Let n ≠ 0, 1 be an integer and Bn be the variety of n-Bell groups defined by the law [ xn, y] [ x, yn ] ^-1= 1. Let Bn be the class of groups in which for any infinite subsets X and Y there exist x ∈ X and y ∈ Y ...Let n ≠ 0, 1 be an integer and Bn be the variety of n-Bell groups defined by the law [ xn, y] [ x, yn ] ^-1= 1. Let Bn be the class of groups in which for any infinite subsets X and Y there exist x ∈ X and y ∈ Y such that [xn,y][x,yn]-1 = 1. In this paper we prove Bn ∩ L： = （Bn U F） M ∩L：, where F and L are the classes of all finite groups and all locally graded groups, respectively.展开更多
In fluid dynamics, plasma physics and nonlinear optics, Korteweg-de Vries (KdV)-type equations are used to describe certain phenomena. In this paper, a coupled KdV-modified KdV system is investigated. Based on the Bel...In fluid dynamics, plasma physics and nonlinear optics, Korteweg-de Vries (KdV)-type equations are used to describe certain phenomena. In this paper, a coupled KdV-modified KdV system is investigated. Based on the Bell polynomials and symbolic computation, the bilinear form of such system is derived, and its analytic N-soliton solutions are constructed through the Hirota method. Two types of multi-soliton interactions are found, one with the reverse of solitonic shapes, and the other, without. Both the two types can be considered elastic. For a pair of solutions to such system, u and v, with the number of solitons N even, the soliton shapes of u stay unvaried while those of v reverse after the interaction; with N odd, the soliton shapes of both u and v keep unchanged after the interaction.展开更多
We present an efficient and simple protocol to unambiguously distinguish 2Nmutual orthogonal N-qubit Greenberger–Horne–Zeilinger states in polarization degree of freedom assisted by the frequency one. This scheme is...We present an efficient and simple protocol to unambiguously distinguish 2Nmutual orthogonal N-qubit Greenberger–Horne–Zeilinger states in polarization degree of freedom assisted by the frequency one. This scheme is based on N single photon Bell state measurements, which can be implemented non-locally. The success probability is100% in principle and our scheme is feasible with current technology. All the advantages make our protocol meaningful and practical in quantum information processing.展开更多
In this paper,the bilinear form of a generalized Kadomtsev-Petviashvili equation is obtained by applying the binary Bell polynomials.The N-soliton solution and one periodic wave solution are presented by use of the Hi...In this paper,the bilinear form of a generalized Kadomtsev-Petviashvili equation is obtained by applying the binary Bell polynomials.The N-soliton solution and one periodic wave solution are presented by use of the Hirota direct method and the Riemann theta function,respectively.And then the asymptotic analysis demonstrates one periodic wave solution can be reduced to one soliton solution.In the end,the bilinear Bcklund transformations are derived.展开更多
文摘Let n ≠ 0, 1 be an integer and Bn be the variety of n-Bell groups defined by the law [ xn, y] [ x, yn ] ^-1= 1. Let Bn be the class of groups in which for any infinite subsets X and Y there exist x ∈ X and y ∈ Y such that [xn,y][x,yn]-1 = 1. In this paper we prove Bn ∩ L： = （Bn U F） M ∩L：, where F and L are the classes of all finite groups and all locally graded groups, respectively.
基金Supported by the National Natural Science Foundation of China under Grant No. 60772023the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02+1 种基金the Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications)the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 200800130006, Chinese Ministry of Education
文摘In fluid dynamics, plasma physics and nonlinear optics, Korteweg-de Vries (KdV)-type equations are used to describe certain phenomena. In this paper, a coupled KdV-modified KdV system is investigated. Based on the Bell polynomials and symbolic computation, the bilinear form of such system is derived, and its analytic N-soliton solutions are constructed through the Hirota method. Two types of multi-soliton interactions are found, one with the reverse of solitonic shapes, and the other, without. Both the two types can be considered elastic. For a pair of solutions to such system, u and v, with the number of solitons N even, the soliton shapes of u stay unvaried while those of v reverse after the interaction; with N odd, the soliton shapes of both u and v keep unchanged after the interaction.
基金Supported by the National Natural Science Foundation of China under Grant No.11004258Fundamental Research Funds for the Central Universities Project under Grant No.CQDXWL-2012-014
文摘We present an efficient and simple protocol to unambiguously distinguish 2Nmutual orthogonal N-qubit Greenberger–Horne–Zeilinger states in polarization degree of freedom assisted by the frequency one. This scheme is based on N single photon Bell state measurements, which can be implemented non-locally. The success probability is100% in principle and our scheme is feasible with current technology. All the advantages make our protocol meaningful and practical in quantum information processing.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10735030 and 11075055Innovative Research Team Program of the National Natural Science Foundation of China under Grant No. 61021004
文摘In this paper,the bilinear form of a generalized Kadomtsev-Petviashvili equation is obtained by applying the binary Bell polynomials.The N-soliton solution and one periodic wave solution are presented by use of the Hirota direct method and the Riemann theta function,respectively.And then the asymptotic analysis demonstrates one periodic wave solution can be reduced to one soliton solution.In the end,the bilinear Bcklund transformations are derived.
