Varieties of modular ortholattices

The bottom of the lattice of varieties of modular ortholattices is described. The theorem that is proved is;THEOREM. Every variety of modular ortholattices which is different from all the MOn, 0n, contains MO.The theorem is proved by translating the problem, at least partially, into the language of regular rings.Communicated by R. Wille     

机械泵驱动两相回路的实时动态模型分析

在航空航天领域,为了加速系统设计及测试进度,通常需要进行半实物实时仿真,即控制器用实物,受控对象采用数学模型。本文开发出了基于Matlab/Simulink的两相传热模块,并用其搭建了某机械泵驱动两相回路的实时动态模型。通过与实验的对比,验证了模型的可靠性,表明该模型满足实时要求,可以在下一步用于半实物仿真。     

Projective orthomodular lattices II

In this paper we continue to investigate projectivity in orthomodular lattices. We prove the somewhat surprising result that no uncountable Boolean algebra is projective in the variety of orthomodular lattices. Received January 7, 1994; accepted in final form July 16, 1996.     

Completions of orthomodular lattices

If K is a variety of orthomodular lattices generated by a finite orthomodular lattice the MacNeille completion of every algebra in K again belongs to K.     

Solubility of water in hydrocarbons as a function of water activity

A method is described for determination of low solubilities of water in organic liquids (such as are used in solvent extraction) by vacuum distillation of a suitably sized equilibrated sample through magnesium perchlorate in a conventional weighing tube. Tritium tracer is used to estimate completeness of water absorption. At the same time, the results serve to evaluate the ratio of tritium and water distribution coefficients for use in collateral determinations of water solubility by simple liquid-liquid distribution. The solubility of water in benzene, n-hexane, and cyclohexane is 0.0363, 0.00362, and 0.00345M respectively. The dissolved water follows Henry's law, the mole fraction constants being 0.00323, 0.000476, and 0.000375 respectively.     

On n-distributive modular ortholattices

Free and finitely presented n-distributive modular ortholattices are discussed. In particular, we show that the free algebra on 3 generators has an unsolvable word problem for n ≥ 14.Dedicated to the memory of Ivan RivalReceived July 6, 2002; accepted in final form January 29, 2004.This revised version was published online in August 2005 with a corrected cover date.     

A second note on the equational theory of modular ortholattices

We show how to alter the material in [4] to prove that every variety of modular ortholattices is generated by its simple members. Supported by NSERC Operating Grant 0041702.