With the aid of the classical Lie group method and nonclassical Lie group method,we derive the classicalLie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS)equation.Usi...With the aid of the classical Lie group method and nonclassical Lie group method,we derive the classicalLie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS)equation.Usingthe symmetries,we find six classical similarity reductions and two nonclassical similarity reductions of the BS equation.Varieties of exact solutions of the BS equation are obtained by solving the reduced equations.展开更多
The transformation groups and symmetries of the baroclinic mode for rotating stratified flow can be obtained via the standard approach. Applying the symmetry group on some special solutions, the newly obtained results...The transformation groups and symmetries of the baroclinic mode for rotating stratified flow can be obtained via the standard approach. Applying the symmetry group on some special solutions, the newly obtained results disprove a known conjecture.展开更多
By Lie symmetry method, the Lie point symmetries and its Kac-Moody-Virasoro (KMV) symmetry algebra of (2+1)-dimensional dispersive long-wave equation (DLWE) are obtained, and the finite transformation of DLWE is given...By Lie symmetry method, the Lie point symmetries and its Kac-Moody-Virasoro (KMV) symmetry algebra of (2+1)-dimensional dispersive long-wave equation (DLWE) are obtained, and the finite transformation of DLWE is given by symmetry group direct method, which can recover Lie point symmetries. Then KMV symmetry algebra of DLWE with arbitrary order invariant is also obtained. On basis of this algebra the group invariant solutions and similarity reductions are also derived.展开更多
The formulations of the finite-field approach to calculate the linear and non-linear optical coefficients (i, (ij, (ijk and (ijkl of a molecular system with different symmetries have been deduced and summarized. The p...The formulations of the finite-field approach to calculate the linear and non-linear optical coefficients (i, (ij, (ijk and (ijkl of a molecular system with different symmetries have been deduced and summarized. The possible choices of the energy sets of the 48 frequent point groups have been optimized and categorized into 11 classes. With the restriction of symmetry operators, a minimum of 9, no more than 21 energy points have to be calculated in order to determine the coefficients, except in the case of the first class to which C1 point group belongs and in which the 34 non-relative energy points selected in our uniform and general scheme are all needed. The symmetric operators that cause some of the tensor components to vanish have been demonstrated as well.展开更多
Let G be a weighted graph with adjacency matrix A=[aij]. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix D=[dij], where for i≠j, dij is the Euclidean distance betwee...Let G be a weighted graph with adjacency matrix A=[aij]. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix D=[dij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for different nuclei. Balasubramanian (1995) computed the Euclidean graphs and their automorphism groups for benzene, eclipsed and staggered forms of ethane and eclipsed and staggered forms of ferrocene. This paper describes a simple method, by means of which it is possible to calculate the automorphism group of weighted graphs. We apply this method to compute the symmetry of tetraammine platinum(II) with C2v and C4v point groups.展开更多
基金Supported by National Natural Science Foundation of China and China Academy of Engineering Physics (NSAF 11076015)
文摘With the aid of the classical Lie group method and nonclassical Lie group method,we derive the classicalLie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS)equation.Usingthe symmetries,we find six classical similarity reductions and two nonclassical similarity reductions of the BS equation.Varieties of exact solutions of the BS equation are obtained by solving the reduced equations.
基金Supported by National Natural Science Foundation of China under Grant Nos.10735030,10675065,and 90503006PCSIRT (IRT0734)+1 种基金the National Basic Research Programme of China under Grant Nos.2007CB814800K.C.Wong Magna Fund in Ningbo University
文摘The transformation groups and symmetries of the baroclinic mode for rotating stratified flow can be obtained via the standard approach. Applying the symmetry group on some special solutions, the newly obtained results disprove a known conjecture.
基金Supported by the Natural Science Foundation of China under Grant No. 10735030Ningbo Natural Science Foundation under Grant No. 2008A610017+3 种基金National Basic Research Program of China (973 Program 2007CB814800)Shanghai Leading Academic Discipline Project under Grant No. B412Program for Changjiang Scholars and Innovative Research Team in University (IRT0734)K.C. Wong Magna Fund in Ningbo University
文摘By Lie symmetry method, the Lie point symmetries and its Kac-Moody-Virasoro (KMV) symmetry algebra of (2+1)-dimensional dispersive long-wave equation (DLWE) are obtained, and the finite transformation of DLWE is given by symmetry group direct method, which can recover Lie point symmetries. Then KMV symmetry algebra of DLWE with arbitrary order invariant is also obtained. On basis of this algebra the group invariant solutions and similarity reductions are also derived.
基金the National Science Foundation of China (69978021), Fujian Provincial National Science Foundation of China (E9910030) and State
文摘The formulations of the finite-field approach to calculate the linear and non-linear optical coefficients (i, (ij, (ijk and (ijkl of a molecular system with different symmetries have been deduced and summarized. The possible choices of the energy sets of the 48 frequent point groups have been optimized and categorized into 11 classes. With the restriction of symmetry operators, a minimum of 9, no more than 21 energy points have to be calculated in order to determine the coefficients, except in the case of the first class to which C1 point group belongs and in which the 34 non-relative energy points selected in our uniform and general scheme are all needed. The symmetric operators that cause some of the tensor components to vanish have been demonstrated as well.
文摘Let G be a weighted graph with adjacency matrix A=[aij]. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix D=[dij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for different nuclei. Balasubramanian (1995) computed the Euclidean graphs and their automorphism groups for benzene, eclipsed and staggered forms of ethane and eclipsed and staggered forms of ferrocene. This paper describes a simple method, by means of which it is possible to calculate the automorphism group of weighted graphs. We apply this method to compute the symmetry of tetraammine platinum(II) with C2v and C4v point groups.
