Triangle-free graphs with no six-vertex induced path

The graphs with no five-vertex induced path are still not understood. But in the triangle-free case, we can do this and one better; we give an explicit construction for all triangle-free graphs with no six-vertex induced path. Here are three examples: the 16-vertex Clebsch graph, the graph obtained from an 8-cycle by making opposite vertices adjacent, and the graph obtained from a complete bipartite graph by subdividing a perfect matching. We show that every connected triangle-free graph with no six-vertex induced path is an induced subgraph of one of these three (modulo some twinning and duplication).     

Comparison of adaptive filters for gas turbine performance monitoring

Kalman filters are widely used in the turbine engine community for health monitoring purpose. This algorithm has proven its capability to track gradual deterioration with a good accuracy. On the other hand, its response to rapid deterioration is either a long delay in recognising the fault, and/or a spread of the estimated fault in several components. The main reason of this deficiency lies in the transition model of the parameters that assumes a smooth evolution of the engine’s condition. The aim of this contribution is to compare two adaptive diagnosis tools that combine a Kalman filter and a secondary system that monitors the residuals. This auxiliary component implements on one hand a covariance matching scheme and on the other hand a generalised likelihood ratio test to improve the behaviour of the diagnosis tool with respect to abrupt faults.     

我国高等教育发展统计特征的PLS通径模型分析

借鉴UNESCO教育指标体系框架,建构我国高等教育发展统计指标体系;采用PLS通径模型这一结构方程建模新技术对建构的指标体系进行验证,并对2006年我国高等教育发展状况进行分析,获得客观统计指标数据特征。     

kQ#k<σ>的Clebsch—Gordan问题

主要讨论斜群代数kQ#k<σ>的Clebsch-Gordan问题.特别地,当Q是A_n,D_n型简图,以及Kronecker简图时,给出kQ#k<σ>的Clebsch-Gordan公式.     

4‐Coloring P6‐Free Graphs with No Induced 5‐Cycles

We show that the 4‐coloring problem can be solved in polynomial time for graphs with no induced 5‐cycle C₅ and no induced 6‐vertex path P₆     

Skew Motzkin paths

In this paper, we study the class S of skew Motzkin paths, i.e., of those lattice paths that are in the first quadrat, which begin at the origin, end on the x-axis, consist of up steps U =(1, 1),down steps D =(1,-1), horizontal steps H =(1, 0), and left steps L =(-1,-1), and such that up steps never overlap with left steps. Let S_n be the set of all skew Motzkin paths of length n and let 8_n = |S_n|. Firstly we derive a counting formula, a recurrence and a convolution formula for sequence{8_n}n≥0. Then we present several involutions on S_n and consider the number of their fixed points.Finally we consider the enumeration of some statistics on S_n.     

THE C-K MODEL WITH SOLVABLE ENDOGENOUS FERTILITY

§ 1　 IntroductionThe relationship of population and economic growth is one of the most importantproblems in modern economic growth theory.Establishing a mathematical model theoreti-cal to study the interrelation of population and economic growth becomes a fundamentalmethod in this field[1～ 7] .In the papers[8,9] ,we obtain the especial C-K models with solv-able endogenous fertility under the specified strongly additive utility function and Cobb-Douglas production function.In the models,th…     

On the Gracefulness of Graph（jC_（4n））∪P_m

The present paper deals with the gracefulness of unconnected graph （jC_（4n））∪P_m,and proves the following result：for positive integers n,j and m with n≥1,j≥2,the unconnected graph（jC_（4n））∪P_m is a graceful graph for m=j-1 or m≥n＋j,where C_（4n） is a cycle with 4n vertexes,P_m is a path with m＋1 vertexes,and（jC_（4n））∪P_m denotes the disjoint union of j-C_（4n） and P_m.     

Note on the longest paths in {K 1,4, K 1,4 + e}-free graphs

A graph G is {K 1,4,K 1,4 + e}-free if G contains no induced subgraph isomorphic to K 1,4 or K 1,4 + e.In this paper,we show that G has a path which is either hamiltonian or of length at least 2δ(G) + 2 if G is a connected {K 1,4,K 1,4 + e}-free graph on at least 7 vertices.