查询词典 structure equations

At the first, it is proved that for an incompressible flow past through a flat plate the solution of the SRNS equations is regular at the point of separation and the SRNS equations are a precise approximation to the CNS equations.

首先，为看清SRNS方程在分离流动中的特点，对其在平板绕流的分离点及其邻域的数学特性进行了研究。

In chapter two, we analyzed the methods for single linear Diophantine equations: Rosser algorithm and Fortenbacher algorithm; the methods for linear Diophantine equations: EMAS algorithm and Contejean algorithm.2. In chapter three, the DLU and IILX algorithms for linear Diophantine equations are given based on the ABS algorithms.

第三章在ABS算法的基础上给出了求解线性丢番图方程组的整隐式LU算法和整隐式LX算法，讨论了相应的ABS性质，并讨论了复杂性分析及其应用。

Based on this, convert the matrix equations problem for row symmetric matrices into ordinary matrix equations problem, the scale of converted matrix equations problem is half of that for the original problem.

在此基础上，将行对称矩阵方程组问题转化为一般的矩阵方程组问题，转化后的一般矩阵方程组问题的规模是原行对称矩阵方程组问题的一半。

Using the properties of base solution vectors of the linear restriction equations, a condition to maintain the same discriminant result between the sampled observations of changed and unchanged was obtained: the disturbed row vector of sampled observations was satisfied all linear equations whose coefficients were the base solution vectors of linear restriction equations.

利用约束条件方程组基础解向量的性质得出了使数据变化前后的判别分类结果保持不变的条件：数据扰动行向量必须满足所有以约束条件方程组的基础解向量为系数的线性方程组。

With the idea of smoothing Newton method, we propose a new class of smoothing Newton methods for the nonlinear complementarity problem based on a class of special functions. In this paper, complementarity problem is converted into a series of smoothing nonlinear equations and a modified smoothing Newton algorithm is used to solve the equations. We use Newton direction and Gradient direction together in the algorithm which guarantees that our method is globally convergent. Also using another smoothing function, we reformulate the generalized nonlinear complementarity problems defined on a polyhedral cone as a system of smoothing equations and a smooth unconstrained optimization problem. Theoretical results that relate the stationary points of the merit function to the solution of the generalized nonlinear complementarity problems are presented, we use the modified smoothing Newton algorithm in generalized nonlinear complementarity problems, under mild hypothesis, a global convergence is proved.

本文一方面基于现有的各种光滑Newton法的思想和半光滑理论，利用著名的F-B互补函数的光滑形式，首先将互补问题的求解转化为求解一系列光滑的非线性方程组，然后给出了一种修正的光滑Newton法，该方法不仅放宽对函数F的要求，在Newton方程不可解时引入初始效益函数的最速下降方向，而且光滑因子的选择也比较简单可行，同时在适当的条件下，证明了其算法具有全局收敛性；另一方面，借助另一种F-B光滑函数，将多面体锥上的广义互补问题转化为一种光滑形式，讨论了优化问题的稳定点与广义非线性互补问题的解之间的理论关系，并将这种修正的光滑Newton法用于求解广义非线性互补问题中，在适当的条件下，该算法同样具有全局收敛性。

By introducing the nonlinear complementarity problem function, the Karush-Kuhn-Tucker conditions of OPF model are transformed equivalently into a set of semismooth nonlinear algebraic equations. Then the set of semismooth equations can be solved by a semismooth L-M method based on the subdifferential. The method belongs to Newton-type method. It can ensure the positive defmitiveness of the iterative coefficient matrix by using the L-M parameter, which avoids the ill-conditioning of iterative equations. The method, requiring only the approximate solution of a linear system at each iteration, is quite applicable to the large-scale cases.

在利用非线性互补函数将OPF模型的KKT条件转化为半光滑非线性代数方程组后，采用基于次微分的半光滑L-M法求解，该方法属于牛顿法范畴，可通过对L-M参数的调整保证迭代系数矩阵的正定性，克服了系数矩阵的奇异引起的"病态"，且该方法在确定搜索方向时只需求解线性系统的加热器近似解，适用于大规模系统的求解。

Based on the surjection of maximal monotone operators, we prove that some semilinear heat equations with weak Lipschitz nonlinear terms are exactly controllable by L〓 0, T: H〓(Ω control; Based on the critical point theorem of coercive convex functionals, we prove that some parabolic equations with Lipschitz nonlinear terms are globally approximately controllable and finite-dimensional exactly controllable by controls acting on mobile supports, and finally, we extend the results to parabolic equations in R〓.

首先利用极大单调算子的满射原理证明了半线性热方程在较弱Lipschitz条件下可通过L〓0.T；H〓(Ω控制实现精确能控。然后通过构造强制凸泛函并利用其临界点理论证明了带Lipschitz非线性项的抛物型方程可通过作用在在移动支集上的控制来实现整体近似能控与有限维精确能控，最后将整体近似能控与有限维精确能控结论推广到无界区域R〓上。

A group of equations of the form are called a system of equations with m linear equations and n unknown variables.

例如的一组方程称为m个线性方程，n个未知数的方程组。

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。

In this paper, beginning with the basic equations of hydrodynamics, turbine and governing system, the author deduced the basic equations of transient process caused by small fluctuation in the inclined ceiling tailrace, then analyzed and calculated the basic equations.

从水力学、水轮机、调速器的基本方程出发，推导了变顶高尾水系统小波动过渡过程的基本方程，并对其进行分析与求解。

There are different types of personal loans available.

有许多不同类型的个人贷款优惠。

The above mentioned teaching model of spiral rising can be used to avoid rigidness in teaching.

上述螺旋式上升的教学模式，可以避免教学形成模式後的僵化现象。