例句與造句

1. In this chapter , a class of mixed monotone operators with a - t type convexity and concavity has been discussed through cone theory and by using the method of lower - upper solutions , the skill of monotone iterative . the sufficient and necessary conditions for existence and uniqueness of their fixed points are given . the results in relevant literatures are generalized or included . these sufficient and necessary conditions are out of the limitation of only giving the sufficient conditions in previous papers , and improve the relevant results essentially ; for a class of mixed monotone operators with general a - t type convexity and concavity , the sufficient and necessary conditions for existence and uniqueness of their fixed points are given by introducing the concept of ? adjoint sequence " . for a class of sublinear mixed monotone operators , the sufficient and necessary conditions for existence and uniqueness of their fixed points are also given by using diagonal process with double - lower ordinate arrangement . and a cl ass of mixed monotone operators with ( a , / 3 ) type convexity and concavity is also studied through some proper transforms , the sufficient and necessary conditions for existence and uniqueness of their fixed points are also given under certain conditions
   通過運用錐理論，采用上下解方法、單調迭代技巧等討論了一類? t型凹凸的混合單調算子，給出了其存在唯一不動點的充分必要條件，含蓋了相關文獻的部分工作，所給的充要條件彌補了以往只給出充分條件的局限性，對文獻中的相關工作做了本質性的改進；對于廣義? t型凹凸混合單調算子，通過引入“伴隨列”的概念，也給出了其存在唯一不動點的充分必要條件；對于次線性混合單調算子，通過運用雙下標排列的對角線方法，也給出了其存在唯一不動點的充分必要條件；通過適當?shù)淖儞Q技巧，討論了( ， )型凹凸混合單調算子，在一定的條件下，給出了其存在唯一不動點的充分必要條件。
2. It's difficult to find diagonal process in a sentence. 用diagonal process造句挺難的