脉冲喷洒杀虫剂的植物病害模型的周期解

本文研究脉冲喷洒杀虫剂的植物病害模型.考虑在传染率随时间周期变化和森林树木总数保持不变的条件下,讨论具有垂直传播的一类具有单个种群的脉冲喷洒农药的SIRS模型,根据单值算子和Bohl-Brouaser不动点理论证明了无病周期解存在性,并且利用单值矩阵,Floquet理论得到其基本再生数并且给出了其无病周期解局部渐近稳定的条件.     

刚性多滞量积分微分方程的Runge-Kutta 方法

本文研究了求解刚性多滞量积分微分方程的Runge-Kutta方法的非线性稳定性和计算有效性.经典Runge—Kutta方法连同复合求积公式和Pouzet求积公式被改造用于求解一类刚性多滞量Volterra型积分微分方程.其分析导出了:在适当条件下,扩展的Runge-Kutta方法是渐近稳定和整体稳定的.此外,数值试验表明所给出的方法是高度有效的.     

基于R/S分析的专利申请量年增长率的相关性研究

Hurst指数是描述分数布朗运动的重要指标.利用R/S分析方法计算出我国专利申请量年增长率的Hurst指数稳定在0.62附近,分形维数稳定在1.38附近.表明我国专利申请量年增长率时间序列,服从分数布朗运动,专利申请量年增长率具有长期相关性.历史数据的影响力随时间间隔的长度增长而缩小,当间隔长度达到10年以上时,历史数据的影响力趋于稳定.     

线性不确定系统的稳定控制鲁棒界和多级稳定鲁棒控制

利用李雅普诺夫稳定性理论研究了线性不确定系统的稳定鲁棒控制问题,得到结果“任何一个稳定控制都是具有一定稳定鲁棒界的稳定控制”.进一步地,根据系统的不确定量的范围,设计了多级稳定鲁棒控制策略.最后给出一个例子说明设计步骤的可行性.     

介紹一种森林測高的方法

当我們要估計一片森林共有多少材积(即森林中木材的总体积)时,就要求出这片森林的平均树高,如果一棵棵地去量,然后求出平均数,这实际上是不可能的,而且也没有必要。往往总是选择几块样地,求出样地上的平均树高,以它来代替全体的平均树高。但由于样地上树木的数目还是非常之多,如果逐一測量,仍須很大的人力和物力,日本有一个森林工作者他想出了一套簡易的方法,这种方法就是現在我們准备介紹的! 如果我們选定了一块样地,它的总面积是D,树木的总数是N。我們用h_i表示第i棵树的树高,那末我     

一类三阶双滞量时滞微分方程的全局渐近稳定性

运用类比法构造Lyapunov函数,讨论了一类三阶双滞量时滞微分方程的全局渐近稳定性,给出了其零解全局渐近稳定的充分性准则.     

高阶张量反卷积非负约束的纤维方向分布估计方法

高阶张量能够以其简单的多项式形式表示多叶函数,被广泛应用于纤维方向分布估计中.但随着高阶张量阶数的增加,现有方法存在难以稳定重构纤维方向和角度分辨率低等缺陷.引入非负约束条件是目前提高稳定性的常用方法,该方法也仅能保证低于6阶时纤维方向的稳定估计.针对以上问题,文章在高阶张量拟合模型基础上引入球面反卷积模型,并提出了一种自适应非负约束迭代算法进行纤维方向分布估计.该算法以高阶张量为基函数拟合纤维扩散分布,沿纤维方向调整非负约束,并自适应训练调整矩阵参数.为了验证本算法的有效性,通过仿真数据与实际临床数据在同等条件下与现有CT-FoD,CSD算法进行角度分辨率,角度误差以及纤维重建对比实验.结果表明,文章所提出的方法在角度分辨率和稳定性方面优于现有的两种方法.     

柔性约束下压杆的一些稳定和不稳定的临界状态

研究了一端固定、一端弹簧约束滑动固定的压杆在Euler临界载荷作用下的稳定性.将系统的势能表示为转角的泛函,将扰动量展开成Fourier级数,将势能的二阶变分表示成一个二次型,得到在临界状态下势能的二阶变分半正定,并求得临界载荷与屈曲模态.进一步研究临界状态下高阶变分的正定性,包括四阶和六阶变分的正定性.结果表明,与刚性约束不同的是,柔性约束压杆临界状态的稳定性与约束的刚度有关,有稳定与不稳定之分,并给出了临界状态是稳定和不稳定的情况下柔性约束相对刚度的范围.     

马尔柯夫链在多介质环境归趋研究中的应用

以开放的环境系统为依托,阐述了马尔柯夫理论在多介质环境归趋研究中的科学性与合理性,并结合国家重点课题—黄河兰州段典型污染物迁移/转化特性及承纳水平研究,研究壬基酚聚氧乙烯醚(nonylphenol polyethoxylates—NPEOs)在黄河兰州段的环境归趋.研究结果表明,利用马尔柯夫模型可以确定污染物在环境介质间的迁移时间、环境介质内的滞留时间、任意时刻污染物在不同环境介质内的含量、给定时间内不同迁移转化过程的迁移量和降解量、环境系统达到稳定的时间、污染物在环境系统内的稳定分布、以及污染物的环境容量或排放标准.     

含尺度变点稳定分布的单位根检验

研究稳定分布噪声模型中含有尺度变点的单位根检验问题.在尺度突变的情形下,给出DF型检验统计量在原假设成立时的渐近分布.结果表明:统计量的渐近分布不仅是Lévy过程的泛函,且依赖尺度变化的位置和跳跃幅度.最后,通过Mente Carlo数值模拟证实,DF检验统计量不再稳健,尺度变点会导致单位根检验的经验水平值发生扭曲.     

