抛物问题的拉格朗日乘子区域分解法

１．引言 近年来,一类新的非重叠区域分解方法一非匹配网格区域分解法,日益引起人们的广泛兴趣,并已成为当今区域分解方法研究的热门课题。这类区域分解方法的特点是：相邻子区域在公共边（或面）上的结点可以不重合,从而能解决许多传统区域分解方法不便解决的问题（如变动网格问题）．目前主要有两类方法来处理这种区域分解的强非协调性：Ｍｏｒｔａｒ无法（见［１－２］和［９－１０］）和拉格朗日乘子法（见［５］,［８］,［１１］和［１２］）．拉格朗日乘子法比Ｍｏｒｔａｒ无法有明显的优点：（１）界面变量（即拉格朗日乘子）…     

依赖时间的Lagrange乘子区域分解法的显式格式

１．引言 近年来,一类新的区域分解法－非匹配网格区域分解法,日益引起人们的广泛兴趣．这类区域分解法的特点是：相邻子区域在公共边（或面）上的结点可以不重合,从而可方便地处理匹配网格区域分解法难以处理的问题：变动网格问题（例如石油勘探中的地层错动问题）和最优网格设计问题（即根据解的性质和实际问题的要求在不同子区域上采用不同的单元类型,不同的网格尺寸和不同阶的逼近多项式）． 在这类区域分解的算法设计中面临着两个困难：界面上非协调性的处理（与通常的协调元不同）和界面上积分的有效计算．现有算法中较引人注目的…     

基于几何非协调分解的Lagrange乘子区域分解方法

本文考虑将Lagrange乘子区域分解方法应用于几何非协调分解的情况来求解二阶椭圆问题.由于采用几何非协调区域分解,每个局部乘子空间关联到多个界面,我们按照一定的规则选取合适的乘子面来定义乘子空间.利用局部正则化技巧,可以消去内部变量,得到关于Lagrange乘子的界面方程.采用一种经济的预条件迭代方法求解界面方程,且相关的预条件子是可扩展的.     

区域分解界面预条件子构造的一般框架

1．引言考虑模型问题：其中ΩR2是多边形区域,常数n≥0．将Ω作非重叠区域分解：Ω＝假定：（i）当i≠j时,（ii）当Ωi与Ωj相邻时,是Ωi和Ωj的一条公共边记称为界面）;（iii）每个闪的尺寸为d,即存在常数co和q,使出包含（包含在）一个直径为C（）（Cod）的圆（国内）．非重叠区域分解方法的实质是,引进两个变量：内部变量。h和界面变量～．先在几上并行未解子问题,将。。消去（即用～表示）,得到～的方程（称为界面方程）;再求解界面方程,得到～的值;最后将～回代,得到。人的值（即原问题的解）．这类区域分解方法是否比重…     

非对称不定问题的非协调多重网格法

１．引言设　是Ｒｄ（ｄ＝２;３）中的有界多角形区域,α是它的边界．考虑下列模型问题此处ｆ∈ＥＬ２（Ω）,系数ＡＥ（Ｃ１（Ω））ｄ×ｄ满足下列一致椭园条件此处α０是正常数．此外假设Ｂ∈（Ｃ１（Ω）ｄ和ｃ∈Ｃ０（Ω）（［１４］）．（１．１）式的变分形式是：找ｕ∈Ｈ０（Ω）使得最近,非对称不定问题的非协调多重网格法吸引了众多的研究,详见问,［７］;［１０］．考虑非协调元多重网格的一个重要原因是混合元和非协调元之间存在着紧密的联系（详见【几问,问）．设ＦＩ是ｆｉ拟一致的Ｈ角形或矩形剖分,是由连接Ｆ'－'（…     

关于具优势对称部分的不定线性代数方程组的分裂极小残量算法

１．引 言 考虑大型稀疏线性代数方程组 为利用系数矩阵的稀疏结构以尽可能减少存储空间和计算开销，Ｋｒｙｌｏｖ子空间迭代算法［１，１６，２３］及其预处理变型［６，８，１３，１８，１９］通常是求解（１）的有效而实用的方法．当系数矩阵对称正定时，共轭梯度法（ＣＧ（     

求解界面方程的Chebyshev加速算法

非重叠区域分解算法在于建立和求解相关的界面方程．建立界面方程在理论上虽。然容易推导，例如某些问题可用Gauss块消去法，但在实际计算时并不可行，所以界面方程在一些算法中是陷式的．而求解界面方程一般要进行预处理，本提出一种区域分解算法，可得出界面方程的显式表达．算法是完全并行的，所得出的界面方程的系数矩阵的条件数已与网参数无关，事实上就是(Sh^（1）)^-1Sh，进而可直接用收敛速度较快的Chebyshev加速算法求解该界面方程，在充分应用并行计算方法的条件下，本算法与[4]中的算法相比计算效率提高．     

