处处不连续又不可测的达布函数类的势

该文提出了一种构造处处不连续，而且在任何区间内取到任一函数值ｃ次的达布函数类的新方法，证明了该函数类的势为２＾ｃ（ｃ为连续统势）；还得到了处处不连续又不可测的达布函数类的势为２＾ｃ。     

模糊Bayes检验

本文对原假设和备择假设中参数是模糊子集的假设检验问题，引入了模糊Ｂａｙｅｓ检验的概念，对简单模糊假设，给出了求模糊Ｂａｙｅｓ检验的方法，讨论了它的性质，并针对一类特殊的隶属函数，得出了检验的具体公式。最后，通过几个数值实例，表明了模糊Ｂａｙｅｓ检验的优良性。     

Parsimonious Least Norm Approximation

A theoretically justifiable fast finite successive linear approximation algorithm is proposed for obtaining a parsimonious solutionto a corrupted linear system Ax=b+p, where the corruption p is due to noise or error in measurement. The proposedlinear-programming-based algorithm finds a solution x by parametrically minimizing the number of nonzeroelements in x and the error Ax-b-p₁.Numerical tests on a signal-processing-based exampleindicate that the proposed method is comparable to a method that parametrically minimizesthe 1-norm of the solution x and the error Ax-b-p₁, and that both methods are superior, byorders of magnitude, to solutions obtained by least squares as well by combinatorially choosing an optimal solution with a specific number of nonzero elements.     

布尔矩阵行空间基数的存在点

设 Ｂｎ 表示所有的ｎ 阶布尔矩阵的集合, Ｒ（ Ａ）表示 Ａ∈ Ｂｎ 的行空间,｜ Ｒ（ Ａ）｜表示 Ｒ（ Ａ）的基数．设ｍ ,ｎ,ｋ 为正整数,本文证明了当ｎ≥９, ｎ＋ ５２ ≤ｋ≤ｎ－ ３ 时,对任意的 ｍ ,２ｋ≤ｍ ≤２ｋ＋ ２ｎ－ ｋ＋ ２＋ ２ｎ－ ｋ＋ １ ＋ …＋ ２３,存在 Ａ∈ Ｂｎ,使得｜ Ｒ（ Ａ）｜＝ ｍ ．     

Polynomial algorithm for sharp upper bound of rainbow connection number of maximal outerplanar graphs

For a finite simple edge-colored connected graph G (the coloring may not be proper), a rainbow path in G is a path without two edges colored the same; G is rainbow connected if for any two vertices of G, there is a rainbow path connecting them. Rainbow connection number, rc(G), of G is the minimum number of colors needed to color its edges such that G is rainbow connected. Chakraborty et al. (2011) [5] proved that computing rc(G) is NP-hard and deciding if rc(G)=2 is NP-complete. When edges of G are colored with fixed number k of colors, Kratochvil [6] proposed a question: what is the complexity of deciding whether G is rainbow connected? is this an FPT problem? In this paper, we prove that any maximal outerplanar graph is k rainbow connected for suitably large k and can be given a rainbow coloring in polynomial time.     

Cardinality of retracts of monounary algebras

For an uncountable monounary algebra (A, f) with cardinality κ it is proved that (A, f) has exactly 2_κ retracts. The case when (A, f) is countable is also dealt with. This work was suported by the the Slovak VEGA Grant No. 1/3003/06. This work was supported by Science and Technology Assistance Agency under the contract No. APVT-20-004104.     

Local analysis,cardinality, and split trick of quasi-biorthogonal frame wavelets

The notion of quasi-biorthogonal frame wavelets is a generalization of the notion of orthogonal wavelets. A quasi-biorthogonal frame wavelet with the cardinality r consists of r pairs of functions. In this paper we first analyze the local property of the quasi-biorthogonal frame wavelet and show that its each pair of functions generates reconstruction formulas of the corresponding subspaces. Next we show that the lower bound of its cardinalities depends on a pair of dual frame multiresolution analyses deriving it. Finally, we present a split trick and show that any quasi-biorthogonal frame wavelet can be split into a new quasi-biorthogonal frame wavelet with an arbitrarily large cardinality. For generality, we work in the setting of matrix dilations.     

变动基数投资组合中的系统误差与估计误差权衡

投资组合选择中的系统误差与估计误差是决定样本期外绩效的重要因素,其权衡受到资产基数N的影响。本文在变动基数的设定下,将Bootstrapping和样本期外滚动的方法应用到均权重、最小方差组合及其误差修正策略的绩效和尾部风险检验过程中,并在不同的市场状态下进行分组讨论。研究发现:(1)最小方差组合与均权重策略的样本期外夏普比率差异与N存在倒U型的关系。(2)最小方差组合的尾部风险随N的扩大而迅速降低,总体来看最小方差组合的尾部风险低于均权重策略。(3)最小方差组合的换手率与N存在正相关关系,盲目增加投资组合选择中的资产基数会带来无谓损失。研究结果表明,投资者应理性选择资产基数,充分利用最小方差组合带来的分散化收益。     

Review of recent results about theκ-centrum of a tree

This paper is concerned with the-centrum of a graph. This concept, related to a particular location problem, generalizes that of the center and that of the median of a graph: the-centrum is the set of points for which the sum of the (weighted) distances from the farthest vertices is minimized. The paper will review some recent results about this problem. In particular, some properties of cardinality, connectivity and, more generally, of the structure of the-centrum of a weighted tree will be presented.