Given a poset P , the set, Γ(P), of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory C of Pos d (the category of posets and Scott-continuous maps) is said to be Γ-faithful if for any posets P and Q in C, Γ(P) ∼ = Γ(Q) implies P ∼ = Q. It is known that the category of all continuous dcpos and the category of bounded complete dcpos are Γ-faithful, while Pos d is ...

As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The main results are as follows: (1) a complete lattice is generalized completely distributive if and...

§0. Introduction Recent work in the general theory of Polish groups has looked for inspiration from the study of countable models, where a major tool in analyzing isomorphism types is provided by the Scott analysis. One has many results that were first proved in the case of the “logic action” on countable models by an appeal to the Scott analysis, and only later generalized to general Polish gr...

In this article, a generalized optimality criteria method is proposed for topology optimization with arbitrary objective function and multiple inequality constraints. This algorithm uses sensitivity information to update both the Lagrange multipliers design variables. Different from conventional method, does not satisfy constraints at every iteration. Rather, it improves variables such that are...