In this paper we investigate Hartman functions on a topological group G. Recall that (ι, C) is a group compactification of G if C is a compact group, ι : G → C is a continuous group homomorphism and ι(G) ⊆ C is dense. A bounded function f : G 7→ C is a Hartman function if there exists a group compactification (ι, C) and F : C → C such that f = F ◦ ι and F is Riemann integrable, i.e. the set of ...

Abstract Twisted étale groupoid algebras have recently been studied in the algebraic setting by several authors connection with an abstract theory of Cartan pairs rings. In this paper we show that extensions ample groupoids correspond a precise manner to Boolean inverse semigroups. particular, discrete twists over certain abelian semigroups, and they are classified Lausch’s second cohomology gr...

We generalize to universal algebra concepts originating from λ-calculus and programming to prove a new result on the lattice λT of λ-theories, and a general theorem of pure universal algebra which can be seen as a meta version of the Stone Representation Theorem. In this paper we introduce the class of Church algebras (which includes all Boolean algebras, combinatory algebras, rings with unit a...

Superconducting rings with exactly Φ0/2 magnetic flux threading are analogous of Ising spins having two degenerate states which can be used to store binary information. When brought close these rings interact by means of magnetic coupling. If the interactions are properly tailored, a system of such superconducting rings can accomplish static quantum logic in the sense that the states of the rin...

In this paper, we present a class of 2k-variable balanced Boolean functions and a class of 2k-variable 1-resilient Boolean functions for an integer k ≥ 2, which both have the maximal algebraic degree and very high nonlinearity. Based on a newly proposed conjecture by Tu and Deng, it is shown that the proposed balanced Boolean functions have optimal algebraic immunity and the 1-resilient Boolean...

We present tractable algorithms for deciding the universal theories of lattices with different notions of complementation by reduction to more standard procedures. The reductions use basic structural properties of lattices. For Boolean algebras, generalised Boolean algebras and atomic distributive lattices we reduce to SAT-procedures. For Brouwerian algebras we reduce to the uniform word proble...