On lattices from combinatorial game theory modularity and a representation theorem: finite case

We show that a self-generated set of combinatorial games, S. may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question "Is there a set which will give a non-distributive but modular lattice?" appears. A useful necessary condition for the existence of a finite non-distributive modular L(S) is proved. We show the existence of S such that L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented. (C) 2014 Elsevier B.V. All rights reserved.

Durability performance of self-compacting concrete (SCC) with binary and ternary mixes of fly ash and limestone filler

The basic objective of this work is to evaluate the durability of self-compacting concrete (SCC) produced in binary and ternary mixes using fly ash (FA) and limestone filler (LF) as partial replacement of cement. The main characteristics that set SCC apart from conventional concrete (fundamentally its fresh state behaviour) essentially depend on the greater or lesser content of various constituents, namely: greater mortar volume (more ultrafine material in the form of cement and mineral additions); proper control of the maximum size of the coarse aggregate; use of admixtures such as superplasticizers. Significant amounts of mineral additions are thus incorporated to partially replace cement, in order to improve the workability of the concrete. These mineral additions necessarily affect the concrete's microstructure and its durability. Therefore, notwithstanding the many well-documented and acknowledged advantages of SCC, a better understanding its behaviour is still required, in particular when its composition includes significant amounts of mineral additions. An ambitious working plan was devised: first, the SCC's microstructure was studied and characterized and afterwards the main transport and degradation mechanisms of the SCC produced were studied and characterized by means of SEM image analysis, chloride migration, electrical resistivity, and carbonation tests. It was then possible to draw conclusions about the SCC's durability. The properties studied are strongly affected by the type and content of the additions. Also, the use of ternary mixes proved to be extremely favourable, confirming the expected beneficial effect of the synergy between LF and FA.