For the propagation of the ultrashort pulses in an inhomogeneous multi-component nonlinear medium, a system of coupled equations is analytically studied in this paper. Painleve analysis shows that this system admits t...For the propagation of the ultrashort pulses in an inhomogeneous multi-component nonlinear medium, a system of coupled equations is analytically studied in this paper. Painleve analysis shows that this system admits the Painleve property under some constraints. By means of the Ablowitz-Kaup-Newell-Segur procedure, the Lax pair of this system is derived, and the Darboux transformation （DT） is constructed with the help of the obtained Lax pair. With symbolic computation, the soliton solutions are obtained by virtue of the DT algorithm. Figures are plotted to illustrate the dynamical features of the soliton solutions. Characteristics of the solitons propagating in an inhomogeneous multi-component nonlinear medium are discussed： （i） Propagation of one soliton and two-peak soliton; （ii） Elastic interactions of the parabolic two solitons; （iii） Overlap two head-on solitons and two head-on two-peak solitons; （v） Two （vi） Decomposition phenomenon of one soliton into two solitons. phenomenon between two solitons; （iv） Collision of different types of interactions of the three solitons; ultrashort-pulse propagation in the inhomogeneous multi-component The results might be useful in the study on the nonlinear media.展开更多
Multi-component mixture(MCM) is a complicated chemical system that contains a great deal of mixture rays with various mixture ratios, and each ray includes many mixtures with different concentration levels.Currently, ...Multi-component mixture(MCM) is a complicated chemical system that contains a great deal of mixture rays with various mixture ratios, and each ray includes many mixtures with different concentration levels.Currently, in combined toxicity field, almost all studies on MCM focus on the mixtures designed by the equivalenteffect concentration ratio(EECR) procedure. However, the EECR mixtures cannot represent the whole mixture system because the EECR mixtures are located on one mixture ray in concentration space formed by multiple components. In our view, some optimal experimental design such as the uniform design(UD) should be used to effectively select many representative mixture rays from the MCM system,instead of single EECR ray. The uniform design ray(UDray) integrating UD idea with fixed-ratio ray design can systematically and comprehensively measure the combined toxicity changes in the MCM system. This review introduces the operation method, construction of uniform table and corresponding usable table, and some cases of application of the UD-ray to help readers easily use UD-ray in their MCM toxicity assessment.展开更多
The authors prove the local unramified correspondence for a new type of construction of CAP representations of even orthogonal groups by a generalized automorphic descent method. This method is expected to work for al...The authors prove the local unramified correspondence for a new type of construction of CAP representations of even orthogonal groups by a generalized automorphic descent method. This method is expected to work for all classical groups.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.60772023by the Open Fund No.BUAA-SKLSDE-09KF-04+2 种基金Supported Project No.SKLSDE-2010ZX-07 of the State Key Laboratory of Software Development Environment,Beijing University of Aeronautics and Astronauticsby the National Basic Research Program of China (973 Program) under Grant No.2005CB321901by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.200800130006,Chinese Ministry of Education
文摘For the propagation of the ultrashort pulses in an inhomogeneous multi-component nonlinear medium, a system of coupled equations is analytically studied in this paper. Painleve analysis shows that this system admits the Painleve property under some constraints. By means of the Ablowitz-Kaup-Newell-Segur procedure, the Lax pair of this system is derived, and the Darboux transformation （DT） is constructed with the help of the obtained Lax pair. With symbolic computation, the soliton solutions are obtained by virtue of the DT algorithm. Figures are plotted to illustrate the dynamical features of the soliton solutions. Characteristics of the solitons propagating in an inhomogeneous multi-component nonlinear medium are discussed： （i） Propagation of one soliton and two-peak soliton; （ii） Elastic interactions of the parabolic two solitons; （iii） Overlap two head-on solitons and two head-on two-peak solitons; （v） Two （vi） Decomposition phenomenon of one soliton into two solitons. phenomenon between two solitons; （iv） Collision of different types of interactions of the three solitons; ultrashort-pulse propagation in the inhomogeneous multi-component The results might be useful in the study on the nonlinear media.
基金supported by the National Natural Science Foundation of China(2117709721207002)Specialized Research Fund for the Doctoral Program of Higher Education(20120072110052)
文摘Multi-component mixture(MCM) is a complicated chemical system that contains a great deal of mixture rays with various mixture ratios, and each ray includes many mixtures with different concentration levels.Currently, in combined toxicity field, almost all studies on MCM focus on the mixtures designed by the equivalenteffect concentration ratio(EECR) procedure. However, the EECR mixtures cannot represent the whole mixture system because the EECR mixtures are located on one mixture ray in concentration space formed by multiple components. In our view, some optimal experimental design such as the uniform design(UD) should be used to effectively select many representative mixture rays from the MCM system,instead of single EECR ray. The uniform design ray(UDray) integrating UD idea with fixed-ratio ray design can systematically and comprehensively measure the combined toxicity changes in the MCM system. This review introduces the operation method, construction of uniform table and corresponding usable table, and some cases of application of the UD-ray to help readers easily use UD-ray in their MCM toxicity assessment.
基金supported by the National Science Foundation Grant(Nos.DMS–1001672,DMS–1301567)the USA-Israel Binational Science Foundation Grant(Nos.2008058,2012019)
文摘The authors prove the local unramified correspondence for a new type of construction of CAP representations of even orthogonal groups by a generalized automorphic descent method. This method is expected to work for all classical groups.
