Practical stabilities for linear fractional impulsive hybrid systems are investigated in detail.The transformation from a linear fractional differential system to a fractional impulsive hybrid system is interpreted.With the help of the Mittag-Leffler functions for matrix-type,several practical stability criteria for fractional impulsive hybrid systems are derived.Finally,a numerical example is provided to illustrate the effectiveness of the results.
A singularly perturbed second-order semilinear differential equation with integral boundary conditions is considered. By the method of boundary functions, the conditions under which there exists an internal transition layer for the original problem are established. The existence of spike-type solution is obtained by smoothly connecting the solutions of left and right associated problems, and the asymptotic expansion of the spike-type solution is also presented.
A clustering algorithm for semi-supervised affinity propagation based on layered combination is proposed in this paper in light of existing flaws. To improve accuracy of the algorithm,it introduces the idea of layered combination, divides an affinity propagation clustering( APC) process into several hierarchies evenly,draws samples from data of each hierarchy according to weight,and executes semi-supervised learning through construction of pairwise constraints and use of submanifold label mapping,weighting and combining clustering results of all hierarchies by combined promotion. It is shown by theoretical analysis and experimental result that clustering accuracy and computation complexity of the semi-supervised affinity propagation clustering algorithm based on layered combination( SAP-LC algorithm) have been greatly improved.
