While every finite lattice-based algebra is dualisable, the same is not true of semilattice-based algebras. We show that a finite semilattice-based algebra is dualisable if all its operations are compatible with the semilattice operation. We also give examples of infinite semilattice-based algebras that are dualisable. In contrast, we present a general condition that guarantees the inherent non...

1. Introduction

We present classes of algebras which may be viewed as weak relation algebras, where a Boolean part is replaced by a not necessarily distributive lattice. For each of the classes considered in the paper we prove a relational representation theorem.

In this article, we study a lattice differential model for a single species with distributed age-structure in an infinite patchy environment. Using method of approaches by Diekmann and Thieme, we develop a comparison principle and construct a suitable sub-solution to the given model, and show that there exists a spreading speed of the system which in fact coincides with the minimal wave speed.

We provide a rigorous mathematical foundation to the study of strongly rational, holomorphic vertex operator algebras V of central charge c = 8, 16 and 24 initiated by Schellekens. If c = 8 or 16 we show that V is isomorphic to a lattice theory corresponding to a rank c even, self-dual lattice. If c = 24 we prove, among other things, that either V is isomorphic to a lattice theory corresponding...

The aim of this work is to study some lattice diagram determinants ∆L(X, Y ) as defined in [5] and to extend results of [3]. We recall that ML denotes the space of all partial derivatives of ∆L. In this paper, we want to study the space M i,j(X, Y ) which is defined as the sum of ML spaces where the lattice diagrams L are obtained by removing k cells from a given partition, these cells being in...