The binding of phosphonic acids at aluminium oxide surfaces and correlation with passivation of aluminium flake

Measurements of adsorption isotherms of a series of thirteen mono- and di-phosphonic acids have shown that these bind strongly to the surface of high surface area aluminium trihydroxide. The incorporation of such phosphonates into a suspension of aluminium flake in an aqueous medium, modelling the continuous phase of a water-based paint, greatly suppresses the evolution of hydrogen. Whilst strong binding of the phosphonate to aluminium oxides is an essential criterion for good passivation, other factors such as the hydrophobicity of the ligand are also important in suppressing hydrogen-evolution.     

A counterexample to the finite height conjecture

There is an infinite subdirectly irreducible lattice which generates a variety that contains only finitely many subvarietes.The author was supported in part by NSF Grant DMS 94-00511     

Doubling convex sets in lattices and a generalized semidistributivity condition

A useful construction for lattices is doubling a convex subsetI of a latticeL, i.e., replacingI byI×2. It is shown that this construction preserves a generalized semidistributivity condition (C). Varieties of lattices in which every lattice satisfies (C) are characterized equationally.This research was supported in part by the NSF (Nation) and NSERC (Day).     

Whaley's Theorem for Finite Lattices

Whaley's Theorem on the existence of large proper sublattices of infinite lattices is extended to ordered sets and finite lattices. As a corollary it is shown that every finite lattice L with |L|≥3 contains a proper sublattice S with |S|≥|L|^1/3. It is also shown that that every finite modular lattice L with |L|≥3 contains a proper sublattice S with |S|≥|L|^1/2, and every finite distributive lattice L with |L|≥4 contains a proper sublattice S with |S|≥3/4|L|. This revised version was published online in June 2006 with corrections to the Cover Date.     

Closure Operators and Lattice Extensions

For closure operators Γ and Δ on the same set X, we say that Δ is a weak (resp. strong) extension of Γ if Cl(X, Γ) is a complete meet-subsemilattice (resp. complete sublattice) of Cl(X, Δ). This context is used to describe the extensions of a finite lattice that preserve various properties. This revised version was published online in September 2006 with corrections to the Cover Date.     

Testing for a Semilattice Term

Order - This paper investigates the computational complexity of deciding if a given finite algebra is an expansion of a semilattice. In general this problem is known to be EXP-TIME complete, and we...