拟线性抛物方程组第一边界问题的有限差分法——V.迭代差分格式的收敛性

对拟线性抛物组第一边界问题构造了迭代差分格式,并证明迭代差分格式的解收敛于问题的唯一解.     

RLW-KdV方程的高阶紧致有限差分格式（英文）

对RLW-KdV方程提出一种新的四阶精度紧致有限差分格式.用离散能量法证明差分格式的能量守恒性、可解性、收敛性和稳定性.在离散L~∞-范数下,所建格式在空间上四阶收敛且在时间上二阶收敛.通过两个数值算例验证了该格式的有效性和可靠性.     

一个新的差分格式的稳定性和收敛性

Douglas给出了三种差分格式并讨论其收敛性和稳定性.[2]中给出了四种既稳定又收敛的差分格式,本文则构造了一个高精度的差分格式,并讨论该格式的收敛性和稳定性.     

奇异摄动问题的加权差分方法

本文对一阶导数引进了新的差分逼近,给出了一族一致收敛的差分格式.     

修正晶体相场模型的二阶线性化差分格式的误差分析

修正晶体相场模型是一类六阶非线性广义阻尼波动方程.首先,基于CrankNicolson格式,利用降阶方法对方程建立线性化隐式差分格式.非线性项通过二阶外推方法进行处理.其次,利用能量分析方法和数学归纳法,对差分格式进行理论分析,证明差分格式的唯一可解性及L~∞范数下的收敛性.收敛阶在时空方向均为二阶.最后,数值算例表明差分格式的有效性及数值收敛阶在L~∞范数下达到二阶.     

RLW-KdV方程的紧致有限差分格式

本文研究了RLW-KdV方程的一个三层线性紧致有限差分格式.该格式是质量守恒和能量守恒的,用离散能量法证明了差分格式的收敛性和稳定性.所建格式的收敛阶为O(τ~2+h~4).数值实验验证了该格式的有效性和可靠性.     

Kuramoto-Sivashinsky方程的线性化L_∞-差分方法

利用有限差分方法研究Kuramoto-Sivashinsky方程初边值问题的数值解.首先,给出了二阶线性化隐式差分格式,该格式在每一时间层均为线性方程组.其次,给出差分格式的守恒性和数值解的有界性.第三,证明差分格式在最大模意义下的收敛性.最后,通过数值算例验证差分格式的收敛阶,并数值模拟方程的混沌解.     

半线性抛物型方程奇异摄动问题的数值解

本文讨论具有抛物边界层的半线性抛物型方程奇异摄动问题的数值解法,在非均匀网格上构造了两层非线性差分格式,证明了差分格式是一致收敛的,给出了一些数值例子.     

小参数在高阶导数项的椭圆型方程第一边值问题的一致收敛差分格式

本文讨论了曲边区域上小参数ε在高阶导数项的椭圆型方程第一边值问题,从一致收敛的必要条件出发构造了特殊的差分格式,证明了差分方程问题解的一致收敛性,估计了收敛的阶数,并讨论了差分方程解的渐近性态.     

KdV-Burgers方程的一类新本性并行差分格式北大核心CSCD

KdV-Burgers方程作为湍流规范方程,具有深刻的物理背景,其快速数值解法具有重要的实际应用价值.针对KdV-Burgers方程,提出了一种新型的并行差分格式.基于交替分段技术,结合经典Crank-Nicolson(C-N)格式、显格式和隐格式,构造了混合交替分段Crank-Nicolson(MASC-N)差分格式.理论分析表明MASC-N格式是唯一可解、线性绝对稳定和二阶收敛的.数值试验表明,MASC-N格式比C-N格式具有更高的精度和效率.与ASE-I和ASC-N差分格式相比,MASC-N并行差分格式有最好的性能.表明该文的MASC-N并行差分方法能有效地求解KdV-Burgers方程.     

ON A THEOREM OF A.A. LYAPUNOV

Abstract

In this note we obtain some extensions and an approximation of the Lyapunov convexity theorem by means of the bilinear integration of a set-valued function. The integration is performed successively with respect to a non-atomic, a direct sum and a Darboux vector measure. The necessary counterexamples are provided.     

A Priori and A Posteriori: A Bootstrapping Relationship

The distinction between a priori and a posteriori knowledge has been the subject of an enormous amount of discussion, but the literature is biased against recognizing the intimate relationship between these forms of knowledge. For instance, it seems to be almost impossible to find a sample of pure a priori or a posteriori knowledge. In this paper, it will be suggested that distinguishing between a priori and a posteriori is more problematic than is often suggested, and that a priori and a posteriori resources are in fact used in parallel. We will define this relationship between a priori and a posteriori knowledge as the bootstrapping relationship. As we will see, this relationship gives us reasons to seek for an altogether novel definition of a priori and a posteriori knowledge. Specifically, we will have to analyse the relationship between a priori knowledge and a priori reasoning, and it will be suggested that the latter serves as a more promising starting point for the analysis of aprioricity. We will also analyse a number of examples from the natural sciences and consider the role of a priori reasoning in these examples. The focus of this paper is the analysis of the concepts of a priori and a posteriori knowledge rather than the epistemic domain of a posteriori and a priori justification.     

有限群的一个类函数的模构造

本文研究了有限群上的一个类函数.通过计算它和不可约特征标的内积,证明了它是特征标并且通过复群代数的中心的正则表示给出了它的一个模构造.     

NAMING A COLUMN ON A SPREADSHEET

Spreadsheets use a meaningful algebra-like notation which, research suggests, can support pupils in developing an understanding of variables. This paper discusses the activity of Year 8 pupils who were taught to name a column on a spreadsheet, and who were asked to reflect upon their activity in a stimulated recall interview. More specifically, it considers the pupils' understanding of notation, such as 'A2' and 'm', which they used when constructing spreadsheet formulae. It is suggested that experience of naming columns may help pupils to develop a clearer sense of the notation as a variable, and to make links between their spreadsheet activity and use of standard algebraic notation [1].     

A REMARK ON A BMO MARTINGALE

Let M = (Mt,Ft) be a uniformly integrable continuous martingale with MO = 0. For1 5 p < cot we setIIMllBMO. = '3p II[E[IMoo ~ MTIplFT]]'/Pll.,where the supremum is taken over all stopping times T.Set BMO. = {M: IIMllBMO. < co}. It is well known that BMO. = BMO, (VI S p 5 q).F'urthermore, all 11.llBMO. norms are equivalent andIIi ~~if;llMllBMO. = SUP T P(T < co)i'where the supremum is taken over all stopping times T satisfying P(T < co) > 0. In the laterwe shall simply …     

A new characterization of A 5

Let G be a group and τ _e (G) the set of numbers of elements of G of the same order. In this paper, by τ _e (G), we give a new characterization of A ₅, where A ₅ is the alternating group of degree 5. We get the theorem following: Theorem. Let G be a group, ${G\cong A_5}$ if and only if τ _e (G) = τ _e (A ₅) = {1, 15, 20, 24}.     

A NOTE ON A COVERING LEMMA OF A CORDOBA AND R FEFFERMAN~(**)

This note simplifies Cordoba-Fefferman's proof on the weak boundedness of strong maximal operator M_8 (with respect to dμ) on L(1+log~(+(n-1))L). Some two-weighted boundedness results on L(1+log~(+α)L) of M_8 are investigated.