Based on the left_right equivalent relation of smooth map_germs in singularity theory, the unfoldings of multiparameter equivariant bifurcation problems with respect to left_right equivalence are discussed. The state ...Based on the left_right equivalent relation of smooth map_germs in singularity theory, the unfoldings of multiparameter equivariant bifurcation problems with respect to left_right equivalence are discussed. The state variables of such an equivariant bifurcation problem were divided into two groups, in which the first can vary independently, while the others depend on the first in the varying process. By applying related methods and techniques in the unfolding theory of smooth map_germs, the necessary and sufficient condition for an unfolding of a multiparameter equivariant bifurcation problem with two groups of state variables to be versal is obtained.展开更多
Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract ...Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six non- equivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.展开更多
In the present study, the dynamic response of a coupled SPM-feeder-cage system under irregular waves and shear currents is analyzed. A numerical model is developed by using the commercial software Orca Flex. Hydrodyna...In the present study, the dynamic response of a coupled SPM-feeder-cage system under irregular waves and shear currents is analyzed. A numerical model is developed by using the commercial software Orca Flex. Hydrodynamics coefficients of the vessel are calculated by using a 3D diffraction/radiation panel program. First- and second-order wave forces are included in the calculations. Morison equation is used to compute the drag force on line elements representing the net. Drag coefficients are determined at every time step in the simulation considering the relative normal velocity between the structural elements and the fluid flow. The dynamic response of the coupled system is analyzed for various environments and net materials. The results of the study show the effects of solidity ratio of the net and vertical positions of the cage on the overall dynamic response of the system, confirming the viability of this type of configuration for future development of offshore aquaculture in deep waters.展开更多
Conservation laws for a class of variable coefficient nonlinear wave equations with power nonlinearities are investigated. The usual equivalence group and the generalized extended one including transformations which a...Conservation laws for a class of variable coefficient nonlinear wave equations with power nonlinearities are investigated. The usual equivalence group and the generalized extended one including transformations which are nonlocal with respect to arbitrary elements are introduced. Then, using the most direct method, we carry out a classification of local conservation laws with characteristics of zero order for the equation under consideration up to equivalence relations generated by the generalized extended equivalence group. The equivalence with respect to this group and the correct choice of gauge coefficients of the equations play the major roles for simple and clear formulation of the final results.展开更多
Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal subgroup of G . For principal fibre bundle (E,p, E/G;G) and (E/H,p′,E/G;G/H), the relation between aut G(E) ...Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal subgroup of G . For principal fibre bundle (E,p, E/G;G) and (E/H,p′,E/G;G/H), the relation between aut G(E) (resp. aut * G(E) ) and aut G/H (E/H) (resp.aut * G/H (E/H)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group F G(E) (resp. E G(E)) while the group F G/H (E/H) is known.展开更多
Differential-difference equations of the form un = Fn（t, un-1,Un,Unn＋1,Un-1,un,Un＋1） are clas- sifted according to their intrinsic Lie point symmetries, equivalence group and some low-dimensional Lie algebras incl...Differential-difference equations of the form un = Fn（t, un-1,Un,Unn＋1,Un-1,un,Un＋1） are clas- sifted according to their intrinsic Lie point symmetries, equivalence group and some low-dimensional Lie algebras including the Abelian symmetry algebras, nilpotent nonAbelian symmetry algebras, solvable symmetry algebras with nonAbelian nilradicals, solvable symmetry algebras with Abelian nilradicals and nonsolvable symmetry al- gebras. Here Fn is a nonlinear function of its arguments and the dot over u denotes differentiation with respect to t.展开更多
文摘Based on the left_right equivalent relation of smooth map_germs in singularity theory, the unfoldings of multiparameter equivariant bifurcation problems with respect to left_right equivalence are discussed. The state variables of such an equivariant bifurcation problem were divided into two groups, in which the first can vary independently, while the others depend on the first in the varying process. By applying related methods and techniques in the unfolding theory of smooth map_germs, the necessary and sufficient condition for an unfolding of a multiparameter equivariant bifurcation problem with two groups of state variables to be versal is obtained.
基金supported by the National Key Basic Research Project of China (973 Program)(No. 2004CB318000)
文摘Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six non- equivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.
基金Kampachi Farms LLC for their support to complete this work and for all the technical information provided to complete the numerical model
文摘In the present study, the dynamic response of a coupled SPM-feeder-cage system under irregular waves and shear currents is analyzed. A numerical model is developed by using the commercial software Orca Flex. Hydrodynamics coefficients of the vessel are calculated by using a 3D diffraction/radiation panel program. First- and second-order wave forces are included in the calculations. Morison equation is used to compute the drag force on line elements representing the net. Drag coefficients are determined at every time step in the simulation considering the relative normal velocity between the structural elements and the fluid flow. The dynamic response of the coupled system is analyzed for various environments and net materials. The results of the study show the effects of solidity ratio of the net and vertical positions of the cage on the overall dynamic response of the system, confirming the viability of this type of configuration for future development of offshore aquaculture in deep waters.
基金Project supported by the National Key Basic Research Program of China (Grant No.2010CB126600)the National Natural Science Foundation of China (Grant No.60873070)+3 种基金the Shanghai Leading Academic Discipline Project,China (Grant No.B114)the Postdoctoral Science Foundation of China (Grant No.20090450067)the Shanghai Postdoctoral Sustentation Foundation,China (Grant No.09R21410600)the Fundamental Research Funds for the Central Universities,China (Grant No.WM0911004)
文摘Conservation laws for a class of variable coefficient nonlinear wave equations with power nonlinearities are investigated. The usual equivalence group and the generalized extended one including transformations which are nonlocal with respect to arbitrary elements are introduced. Then, using the most direct method, we carry out a classification of local conservation laws with characteristics of zero order for the equation under consideration up to equivalence relations generated by the generalized extended equivalence group. The equivalence with respect to this group and the correct choice of gauge coefficients of the equations play the major roles for simple and clear formulation of the final results.
文摘Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal subgroup of G . For principal fibre bundle (E,p, E/G;G) and (E/H,p′,E/G;G/H), the relation between aut G(E) (resp. aut * G(E) ) and aut G/H (E/H) (resp.aut * G/H (E/H)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group F G(E) (resp. E G(E)) while the group F G/H (E/H) is known.
基金Supported by the National Natural Science Foundation of China(No.11001240,11371323)
文摘Differential-difference equations of the form un = Fn（t, un-1,Un,Unn＋1,Un-1,un,Un＋1） are clas- sifted according to their intrinsic Lie point symmetries, equivalence group and some low-dimensional Lie algebras including the Abelian symmetry algebras, nilpotent nonAbelian symmetry algebras, solvable symmetry algebras with nonAbelian nilradicals, solvable symmetry algebras with Abelian nilradicals and nonsolvable symmetry al- gebras. Here Fn is a nonlinear function of its arguments and the dot over u denotes differentiation with respect to t.
