解析函数

Eular -Bernonulli beam model and Tomosimko beam model were adapted to study the inherence vibration properties of the pipelines under dynamical loads, and the analytical answers of the chanmical results were brought out in the fifth chapter. And gave priority to the Eular -Bernonulli beam model, the simply and convenient analytical resolution for the response of the pipelines under dynamical traffic loads through the impulse function and the congruence method of the vibration form and so on.

本文采用Eular-Bernonulli梁模型和Tomosimko梁模型对动力下Kelvin粘弹性地基中管道固有振动性状进行了分析，提出了各力学结果描述的解析式；并以Eular-Bernonulli梁模型为主，基于脉冲函数、振型迭加法等对管道在动力交通荷载作用下的管道响应问题提出简单便捷的解析算法；在管道受力结果的分析中，考虑管道响应输出的随机性，将管道响应用随机过程来描述其概率特征，使得结果描述更加真实准确。

Two sets of analytic functions are used in the horizontal directions and the method of discreteness is used in vertical direction.

用半解析单元法分析了矩形薄板与无限层土地基的静动力相互作用，提出了板单元和地基单元半解析位移函数。

Utilizing plane sectorial domain Hamilton system function via variable substitutes and eigenfunction expansion method, an analytical element is proposed in this paper for the crack analysis of reinforced concrete structures combining the bridging model and Dugdale model. Combined with finite element, nolinear crack problems of reinforced concrete structure can be analyzed.

利用平面扇形域哈密顿体系方程，通过分离变量法及共轭辛本征函数向量展开法，结合Dugdale模型和桥联力模型，推导了钢筋混凝土结构裂纹尖端的解析元列式，将此解析元与普通有限元结合，可用于分析钢筋混凝土的非线性断裂问题。

Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques are employed to develop a novel analytical finite element for the fictitious crack propagation linear force model in fracture mechanics of concrete in this paper.

利用平面扇形域哈密顿体系的方程，通过分离变量法及共轭辛本征函数向量展开法，以解析的方法推导出基于混凝土虚拟裂缝扩展线性粘聚力模型的平面裂缝解析元列式。

Based on the Betti-Rayleigh dynamic reciprocal theorem, the reciprocal property of the Green function is demonstrated; and the analytical solution of soil vibration subjected to moving loads is deduced. By means of double Fourier integral transform, the problem is firstly transformed into wave number-frequency domain, which makes it very convenient to derive the solution and furthermore to analyze the frequency characteristics of soil vibration.

基于Betti-Rayleigh动力互易定理，论证了地基土Green函数的互易性，推导了移动荷载引起的地基土振动解析解，进而推证出移动常力荷载和移动简谐荷载作用下地基于表面振动在波数－频率域内和空间－时间域内的解析表达式，并采用Matlab对其进行数值计算。

The dissertation includes the work as follows: Firstly, we present a random graph model with spatial reuse for a dense MANET which using directional antennas. The analytic formula of several important performance parameters for the MANET are obtained under the DSR routing protocol, such as the average flooding distance, the probability generating function of the flooding distance, the probability of a flooding route to be symmetrically valid, the average time to find a symmetrically valid route and the cost to successfully route a data packet to its destination. We compare the two models with spatial reuse and without spatial reuse by evaluating these parameters. It is shown that the spatial reuse model is much more effcctive in terms of the performance of the dense network with directional antenna, because the bigger is the degree of spatial reuse, the smaller is the average flooding distance.

在定向天线技术的支持下，建立了移动自组网络空间可重用的贝努利随机图模型，获得了DSR路由协议下平均泛洪距离的解析公式和泛洪距离的概率母函数：给出了有效对称路由概率、发现有效路由平均时间、成功路由代价等关键性能参数的解析分析；在网络性能参数定量分析的基础上，对空间可重用和无重用的网络进行了比较分析，结果显示空间重用度增大，则平均泛洪距离、路由发现时延、网络代价减少。

In this note, a new approach is presented which calculates analytically the experiment estimator distribution via a Fourier transform, using the likelihood ratio as an ordering estimator. The analytic approach enjoys an enormous speed advantage over the toy Monte Carlo method, making it possible to quickly and precisely calculate confidence level results.

本文则介绍一种新的计算方法，通过定义似然函数比为实验的估计值，并应用Fourier变换，用解析的方法计算出置信度，与toy Monte Carlo方法相比，解析方法可极大地提高计算的速度和精度。

This paper presents analytical solutions of internal forces of a solid three hinged arch subjected to complex loadings by a singular function method.

用奇异函数法导出了实体三铰拱在复杂载荷作用下内力的解析解，与传统的数解法相比，由于用统一的解析式表达内力，便于编程计算，也便于根据已知外载情况合理地设计拱轴

The analytical potential energy functions of the C2S+、A2and B2S+ states of the halogenate calcium molecules CaX (X=Br, Cl, F) are studied using the energy consistent method.

采用研究解析势能函数的能量自洽法Energy Consistent Method，研究了部分卤化钙分子CaX (X=Br， Cl， F)的C2S+、A2和B2S+态等基态和低激发态的解析势能曲线。

The results show that the calculated thickness of elastic foundation should be ten times as much as the radius of thick rounded plate , and calculated area of elastic foundation should be thirt.

用半解析元法分析了厚圆板基础与无限层土地基的三维动力相互作用，提出了一种新的半解析位移函数。

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