查询词典 differential operator

The theory of maximal monotone operator is one of the most importance successes in the area of nonlinear analysis. It provides a powerful general framework for the study of nonlinear partial differential equations, nonlinear integral equations, control theory, optimization. Practically, it has be applied abroad in physics, economics and engineering.

极大单调算子理论是非线性分析领域的有效工具之一，已被广泛应用于非线性偏微分方程、非线性积分方程、控制论、最优化理论等学科，在物理学、经济学、工程学等应用学科也有着广泛的应用。

The abstract result contains several concrete results in the literature and can also be used to deal with some new cases for resonant differential equations.In the introduction, we briefly introduce the development process of the variational methods. In Chapter 2, we list some basic knowledges refering to the variational methods, including the Sobobev space,—△ operator, the weak solution and the minimizing sequence methods and some minimax theorems. In Chapter 3, we introduce the research process of Hamiltonian system of second order and the semilinear elliptic problems, using the methods introduced previously. In Chapter 4, we prove the main theorem of the thesis, and apply it to the problems in the previous Chapter, and can also be applied to some new resonant cases.

在前言中，简要介绍了变分法的产生、发展过程，在第二章中我们介绍了有关变分法的一些基本知识，包括Sobolev空间，—△算子，弱解，极小化序列方法和一些极小极大定理，在第三章中我们介绍了非线性项有界或满足次线性条件，以及它满足推广的Ahmad-Lazer-Paul条件时，二阶Hamiltonian系统和半线性椭圆问题的研究历程，最后在第四章中我们证明了本论文的主要定理，并把它应用到第三章的问题中，使得前面的几种共振的情形都可以统一到这个抽象的结果中。

Thus, filtering as a regularizing operator must be performed first at one scale and filtering at different scales must be performed after the differential operation.

因此，过滤使操作员合法化一定是在一刻度方面首先履行和在不同刻度方面透入一定是在有区别运作以后履行。

After the brief retrospect of spectral methods applied to get the numerical solutions of partial differential equations, the Walsh spectral methods are extensively studied. A new method of designing the "derivate operator" and a new Walsh spectral method based on quasi-Walsh order are proposed, which primarily prove the special uses of it.

回顾了数值求解偏微分方程的谱方法，比较深入地考察了数值求解偏微分方程的Walsh谱方法，提出了一种新的设计"求导算子"的方法，基于这样设计出来的"求导算子"，提出了一种新的基于类Walsh序的Walsh函数的Walsh谱方法，初步验证了这种序的特殊价值。

In Chapter 3, by establishing a L-operator inequality and using the properties of M-matrix and stochastic analysis techniques, some sufficient conditions ensuring the exponential dissipativity in mean square of impulsive stochastic functional differential equations of Ito-type are obtained.

第三章，通过建立L-算子不等式，运用M-矩阵的理论和随机分析技巧，获得了一类脉冲随机泛函微分方程均方指数耗散的充分条件。

The self-adjoint boundary-value problems and spectral theory of differential operators are important and fundamental problems in the operator theory.

微分算子自伴边值问题及谱理论是算子理论的重要而基本问题，它是同微分方程、数学物理和量子力学的某些重要问题相联系而发展起来的。

Using 〓-theory in partial differential equation,I find out a sufficient condition on A,B,under which ican be extended to andreplaced by a self-adjoint operator.

利用偏微分方程中的〓理论，我对算子A和B找到了一个充分条件，在该条件下，i可以扩张成一个自共轭算子。

It is embodied in the three research programs of modern physics:(1) According to the program of geometrization of physics, the essence of the Curved Space in gravitational field needs to be explicated by Riemannian geometry, differential geometry, tensor analysis;(2)According to the program of quantum field theory, the generation and annihilation operator can represen...

它分别体现在现代物理学的三大研究纲领中：(1)根据物理学的几何化纲领，引力场弯曲空间的奥秘需要通过黎曼几何、微分几何与张量分析来解读；(2)根据量子场论纲领，场理论的&产生和湮灭&算符，能方便而精确地表征和重构相关的微观作用机制；&场的本体论&和&生成辩证法&同时得到体现。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。