closed half space

:In this paper,we introduced a new concept the Biclosed simiring with two infinite sum operations and proved that both P(∑*)={L|L is a language over ∑ where ∑ is an alphabet} and B 《∑*》={r|r is a formal power series with coefficients in B={0,1} and variables in ∑} are near Biclosed semirings and both are isomorphic.

该文建立含两个无穷和代数运算的双闭半环概念，证明了：字母表∑上全体语言之集Ｐ（∑）与布尔半环Ｂ＝｛０，１｝上的形式幂级数全体之集Ｂ《∑》近双闭半环同构，进而用半环对∑上的前（后）缀码给出了刻划。

And we discussed the ultraproductof divisible closed semirings envelope of an element and an embedding theorem.

本文讨论了可除闭半环的分类、无限超积、元素的闭包和嵌入定理，这些结果为研究与应用可除半环提供了有用的基础。

The acoustic eigen frequencies of the hermetic and half-hermetic spaces and its change with dimensions of the clapborad are simulated.

通过分析封闭、半封闭空间中气体的声学特性,针对当其固有声学频率与激振频率一致时,由于气体共振产生的共鸣音,提出了移频降噪理论。