Notes on planar semimodular lattices. VI. On the structure theorem of planar semimodular lattices

In a recent paper, G. Czédli and E. T. Schmidt present a structure theorem for planar semimodular lattices. In this note, we present an alternative proof.     

The order of principal congruences of a bounded lattice

We characterize the order of principal congruences of a bounded lattice (also of a complete lattice and of a lattice of length 5) as a bounded ordered set. We also state a number of open problems in this new field.     

A technical lemma for congruences of finite lattices

The classical Technical Lemma for congruences is not difficult to prove but it is very efficient in its applications. We present here a Technical Lemma for congruences on finite lattices. This is not difficult to prove either but it already has proved its usefulness in some applications.     

Lattice tolerances and congruences

We prove that a tolerance relation of a lattice is a homomorphic image of a congruence relation.     

Growth, thermal stability and structure of ultrathin Zn-layers on Pd(1 1 1)

Low-energy ion scattering with monolayer sensitivity was applied to investigate ultrathin films of zinc on Pd(1?1?1). Uptake curves taken at 150?K indicate the simultaneous growth of multilayers with negligible interlayer transport. Annealing experiments for two-monolayer films reveal a rapid decrease in the zinc content on the surface layer at temperatures above 300?K, forming a metastable state with a Pd:Zn surface ratio of approx. 1:1 in the temperature region between 400 and 550?K. This state is most easily explained as a slightly buckled p(2?×?1)-PdZn surface alloy, with Zn atoms located approx. 0.25?? above their Pd counterparts.     

Do we need complete-simple distributive lattices?

Presented by R. Freese.