A Dirac comb of point measures in Euclidean space with bounded complex weights that is supported on a lattice Γ inherits certain general properties from the lattice structure. In particular, its autocorrelation admits a factorization into a continuous function and the uniform lattice Dirac comb, and its diffraction measure is periodic, with the dual lattice Γ ∗ as lattice of periods. This state...

The Grätzer-Schmidt theorem of lattice theory states that each algebraic lattice is isomorphic to the congruence lattice of an algebra. A lattice is algebraic if it is complete and generated by its compact elements. We show that the set of indices of computable lattices that are complete is Π 1 -complete; the set of indices of computable lattices that are algebraic is Π 1 -complete; and that th...

A method to determine the type of knot formed by a compact lattice chain is described. The compact lattice chain refers to a lattice self−avoiding walk that visits ever lattice site within a cubic region. The method is implemented in computer code as C++ and Java programs. As a first measure of knot complexity, the average number of crossings in the knot projection for a range of chain sizes is...

We initiate a study of topological orthoalgebras (TOAs), concentrating on the compact case. Examples of TOAs include topological orthomodular lattices, and also the projection lattice of a Hilbert space. As the latter example illustrates, a lattice-ordered TOA need not be a topological lattice. However, we show that a compact Boolean TOA is a topological Boolean algebra. Using this, we prove th...

The least element 0 of a finite meet semi-distributive lattice is a meet of meet-prime elements. We investigate conditions under which the least element of an algebraic, meet semi-distributive lattice is a (complete) meet of meet-prime elements. For example, this is true if the lattice has only countably many compact elements, or if |L| < 2א0 , or if L is in the variety generated by a finite me...