Boolean Differential Operators

We consider four combinatorial interpretations for the algebra of Boolean differential operators. We show that each interpretation yields an explicit matrix representation for Boolean differential operators

Consistent discrete gravity solution of the problem of time: a model

The recently introduced consistent discrete lattice formulation of canonical general relativity produces a discrete theory that is constraint-free. This immediately allows to overcome several of the traditional obstacles posed by the ``problem of time'' in totally constrained systems and quantum gravity and cosmology. In particular, one can implement the Page--Wootters relational quantization. This brief paper discusses this idea in the context of a simple model system --the parameterized particle-- that is usually considered one of the crucial tests for any proposal for solution to the problem of time in quantum gravity.Comment: 15 pages, no figure

Fundamental decoherence in quantum gravity

A recently introduced discrete formalism allows to solve the problem of time in quantum gravity in a relational manner. Quantum mechanics formulated with a relational time is not exactly unitary and implies a fundamental mechanism for decoherence of quantum states. The mechanism is strong enough to render the black hole information puzzle unobservable.Comment: 6 pages, to appear in the proceedings of DICE 2004 (Piombino, Italy

Fundamental decoherence from quantum gravity: a pedagogical review

We present a discussion of the fundamental loss of unitarity that appears in quantum mechanics due to the use of a physical apparatus to measure time. This induces a decoherence effect that is independent of any interaction with the environment and appears in addition to any usual environmental decoherence. The discussion is framed self consistently and aimed to general physicists. We derive the modified Schroedinger equation that arises in quantum mechanics with real clocks and discuss the theoretical and potential experimental implications of this process of decoherence.Comment: 9 pages, dedicated to Octavio Obregon on his 60th birthda

Commensurability effects for fermionic atoms trapped in 1D optical lattices

Fermionic atoms in two different hyperfine states confined in optical lattices show strong commensurability effects due to the interplay between the atomic density wave (ADW) ordering and the lattice potential. We show that spatially separated regions of commensurable and incommensurable phases can coexist. The commensurability between the harmonic trap and the lattice sites can be used to control the amplitude of the atomic density waves in the central region of the trap.Comment: Accepted for publication in Physical Review Letter

Vanishing ideals over graphs and even cycles

Let X be an algebraic toric set in a projective space over a finite field. We study the vanishing ideal, I(X), of X and show some useful degree bounds for a minimal set of generators of I(X). We give an explicit description of a set of generators of I(X), when X is the algebraic toric set associated to an even cycle or to a connected bipartite graph with pairwise disjoint even cycles. In this case, a fomula for the regularity of I(X) is given. We show an upper bound for this invariant, when X is associated to a (not necessarily connected) bipartite graph. The upper bound is sharp if the graph is connected. We are able to show a formula for the length of the parameterized linear code associated with any graph, in terms of the number of bipartite and non-bipartite components

Regularity and algebraic properties of certain lattice ideals

We study the regularity and the algebraic properties of certain lattice ideals. We establish a map I --> I\~ between the family of graded lattice ideals in an N-graded polynomial ring over a field K and the family of graded lattice ideals in a polynomial ring with the standard grading. This map is shown to preserve the complete intersection property and the regularity of I but not the degree. We relate the Hilbert series and the generators of I and I\~. If dim(I)=1, we relate the degrees of I and I\~. It is shown that the regularity of certain lattice ideals is additive in a certain sense. Then, we give some applications. For finite fields, we give a formula for the regularity of the vanishing ideal of a degenerate torus in terms of the Frobenius number of a semigroup. We construct vanishing ideals, over finite fields, with prescribed regularity and degree of a certain type. Let X be a subset of a projective space over a field K. It is shown that the vanishing ideal of X is a lattice ideal of dimension 1 if and only if X is a finite subgroup of a projective torus. For finite fields, it is shown that X is a subgroup of a projective torus if and only if X is parameterized by monomials. We express the regularity of the vanishing ideal over a bipartie graph in terms of the regularities of the vanishing ideals of the blocks of the graph.Comment: Bull. Braz. Math. Soc. (N.S.), to appea

Grau de conhecimento sobre fatores de risco cardiovascular e motivação à prática esportiva entre os participantes do grupo de caminhada do Centro de Saúde Córrego Grande-Florianópolis

Trabalho de Conclusão de Curso - Universidade Federal de Santa Catarina. Curso de Medicina. Departamento de Saúde Pública