解含非线性源项的变分不等式问题的非重叠区域分解法

１．引言 近十几年来,变分不等式区域分解算法方面的研究取得了很多成果．特别是重叠型区域分解法方面的研究更是硕果累累,读者可参阅［１－８］等文献．而非重叠型区域分解法方面的研究目前相关结论不多,只有文献［９］针对线性算子单障碍问题提出了一类多子域非重叠区域分解算法（该方法的基本思想来自于工程中早已运用的子结构法）,证明了它的收敛性,并给出了收敛速度分析． 本文将针对含非线性源项的变分不等式问题提出一类多子域非重叠区域分解算法,并给出其收敛性和收敛速度分析． ２．问题及其有限元逼近 设ｎ为ＲＺ中有界凸多…     

耗散Zakharov方程组柯西问题的指数吸引子

文［１］中证明了耗散Ｚａｋｈａｒｏｖ方程组的最大吸引子的存在性．该文采用算子分解技术和构造犎２×犎１×犔２（犚）中渐进紧不变集的方法,得到了一维无界区域上耗散Ｚａｋｈａｒｏｖ方程组柯西问题的指数吸引子．     

椭圆外区域上的自然边界元法

１．引言 二十年来,自然边界元法已在椭圆问题求解方面取得了许多研究成果。它可以直接用来解决圆内（外）区域、扇形区域、球内（外）区域及半平面区域等特殊区域上的椭圆边值问题［１,２,５］,也可以结合有限元法求解一般区域上的椭圆边值问题,例如基于自然边界归化的耦合算法及区域分解算法就是处理断裂区域问题及外问题的一种有效手段［２－４,６］。 人们在设计求解外问题的耦合算法或者区域分解算法时,通常选取圆周或球面作人工边界。但对具有长条型内边界的外问题,以圆周或球面作人工边界显然并非最佳选择,它将会导致大量的…     

Rigid isotopy classification of real algebraic curves of bidegree (3,3) on quadrics

A rigid isotopy of nonsingular real algebraic curves on a quadric is a path in the space of such curves of a given bidegree. We obtain the rigid isotopy classification of nonsingular real algebraic curves of bidegree (3, 3) on a hyperboloid and on an ellipsoid. We also study of the space of real algebraic curves of bidegree (3, 3) with a single node or cusp. Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 810–815, December, 1999.     

Bounds of the Hausdorff Measure of Sierpinski carpet

By means of the idea of [2]（Jia Baoguo,J.Math.Anal.Appl.In press） and the self.similarity of Sierpinski carpet, we obtain the lower and upper bounds of the Hausdorff Measure of Sierpinski carpet, which can approach the Hausdorff Measure of Sierpinski carpet infinitely.     

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X     

Toward eudaimonology: notes on a quantitative framework for the study of happiness

After noting factors (concern for others, ignorance, irrationality) accounting for the divergences between preference and happiness, the question of representing the preference of an individual by a utility function is discussed, taking account of lexicographic ordering, imperfect discrimination and the corresponding concepts of semiorder and sub-semiorder. Methods to improve upon the interpersonal comparability of measures of happiness such as pinning down the dividing line of zero happiness and the use of a just perceivable increment of happiness are discussed. The relation of social welfare to individual welfare (i.e. happiness) is then considered. Some reasonable set of axioms ensuring that social welfare is a separable function of and indeed an unweighted sum of individual welfares are reviewed. Finally, happiness is regarded as a function of objective, institutional and subjective factors; an interdisciplinary approach is needed even for an incomplete analysis.     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

The use of phase portraits to visualize and investigate isolated singular points of complex functions

ABSTRACT

Undergraduate students usually study Laurent series in a standard course of Complex Analysis. One of the major applications of Laurent series is the classification of isolated singular points of complex functions. Although students are able to find series representations of functions, they may struggle to understand the meaning of the behaviour of the function near isolated singularities. In this paper, I briefly describe the method of domain colouring to create enhanced phase portraits to visualize and study isolated singularities of complex functions. Ultimately this method for plotting complex functions might help to enhance students' insight, in the spirit of learning by experimentation. By analysing the representations of singularities and the behaviour of the functions near their singularities, students can make conjectures and test them mathematically, which can help to create significant connections between visual representations, algebraic calculations and abstract mathematical concepts.     

ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.     

Absolute Continuity of Measures in the Class of Markov and Semi-Markov Processes of Diffusion Type

The property of absolute continuity of measures in the class of one-dimensional semi-Markov processes of diffusion type is investigated. The measure of such a process can be composed of two measures. The first one is a distribution of a random track, and the second one is a conditional distribution of a time run along the track. The desired density is represented in the form of product of two corresponding densities.     

Schreier rewriting beyond the classical setting

Using actions of free monoids and free associative algebras, we establish some Schreiertype formulas involving ranks of actions and ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish a generalization of the Schreier formula in the case of subgroups of infinite index. We also study and apply large modules over free associative and free group algebras. This work was supported by Natural Sciences and Engineering Research Council of Canada (Grant No. 227060-04), Yuri Bahturin, National Science Foundation (Grant No. DMS-0700811) and Russian Fund for Basic Research (Grant No. 08-01-00573), Alexander Olshanskii