strong completeness and uniform bounds

ABSTRACT. We consider a classical system of point particles interacting by means of a short range potential. We prove that, in the low–density (Boltzmann–Grad) limit, the system behaves, for short times, as predicted by the associated Boltzmann equation. This is a revisitation and an extension

The origin of the spacetime metric: Bell’s ‘Lorentzian pedagogy ’ and its significance in general relativity ∗

The origin of the spacetime metric: Bell’s ‘Lorentzian pedagogy ’ and its significance in general relativity ∗

Abstract not found

Abstract. We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework

and (2) the gas is near an abso-lute equilibrium — a spatially uniform, stationary state. When we consider regimes in which both the transport scales and Re vanish, we derive the weakly compressible Stokes approximation — a linear system. When we consider regimes in which the transport scales vanish

We study highly expressive query languages for unordered data trees, using as formal vehicles Active XML and extensions of languages in the while family. All languages may be seen as adding some form of control on top of a set of basic pattern queries. The results highlight the impact and interplay of different factors: the expressive power of basic queries, the embedding of computation into data (as in Active XML), and the use of deterministic vs. nondeterministic control. All languages are Turing complete, but not necessarily query complete in the sense of Chandra and Harel. Indeed, we show that some combinations of features yield serious limitations, analogous to FO k definability in the relational context. On the other hand, the limitations come with benefits such as the existence of powerful normal forms. Other languages are “almost ” complete, but fall short because of subtle limitations reminiscent of the copy elimination problem in object databases.

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that the degree of assortative matching among married couples has increased significantly 1 . Even more important are the evolutions in education and human capital, particularly in terms of composition by gender. During the first half of the twentieth century, college attendance increased for both genders