单调线性互补问题的最小原则(II)

在文［１］的基础上，对单调线性互补问题（ＭＬＣＰ）给出了不同于文［１７］的最小原则的另一形式，并提出了一个在有限步内求出单调线性互补问题解集的新算法；给出了单调线性互补问题的三个误差界公式．这些公式推广了文［６］的有关结果，并且较文［８］中的误差界表示形式简洁和易于检验．     

求解退化单调线性互补问题极大互补解的复杂性

本文考虑求解退化单调线性互补问题的一类不可行内点算法，其中嵌入一个恢复算法，给出了用这类算法产生所考虑问题的一个精确极大互补解的复杂性．     

具简单界约束变分不等式的拟牛顿算法的收敛性分析

１．引言 牛顿型方法是解变分不等式的一类重要数值迭代算法．其局部收敛性质的研究也取得了很好的成果（见［５］等）．近几年来,此类算法的全局收敛性研究也得到了许多进展．如阻尼牛顿法的局部超线性乃至二阶收敛性质的研究（见［４,６,９; １１, １２, １４; １６］等）．然而,对于计算上更为实用的拟牛顿法的研究还不多见．文［１８］基于祁力群等在［１４］中给出的逐次逼近牛顿型法,建立了一种解非线性互补问题的拟牛顿法,并得到了类Ｂｒｏｙｄｅｎ算法的全局收敛性．但是,该方法有以下两个缺陷：１．线搜索可能不能实现…     

一类线性约束凸规划的内椭球算法

1引言自从1984年Karmarkar的著名算法——梯度投影算法发表以来,由其理论上的多项式收敛性及实际计算的有效性,使得内点算法成为近十几年来优化界研究的热点（［1］）．通过中外学者的深入研究,线性规划与凸二次规划的内点算法研究已取得了不少成果（［2」、［3〕）．这些算法大致可分为四种类型：梯度投影算法、仿射尺度算法、路径跟踪法和势函数减少法吸3］、〔9〕）．近来,人们开始着手将这些方法推广到非线性规划中的凸规划问题、线性互补问题和非线性互补问题（【6」、［7」、〔sj、［10」、Ill〕）．例如：文［8」对一类凸可分规…     

一类非线性代数方程组的并行迭代算法

１．引言考虑非线性代数方程组这里,　　　　　　　　　　　　　　　　　　　　　　　　　　　　为连续的对角映射,二者的导函数均存在,但并不一定连续．这类非线性代数方程组具有丰富的实际背景．譬如,Ｓｔｅｆａｎ问题和许多弱非线性椭圆型偏微分方程,就可归结为（１．１）的数值求解问题．根据方程组（１．１）的特殊结构,并利用矩阵多重分裂思想,文ｔＺ］讨论了一类并行非线性Ｇａｕｓｓ－Ｓｅｉｄｅｌ型迭代算法．这类算法具有很好的数值性质和较高的并行效率·在此基础上,运用松弛加速技术,文［８］进一步研究了一类并行多分…     

求反三角函数值方法的再改进

形如ａｒｃｓｉｎ（ｓｉｎｘ）（ｘ∈Ｒ）的一类式子的求值问题已有一些文章提到了它们的重要性，并讨论了解答这些问题的公式和方法，如文［１］就给出了八个公式．但正如文［２］指出的那样，文［１］给出的八个公式太繁琐，不容易付诸教学和应用．文［２］也给出了改进...     

形状记忆合金问题的有限元逼近

１．引言本文讨论非线性微分方程其中　系数　是给定常数,ｆ,ｆ为已知函数．这是形状记忆合金问题的数学模型,未知量ｕ,θ代表位移及Ｋｅｌｖｉｎ温度,其物理背景及数学模型的建立,参见文献［３,４］．最近,文［１,２］讨论了方程组（１．１）－（１．５）的数值求解,提出全离散格式．文［２］用Ｇａｌｅｒｋｉｎ方法,位移ｕ用四阶微分方程的有限个特征向量张成的空间,温度θ用分段线性多项式（折线）空间来近似,给出一个全离散格式,证明了离散近似解的存在唯一性,定性说明收敛于原问题的精确解．文［１］采用［２］中的离散…     

求解互补问题的不可行内点法及其计算复杂性

给出了求解一类非单调非线性互补问题的一种不可行内点法,讨论了该算法的收敛性及计算复杂性.分析结果表明,所给方法是一多项式时间算法.     

