参数方程

In the present work,the existence and uniqueness results aboutperiodic boundary value problems for different kinds of the nonlin-ear periodically perturbed nonconservative systems are establishedthrough the discretization technique,under suitable assumptions,by using global inverse function theorem and result about the ex-istence and uniqueness of periodic solution for nonhomogeneouslyfirst order linear periodic boundary value problem.

本文的第一章概述了在讨论原问题解的存在唯一性过程中以及构造和分析相关的数值求解方法时将要用到的全局反函数定理、有关矩阵特征值的若干重要引理、线性常微分方程非齐次周期问题解的存在唯一性定理和单参数影射方法及有关结论，并简单回顾了已有的证明非线性微分方程周期边值问题解的存在唯一性的方法，其中包括谱理论、最大最小化形式方法、摄动技术和全局反函数理论方法，最后，介绍了两类数值求解非线性微分方程问题的方法。

In this paper, Newton iteration formula for computing normal depth and critical depth was put forward by mathematical transformation of uniform flow equation and critical flow equation of circular section tunnel. Then, the relationship between the corresponding central angle and the introduced parameters was analyzed. An approximate formula for angle was obtained according to optimal uniform approximation principle. Using this approximate formula as initial value of iteration formula, a direct formula for calculating normal depth and critical depth of circular section tunnel was established after its first iterative.

该文通过对圆形断面均匀流方程与临界流方程的数学变换，分别得到其正常水深与临界水深的牛顿迭代公式，同时，通过对正常水深与临界水深对应的中心角与引入参数之间关系的分析及数值计算，利用最优一致逼近原理分别得到了正常水深与临界水深对应中心角的近似计算式，并以此近似计算式为初值，用迭代方程进行一次迭代得到了圆形断面均匀流水深与临界流水深的直接计算公式。

Based on the principle of optimality,the search problem is then transformed to an equivalent problem of deterministic distributed parameters system,represented by a second order PDE.

采用分析的方法来研究随机运动目标的最优搜索问题，并将原问题转化为由一个二阶偏微分方程所表示的确定性分布参数系统的等价问题，推导出随机运动目标的最优搜索问题的HJB方程，并证明了该方程的解即是所寻求的最优搜索策略。

Let the obtained modality parameters be substituted into the coupling vibration partial differential equation and transform the complex partial differential equation into the variable coefficient nonlinear or...

把所得模态参数代入耦合振动偏微分方程中，将复杂的偏微分方程转化为变系数非线性常微分方程组，用Runge-Kutta方法获得方程的数值解。

Using PH linearization ,the nonlinear partial differential equation was transformed into linear partial differential equation,and then,by introducing a complex function,it was further transformed into a set of two linear differential equations.

应用 PH线性化方法，将非线性偏微分方程转化为线性偏微分方程，引入复函数将复常数偏微分方程变为两个线性实常数微分方程组，并采用小参数迭代法进行求解，近似求得了螺旋槽内气体动压分布的解析解。

When the geometric similitude ratio of the model to the prototype was determined and the loading similitude condition was satisfied by using similitude theory in structure modeling and experimental techniques, the prototype soil parameters were derived according to the model test result. The vibrating wheel compelled by harmonic exciting force was treated as a lumped mass vibrating system by equation equity method. By using this mechanical model in vibrating compaction, soil parameters were identified according to the equivalence of vibrating differential equation. The curve fitting method of amplitude versus frequency response was used for dynamic simulation based on the systematic dynamic equation of vibrating roller-soil system.

用相似理论与模型试验法在确定了模型与原型之间的几何相似比并满足载荷相似条件后，根据模型试验结果推导出了原型土体参数；用方程对等法把受简谐激振力作用的振动轮等效为集中质量振动系统，以此作为振动压实过程的力学模型，根据振动微分方程的等效条件进行识别；用幅频特性曲线拟合法以振动压路机－土壤系统动力学方程为基础，用计算机进行动态仿真。

The Fourier transfermation about the azimuthal angle and Hankeltransfermation about the radial dirction have been used to turn the basic dis-placement equatioons and constitutive equations under cylindrical coordinatesystem into a system of second order ordinary differential equations in thewavenumber domain,by use of the initial prarameter method to solve differ-ential equations.

利用关于方位角的Fourier变换及关于径向的Hankel变换，将柱坐标系下位移基本方程和本构方程转化为波数域内二阶常微分方程组，利用求解微分方程的初参数法，建立了介质层的传递矩阵，导出了层状弹性半空间在地表作用任意静荷载情形下的解析解。

The nonlinear dynamic system with quadratic and cubic nonlinearities is obtained by applying mathematical transformation to the equation.

基於Karman方程的动态比拟，运用Galerkin法，选用合适的正交函数将控制薄板振动的偏微分方程离散化为常微分方程，得到一带有平方和立方非线性的参数激励和外激励联合作用的非线性动力学系统。

The critical nitrogen content in heading period was used to calculate the biggest accumulation quantity of nitrogen. The latent distribution index of leaf and stem, which was the variety heredity parameter, were used to distinguish the difference in nitrogen assignment in different varieties. The dynamic content of the nitrogen accumulation before anthesis could be described with a Richards model. The dynamic content of the nitrogen remobilization in leaf with leaf area index could be described with a power model, and the nitrogen absorption of grain from soil with dry weight could be described with a power model. The dynamic content of nitrogen density in stem and spike with physiological development time could be described with a nonlinear model.

模型利用抽穗期植株临界含氮量来表达氮素最大积累量，引入叶片潜在分配指数和茎鞘潜在分配指数2个品种遗传参数来区别不同品种在器官间的氮素分配差异，采用Richards方程来描述大麦花前氮素积累动态变化；采用指数函数方程来描述叶片氮的转移量随叶面积指数的动态变化以及籽粒从土壤中吸收的氮量随干物重的动态变化；采用非线性函数方程描述茎鞘和穗部的氮浓度随生理发育时间的动态变化。

Rate constants, correlation coefficients, equilibrium adsorption capacities and kinetic parameters, for each kinetic equation were calculated and discussed. It shows that the adsorption of MB onto industry debarked hemp could be described by the pseudo-second-order equation.

在不同初始浓度下，运用准一级动力学方程和准二级动力学方程对数据进行拟合，并计算和分析速率常数、相关系数、平衡吸附量和动力学参数，说明吸附过程符合准二级动力学方程。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。