算子方程

This method consists of solving a Cauchy problem for a linear operator equation.

3，4」中，提出了解右端数据有扰动的线性算子方程的动态系统方法·实际间题中，算子与右端数据通常是近似已知的。

Firstly, by constructing an abstract operator, the original problem can be transformed into a Cauchy problem for an abstract operator equation.

首先，通过构造了一个抽象算子，将原问题转化为一个抽象算子方程的Cauchy问题。

Weak formulation of equilibrium equations including boundary conditions of laminated cylindrical shell is presented, thermal stresses mixed equation of closed continuous cylindrical shell is established.

建立了弹性力学基本方程的弱形式，从而得到叠层连续柱壳混合状态方程和边界条件放在一起的算子方程，扩大了求解的空间，给出了叠层连续闭口柱壳在热荷载和机械荷载作用下的解析解。

Beginning with some cases, the article gives basic definitions of inverse problems and ill-posed problems. Then it discusses the Moore-Penrose generalized solution and the Moore-Penrose generalized inverse, and makes a conclusion that linear compact operator equations are ill-posed, that is, the Moore-Penrose generalized solution is unstable.

本文从一些实例出发，介绍了反问题和不适定问题的基本概念，并讨论了方程的Moore-Penrose广义解和Moore-Penrose广义逆，得出了线性紧算子方程的不适定性，即Moore-Penrose广义解的不稳定性的结论。

A complete boundary integral formulation for incompressible Navier Stokes equations with time discretization by operator splitting is developed by using the fundamental solutions of the Helmhotz operator equation with different orders.

利用不同阶次的Helmhotz算子方程的基本解，建立了时间离散不可压缩Navier－Stokes方程的完全边界积分表示式。

We establish the equivalent integral equations to these problems, and prove that the defined operator is completely continuous.

建立了与这些问题等价的算子方程，并证明了所定义的算子是全连续的。

Every existence theorem of them is proved, respectively.

本文所获的一些结果不仅是非线性泛函分析领域中一系列重要定理的推广，而且它们为随机微分方程、随机积分方程及随机算子方程的研究提供重要的工具。

This dissertation studies perturbation bounds of infinite dimensional operatorsand operator equations.We obtained the following main results.

本文讨论了Hilbert空间和Banach空间上线形有界算子和算子方程的扰动理论，得到了一系列结果。

So one topic of this thesis is to further study Ishikawa and Mann iterationmethods for solutions to nonlinear equations involving single-valued m ?

长期以来，许多作者用Ishikawa和Mann迭代法去逼近非线性算子方程的解以及非线性算子的不动点。

Based on the theory of nonequilibrium statistics and density operator equation, the generalized master characteristic function for the nonextensive reaction-diffusion systems affected by pressure is derived by equation satisfied by calculating the time variation of probability distribution function, where the pressure of the nonextensive systems is given in the framework of Tsallis statistics.

依据非平衡统计及密度算子方程，通过计算概率分布函数的时间变化，得到了非广延反应扩散系统在压力作用时其特征函数满足的广义主方程，其中非广延反应扩散系统的压力在Tsallis统计的框架下给出。与唯象理论中的主方程比较，新得到的方程不仅依赖于非广延参量q而且有更多的非线性项，因此更具有普遍性。

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。