In the system of two energy levels atom, based on the quantum theory and considering the effects of the outfield on the atom system, we can get the conclusion that the direction of external force is contrary to average acceleration, which conflicts with quantum Newton equation.

In this paper the scattered angle in central force field is calculated by using calculus of functional vector analysis on base of Newton equation and the law of conservation of angular momentum, it avoides complex calculations in general textbook on basics of orbital equation of central force field.

In this paper,we propose a new quasi-Newton equation by doing the four-order Taylor series expansion for the objective function,and present a new quasi-Newton method based on the equation.

A class of modified BFGS algorithm based on the new quasi-Newton equation Bk+1sk=k=yk+γksTksksk is presented in this paper to solve the unconstrained optimization problem, and the global convergence is proved under the condition that the objective function is uniformly convex, the parameter k satisfies |1-k|≤t′‖sk‖ (t′ is a constant).

As we all know, Quasi-Newton equations lay the basis ofQuasi-Newton methods, according to the time when the Quasi-Newton equations appear, wecan classify them as :the original and the new ones.

It is proved that the formula is the unique solution for which satisfiy pseudo-Newton equations.

Based on the basin of attraction,the Newtonian equation is related to an initial value problem in terms of which a new set of sufficient condition for the existence of a unique 2π-periodic solution in this paper.

Based on the basin of attraction,this paper proves sufficient condition for the existence of a periodic solution of the Newtonian equation u″(t)+gradG(u(t))=p(t) by Shen Z H.