In this paper, the authors investigate the invariant cones of quadratic homoge- neous polynomial vector fields in three variables. Necessary and sufficient conditions for the existence of non-isolated invariant closed...In this paper, the authors investigate the invariant cones of quadratic homoge- neous polynomial vector fields in three variables. Necessary and sufficient conditions for the existence of non-isolated invariant closed cones are obtained by the algebraic expressions in terms of the coefficients of certain quadratic homogeneous polynomials.展开更多
For planar analytic homogcneous vector fields, the existence of periodic orbits and the noncxistence of limit sets arc verilied. It is concluded that spacial analytic homlogencous vector tleld of order in has no limit...For planar analytic homogcneous vector fields, the existence of periodic orbits and the noncxistence of limit sets arc verilied. It is concluded that spacial analytic homlogencous vector tleld of order in has no limit sets for any m>1. Similar results arc extended to highel-dimensional polynomial homogeneous vector fields under certain conditions.展开更多
The Fourier transform for homogeneous vector bundles over quaternion unit disk is studied, and the corresponding inversion formula and Plancherel formula are established.
In this paper, we investigate the invariant cones of cubic homogeneous polynomial vector fields with three variables. Sufficient conditions for the existence of invariant non-isolated closed cones are obtained as alge...In this paper, we investigate the invariant cones of cubic homogeneous polynomial vector fields with three variables. Sufficient conditions for the existence of invariant non-isolated closed cones are obtained as algebraic expressions in terms of the coefficients of certain cubic homogeneous polynomials.展开更多
The paper discusses an extended entropy model for the prediction of trip amount and provides a method to solve it, called the simple block iterative algorithm, from the point of view of the system of nonlinear equatio...The paper discusses an extended entropy model for the prediction of trip amount and provides a method to solve it, called the simple block iterative algorithm, from the point of view of the system of nonlinear equations. Because the algorithm gives consideration to the characteristic of the model, it has better effect in our practice. The paper also studies the existence and uniqueness of the solution and convergence of the algorithm.展开更多
文摘In this paper, the authors investigate the invariant cones of quadratic homoge- neous polynomial vector fields in three variables. Necessary and sufficient conditions for the existence of non-isolated invariant closed cones are obtained by the algebraic expressions in terms of the coefficients of certain quadratic homogeneous polynomials.
文摘For planar analytic homogcneous vector fields, the existence of periodic orbits and the noncxistence of limit sets arc verilied. It is concluded that spacial analytic homlogencous vector tleld of order in has no limit sets for any m>1. Similar results arc extended to highel-dimensional polynomial homogeneous vector fields under certain conditions.
文摘The Fourier transform for homogeneous vector bundles over quaternion unit disk is studied, and the corresponding inversion formula and Plancherel formula are established.
文摘In this paper, we investigate the invariant cones of cubic homogeneous polynomial vector fields with three variables. Sufficient conditions for the existence of invariant non-isolated closed cones are obtained as algebraic expressions in terms of the coefficients of certain cubic homogeneous polynomials.
文摘The paper discusses an extended entropy model for the prediction of trip amount and provides a method to solve it, called the simple block iterative algorithm, from the point of view of the system of nonlinear equations. Because the algorithm gives consideration to the characteristic of the model, it has better effect in our practice. The paper also studies the existence and uniqueness of the solution and convergence of the algorithm.
