精确解

In this paper, the idea of " centrifugal potential field ",which induced by large overall rotation is introduced, and the motion equation of a coupled rigid-flexible system by employing Hamilton's principle is established.

本文从离心力势场的概念出发，应用Hamilton原理建立了具有动力刚化效应的刚柔耦合系统的运动方程，证明了该方程解的周期性，并采用了Frobenius方法给出了其精确解的一般形式。

And based on a class of oscillator of ENSO models, employing the method of homotopic mapping, the approximate and exact of solution of corresponding problem is studied.

并在这基础上借助同伦映射方法研究了一类ENSO模型振子模型的近似解与精确解。

Firstly, the fully discrete standard finite element Galerkin method and the nonlinear finite element Galerkin method and the modified finite element Galerkin method in which time is discretized by the Euler implicit difference scheme are considered, and the - and - global relative errors and CPU time corresponding to the SG method, the NG method and the MNG method are computed respectively.

首先，对于全离散(时间离散是欧拉显式格式)标准有限元Galerkin方法和非线性有限元Galerkin方法以及修正有限元非线性Galerkin方法，分别进行数值计算，并比较了三种算法的计算解与精确解的误差估计及所耗费的CPU时间，结果验证了MNG方法要优于NG方法，而NG方法又优于SG方法。

The advantages of this method are:① the range of the exponent i of the undefined functions f from-N to N;② the indeterminate specific form of function so that we can get more new exact solutions.

点在于：①待定函数f的指数i的范围从N扩大到－N；②可以不必给出函数f的具体表达式求解方程，这样便于寻找更多的解。本文就是利用了这一特点，选择合适的参数，得到一些mBBM方程新的精确解。

Firstly, by adopting the thought of Adomian's decomposition method, the generic dynamic model in mechanical systems are transformed into a standard first-orderdifferential-equations, and then the inverse operator method for the approximate analytic solution of nonlinear mechanical system is developed based on the exact solution in form.

主要研 究工作如下：利用Adomian的分解方法的思想，把机械系统中最一般的动力学模型转化为一阶标准型微分方程组，以形式上的精确解的表达式为基础构造了求解机械系统非线性模型近似解析解的逆算符方法；针对机械系统非线性模型的特点，提出了直接处理高阶方程的不降阶逆算符方法；证明了该方法的收敛性。

The result for an aluminum sphere with gaussian pulse incident wave was compared to the theor y value obtained by inverse Fourier transform from the product of Rayleigh serie s with incident wave in the frequency domain, which shows a good agreement.

计算了高斯形脉冲入射下弹性铝球的无量纲反向散射声压，并和由频域的Rayleigh 简正级数解与入射波的频谱的乘积作反变换得到的精确解做了比较，两者趋势基本一致。

The Lagrange motion equation of the system is established, and synchronous movement is studied. Exact solution of synchronous movement is presented and movement disciplinarian is studied. It proved that under certain condition, it exist periodic motion.

在本文中对该模型建立Lagrange运动方程，主要研究其同步运动，求出同步运动的精确解，并分析其运动规律，证明了在一定条件下存在周期解。

To solve the problem encountered in finding a proper rotation matrix and translation vector, approximate and precise solutions are provided successively. The approximate one has the advantage of utilizing existing solution, with limited range of weight to choose from. The precise one has no limit to weight, and can also prevent the problem of obtaining a mirror matrix of the correct one. Besides, it permits the'hat'to be amplified to fit the size of'head'.

其中近似解可以直接套用现成的公式计算，但是权重的选择余地不大，而精确解则无此限制，而且从理论上解决了不同权重下求解旋转矩阵和平移向量时，可能出现错误的旋转矩阵的问题，并允许在配准时对"帽"进行缩放以适应"头"和"帽"的大小不匹配的问题。

By using the resolvent operator technique associated with relaxed-monotone operators, we construct a new iterative algorithm for solving the system of generalized mixed quasi-variational-like inclusions. We also prove the existence of solutions and the convergence of iterative sequences generated the iterative algorithm.

利用松弛－-单调算子的豫解算子技巧，给出了求解这类广义混合拟似变分包含组的迭代算法，并证明了由迭代算法生成的迭代序列强收敛于该变分包含组的精确解。

Using the resolvent operator technique, we establish the equivalence between the generalized set-valued quasi variational inclusions in Banach spaces and the fixed point problems, and some perturbed iterative algorithms, prove that its proximate solution converges to its exact solution in real Banach spaces.

利用这种等价性，建立了一些摄动迭代算法，并证明了近似解序列强收敛于精确解。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。