In this section, we present numerical results to evaluate the distributed algorithms of Section 3 as well as the centralized and BNB-based solutions of Section 4 and Section 5, respectively.
Section 2 describes the objective prejudgment model of intrusion detections, Section 3 proposes solution of intrusion detections, Section 4 involves simulations, and Section 5 includes a conclusion.
This result will be employed in Section 4 and Section 5, namely to prove the existence of oscillatory solutions of (2) (Section 4) and the uniqueness of solutions of (1), which have the same asymptotics as solutions of (2) (Section 5).
In this section, we first introduce the concepts of the essential solution of Ky Fan's section theorem and the essential Ky Fan point with respect to (rho_{s}^{u}) and (rho_{k}^{u}).
Further, (y_{0}inbigcap_{xin X}{yin X| x,y in A}=bigcap_{xin X}E_{A}(x)) is solution of Ky Fan's section theorem with respect to A. Denote the set of all solutions of Ky Fan's section theorem by (F_{s}(E_{A})=bigcap_{xin X}{yin X| x,y in A}=bigcap_{xin X}E_{A}(x)).
The point (y_{0}) is called solution of Ky Fan's section theorem with respect to A. We introduce now an alternative form of Ky Fan's section theorem, i.e., the famous Ky Fan's inequality theorem.
