This paper mainly focuses on the entire solutions of a nonlocal dispersal equation with asymmetric kernel and bistable nonlinearity. Compared with symmetric case, the asymmetry of the dispersal kernel function makes m...This paper mainly focuses on the entire solutions of a nonlocal dispersal equation with asymmetric kernel and bistable nonlinearity. Compared with symmetric case, the asymmetry of the dispersal kernel function makes more diverse types of entire solutions since it can affect the sign of the wave speeds and the symmetry of the corresponding nonincreasing and nondecreasing traveling waves.We divide the bistable case into two monostable cases by restricting the range of the variable, and obtain some merging-front entire solutions which behave as the coupling of monostable and bistable waves. Before this, we characterize the classification of the wave speeds so that the entire solutions can be constructed more clearly. Especially, we investigate the influence of the asymmetry of the kernel on the minimal and maximal wave speeds.展开更多
Projection temporal logic(PTL) is an extension of interval temporal logic(ITL) with a new projection operator prj and infinite intervals which has been well investigated in the past ten years.In this paper,we review t...Projection temporal logic(PTL) is an extension of interval temporal logic(ITL) with a new projection operator prj and infinite intervals which has been well investigated in the past ten years.In this paper,we review the work on PTL in four aspects:(1) decidability,complexity and expressiveness of propositional PTL(PPTL);(2) modeling,simulation and verification language(MSVL);(3) formal verification approaches with MSVL and PPTL;and(4) supporting toolkit MSV.展开更多
基金Supported by the National Natural Science Foundations of China （No. 60773003, 60970120, 60903180）, the Natural Science Basic Research Plan in Shanx/Province of China （No. S JOB -ZTI4 ）, and the Fundamental Research Funds For the Central Universities and the 111 Project （ No. B08038 ）.
基金partially supported by FRFCU(300102128108)the NSF of China(Grant No.11801038)+2 种基金partially supported by the NSF of China(Grant Nos.11671180 and 11731005)partially supported by the NSF of China(Grant No.11371179)partially supported by the NSF of China(Grant No.11201359)
文摘This paper mainly focuses on the entire solutions of a nonlocal dispersal equation with asymmetric kernel and bistable nonlinearity. Compared with symmetric case, the asymmetry of the dispersal kernel function makes more diverse types of entire solutions since it can affect the sign of the wave speeds and the symmetry of the corresponding nonincreasing and nondecreasing traveling waves.We divide the bistable case into two monostable cases by restricting the range of the variable, and obtain some merging-front entire solutions which behave as the coupling of monostable and bistable waves. Before this, we characterize the classification of the wave speeds so that the entire solutions can be constructed more clearly. Especially, we investigate the influence of the asymmetry of the kernel on the minimal and maximal wave speeds.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 61373008, 11201359, 61562069）, the Natural Science Basic Research Plan in Shaanxi Province of China （Grant No. 2012JM8013）, the 111 Project （Grant No. B08038）, and the Science and Technology on Communication Security Laboratory （Grant No. 9140C110203140C11049）.
基金supported by the National Natural Science Foundation of China(Grant Nos.61133001,61272117,61202038,61322202,61420106004 and 91418201)
文摘Projection temporal logic(PTL) is an extension of interval temporal logic(ITL) with a new projection operator prj and infinite intervals which has been well investigated in the past ten years.In this paper,we review the work on PTL in four aspects:(1) decidability,complexity and expressiveness of propositional PTL(PPTL);(2) modeling,simulation and verification language(MSVL);(3) formal verification approaches with MSVL and PPTL;and(4) supporting toolkit MSV.
