等离子体流注入实验

本文叙述简单磁镜中,等离子体流注入的实验结果。被磁镜场捕获的等离子体驱动了m=1的交换不稳定性,等离子体发生破裂的临界β值约5％,导电壁的线结效应对交换模有稳定作用。     

Families of methods for ordinary differential equations based on trigonometric polynomials

We consider the construction of methods based on trigonometric polynomials for the initial value problems whose solutions are known to be periodic. It is assumed that the frequency w can be estimated in advance. The resulting methods depend on a parameter ν = hw, where h is the step size, and reduce to classical multistep methods if ν → 0. Gautschi [4] developed Adams and Störmer type methods. In our paper we construct Nyström's and Milne-Simpson's type methods. Numerical experiments show that these methods are not sensitive to changes in w, but require the Jacobian matrix to have purely imaginary eigenvalues.     

Note on a proposed weighted residual method for solving nonlinear differential boundary problems

A proposed iterative method for solving nonlinear differential two-point boundary value problems is generalized and shown to be equivalent to using the standard method of adjoints on a linearized form of the nonlinear boundary-value problem.     

An evasion game with a destination

This paper solves an aiming and evasion game in which a gunner with a number of shots attempts to hit an evader moving along the positivex-axis. The gunner's aiming of the evader is complicated by the fact that there is a delay due to the time taken for the shot to reach the evader from the gunner.     

非线性Schrodinger方程耦合组初边值问题整体解的存在唯一性

本文讨论非线性Schrodinger方程耦合组初边值问题,使用积分估计,得到了整体解的存在唯一性。     

Integral operators with Green's function type kernel

A variant of the Nyström method based on Simpson's rule is presented. This is designed to deal with integral operators with kernels k(s, t) that are not continuous along the diagonal s = t. A complete analysis is carried out, generalizations for other interpolatory quadrature rules are proposed; also a variant using Gaussian quadrature is considered and examples are given.     

Generalization of the main equation of differential game theory

We consider feedback, two-person, zero-sum differential games. We obtain two inequalities for the directional derivatives of the nonsmooth value function. We show that these inequalities, together with the boundary conditions, constitute necessary and sufficient conditions which the value function must satisfy. In the region where the value function is differentiable, the inequalities become the well-known main equation of differential game theory (Isaacs-Bellman equation). The results obtained here may be useful in the approximation of the value function by piecewise smooth splines and also in the classification of singular surfaces.The author would like to thank Academician N. N. Krasovskii for his valuable advice and encouragement.