算子方程

In this paper, firstly we recount properties about the collision operator and listthe gained results of the Boltzmann equation in semiconductor.

在本文中，第一部分综合叙述了半导体Boltzmann方程中碰撞算子的一些基本性质以及半导体Boltzmann方程已得到的结果。

The existence of solutions to a type of nonlinear ordinary differential equations four-point boundary value problems with p-Laplace operator was studied by means of the extension of Mawhin s continuation theorem with sufficient conditions obtained for the existence of solution.

利用Mawhin连续引理的推广形式，研究一类具 p-Laplace算子的非线性常微分方程四点边值问题解的存在性，得到了方程解存在的充分条件。

The purpose of this paper is to prove the existence of non-oscillatory solutions to second-order neutral time-lag differential equation with positive/negative coefficient by using contraction-image principle through defining an operator from a bounded,closed,and convex subset into Banach space.

通过定义有界闭凸子集到B anach空间上的一个算子，应用压缩映像原理讨论了带有正负系数的二阶中立型时滞微分方程非振动解的存在性，得到该方程非振动解存在的一个充分条件。

A integral equation formulation is derived based on modified Green's operator with norm less or equal to one. The integral equation is convergent for any conductivity distribution and frequency if iterative solvers are used.

利用范数小于或等于1的修正Green算子得到各向异性地层中的新积分方程，由于满足压缩映射条件，该积分方程在任意参数条件下总是迭代收敛的。

Finally, we study the eventual differentiability of a C_0-semigroup associated to a waveequation with boundary dissipation.

最后，我们讨论了一类具边界耗散的线性双曲型方程生成的算子半群的最终可微性，并利用这个结果得到了方程的解具有最终正则性以及半群满足谱决定增长条件。

The proposed method is sample and does not need to compute both complex partial differential equation and operator equation of Riccati.

该方法计算简单，无须计算复杂的偏微分Riccati方程或算子Riccati方程。

In this paper we review some recent progress on the nucleation of zeros and the structure of the nodal sets of the complex-valued solutions of Ginzburg-Landau system for superconductivity and of more general partial differential equations with magnetic Schrodinger operator.

本文考察了近年来对超导的Ginzburg-Landau方程复值解的零点的产生与零点集的结构的研究进展，也考察了含有磁Schrodinger算子的更一般的偏微分方程的相关问题。

In Chapter 4, we introduce the definition of implicit complementarity problems and struct an equivalent projection differential equation system. And then we prove the equilibrium point of system is exact the solution of the implicit complementarity problem.

本文的第4章介绍了有关隐式互补问题的相关知识，并且利用投影算子建立了与之等价的微分方程系统，这个微分方程系统的平衡点就是隐互补问题的解。

In constructing new solutions of Feigenbaum renor- malization group equation, it is important to know which operator commute s with the iterative operator,This paper presents a theorem about the structure of the ab.

本文揭示了与迭代算子对易的算子集合在构造Feigenbaum重整化群方程新解中的重要性。

Finally, combining PDE with Differential Geometry, parametrically representing the surface, tensor based image processing techniques have been proposed, such as edge detection , morphological operation? implicitly representing the surface as the level-set of the higher dimensional function, the variational problems and partial differential equations that define maps onto the given generic surface have been discussed.

本文结合微分几何学，基于曲线坐标系下的微分算子将平面上的图像处理框架推广到曲面上，得到了参数化曲面上的图像处理框架，并给出了边缘检测和形态学运算的算例；在已知给定曲面的隐式表达时，探讨了定义在任意曲面上的偏微分方程，解决了任意曲面上数据场的扩散问题。

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。