We study property RD in terms of rapid decay of matrix coefficients. We give new formulations of property RD in terms of a L-integrability condition of a Banach representation. Combining this new definition with the existence of cyclic subgroups of exponential growth in non-uniform lattices in semisimple Lie groups, we deduce that there exist matrix coefficients associated to several kinds of q...

in this paper, we establish the theory of fuzzy ideal convergence on completely distributive lattices and give characterizations of some topological notions. we also study fuzzy limit structures and discuss the relationship between fuzzy co-topologies and fuzzy limit structures.

We deal with the following question: What is the proper way to introduce symmetric difference in orthomodular lattices? Imposing two natural conditions on this operation, six possibilities remain: the two (commutative) normal forms of the symmetric difference in Boolean algebras and four noncommutative terms. It turns out that in many respects the non-commutative forms, though more complex with...

The dynamics of cold atoms in conservative optical lattices obviously depends on the geometry of the lattice. But very similar lattices may lead to deeply different dynamics. In a 2D optical lattice with a square mesh, it is expected that the coupling between the degrees of freedom leads to chaotic motions. However, in somme conditions, chaos remains marginal. The aim of this paper is to unders...

A study of the phase transition in 4D pure compact U(1) LGT on toroidal and spherical lattices. Abstract We have performed a systematic study of the phase transition in the pure compact U(1) lattice gauge theory in the extended coupling parameter space (β, γ) on toroidal and spherical lattices. The observation of a non-zero latent heat in both topologies for all investigated γ ∈ [+0.2, −0.4], t...

We discuss the question whether every finite interval in the lattice of all topologies on some set is isomorphic to an interval in the lattice of all topologies on a finite set – or, equivalently, whether the finite intervals in lattices of topologies are, up to isomorphism, exactly the duals of finite intervals in lattices of quasiorders. The answer to this question is in the affirmative at le...

The main goal of this paper is to explain the link between the algebraic and the Kripke-style models for certain classes of propositional logics. We start by presenting a Priestley-type duality for distributive lattices endowed with a general class of well-behaved operators. We then show that nitely-generated varieties of distributive lattices with operators are closed under canonical embedding...

A study of the phase transition in 4D pure compact U(1) LGT on toroidal and spherical lattices. Abstract We have performed a systematic study of the phase transition in the pure compact U(1) lattice gauge theory in the extended coupling parameter space (β, γ) on toroidal and spherical lattices. The observation of a non-zero latent heat in both topologies for all investigated γ ∈ [+0.2, −0.4], t...

We present a new Priestley-style topological duality for bounded N4-lattices, which are the algebraic counterpart of paraconsistent Nelson logic. Our duality differs from the existing one, due to Odintsov, in that we only rely on Esakia duality for Heyting algebras and not on the duality for De Morgan algebras of Cornish and Fowler. A major advantage of our approach is that for our topological ...

The O(n) non-linear σ-model is simulated on 2-dimensional regular and random lattices. We use two different levels of randomness in the construction of the random lattices and give a detailed explanation of the geometry of such lattices. In the simulations, we calculate the mass gap for n = 3, 4 and 8, analysing the asymptotic scaling of the data and computing the ratio of Lambda parameters Λ r...