查询词典 nonlinear equation

But it is a hard task to solve this equation, one reason is that the TV-norm is nondifferentiable when |▽_u|= 0, so we cant apply a linearizationtechnique such as the Newton method. The other reason is that the Euler-Lagrange equation has a highly nonlinear term. The Newton method for such equation is known to have a very small domain of convergence, and it is very difficult to make sure that the initial value such as the observed image belongs to this domain. So the Newton method is not an ideal method for solving this equation.

但是求解它比较困难，主要是因为TV-范数在|▽u|=0处不可微，不能用诸如牛顿法之类的方法将其线性化；且Euler-Lagrange方程含有一个高度非线性的项，牛顿法只有局部收敛性，对于高度非线性问题它的收敛域很小，因此难以保证所取的初始点在它的收敛域内，故一般不用牛顿法直接求解。

In this paper, we used the regularization method and the best disturbed iteration to solve such more extensive equations: every kind of positive problems and inverse problems of the hyperbolic partial differential equation and parabolic equation. We give homologous methods to solve the positive problems and inverse problems of nonlinear Burgers equation and Boussinesq equation.

本文应用正则化方法和最佳摄动量法，解决了一类更广泛的双曲型和抛物型偏微分方程的各类正问题及反问题，对非线性的Burgers方程及Boussinesq方程的正问题及反问题，也给出了相应的求解方法。

Based on the magnetic-elasticity nonlinear kinetic equations, physical equations, electrical kinetic equations and the expression of Lorentz forces, the magnetic-elasticity kinetic buckling equation of a current-carrying plate applied mechanical load in a magnet field were derived. The equation was transformed into the standard Mathieu equation by using Galerkin method. Thus, the magnetic-elasticity kinetic problem was changed into a problem of solving the Mathieu equation.

在载流薄板的磁弹性非线性运动方程、物理方程、洛仑兹力表达式及电动力学方程的基础上，导出了载流薄板磁弹性动力屈曲方程，并应用Galerkin原理把屈曲方程整理为Mathieu方程的标准形式，将载流矩形薄板在电磁场与机械荷载共同作用下的磁弹性屈曲问题归结为对Mathieu方程的求解问题。

Based on the magneticelasticity nonlinear kinetic equations, physical equations, electrical kinetic equations and the expression of Lorentz forces, the magneticelasticity kinetic buckling equation of a currentcarrying plate applied mechanical load in a magnet field were derived. The equation was transformed into the standard Mathieu equation by using Galerkin method. Thus, the magneticelasticity kinetic problem was changed into a problem of solving the Mathieu equation.

在载流薄板的磁弹性非线性运动方程、物理方程、洛仑兹力表达式及电动力学方程的基础上，导出了载流薄板磁弹性动力屈曲方程，并应用Galerkin原理把屈曲方程整理为Mathieu方程的标准形式，将载流矩形薄板在电磁场与机械荷载共同作用下的磁弹性屈曲问题归结为对Mathieu方程的求解问题。

For overcome nonlinear terms of any degree in the equation, we made a proper transformation according to the structure of the equation at first, make the equations into ordinary differential equation. Then solve the ordinary differential equation exactly, by auxiliary functions method and undetermined the coefficient method and algebraic computer system Mathematica.

为了克服方程中非线性项的任意次幂，我们采用的方法是首先根据方程的特点，做适当的变换，使原问题转化为常微分方程的问题，其次对该常微分方程再进行各类变换，如辅助函数法以及待定系数法……。

In the solution of the problems in algebraic equation, differential equation and integral equation, we usually resort the sotution of equation to the fixed point of mapping in metric space. The contraction mapping principle can be used to solve many problems of the existence and uniqueness of equation solution.

