Using those properties obtained,the following result is proved by a constructive method: Let X be a completely metric space with a fixed point,if f is a topological transitive continuous self-map on X,then there exists a dense infinitely-expansive LY-scrambled set consisting of transitive points of f.

Several works suggest proving termination by using triggering and activation graphs at compile-time, and computing an irreducible rule set is the key technique.

Most papers on detection intrusion problems made by past researchers usually employ rule portfolio to match attack data packages and appear unable to keep the system in optimized detection status when the detection probability is unknown or varying.

In this paper,an optimization method is provided based on study how to select rule portfolio in real-time intrusion detection system,this method can improve the function for IDS under the condition of flood data.

Based on the command and control theory in the information age,the value and working mechanism of self-synchronization in improving the battle effectiveness of troops is discussed,and the self-synchronization realization methods and principles based on rule set are brought forward.

No cycles in TG is a sufficient condition of the termination of rule sets, but it is not a necessary condition.

Through the study of the confluence of active rule set,the analysis of its interchange bility and the execution graph,this paper presents the deciding theorem of confluence.

Besides,the integration rule and transformation algorithm of heterogeneous data .