• 1. second necessary condition: 第二必要条件
• 2. second order necessary condition: 二阶必要条件
• 3. weak second-order necessary condition: 弱二阶必要条件

• 1.In this paper, We prove that the orthogonal condition to solve the uniform asymptotic solution of second order linear P. D. E in periodic region is the necessary and sufficient condition.
  本文证明了求解周期区域上的二阶线性偏微分方程的一致有效渐近解的正交条件是充分和必要的。
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• 2.Then, the latter necessary and sufficient condition is generalized to the case for the two different point ranges of degenerate second order curve.
  然后，再将非退化二阶曲线到自身的双射为对合的充要条件推广到退化二阶曲线两相异点列的情形。
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