最小树的一般算法

本文根据设计并行算法的基本原则,给出了最小树的两个对偶定理.在此基础上,建立了两种对偶的同步并行算法的雏型.这两种算法恰恰在对偶的意义下,概括了以往的最小树算法.     

Chromatic Uniqueness of the Complement of T_m(l, 4, m - 6)

In the paper, we prove that the complement of Tm(1,4,m - 6)(m > 10) is chromatically unique if and only if m ≠5k(k ≥ 2).     

带有边集限制的最均匀支撑树问题

本在无向网络中，建立了带有边集限制的最均匀支撑树问题的网络模型．中首先解决最均匀支撑树问题，并给出求无向网络中最均匀支撑树的多项式时间算法；然后，给出了求无向网络中带有边集限制的最小树多项式时间算法；最后，在已解决的两个问题的基础上解决了带有边集限制的最均匀支撑树问题．     

On the Spectral Radius of Trees with the Given Diameter d

Let T denote a tree with the diameter d(d≥2) and order n. Let P^*d,r,n-d-1denote the tree obtained by identifying the rth vertex of path Pd l and the center of starKl,K1,n-d-1, where r = r(d) is the integer part about d 2/2. Then p(T)≤ p(P^*d,r,n-d-1), andequality holds if and only if T≌P^*d,r,n-d-1     

The Computable Dimension of I-Trees of Infinite Height

We study computable trees with distinguished initial subtree (briefly, I-trees). It is proved that all I-trees of infinite height are computably categorical, and moreover, they all have effectively infinite computable dimension.     

Identifying phylogenetic trees

A central problem that arises in evolutionary biology is that of displaying partitions of subsets of a finite set X on a tree whose vertices are partially labelled with the elements of X. Such a tree is called an X-tree and, for a collection of partitions of subsets of X, characterisations for the existence and uniqueness of an X-tree that displays have been previously given in terms of chordal graphs. In this paper, we obtain two closely related characterisations also in terms of chordal graphs. The first describes when identifies an X-tree, and the second describes when a compatible subset of is of maximum size.     

最小费用k度限制树对策

本在Glover—Klingman算法及最小费用支撑树对策的基础上，讨论了最小费用k度限制树对策问题．利用威胁、旁支付理论制订了两种规则，并利用优超、策略等价理论分别给出了在这两种规则下最小费用k度限制树对策核心中的解，从而证明了在这两种规则下其核心非空．     

有消费或投资的华氏宏观经济模型

本文对华罗庚教授的宏观经济模型进行了推广 ,在原来模型的基础上 ,分别增加了消费、投资 ,得到两种不同的模型 ,并对模型具有经济意义的解进行了研究     

Regression quantiles for unstable autoregressive models

This paper investigates regression quantiles (RQ) for unstable autoregressive models. The uniform Bahadur representation of the RQ process is obtained. The joint asymptotic distribution of the RQ process is derived in a unified manner for all types of characteristic roots on or outside the unit circle. It involves stochastic integrals in terms of a sequence of independent and identically distributed multivariate Brownian motions with correlated components. The related L-estimator is also discussed. The asymptotic distributions of the RQ and the L-estimator corresponding to the nonstationary componentwise arguments can be transformed into a function of a normal random variable and a sequence of i.i.d. univariate Brownian motions. This is different from the analysis based on the LSE in the literature. As an auxiliary theorem, a weak convergence of a randomly weighted residual empirical process to the stochastic integral of a Kiefer process is established. The results obtained in this paper provide an asymptotic theory for nonstationary time series processes, which can be used to construct robust unit root tests.     

Vector Lattices on a Set of Two Generators

It is proved that the center of an automorphism group Aut(FVL2) of a free vector lattice FVL2 on a set of two free generators is isomorphic to a multiplicative group of positive reals. It is shown that the free vector lattice FVL2 has an isomorphic representation by continuous piecewise linear functions of the real line; as a consequence, the ideal lattice and the root system for rectifying ideals in FVL2 are amply described. Similar results are obtained for a free vector lattice FVL2 _Q 2 generated by two elements over a field of rational numbers.