Let Γm，n^* denote all m × n strongly connected bipartite tournaments and a(m, n) the maximal integer k such that every m × n bipartite tournament contains at least a k × k transitive bipartite subtour...Let Γm，n^* denote all m × n strongly connected bipartite tournaments and a(m, n) the maximal integer k such that every m × n bipartite tournament contains at least a k × k transitive bipartite subtournament. Let t ( m, n, k, l ) = max{t( Tm,n，k, l ) : Tm,n∈Γm，n^*}, where t ( Tm,n, k, l ) is the number of k × l(k≥2,l≥2) transitive bipartite subtournaments contained in Tm,n∈Γm，n^*. We obtain a method of graph theory for solving some integral programmings, investigate the upper bounds of a(m,n) and obtain t (m,n, k，l).展开更多
The authors discuss the stability radius of the non-smooth Pritchard-Salamon systemsunder structured perturbations.A formula for the stability radius in terms of t he norm of a certaininput-output operator is obtained...The authors discuss the stability radius of the non-smooth Pritchard-Salamon systemsunder structured perturbations.A formula for the stability radius in terms of t he norm of a certaininput-output operator is obtained.Furthermore,the relationship between stability radius and thesolvability of some type of algebraic Riccati equations is given.展开更多
文摘Let Γm，n^* denote all m × n strongly connected bipartite tournaments and a(m, n) the maximal integer k such that every m × n bipartite tournament contains at least a k × k transitive bipartite subtournament. Let t ( m, n, k, l ) = max{t( Tm,n，k, l ) : Tm,n∈Γm，n^*}, where t ( Tm,n, k, l ) is the number of k × l(k≥2,l≥2) transitive bipartite subtournaments contained in Tm,n∈Γm，n^*. We obtain a method of graph theory for solving some integral programmings, investigate the upper bounds of a(m,n) and obtain t (m,n, k，l).
基金supported by the National Natural Science Foundation of China under Grant Nos. 10626057 and 10571165
文摘The authors discuss the stability radius of the non-smooth Pritchard-Salamon systemsunder structured perturbations.A formula for the stability radius in terms of t he norm of a certaininput-output operator is obtained.Furthermore,the relationship between stability radius and thesolvability of some type of algebraic Riccati equations is given.
