查询词典 galerkin equations

Two basic theorems are given by researching Hamilton's two steps linear differential equations of bender equations which provide widespread application methods of normal differential operator correspond to ladder operators,then the solutions of general equations are obtained by taking advantage of the two above theorems: The energy eigenvalue equation of one-dimensional oscillator; the common state of ; the radial equation of a bondage state of hydrogen atom; the radial equation isotropic three-dimensional harmonic oscillator; the infinity deep potential well of ball

本文通过研究束缚态本征方程里的哈密顿算符的二阶线性常微分形式，给出两个基本定理并证明，提供构造二阶线性常微分算符相应的阶梯算符的普遍实用的方法，然后利用这两个定理构造量子力学中常见力学量的阶梯算符，并用以计算其能量本征值和对应本征函数：一维谐振子的能量本征方程；共同本征态；氢原子束缚态径向方程；三维各向同性谐振子的径向方程；无限深球势阱。

Linear differential equations of the principle of superposition theory of linear differential equations play an important role, especially in solving linear differential equations of the nature and structure of play to solve the problem of reducing the complexity and difficulty of the role.

请帮忙翻译一下摘要，跪谢线性微分方程解的叠加原理在线性微分方程理论中占有重要地位，尤其是在解决线性微分方程解的性质和结构问题中起到了降低解决问题的复杂度以及难度的作用。

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。

Therefore, basic methodologies for stochastic seismic and filtering responses of nonlinear structure are studied, the approximate solution methodologies and their practical applications are investigated in the dissertation employing equivalent linearization and moment equations method based on FPK equations and Ito stochastic differential equations. The research works are mainly concerned with the following aspects:Firstly, the differential expression of bilinear hysteretic is studied and a new differential expression is developed, then they are demonstrated.

因此，本文基于FPK方程和伊藤随机微分方程，研究了滞后结构物的随机地震反应和随机滤波问题的基本方法，并利用等效线性化法和矩方程法，研究了非线性结构随机地震反应分析和随机滤波分析的近似解法及它们的工程应用。

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。

Salt is good, but if the salt becomes flat and tasteless, with what do you season it?

14：33 盐本是好的，盐若失了味，可用什么叫它再咸呢？

He reiterated that the PLA is an army of the people under the leadership of the Communist Party of China.

他重申，人民解放军是在中国共产党领导下的人民军队。