In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation...In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.展开更多
This paper proposes a new method to reduce the dimensionality of input and output spaces in DEA models. The method is based on Yanai’s Generalized Coefficient of Determination and on the concept of pseudo-rank of a m...This paper proposes a new method to reduce the dimensionality of input and output spaces in DEA models. The method is based on Yanai’s Generalized Coefficient of Determination and on the concept of pseudo-rank of a matrix. In addition, the paper suggests a rule to determine the cardinality of the subset of selected variables in a way to gain the maximal discretionary power and to suffer a minimal informational loss.展开更多
Presented here are the Generalized BCS Equations incorporating Fermi Energy for the study of the {Δ, Tc, jc(T)} values of both elemental and composite superconductors (SCs) for all T ≤ Tc, where Δ, Tc and jc(T) den...Presented here are the Generalized BCS Equations incorporating Fermi Energy for the study of the {Δ, Tc, jc(T)} values of both elemental and composite superconductors (SCs) for all T ≤ Tc, where Δ, Tc and jc(T) denote, respectively, one of the gap values, the critical temperature and the T-dependent critical current density. This framework, which extends our earlier study that dealt with the {Δ0, Tc, jc(0)} values of an SC, is also shown to lead to T-dependent values of several other related parameters such as the effective mass of electrons, their number density, critical velocity, Fermi velocity (VF), coherence length and the London penetration depth. The extended framework is applied to the jc(T) data reported by Romijn et al. for superconducting Aluminium strips and is shown not only to provide an alternative to the explanation given by them, but also to some novel features such as the role of the Sommerfeld coefficient γ(T) in the context of jc(T) and the role of VF(T) in the context of a recent finding by Plumb et al. about the superconductivity of Bi-2212.展开更多
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant Nos. 2004zx16 and Q2005A01
文摘In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.
文摘This paper proposes a new method to reduce the dimensionality of input and output spaces in DEA models. The method is based on Yanai’s Generalized Coefficient of Determination and on the concept of pseudo-rank of a matrix. In addition, the paper suggests a rule to determine the cardinality of the subset of selected variables in a way to gain the maximal discretionary power and to suffer a minimal informational loss.
文摘Presented here are the Generalized BCS Equations incorporating Fermi Energy for the study of the {Δ, Tc, jc(T)} values of both elemental and composite superconductors (SCs) for all T ≤ Tc, where Δ, Tc and jc(T) denote, respectively, one of the gap values, the critical temperature and the T-dependent critical current density. This framework, which extends our earlier study that dealt with the {Δ0, Tc, jc(0)} values of an SC, is also shown to lead to T-dependent values of several other related parameters such as the effective mass of electrons, their number density, critical velocity, Fermi velocity (VF), coherence length and the London penetration depth. The extended framework is applied to the jc(T) data reported by Romijn et al. for superconducting Aluminium strips and is shown not only to provide an alternative to the explanation given by them, but also to some novel features such as the role of the Sommerfeld coefficient γ(T) in the context of jc(T) and the role of VF(T) in the context of a recent finding by Plumb et al. about the superconductivity of Bi-2212.