关于非齐次线性方程组的又一类反问题

关于非齐次线性方程组的又一类反问题王卿文（山东昌潍师专数学系２６１０４３）李森林先生在文［１］中给出了非齐次线性方程组Ａｘ＝ｂ的一类反问题，文［２］－［４］对此做了很出色的工作．本文旨在提出并解决非齐次线性方程组的另一类反问题（简称反问题Ⅱ）：给定一...     

求解一类非单调线性互补问题的宽邻域内点方法及其计算复杂性

对于一类非单调线性互补问题给出了一种新的算法——宽邻域内点算法，并讨论了其计算复杂性。     

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.     

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 …     

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].     

简化摩擦接触问题的对称弱超内罚间断Galerkin方法的先验和后验误差估计

本文讨论了简化摩擦接触问题的一类对称弱超内罚间断Galerkin方法.首先,在能量范数意义下得到最优先验误差估计.进一步,我们推导了一类残量型后验误差估计子,并证明了它的可靠性和有效性.     

A SOLUTION OF A GENERAL EQUILIBRIUM PROBLEM

Under the framework of a real Hilbert space, we introduce a new iterative method for finding a common element of the set of solution of a general equilibrium problem and the set of fixed points of a nonexpansive semigroup. Moreover, a numerical example is presented. This example grantee the main result of the paper.     

一类中心循环的有限p-群的自同构群的研究

本文研究了一类中心循环的有限p-群G的自同构群.利用在G的导群上作用平凡的自同构以及环上的辛群和正交群,确定了G的自同构群的结构,这推广了Bornand的相应结果.     

论射影平坦空间的一个特征

<正> §1.如所周知,黎曼空间中关于平面公理的嘉当(E.Cartan)定理可以拓广到更一般的空间中去,满足平面公理的 m 维黎曼空间在它的每点容有∞~(m-1)张全测地超曲面.柏尔特拉米(Beltrami)给出常曲率空间的另一特征,只有常曲率空间才能与欧氏空     

A RIEMANN-HILBERT PROBLEM IN A RIEMANN SURFACE

One of the inspirations behind Peter Lax’s interest in dispersive integrable systems, as the small dispersion parameter goes to zero, comes from systems of ODEs discretizing 1-dimensional compressible gas dynamics [17]. For example, an understanding of the asymptotic behavior of the Toda lattice in different regimes has been able to shed light on some of von Neumann’s conjectures concerning the validity of the approximation of PDEs by dispersive systems of ODEs. Back in the 1990s several authors have worked on the long time asymptotics of the Toda lattice [2, 7, 8, 19]. Initially the method used was the method of Lax and Levermore [16], reducing the asymptotic problem to the solution of a minimization problem with constraints (an "equilibrium measure" problem). Later, it was found that the asymptotic method of Deift and Zhou (analysis of the associated Riemann-Hilbert factorization problem in the complex plane) could apply to previously intractable problems and also produce more detailed information. Recently, together with Gerald Teschl, we have revisited the Toda lattice; instead of solutions in a constant or steplike constant background that were considered in the 1990s we have been able to study solutions in a periodic background. Two features are worth noting here. First, the associated Riemann-Hilbert factorization problem naturally lies in a hyperelliptic Riemann surface. We thus generalize the Deift-Zhou "nonlinear stationary phase method" to surfaces of nonzero genus. Second, we illustrate the important fact that very often even when applying the powerful Riemann-Hilbert method, a Lax-Levermore problem is still underlying and understanding it is crucial in the analysis and the proofs of the Deift-Zhou method!