解析函数

Properties of the reciprocal of δ_k function and it' s mean value are study, using analytic methods give an exact calculating formula for the reciprocal of δ_k function.

研究了δ_k函数倒数的性质及其均值估计问题，利用解析的方法得到关于δ_k函数倒数的一个精确的计算公式。

We take sech form ansatz and solve the CNLS equations through variational approach. We obtain the analytical expression of nonlinear coupling term, which is in the lagrangian of CNLS. We apply a potential well model to analyze the interaction properties of self-trapping beams in detail, the results show that the interaction do not change the profile of the beams, two beams keep oscillating around their collective center periodically. The amplitude and period of this oscillation are both determined by initial separation of two beams.

我们采用Sech函数为试探函数，用变分法求解CNLS方程，（1）给出了CNLS方程所对应的拉格朗日中的非线性耦合项的解析表达，（2）利用势阱模型详细分析两自陷光束之间相互作用的特性，结果表明，相互作用没有改变孤子的形态，它们分别在与传播方向垂直的方向上绕它们的公共中心做往复振动，振动幅度及周期都取决于两光束的初始分隔。

In order to get the formulation,the B3 spline function is used to distribute the contact problem,and numerical examples are analyzed to show the effectiveness of the method.

该方法充分利用了样条函数的解析和数值双重性及连续性强的优点来构造杆的位移函数，因此可推广应用于分析结构在冲击荷载下的动力响应问题。

As the main part of this thesis, based on RSJ model, a symmetric DC SQUID is theoretically studied through two-dimensional Fokker-Planck equations, by using the "potential condition" in the case of steady state, the stationary probability distribution function of this system is obtained firstly in the accurate theory, meanwhile, the expressions of all the SQUID characteristics functions are obtained, for example, the circulating current, total normalized voltage and transfer function.

作为本论文的主体工作，我们以RSJ模型为基础，利用二维Fokker—Planck方程从理论上研究了对称型双结超导量子干涉器件，利用定态条件下的"势条件"得到了系统定态概率分布的精确解析表达式，进而得到了该系统所有特性函数如环路电流、总电压、调制函数的统计表达式，利用数值计算讨论了各种参数对DC SoL71D系统特性的影响。

Based on the dynamic equation, the transport and acceleration of out-flowing ionospheric ions in the magnetosphere are studied by means of finding the ion distribution function. They include two parts: the study of static ion distribution with analysis and numerical compute; the study of ion acceleration by induced electric feild in the period of dipolarization of taillike geomagnetic lines in the substorm expansion phase with the numerical simulation of the ion distribution function.

本文在磁层中上行离子的加速与传输理论研究领域中，采用动力论方程，用求解离子分布函数的方法来研究问题：(1)用解析求解和数值计算的方法，对上行离子在不同Kp指数条件下磁场位形中的定态分布进行了研究；(2)用数值模拟计算分布函数的方法，对上行离子在亚暴膨胀相磁场向偶极形驰豫过程中受磁尾的感应电场加速进行了研究。

Based on the perturbation theory,the influences of the Fermi resonance interaction between the two and three vibronic levels on the level energy,wavefunction,and the spectral line intensity are investigated in detail respectively.

本文考虑了分子振动非谐性所引起的振动能级之间的费米共振相互作用，利用定态微扰论，从理论上系统地分析了两态和三态之间的费米共振相互作用对能级能量、态函数和谱线强度的影响，在三阶非谐性近似下，得到了计及费米共振相互作用在内的能级能量、态函数和谱线强度的数学解析表达式。

As their application, we obtain some indentities for the infinite products from the new expression in the special cases of these fuctions, and establish simultaneously a kind of inequalities with their convexities.

作为应用，在特殊情况下得出了这些广义函数的新的表达式，由此出发得到了一些关于自然数和合数的无穷乘积的恒等式，同时由广义函数各种凸性建立了若干解析不等式。

This paper establishes cubic spline function, analyzes subsection curve function and curve slope and curvature, at last decides to place the curve especial points which can be obtain easement curve length and other line parameters, such as the ZH point (end of line and beginning of transition curve), the HY point (end of transition curve and beginning of circular curve), the QZ point, the YH point (end of circular curve and beginning of transition curve), the HZ point (end of transition curve and beginning of line).

针对公路平面线形的8种组合类型，其线形元素特征则由最基本的直线、圆曲线、缓和曲线组成的特点，解析三次样条函数模型，得分段曲线函数、曲线斜率、曲率，从而确定曲线特征点（直缓ZH点、缓圆HY点、曲中QZ点、圆缓YH点、缓直HZ点）位置，进而得到曲线缓和曲线长度及其他线形参数。

In the third chapter, using the methods of nonlinear feedback functions and Lyapunov functions and combining analytical with numerical methods, the nonlinear feedback methods are introduced and the synchronizations of chaos in Hadley system of aerographs and LFRBM system of physics are realized. Some of nonlinear feedback functions are constructed.

第三章在介绍非线性反馈方法原理的基础上，应用非线性控制的基本思想及Lyapunov函数方法，将解析法与数值法相结合，分别对气象学中著名的Hadley环流和物理学中的LFRBM系统进行研究，找到了一类非线性反馈函数，实现了混沌自同步，并利用Mathematica软件进行仿真实验，数值结果说明了该方法的有效性。

Combined with the boundary conditions of soil surface under unit impulse excitation,the Green's functions for ground displacements in wavenumber-frequency domain are deduced.The Green's functions obtained are implemented by MATLAB,and their preliminary characteristics are presented via an example.

结合单位脉冲荷载作用下地基土表面的边界条件，推导出波数-频率域内地基土表面位移Green函数的解析解，用Matlab程序语言对理论进行实现并通过算例对地基土表面位移Green函数的特征进行了分析和总结。

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％。