非性性奇异边值问题

对一类奇异两点边值问题,在很一般的条件下,证明了摄动问题的可解性与一类全连续映象不动点的存在性是等价的,并且给出了摄动问题的可解性与原问题的可解性之间的关系．     

奇性边值问题的正解存在性

本文考虑具有奇性的两点边值问题,主要依据锥映射理论中的一个不动点定理,构造了一系列解的存在性条件,并在最后又证明了单减条件下奇性边值问题解的存在性的一个简明定理．     

平均跟踪性与双曲线性同胚

本文研究了双曲线性自同胚的平均跟踪性,利用双曲线性映射的性质和压缩映射定理,得到了在有界的Banach空间上的双曲线性自同胚具有平均跟踪性.另外,证明了在一般的度量空间上的压缩映射也具有平均跟踪性.     

均匀性度量中的密集性偏差与稀疏性偏差

该文根据王元，方开泰［２］的近似偏差（discrepancy）的均匀性准则，定义了理想布点情况下的标准半径，定义了ｍ 维单位子空间Ｃｍ＝［０，１］中两点间的ｆ距离和ｇ距离，由此定义了最大空穴半径和最小空穴半径，提出了均匀性度量的密集性偏差与稀疏性偏差．给出了二维情况 下的计算结果．我们的方法计算量不大，不仅能较好地度量布点的均匀性以及布点在低维投影的均匀性，而且能指导如何调整布点使之尽可能与理想布点接近．     

原函数存在性与可积性概念辨析

讨论函数可积性和原函数存在性问题,并结合具体实例分析原函数存在性和可积性之间的相互关系.     

滞后控制系统的完全能控性、毕竟能控性、最终能控性和拟能控性

讨论时滞控制系统的能控性 .指出与无时滞系统不同的是 ,该类系统的能控性与终点时刻有一定的关系 .由此给出一系列与终点时刻有关的能控性 ,即完全能控性、毕竟能控性、最终能控性等 ,并得到一些判定定理 .     

半群的拟紧性和不可约性

利用算子半群生成元的边界扰动方法,给出了Banach格上C0半群的拟紧性和不可约性的充分条件.并利用该结果对一串联可修复系统的拟紧性和不可约性进行了研究.     

渐近线性Klein-Gordon-Maxwell系统正解的存在性

研究如下Klein-Gordon-Maxwell系统■其中ω>0是一个常数,λ≥1是一个参数.当非线性项在无穷远处满足渐近线性增长时,利用变分方法获得了系统正解的存在性结果.完善了此系统解存在性的已有结果.     

边值系统的能控性与能观测性问题

把抽象系统的能控性和能观测性推广到由强连续双半群描述的抽象边值系统,给出了相应的边值系统能控性的充要条件,并研究了能观测性与能控性之间的对偶关系.最后作为例子,研究了双曲系统能控性.文中所得的结果可用于讨论现代物理系统中出现一类边值系统的能控性与能观测性问题.     

一类二阶非线性差分方程的振动性与渐近性

研究了一类二阶非线性差分方程解的振动性与渐近性,建立了三个新的振动性与渐近性定理,推广和改进了已知的一些结果.     

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     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

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.     

Nonexistence in power and gamma density regression, sum of nonnegative terms

When we use the power function α(c x)^b and gamma density αx^be^-cx to fit the data by the least squares method, we have to address the question of existence. The closure of the set of each type of these functions defined on a finite domain is determined. We derive a way to determine the closure of a sum of nonnegative functions if the closures of the summands are available.     

Sur l'existence, l'unicité, la stabilité et les propriétés de grandes déviations des solutions d'équations différentielles stochastiques rétrogrades à horizon aléatoire. Application à des problèmes de perturbations singulières

We study the existence, uniqueness and stability of solutions of backward stochastic differential equations with random terminal time under new assumptions; then we establish a large deviation principle for the solutions of such equations, related to a family of Markov processes, the diffusion coefficient of which tends to zero. Finally we apply these results to the analysis of some singular perturbation problems for a class of nonlinear partial differential equations.     

Schreier rewriting beyond the classical setting Dedicated to our teacher Alfred Lvovich Shmelkin on his 70th birthday

Using actions of free monoids and free associative algebras, we establish some Schreier-type 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.     

A quantum spin system with random interactions I

We study a quantum spin glass as a quantum spin system with random interactions and establish the existence of a family of evolution groups {τ_t(ω)}_ω∈/Ω of the spin system. The notion of ergodicity of a measure preserving group of automorphisms of the probability space Ω, is used to prove the almost sure independence of the Arveson spectrum Sp(τ(ω)) of τ_t(ε). As a consequence, for any family of (τ(ω),β) — KMS states {ρ(ω)}, the spectrum of the generator of the group of unitaries which implement τ(ω) in the GNS representation is also almost surely independent of ω.     

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.     

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.     

Clustering Methods in Microarrays

Summary DCT Given a finite set of points in an Euclidean space the \emph{spanning tree} is a tree of minimal length having the given points as vertices. The length of the tree is the sum of the distances of all connected point pairs of the tree. The clustering tree with a given length of a given finite set of points is the spanning tree of an appropriately chosen other set of points approximating the given set of points with minimal sum of square distances among all spanning trees with the given length. DCM A matrix of real numbers is said to be column monotone orderable if there exists an ordering of columns of the matrix such that all rows of the matrix become monotone after ordering. The {\emph{monotone sum of squares of a matrix}} is the minimum of sum of squares of differences of the elements of the matrix and a column monotone orderable matrix where the minimum is taken on the set of all column monotone orderable matrices. Decomposition clusters of monotone orderings of a matrix is a clustering ofthe rows of the matrix into given number of clusters such that thesum of monotone sum of squares of the matrices formed by the rowsof the same cluster is minimal.DCP A matrix of real numbers is said to be column partitionable if there exists a partition of the columns such that the elements belonging to the same subset of the partition are equal in each row. Given a partition of the columns of a matrix the partition sum of squares of the matrix is the minimum of the sum of square of differences of the elements of the matrix and a column partitionable matrix where the minimum is taken on the set of all column partitionable matrices. Decomposition of the rows of a matrix into clusters of partitions is the minimization of the corresponding partition sum of squares given the number of clusters and the sizes of the subsets of the partitions.