步映射的纹理坐标。

For example, using the raised consine roll off function as the system pulse response, the feasiblity and effectiveness on the interpolation formula has been certified by theoretical and numerical analysis. The computer simulation result on 16-QAM signal is given.

以系统脉冲响应为升余弦滚降函数为例，利用理论分析和数值分析的方法验证了插值公式的可行性和有效性，并给出了16-QAM信号的计算机仿真结果。

As an application of the interpolation criteria, the interpolation formula of bandlimited transmission signals which satisfied the condition of the Nyquist first criteria has been presented.

在信号插值问题上，首先利用基本的信号模型和Nyquist第一准则，导出了一个插值准则，作为插值准则的应用，对满足Nyquist第一准则的带限传输信号给出了一个通用的插值公式，以升余弦滚降函数为成形滤波函数的限带传输信号作为一个特例，通过计算机仿真验证了插值算法的可行性和有效性。

The general analytical expression of the deformed high-order Bessel beam and its propagation properties of in self-focusing lens self-imaging process in free space wer.

从产生高阶贝塞尔光束的典型光路着手，通过将高阶贝塞尔光束分解为高阶贝塞尔余弦光束和高阶贝塞尔正弦光束，利用柱坐标下的Collins公式，分析了变形高阶贝塞尔光束的解析表达式和在自聚焦透镜中的传播。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。