Forest covers and a polyhedral intersection theorem

Aforest cover of a graph is a spanning forest for which each component has at least two nodes. We consider the convex hull of incidence vectors of forest covers in a graph and show that this polyhedron is the intersection of the forest polytope and the cover polytope. This polytope has both the spanning tree and perfect matching polytopes as faces. Further, the forest cover polytope remains integral with the addition of the constraint requiring that, for some integerk, exactlyk edges be used in the solution.Research done while thae authors were visiting the Institut für Ökonometrie und Operations Research, Universität Bonn, West Germany.Financial support provided by the Natural Sciences and Engineering Research Council, Canada and the German Research Association (Deutsche Forschungsgemeneinschaft, SFB 303).     

In and out forests on combinatorial landscapes

Fitness landscape theory is a mathematical framework for numerical analysis of search algorithms on combinatorial optimization problems. We study a representation of fitness landscape as a weighted directed graph. We consider out forest and in forest structures in this graph and establish important relationships among the forest structures of a directed graph, the spectral properties of the Laplacian matrices, and the numbers of local optima of the landscape. These relationships provide a new approach for computing the numbers of local optima for various problem instances and neighborhood structures.     

森林的致命性病虫害模型

本文讨论了森林的传染病方程 ,建立了森林的致命性病虫害偏微分方程模型     

食叶昆虫与树叶的动态模型

落叶林经常遭受食叶昆虫的危害.建立了六个模型,通过对它们的分析来预测在什么条件下食叶昆虫会吃光落叶林的树叶.     

森林补图的最小填充

本文研究森林补图的最小填充问题,并给出了森林补图的填充数的表达式.     

The quotient algebra of labeled forests modulo <Emphasis Type="Italic">h</Emphasis>-equivalence

We introduce and study some natural operations on a structure of finite labeled forests, which is crucial in extending the difference hierarchy to the case of partitions. It is shown that the corresponding quotient algebra modulo the so-called h-equivalence is the simplest non-trivial semilattice with discrete closures. The algebra is also characterized as a free algebra in some quasivariety. Part of the results is generalized to countable labeled forests with finite chains. Supported by a DAAD project within the program “Ostpartnerschaften.” __________ Translated from Algebra I Logika, Vol. 46, No. 2, pp. 217–243, March–April, 2007.     

The boundary of iterates in Euclidean growth models

This paper defines a general Euclidean growth model via a translation invariant, monotone and local transformation on Borel subsets of . The main result gives a geometric condition for the boundary curvature of the iterates to go to 0. Consequences include estimates for the speed of convergence to the asymptotic shape, and a result about survival of Euclidean deterministic forest fires.

     

林木病虫害的动力学模型

本文讨论森林病虫害方程 ,建立了森林病虫害的一些常微分方程模型 ,并讨论了模型解的性质 .     

Use of stochastic control theory to model a forest management system

A forest management problem due to Hellman has been modelled as a stochastic control problem with one state variable (inventory level) and one control variable (consumption rate of wood by the factories). The stochastic process governing the evolution of the inventory level is transformed into an Itô stoachastic differential equation by approximating the compound Poisson process of wood arrivals into the depot as a Wiener process. The resulting stochastic control problem is solved by using the Hamilton-Jacobi-Bellman equation of stochastic dynamic programming. Two numerical examples illustrate the results.     

最大度大于等于7的平面图的线性荫度

图的染色问题在组合优化、计算机科学和Hessians矩阵的网络计算等方面具有非常重要的应用。其中图的染色中有一种重要的染色——线性荫度,它是一种非正常的边染色,即在简单无向图中,它的边可以分割成线性森林的最小数量。研究最大度$\bigtriangleup（G）\geq7$的平面图$G$的线性荫度,证明了对于两个固定的整数$i$,$j\in\{5,6,7\}$,如果图$G$中不存在相邻的含弦$i$,$j$-圈,则图$G$的线性荫度为$\lceil\frac\bigtriangleup2\rceil$。     

带生长函数的非定常森林发展系统

讨论非定常森林发展系统的动力学模型,证明了方程解的存在唯一性,并用Lyapunov稳定性理论讨论了系统的稳定性.     

The acircuitic directed star arboricity of subcubic graphs is at most four

A directed star forest is a forest all of whose components are stars with arcs emanating from the center to the leaves. The acircuitic directed star arboricity of an oriented graph G (that is a digraph with no opposite arcs) is the minimum number of arc-disjoint directed star forests whose union covers all arcs of G and such that the union of any two such forests is acircuitic. We show that every subcubic graph has acircuitic directed star arboricity at most four.     

非线性半离散森林系统的可控性

讨论森林发展系统的一类非线性林龄面积结构的半离散模型,利用矩阵的秩判据证明了森林半离散系统的可控性.     

非线性半离散森林系统的稳定性

讨论森林发展系统的一类非线性林龄面积结构的半离散模型 ,给出了非线性半离散系统稳定的一些充分条件 .     

Stable Solution of Nonlinear Age-structured Forest Evolution System

This paper studies the dynamical behavior of a class of total area dependent nonlinear age-structured forest evolution model. We give the problem of equal value for the forest system, and discuss the stable solution of system. We obtained the necessary and sufficient conditions for there exists the stable solution.     

森林发展系统的一个非线性半离散模型

本文建立了森林发展系统的一类非线性林龄面积结构的半离散模型 ,并讨论了半离散系统解的存在唯一性 ,给出了线性半离散系统稳定的一些充分条件