Sharp Condition for Global Existence of Supercritical Nonlinear Schrodinger Equation with a Partial Confinement

We study the L^(2)-supercritical nonlinear Schrodinger equation(NLS) with a partial confinement,which is the limit case of the cigar-shaped model in Bose-Einstein condensate(BEC). By constructing a cross constrained variational problem and establishing the invariant manifolds of the evolution fow, we show a sharp condition for global existence.

变差可积鞅及条件变差可积鞅的最优系数不等式

设f是条件变差可积鞅 ,则有‖f‖p≤ 1P‖f‖ap 0 <P≤ 1当P≠ 1时 ,不等式是严格的 ,同时系数 1P是最优的 ,若f是变差可积鞅 ,则‖f‖Ap ≤ 1P‖f‖ap 0 <P ≤ 11P‖f‖ap ≤‖f‖Ap P≥ 1同样当P≠ 1时 ,不等式是严格的 ,且系数

Delay Model for Competitive Economic Systems

In this paper, a delay model for competitive economyic system is presented to replace the Walras-Samuelson Model, some analyses are given and a stability criterion is given. Finally,some remarks are given to show the superiority of this criterion and the delay model.