If a locale is presented by a “flat site”, it is shown how its frame can be presented by generators and relations as a dcpo. A necessary and sufficient condition is derived for compactness of the locale (and also for its openness). Although its derivation uses impredicative constructions, it is also shown predicatively using the inductive generation of formal topologies. A predicative proof of ...

the concepts of structural optimization was introduced about sixty years ago. smiths from the university of los angeles (california) for the first time has offered the combination of finite element method and optimization techniques to design optimum structures (1960). at present time, this techniques are generally understood and many softwares for this perpose have been developed. in this pape...

In Danish aspectual differences are expressed by certain verbal constructions. Such aspectual constructions have not received much attention in the Danish literature, but cf. Diderichsen (1946, p. 156), Hansen (1967, vol. 3, pp. 30–31), Jensen (1985, p. 113), Brandt (1992) and Jørgensen (2001). (1) is an example of such an aspectual construction which is used to express imperfective aspect, and...