基于微分形式的广义有限体积方法

本文研究基于微分形式的广义有限体积方法,证明了该方法具有保结构性质,给出了它和其他保结构算法间的关系.并且指出了该方法具有变分性质,所以可视为是有限元方法和混合有限元方法.数值试验表明了该方法的有效性.     

自适应Fuzzy系统及其逼近性能分析

本文提出了一种新的Fuzzy推理方法——自适应Fuzzy推理方法,基于该方法构造了自适应Fuzzy系统,证明了该系统不但具有泛逼近性,而且具有光滑性.基于该方法也得到了一种构造Fuzzy系统推理前件Fuzzy集的方法.使用该前件,CRI方法也具有光滑性,这使得CRI方法具有更广泛的意义.     

新的投影混合稳定化方法在抛物问题中的应用

针对抛物问题提出一种新的投影混合稳定化方法.该方法基于等阶的混合有限元,相比通常的局部投影稳定化方法,增加了新的投影稳定项及压力跳跃项,有效地克服了等阶有限元不满足inf-sup条件而导致的解的不稳定性,也保证了该方法不仅对连续的压力空间适用,且对不连续的压力空间亦适用.本文证明了该方法的稳定性,并给出了误差估计.最后,数值算例验证了该方法的理论分析及有效性.     

Sobolev 方程的$H^1$-Galerkin混合有限元方法

对Sobolev方程采用H1-Galerkin混合有限元方法进行数值模拟．给出了一维空间中该方法的半离散和全离散格式及其最优误差估计;并将该方法推广到二维和三维空间．与H1-Galerkin有限元方法相比,该方法不仅降低了对有限元空间的连续性要求;而且与传统的混合有限元方法具有相同的收敛阶,但其有限元空间的选取却不需要满足LBB相容条件．数值例子将进一步说明该方法的可行性与有效性．     

多源验前信息下先验分布的稳健融合方法

根据多种先验分布与似然函数尾部特性的比较,给出了多源验前信息下先验分布的稳健融合方法.讨论了由该方法得到的融合先验分布的后验稳健性问题.最后的数值例子表明,由该方法得到的融合先验分布具有较好的稳健性,进一步验证了该方法的有效性.     

不可微规划的极大熵不动点算法

本文将极大熵逼近方法和不动点计算方法有机地结合,提出了一种不可微规划计算方法．该方法同样也适用于求解可微规划,而后给出了该方法的收敛性     

建立在修正BFGS公式基础上的新的共轭梯度法

共轭梯度法是一类非常重要的用于解决大规模无约束优化问题的方法. 本文通过修正的BFGS公式提出了一个新的共轭梯度方法. 该方法具有不依赖于线搜索的充分下降性. 对于一般的非线性函数, 证明了该方法的全局收敛性. 数值结果表明该方法是有效的.     

平稳增广混合回归模型参数估计的一种新方法及其应用

本文提出平稳增广混合回归模型参数估计的一种新方法,该方法采用逐次投影分离参数的方法直接给出模型中自回归部分参数的估计,并由此而获得回归部分参数的估计。该方法克服了以往解此类问题时只能用近似求解方法的缺点。将该方法用到雷达使用有效度预测方程的参数估计中,取得令人满意的效果。     

“四环递进”教学法在农科高等数学教学中的尝试

简要介绍在中学理科教学中广泛使用的一种方法——"四环递进"教学法.结合教学实际,阐述在农科院校高等数学教学中应用该方法的必要性与可行性.通过实例说明如何使用该方法,并通过实际数据说明该方法在高等数学教学中的有效性.     

基于当地笛卡尔架构的无网格方法

提出了一种新的无网格方法,该方法是自动地在每一样点建立一个局部笛卡尔架构并选取相应的邻近点,然后运用全导数公式构造该样点的所有导数,它不需要任何网格单元,所以是彻底的无网格方法．数值算例表明,该方法具有很高的精度．     

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.