算子方程

In this paper,using inverse differential operator and its linear property,we present the particular solution of n-th order general inhomogeneous linear ordinary differential equation with constant coefficient.

利用逆微分算子及其线性性质，给出了求n阶常系数线性一般非齐次项微分方程特解公式。

In this course we shall develop theoretical methods suitable for the description of the many-body phenomena, such as Hamiltonian second-quantized operator formalism, Greens functions, path integral, functional integral, and the quantum kinetic equation.

在本课程中，我们将会建立一种适合描述多体问题的理论方法，诸如哈密顿二次量子化算子形式、格林函数、路径积分、泛函积分和量子动力方程等。

Based on the analogy of structural mechanics and optimal contro1, and a1so based on carrying the minimum potential energy variational principle in elastici- ty to the generalized one, the theory of Hami1tonian system can be introduced into theory of e1asticity and e11iptic PDE. The transverse eigensolutions of the Hamiltonian operator matrix and its expansion solution method can be deduced.

利用结构力学与最优控制相模拟的理论，将弹性力学势能变分原理导向部分一般变分原理，并将哈密尔顿体系的理论引入到弹性力学与椭圆型偏微分方程之中，导出一套横向哈密尔顿算子矩阵的本征函数向量展开解法。

Special considerations are given to spatial discretization of hyperbolic equation with non self-adjoint operator nature.

同时构造了一个用于求解此耦合过程的统一混合弱形式，并且针对其中具有非自伴随算子特性的双曲线控制方程的空间离散进行了特殊考虑。

Specially, in Hilbert spaces, some necessaryand sufficient conditions are given in terms of the uniformly square integrability anduniform boundness of the resolvent on the imaginary axis respectively. Furthermore,we consider this robustness fordifferential equations with unbounded operatorin the delay term.

我们进一步研究了时滞项含无界算子的抽象微分方程的小时滞鲁棒稳定性，获得了一些充分必要条件，并应用所得结论讨论了具解析半群生成元的时滞系统。

The conclusion derived from the comparison between the two methods is useful to the integral operator solution .

积分算子解法是求解粘弹性问题的一种重要的解析方法，推演材料的积分型本构方程是此种求解方法的重要步骤。

In this PhD thesis, we first study the following BVP for first-order dynamic equation on time scaleThe corresponding integral operator is constructed and its completely continuity is proved.

本文首先研究了测度链T上的一阶动力方程边值问题构造了相应的积分算子并证明了其全连续性。

It is well-known that the generalized inverses of a matrix have wide applications in many areas such as differential and integral equations, operator theory, statics, optimal theory, control theory, Markov chains and etc.

众所周知，矩阵广义逆在许多领域中有广泛应用，如在微分和积分方程、算子理论、统计学、控制论、Markov链、最优化等。

The main content includes that the accuracy of interpolation operators is creased since defect equations introduce less error: Gauss-Seidel solution can save effectively the computational time, in particular, the CPU-time for the setup phase; Jacobi-relaxation interpolation contributes to efficient and robust algebraic multigrid methods by a simple and purely algebraic mean.

最主要的内容是基于亏量方程引入的误差较小，从而进一步提高插值算子的精度；采用Gauss-Seidel解法有利于节省计算时间，特别是预备阶段的CPU时间；插值的松驰以一种简单的纯代数的方式获得高效且稳健的代数多重网格算法。

Meanwhile, we obtain some properties of the linear operator from the transformed second order ordinary differential equation.

同时，得到了变换后二阶常微分方程线性算子的一些性质。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。