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 ...

This note is a sequel to [1] . First let us recall some of the notations . Denote by G(n, in) a graph with n vertices and m edges. Let K d (r,, . . ., rd ) be the complete dpartite graph with r ; vertices in its i-th class and put K,(t) = K d (t, . . ., t), K d = Kd (1) . Given integers n > d(> 2), let in d(n) be the minimal integer with the property that every G(n, in), where an > na d (n), co...

Let G be a connected d-regular graph with k vertices. We investigate the behaviour of a spanning random subgraph Gp of G n, the n-th Cartesian power ofG, which is constructed by deleting each edge independently with probability 1−p. We prove that lim n→∞ P[Gp is connected] = e−λ, if p = p(n) = 1− ( λ 1/n n k )1/d and λn → λ > 0 as n → ∞. This extends a result of L. Clark, Random subgraphs of ce...

The commuting graph C(G,X), where G is a group and X is a subset of G, is the graph with vertex set X and distinct vertices being joined by an edge whenever they commute. Here the diameter of C(G,X) is studied when G is a symmetric group and X a conjugacy class of elements of order 3.

We prove a Nullstellensatz for the ring of polynomial functions in n non-commuting variables over Hamilton's real quaternions. also characterize generalized identities which hold quaternions, and more generally, any division algebra .

BACKGROUND: Children's active commuting to school, i.e. walking or cycling to school, was associated with greater moderate-to-vigorous physical activity, although studies among ethnic minorities are sparse. OBJECTIVES: Among a low-income, ethnic minority sample of fourth grade students from eight public schools, we examined (1) correlates of active commuting to school and (2) the relationship b...

Let H be a hypergraph with n vertices. Suppose that d1, d2, . . . , dn are degrees of the vertices of H. The t-th graph entropy based on degrees of H is defined as

We prove the logarithmic concavity of the Duistermaat-Heckman measure of an Hamiltonian (n− 2)-dimensional torus action for which there exists an effective commuting symplectic action of a 2-torus with symplectic orbits. Using this, we show that any symplectic (n− 2)-torus action with non-empty fixed point set which satisfies this additional 2-torus condition must be Hamiltonian.