Supply network planning in the forest supply chain with bucking decisions anticipation

We consider a two-echelon timber supply chain in which the first echelon consists of several stands to be harvested and the second echelon consists of mills to be supplied with logs of different length. This problem aims at minimizing harvesting and transportation costs for one production period, while satisfying demand expressed as a mix of volumes of specific log types. Harvesting cost, which includes felling, bucking and hauling to roadside, depends upon the number of log type to be produced and sorted. Each stand to be harvested is modeled individually with a limited number of trees of various classes of diameter and total length, which affects the productivity factors of the bucking patterns to be used. To take these characteristics into account, we propose heuristics based on columns generation to solve the supply network problem at the forest level with an anticipation of bucking operations at the stand level.     

The maximum multiplicity of the largest k-th eigenvalue in a matrix whose graph is acyclic or unicyclic

Given a graph $G$ we are interested in studying the symmetric matrices associated to $G$ with a fixed number of negative eigenvalues. For this class of matrices we focus on the maximum possible nullity. For trees this parameter has already been studied and plenty of applications are known. In this work we derive a formula for the maximum nullity and completely describe its behavior as a function of the number of negative eigenvalues. In addition, we also carefully describe the matrices associated with trees that attain this maximum nullity. The analysis is then extended to the more general class of unicyclic graphs. Further our work is applied to re-describing all possible partial inertias associated with trees, and is employed to study an instance of the inverse eigenvalue problem for certain trees.     

The number of maximum matchings in a tree

We determine upper and lower bounds for the number of maximum matchings (i.e., matchings of maximum cardinality) m(T) of a tree T of given order. While the trees that attain the lower bound are easily characterised, the trees with the largest number of maximum matchings show a very subtle structure. We give a complete characterisation of these trees and derive that the number of maximum matchings in a tree of order n is at most O(1.391664ⁿ) (the precise constant being an algebraic number of degree 14). As a corollary, we improve on a recent result by Górska and Skupień on the number of maximal matchings (maximal with respect to set inclusion).     

The Estrada index of trees

The Estrada index of a graph G is defined as , where λ₁,λ₂,…,λ_n are the eigenvalues of its adjacency matrix. We determine the unique tree with maximum Estrada index among the set of trees with given number of pendant vertices. As applications, we determine trees with maximum Estrada index among the set of trees with given matching number, independence number, and domination number, respectively. Finally, we give a proof of a conjecture in [J. Li, X. Li, L. Wang, The minimal Estrada index of trees with two maximum degree vertices, MATCH Commun. Math. Comput. Chem. 64 (2010) 799-810] on trees with minimum Estrada index among the set of trees with two adjacent vertices of maximum degree.     

Maximizing the number of independent subsets over trees with bounded degree

The number of independent vertex subsets is a graph parameter that is, apart from its purely mathematical importance, of interest in mathematical chemistry. In particular, the problem of maximizing or minimizing the number of independent vertex subsets within a given class of graphs has already been investigated by many authors. In view of the applications of this graph parameter, trees of restricted degree are of particular interest. In the current article, we give a characterization of the trees with given maximum degree which maximize the number of independent subsets, and show that these trees also minimize the number of independent edge subsets. The structure of these trees is quite interesting and unexpected: it can be described by means of a novel digital system—in the case of maximum degree 3, we obtain a binary system using the digits 1 and 4. The proof mainly depends on an exchange lemma for branches of a tree. © 2008 Wiley Periodicals, Inc. J Graph Theory 58: 49–68, 2008     

A greedy algorithm for multicut and integral multiflow in rooted trees

We present an O(min(Kn,n²)) algorithm to solve the maximum integral multiflow and minimum multicut problems in rooted trees, where K is the number of commodities and n is the number of vertices. These problems are NP-hard in undirected trees but polynomial in directed trees. In the algorithm we propose, we first use a greedy procedure to build the multiflow then we use duality properties to obtain the multicut and prove the optimality.     

The number of spanning trees of a graph

In this paper, we present some sharp upper bounds for the number of spanning trees of a connected graph in terms of its structural parameters such as the number of vertices, the number of edges, maximum vertex degree, minimum vertex degree, connectivity and chromatic number.     

Null decomposition of trees

Let $T$ be a tree. We show that the null space of the adjacency matrix of $T$ has relevant information about the structure of $T$. We introduce the Null Decomposition of trees, which is a decomposition into two different types of trees: N-trees and S-trees. N-trees are the trees that have a unique maximum (perfect) matching. S-trees are the trees with a unique maximum independent set. We obtain formulas for the independence number and the matching number of a tree using this decomposition. We also show how the number of maximum matchings and the number of maximum independent sets in a tree are related to its null decomposition.     

On the weighted trees with given degree sequence and positive weight set

We determine the (unique) weighted tree with the largest spectral radius with respect to the adjacency and Laplacian matrix in the set of all weighted trees with a given degree sequence and positive weight set. Moreover, we also derive the weighted trees with the largest spectral radius with respect to the matrices mentioned above in the sets of all weighted trees with a given maximum degree or pendant vertex number and so on.     

An optimization problem in forest management

A mathematical model', in the form of a system of differential equations, for the growth of a forest is suggested. The model is based among other things on the fact that the growth of the trees slows down as the crowns of trees get into touch with each other. By using the model the following problem is treated. To be found are the density of trees at time of planting, the policy of thinning of the forest, and the moment of time when the felling of the trees takes place such that the yield from the forest becomes maximal. The problem is an optimal control problem with an unknown parameter and with an unknown terminal time. A comparison with experimental data shows a reasonably good agreement.