在代数方程、微分方程和积分方程的求解问题中，通常把所求的解归结为度量空间中映射的不动点，然后应用压缩映象原理来统一处理许多方程解的存在性和唯一性问题。

On the basis of gas migration equation -Darcy Law,coal seam gas content equation -parabola equation ,ideal gas state equation and the continuity equation s of the gas flow,a dynamic model of gas unilateral flow in the coal seam is set .

根据基本假设，对煤层瓦斯流动规律进行了研究，运用瓦斯运动方程—达西定律、煤层瓦斯含量方程—抛物线方程、理想气体状态方程以及气体流动的连续性方程，建立了煤层单向瓦斯流动的动力学模型，并根据边界条件和初始条件，对动力学模型进行了求解，推导出煤壁单位面积的瓦斯涌出量的计算公式，分析了瓦斯涌出量的影响因素，利用测得的数据，进行了实例计算，并用vc编制了计算机程序。

In order to obtain more general solution of second order linear differential equation with constant coefficients, which is important in theory and practice, on the basis of knowing a special of the second order linear differential equation with constant coefficients and by using the method of variation of constant, the second order linear differential equation with constant coefficients is transferred to the reduced differential equation and a general formula of the second order linear differential equation with constant coefficients is derived.

为了更多地得到理论上和应用上占有重要地位的二阶常系数线性非齐次微分方程的通解，这里使用常数变易法，在先求得二阶常系数线性齐次微分方程一个特解的情况下，将二阶常系数线性非齐次微分方程转化为可降阶的微分方程，从而给出了一种运算量较小的二阶常系数线性非齐次微分方程通解的一般公式，并且将通解公式进行了推广，实例证明该方法是可行的。

Thirdly, according to the development of the frozen soil, the coupling model of single freezing pipe of axial symmetry of temperature field, stress field and moisture migration is put forward firstly. Then, by means of the progressing principle of potential field, the coupling model of temperature field, stress field and moisture migration which is under the condition of the multi-freezing pipes is extended. At last, the energy balance equation, stress balance equation, quality balance equation, geometric equation, physical equation, initial and boundary conditions etc are adopted to give the analytic solution to the problem of plane axial symmetry of single freezing pipe.

第三，在对室内试验和现场实测结果研究的基础上，分析了土体冻结过程中温度场、应力场、水分场耦合原理，并按照冻土体形成发展过程，首先建立了单一冷源冻结轴对称温度、应力、水分场耦合模型；接着利用势场的迭加原理，将单一冷源情况的三场耦合问题推广到多冷源情况的三场耦合；最后根据能量守恒平衡方程、应力平衡方程、质量守恒平衡方程、几何方程、物理方程、初始及边界条件，解出了单一冷源平面轴对称问题的解析解。

Under the condition of the slide between pile and soil around pile is taked into account,five equations are established, including the equation of compatibility between the settlement of pile cap soil and the settlement of pile cap; the equation of compatibility between the settlement of pile head soil and the settlement of pile head; the physical equation between the settlement of soil around pile shaft and the settlement of pile shaft;the equation of equilibrium between loads on the pile cap, side frictional stress and restraints of pile head; the equation of compatibility between the deformation of the pile body and the subtraction between the settlement of pile cap and the settlement of pile heap.

桩身单元和土单元存在着相互作用，在允许桩土相对滑移的前提下，建立桩顶土体沉降与桩顶沉降的协调方程、桩底土体沉降与桩端沉降的协调方程、桩土相对位移与桩侧摩阻力的物理方程、桩身力的平衡方程、桩身压缩和桩顶沉降与桩端沉降之差的协调方程。

The witness also told the jury at the Royal Courts of Justice in London that he saw a paparazzo fighting with a member of the public who was trying to stop him taking pictures in the minutes before the emergency services arrived.

他还告诉在伦敦皇家法庭的陪审团，在急救服务到来之前，他当时看见一个狗仔队正和一群阻止他拍照的人打架。

The entire N／C program on a tape is made up of an accumulation of these successive data blocks.

纸带上的整个数控程序由这些连续数据单元连接而成。