Dipole words are sequences of magnetic dipoles, in which alike elements repel and opposite elements attract. Magnetic dipoles contrast with more general sets of bonding types, called glues, in which pairwise bonding strength is specified by a glue function. We prove that every glue function g has a set of dipole words, called a dipole code, that attractively encodes g: the pairwise attractions ...

Active commuting could contribute to increasing physical activity. The objective of this study was to characterise patterns of active commuting to and from schools in children and adolescents in Chile. A total of 453 Chilean children and adolescents aged between 10 and 18 years were included in this study. Data regarding modes of commuting and commuting distance was collected using a validated ...

BACKGROUND Vehicular traffic is a major source of outdoor air pollution in urban areas, and studies have shown that air pollution is worse during hours of commuting to and from work and school. However, it is unclear to what extent different commuting behaviors are a source of air pollution compared to non-commuters, and if air pollution exposure actually differs by the mode of commuting. This ...

LetA be a ν-vector of self-adjoint, pairwise commuting operators andB a bounded operator of classCn0 (A). We prove a Taylor-like expansion of the commutator [B, f(A)] for a large class of functions f : Rν → R, generalising the one-dimensional result where A is just a self-adjoint operator. This is done using almost analytic extensions and the higher-dimensional Helffer-Sjöstrand formula.

We present a construction of high order finite elements for H1, H(curl), H(div) (and L2) on a pyramid, which are compatible with existing tetrahedral and hexahedral high order finite elements and satisfy the commuting diagram property.

The commuting graph of a group G, denoted by Γ(G), is a simple graph whose vertices are all non-central elements of G and two distinct vertices x, y are adjacent if xy = yx. In [1] it is conjectured that if M is a simple group and G is a group satisfying Γ(G) ∼= Γ(M), then G ∼= M . In this paper we prove this conjecture for many simple groups.

Maxwell equations are posed as variational boundary value problems in the function space H(curl) and are discretized by Nédélec finite elements. In Beck et al., 2000, a residual type a posteriori error estimator was proposed and analyzed under certain conditions onto the domain. In the present paper, we prove the reliability of that error estimator on Lipschitz domains. The key is to establish ...

We propose a novel protocol for quantum key distribution based on the quantum polarization properties of coherent states. The key elements are encoded either in the component amplitude difference or in the phase difference of Gaussian-modulated strong coherent fields. The quantum counterpart (Stokes operators) of the classical parameters which represent the preponderance of xlinear polarization...

| The purpose of this note is to present a new sampling technique and to demonstrate some of its properties. The new technique consists of picking two elements at random, and de-terministically generating (from them) a long sequence of pairwise independent elements. The sequence is guarantees to intersect, with high probability, any set of non-negligible density.

A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin–Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables x1, x2, . . .. This construction provides explicit expressions for the Hamiltonians in terms of the power sum symmetric functions pn = x n 1 + x n 2 + · · · and is ba...