典型液压系统在功率键合图中的应用

在工程系统动态特性的理论研究中,常用的方法有传递函数法和状态方程法。但对液压系统来说,具有一定的局限性。而功率键合图,则可以直接从液压原理图有条不紊地画出来。本文给出了一典型液压系统的功率键合图,同时给出了影响系统动态特性的各个因素和系统的方程。     

正则图的剖分图的秩

讨论几类正则图的剖分图的邻接矩阵的秩。主要有:圈,路,完全图,完全二部图和多部图,度为3与4的循环图。     

轮和完全等二部图联图的若干染色问题

图的染色理论是图论的一个重要分支。本文使用分析的方法得到了轮和完全等二部图联图的全色数、均匀全色数和邻点可区别边色数。     

古朴简雅、自然圆润——简析钟道宇端砚系列小说的语言艺术

钟道宇的端砚系列小说语言非常简朴、清新。使用古汉语的表达方式而显得蕴藉典雅;运用各类修辞手法及吸收端州地方语言的质朴与灵活,增强了表现力。     

Optimal Augmentation of a 2-Vertex-Connected Multigraph to a k-Edge-Connected and 3-Vertex-Connected Multigraph

Given an undirected multigraph G = (V, E) and two positive integers and k, we consider the problem of augmenting G by the smallest number of new edges to obtain an -edge-connected and k-vertex-connected multigraph. In this paper, we show that the problem can be solved in Õ(mn²) time for any fixed and k = 3 if an input multigraph G is 2-vertex-connected, where n = |V| and m is the number of pairs of adjacent vertices in G.     

The Steiner Tree Problem in Kalmanson Matrices and in Circulant Matrices

We investigate the computational complexity of two special cases of the Steiner tree problem where the distance matrix is a Kalmanson matrix or a circulant matrix, respectively. For Kalmanson matrices we develop an efficient polynomial time algorithm that is based on dynamic programming. For circulant matrices we give an -hardness proof and thus establish computational intractability.     

Improved Approximation for Breakpoint Graph Decomposition and Sorting by Reversals

Sorting by Reversals (SBR) is one of the most widely studied models of genome rearrangements in computational molecular biology. At present, is the best known approximation ratio achievable in polynomial time for SBR. A very closely related problem, called Breakpoint Graph Decomposition (BGD), calls for a largest collection of edge disjoint cycles in a suitably-defined graph. It has been shown that for almost all instances SBR is equivalent to BGD, in the sense that any solution of the latter corresponds to a solution of the former having the same value. In this paper, we show how to improve the approximation ratio achievable in polynomial time for BGD, from the previously known to for any > 0. Combined with the results in (Caprara, Journal of Combinatorial Optimization, vol. 3, pp. 149–182, 1999b), this yields the same approximation guarantee for n! – O((n – 5)!) out of the n! instances of SBR on permutations with n elements. Our result uses the best known approximation algorithms for Stable Set on graphs with maximum degree 4 as well as for Set Packing where the maximum size of a set is 6. Any improvement in the ratio achieved by these approximation algorithms will yield an automatic improvement of our result.     

Finding a Noncrossing Steiner Forest in Plane Graphs Under a 2-Face Condition

Let G = (V,E) be a plane graph with nonnegative edge weights, and let be a family of k vertex sets , called nets. Then a noncrossing Steiner forest for in G is a set of k trees in G such that each tree connects all vertices, called terminals, in net N _i, any two trees in do not cross each other, and the sum of edge weights of all trees is minimum. In this paper we give an algorithm to find a noncrossing Steiner forest in a plane graph G for the case where all terminals in nets lie on any two of the face boundaries of G. The algorithm takes time if G has n vertices and each net contains a bounded number of terminals.     

Fast On-Line/Off-Line Algorithms for Optimal Reinforcement of a Network and its Connections with Principal Partition

The problem of computing the strength and performing optimal reinforcement for an edge-weighted graph G(V, E, w) is well-studied. In this paper, we present fast (sequential linear time and parallel logarithmic time) on-line algorithms for optimally reinforcing the graph when the reinforcement material is available continuously on-line. These are the first on-line algorithms for this problem. We invest O(|V|³|E|log|V|) time (equivalent to (|V|) invocations of the fastest known algorithms for optimal reinforcement) in preprocessing the graph before the start of our algorithms. It is shown that the output of our on-line algorithms is as good as that of the off-line algorithms. Thus our algorithms are better than the fastest off-line algorithms in situations when a sequence of more than (|V|) reinforcement problems need to be solved. The key idea is to make use of ideas underlying the theory of Principal Partition of a Graph. Our ideas are easily generalized to the general setting of polymatroid functions. We also present a new efficient algorithm for computation of the Principal Sequence of a graph.     

The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers

Let k 5 be a fixed integer and let m = (k – 1)/2. It is shown that the independence number of a C _k-free graph is at least c ₁[ d(v)^{1/(m – 1)}]^{(m – 1)/m} and that, for odd k, the Ramsey number r(C _k, K _n) is at most c ₂(n ^{m + 1}/log n)^1/m , where c ₁ = c ₁(m) > 0 and c ₂ = c ₂(m) > 0.