In this paper we acquaint the reader first with the algebraic semantics which is corre-sponding to the Kripke`s semantic having nested domaius. By an application of the completenesstheorem on relational semantics of the quantified normal modal systems with nested domains proved in Hughes and Cresswell`s method to prove a completeness theorem on relational algebraic semantics of those system. Next for normal systems with semantics which admits arbi-trarily variable domains we use Henkin`s method to prove a c...
本文首先讨论嵌套论域语义的相应代数语义并由Hughes和Cresswell在［5］中建立的关于具有嵌套论域的正规量词模态系统的关系语义完全性定理推出其相应的代数语义完全性定理：然后对于具有任意可变论域语义的正规系统，我们用Henkin方法给出其关于狭义Kripke语义的关系语义完全性定理，由此通过将关系语义转化为代数语义从而亦推得其代数语义完全性定理。
Synthetic natural environment (SNE) includes four primary domains: terrain, ocean, air and space. As an important part of air environment, variable wind field would affect the performance of aircraft.
综合自然环境包括地形、大气/气象、海洋、空间四大领域，变化风场作为大气环境中的重要组成部分，其对飞行器使用性能的影响不容忽视。Air（初三适用）
When the domains is a general domain and the angular velocities are variable, we obtain existence theorems for the isentropic equations of state by monotone method.
最后，在一般的区域中用上下解方法得到了：当角速度不是常数，等熵情形时方程组（0.1）解的存在性。