函数振幅的性质与应用

函数振幅是微积分中最基本的概念之一,它的性态决定了函数许多解析性质．本文中扩充了函数振幅的定义．并利用它定义了函数振动性强弱的概念．作为这一概念的应用,建立起判定函数连续性、一致连续性、可积性、有界变差性的比较判别法,并给出了一些应用实例．     

指数有界的双连续n次积分C-半群及其生成定理

在双连续半群和n次积分C-半群的基础上,引入了指数有界的双连续n次积分C-半群,并讨论了其性质和生成定理.     

f-ergodicity of Markov Process by Coupling Method北大核心CSCD

We first study the basic coupling and obtain an equation between total variation norm and the basic coupling. Then by use this equation we investigate the ergodicity property of continuous time Markov processes in general state space. For an ergodic continuous-time Markov processes, adding condition π(f) < ∞, by using the coupling method, there exists the full absorption set, such that the continuous time Markov processes are f-ergodic on it. © 2022 Chinese Academy of Sciences. All rights reserved.     

奇异算子Q-变差在齐型空间上的最优加权估计（英文）

我们将齐型空间上的A_p理论的最优权有界性推广到了平均算子和Calder■n–Zygmund算子的q变差.这些结果利用了Lorist和Omisboand在齐型空间上给出的新的稀疏控制技术[1]以及[2].最后我们还讨论了这些理论的应用.     

关于可压液晶方程组的能量有界性

考察可压液晶方程组有关能量的基本性质.证明了只要初始能量有界,此系统的能量就是一个与时间无关的有界量.     

EXISTENCE AND UNIQUENESS OF STRONG PERIODIC SOLUTION OF THE EVOLUTION SYSTEM DESCRIBING GEOPHYSICAL FLOW—PART I： IN BOUNDED DOMAINS

61. IntroductionDiscovered by R. HideI3], the following evolution system has been used to describe thegeophysical flow:where u = u(xl,',XN,t) = (ul,',UN) and B = B(xl,',XN,t) = (BI,',BN) arethe velocity vectors Of Eulerian flow and magnetic fields respectively. p(x, t) and q(x, t) arepressures. j(x, t) and g(x,t) are volUme forces. p and u are the constants of density andviscosity of the flow respeCtively, p is the constant of magnetic permeability and A = f withelectrical resis…     

非线性应变波方程与薛定谔方程耦合组在~3上的极大吸引子

本文研究了非线性应变波方程与薛定谔方程耦合组在~３上的柯西问题与极大吸引子存在性．     

单边奇异积分交换子的加权变差不等式

本文主要研究了单边Calder\''{o}n-Zygmund奇异积分交换子的加权变差不等式,即建立了单边Calder\''{o}n-Zygmund奇异积分与Lipschitz函数生成的交换子的加权变差不等式, 同时,利用权的外推法得到了该交换子在Triebel-Lizorkin空间上的加权变差不等式.     

ENTROPY SOLUTIONS FOR FIRST-ORDER QUASILINEAR EQUATIONS RELATED TO A BILATERAL OBSTACLE CONDITION IN A BOUNDED DOMAIN

This paper is devoted to the existence and the uniqueness of the entropy solution for a general scalar conservation law associated with a forced bilateral obstacle condition in a bounded domain of R^P, p ≥ 1. The method of penalization is used with a view to obtaining an existence result. How-ever, the former only gives uniform L^∞-estimates and so leads in fact to look for an Entropy Measure-Valued Solution, according to the specific properties of bounded sequences in L^∞. The uniqueness of this EMVS is proved. Classically, it first ensures the existence of a bounded and measurable function U entropy solution and then the strong convergence in La of approximate solutions to U.     

有极大次数的传递置换群

本文研究有有界运动的置换群,给出了非单位元恰有两个运动的有极大次数的传递置换群的结构和分类,推广了文献[1]的结果.