The original motivation of this paper, as presented in [15], was to compute the dual space of a lattice of subsets of some free monoid A. According to StonePriestley duality, the dual space of a lattice can be identified with the set of its prime filters, but it is not always the simplest way to describe it. Consider for instance the Boolean algebra generated by the sets of the form uA, where u...

We present pseudopotential coefficients for the first two rows of the Periodic Table. The pseudopotential is of an analytic form that gives optimal efficiency in numerical calculations using plane waves as a basis set. At most, seven coefficients are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property,...

In [15] M. Schellekens introduced the complexity (quasi-metric) space as a part of the research in Theoretical Computer Science and Topology, with applications to the complexity analysis of algorithms. Later on, S. Romaguera and M. Schellekens ([13]) introduced the so-called dual complexity (quasi-metric) space and established several quasi-metric properties of the complexity space via the anal...

I propose that self–duality in quantum phase–space provides the criteria for the selection of the quantum gravity vacuum. The evidence for this assertion arises from two independent considerations. The first is the phenomenological success of the free fermionic heterotic–string models, which are constructed in the vicinity of the self–dual point under T–duality. The relation between the free fe...