Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This ...Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation.展开更多
We propose an algebraic model, presenting individual contributions separately in the system of interest, for the exact solutions of one-dimensional Poisson-Schr?dinger equations used generally in semiconductor device ...We propose an algebraic model, presenting individual contributions separately in the system of interest, for the exact solutions of one-dimensional Poisson-Schr?dinger equations used generally in semiconductor device simulations. The model presented here reveals an interesting relation between the corresponding Poisson and Schr?dinger equation for the physical structure considered, which leads to closed solutions without solving the required electrostatic equation.展开更多
Understanding how electrons form pairs in the presence of strong electron correlations demands going beyond the BCS paradigm.We study a correlated superconducting model where the correlation effects are accounted for ...Understanding how electrons form pairs in the presence of strong electron correlations demands going beyond the BCS paradigm.We study a correlated superconducting model where the correlation effects are accounted for by a U term local in momentum space.The electron correlation is treated exactly while the electron pairing is treated approximately using the mean-field theory.The self-consistent equation for the pair potential is derived and solved.Somewhat contrary to expectation,a weak attractive U comparable to the pair potential can destroy the superconductivity,whereas for weak to intermediate repulsive U,the pair potential can be enhanced.The fidelity of the mean-field ground state is calculated to describe the strength of the elelectron correlation.We show that the pair potential is not equal to the single-electron superconducting gap for the strongly correlated superconductors,in contrast to the uncorrelated BCS limit.展开更多
The exact solution of the U(5)-O(6)transitional description in the interacting boson model with twoparticle and two-hole configuration mixing is derived based on the Bethe ansatz approach.The Bethe ansatz equations ar...The exact solution of the U(5)-O(6)transitional description in the interacting boson model with twoparticle and two-hole configuration mixing is derived based on the Bethe ansatz approach.The Bethe ansatz equations are provided to determine the model’s eigenstates and corresponding eigen-energies.N=2 and N=4 cases are considered as examples to demonstrate the solution features.As an example of the application,some low-lying level energies and B(E2)ratios of 108Cd are fitted and compared with the corresponding experimental data.展开更多
Let G be a finite group. The degree(vertex) graph Γ(G) attached to G is a character degree graph.Its vertices are the degrees of the nonlinear irreducible complex characters of G, and different vertices m, n are adja...Let G be a finite group. The degree(vertex) graph Γ(G) attached to G is a character degree graph.Its vertices are the degrees of the nonlinear irreducible complex characters of G, and different vertices m, n are adjacent if the greatest common divisor(m, n) > 1. In this paper, we classify all graphs with four vertices that occur as Γ(G) for nonsolvable groups G.展开更多
基金Supported by the Key Foundation of Anhui Education Bureau under Grant No.KJ2013A028the 211 Project of Anhhui University under Grant No.J18520104+2 种基金Scientific Training Project for University StudentsNational Natural Science Foundation of China under Grant Nos.11471015,11571016Natural Science Foundation of Anhui Province under Grant No.1408085MA02
文摘Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation.
文摘We propose an algebraic model, presenting individual contributions separately in the system of interest, for the exact solutions of one-dimensional Poisson-Schr?dinger equations used generally in semiconductor device simulations. The model presented here reveals an interesting relation between the corresponding Poisson and Schr?dinger equation for the physical structure considered, which leads to closed solutions without solving the required electrostatic equation.
基金supported by the National Natural Science Foundation of China(Grant No.11274379)the Research Funds of Renmin University of China(Grant No.14XNLQ07)。
文摘Understanding how electrons form pairs in the presence of strong electron correlations demands going beyond the BCS paradigm.We study a correlated superconducting model where the correlation effects are accounted for by a U term local in momentum space.The electron correlation is treated exactly while the electron pairing is treated approximately using the mean-field theory.The self-consistent equation for the pair potential is derived and solved.Somewhat contrary to expectation,a weak attractive U comparable to the pair potential can destroy the superconductivity,whereas for weak to intermediate repulsive U,the pair potential can be enhanced.The fidelity of the mean-field ground state is calculated to describe the strength of the elelectron correlation.We show that the pair potential is not equal to the single-electron superconducting gap for the strongly correlated superconductors,in contrast to the uncorrelated BCS limit.
基金Support from the National Natural Science Foundation of China(11675071,11975009,11575076)the Liaoning Provincial Universities Overseas Training Program(2019-46)+3 种基金the U.S.National Science Foundation(OIA-1738287 and ACI-1713690),U.SDepartment of Energy(DE-SC0005248)the Southeastern Universities Research Associationthe LSU-LNNU joint research program(9961)is acknowledged。
文摘The exact solution of the U(5)-O(6)transitional description in the interacting boson model with twoparticle and two-hole configuration mixing is derived based on the Bethe ansatz approach.The Bethe ansatz equations are provided to determine the model’s eigenstates and corresponding eigen-energies.N=2 and N=4 cases are considered as examples to demonstrate the solution features.As an example of the application,some low-lying level energies and B(E2)ratios of 108Cd are fitted and compared with the corresponding experimental data.
基金supported by National Natural Science Foundation of China(Grant No.10871032)
文摘Let G be a finite group. The degree(vertex) graph Γ(G) attached to G is a character degree graph.Its vertices are the degrees of the nonlinear irreducible complex characters of G, and different vertices m, n are adjacent if the greatest common divisor(m, n) > 1. In this paper, we classify all graphs with four vertices that occur as Γ(G) for nonsolvable groups G.
