In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix eleme...In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.展开更多
In this paper we investigate the complexity of several problems concerning 2CNF formulas. At first, we show that the minimal unsatisfiability problem for 2CNF formulas can be solved in linear time. Then we prove that ...In this paper we investigate the complexity of several problems concerning 2CNF formulas. At first, we show that the minimal unsatisfiability problem for 2CNF formulas can be solved in linear time. Then we prove that the problem determining if a 2CNF formula can be transformed to a minimal unsatisfiable formula is also solvable in linear time. Thirdly, we show the polynomial solvability of the satisfiability problem for symmetric monotone formulas in which all clauses has length 2 or ? n - k ( n is the ...展开更多
A class of parallel implicit Runge-Kutta formulas is constructed for multiprocessor system. A family of parallel implicit two-stage fourth order Runge-Kutta formulas is given. For these formulas, the convergence is pr...A class of parallel implicit Runge-Kutta formulas is constructed for multiprocessor system. A family of parallel implicit two-stage fourth order Runge-Kutta formulas is given. For these formulas, the convergence is proved and the stability analysis is given. The numerical examples demonstrate that these formulas can solve an extensive class of initial value problems for the ordinary differential equations.展开更多
In this paper, two recurrence formulas for radial average values of N-dimensional hydrogen atom are derived. Explicit expressions for <n rJ N-2 |r s|n rJ N-2 > are given for 3≥s≥-6. These results can be applie...In this paper, two recurrence formulas for radial average values of N-dimensional hydrogen atom are derived. Explicit expressions for <n rJ N-2 |r s|n rJ N-2 > are given for 3≥s≥-6. These results can be applied to discuss average value of centrifugal potential energy and other physical quantities. The relevant results of the usual hydrogen atom are contained in more general conclusion of this paper as special cases.展开更多
文摘In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.
文摘In this paper we investigate the complexity of several problems concerning 2CNF formulas. At first, we show that the minimal unsatisfiability problem for 2CNF formulas can be solved in linear time. Then we prove that the problem determining if a 2CNF formula can be transformed to a minimal unsatisfiable formula is also solvable in linear time. Thirdly, we show the polynomial solvability of the satisfiability problem for symmetric monotone formulas in which all clauses has length 2 or ? n - k ( n is the ...
基金Project supported by the National Natural Science Foundation of China
文摘A class of parallel implicit Runge-Kutta formulas is constructed for multiprocessor system. A family of parallel implicit two-stage fourth order Runge-Kutta formulas is given. For these formulas, the convergence is proved and the stability analysis is given. The numerical examples demonstrate that these formulas can solve an extensive class of initial value problems for the ordinary differential equations.
文摘In this paper, two recurrence formulas for radial average values of N-dimensional hydrogen atom are derived. Explicit expressions for <n rJ N-2 |r s|n rJ N-2 > are given for 3≥s≥-6. These results can be applied to discuss average value of centrifugal potential energy and other physical quantities. The relevant results of the usual hydrogen atom are contained in more general conclusion of this paper as special cases.
