Geometric properties of boundary sections of solutions to the Monge--Amp\`ere equation and applications

In this paper, we establish several geometric properties of boundary sections of convex solutions to the Monge-Amp\`ere equations: the engulfing and separating properties and volume estimates. As applications, we prove a covering lemma of Besicovitch type, a covering theorem and a strong type $p-p$ estimate for the maximal function corresponding to boundary sections. Moreover, we show that the Monge-Amp\`ere setting forms a space of homogeneous type.Comment: 24 page

A stochastic Lagrangian representation of the 3-dimensional incompressible Navier-Stokes equations

In this paper we derive a representation of the deterministic 3-dimensional Navier-Stokes equations based on stochastic Lagrangian paths. The particle trajectories obey SDEs driven by a uniform Wiener process; the inviscid Weber formula for the Euler equations of ideal fluids is used to recover the velocity field. This method admits a self-contained proof of local existence for the nonlinear stochastic system, and can be extended to formulate stochastic representations of related hydrodynamic-type equations, including viscous Burgers equations and LANS-alpha models.Comment: v4: Minor corrections to bibliography, and final version that will apear in CPAM. v3: Minor corrections to the algebra in the last section. v2: Minor changes to introduction and refferences. 14 pages, 0 figure

Emissions from pre-Hispanic metallurgy in the South American atmosphere

Peer reviewedPublisher PD

Testing demand responsive shared transport services via agent-based simulations

Demand Responsive Shared Transport DRST services take advantage of Information and Communication Technologies ICT, to provide on demand transport services booking in real time a ride on a shared vehicle. In this paper, an agent-based model ABM is presented to test different the feasibility of different service configurations in a real context. First results show the impact of route choice strategy on the system performance

Local scales on curves and surfaces

In this paper, we extend our previous work on the study of local scales of a function to studying local scales on curves and surfaces. In the case of a function f, the local scales of f at x is computed by measuring the deviation of f from a linear function near x at different scales t's. In the case of a d-dimensional surface E, the analogy is to measure the deviation of E from a d-plane near x on E at various scale t's. We then apply the theory of singular integral operators on E to show useful properties of local scales. We will also show that the defined local scales are consistent in the sense that the number of local scales are invariant under dilation

A stochastic perturbation of inviscid flows

We prove existence and regularity of the stochastic flows used in the stochastic Lagrangian formulation of the incompressible Navier-Stokes equations (with periodic boundary conditions), and consequently obtain a \holderspace{k}{\alpha} local existence result for the Navier-Stokes equations. Our estimates are independent of viscosity, allowing us to consider the inviscid limit. We show that as $\nu \to 0$, solutions of the stochastic Lagrangian formulation (with periodic boundary conditions) converge to solutions of the Euler equations at the rate of $O(\sqrt{\nu t})$.Comment: 13 pages, no figures

Indexing, browsing and searching of digital video

Video is a communications medium that normally brings together moving pictures with a synchronised audio track into a discrete piece or pieces of information. The size of a “piece ” of video can variously be referred to as a frame, a shot, a scene, a clip, a programme or an episode, and these are distinguished by their lengths and by their composition. We shall return to the definition of each of these in section 4 this chapter. In modern society, video is ver

A general model for the identification of specific PAHs in the far-IR

Context. In the framework of the interstellar PAH hypothesis, far-IR skeletal bands are expected to be a fingerprint of single species in this class. Aims. A detailed model of the photophysics of interstellar PAHs is required for such single-molecule identification of their far-IR features in the presently available Infrared Space Observatory data and in those of the forthcoming Herschel Space Observatory mission. Methods. We modelled the detailed photophysics of a vast sample of species in different radiation fields, using a compendium of Monte-Carlo techniques and quantum-chemical calculations. This enabled us to validate the use of purely theoretical data and assess the expected accuracy and reliability of the resulting synthetic far-IR emission spectra. Results. We produce positions and intensities of the expected far-IR features which ought to be emitted by each species in the sample in the considered radiation fields. A composite emission spectrum for our sample is computed for one of the most favourable sources for detection, namely the Red Rectangle nebula. The resulting spectrum is compared with the estimated dust emission in the same source, to assess the dependence of detectability on key molecular parameters. Conclusions. Identifying specific PAHs from their far-IR features is going to be a difficult feat in general, still it may well be possible under favourable conditions.Comment: 14 pages, 9 figures + 18 pages of online appendix. Accepted for publication in A&A (09/06/2006

Closure Theorem for Sequential-Design Processes

This chapter focuses on stochastic control and decision processes that occur in a variety of theoretical and applied contexts, such as statistical decision problems, stochastic dynamic programming problems, gambling processes, optimal stopping problems, stochastic adaptive control processes, and so on. It has long been recognized that these are all mathematically closely related. That being the case, all of these decision processes can be viewed as variations on a single theoretical formulation. The chapter presents some general conditions under which optimal policies are guaranteed to exist. The given theoretical formulation is flexible enough to include most variants of the types of processes. In statistical problems, the distribution of the observed variables depends on the true value of the parameter. The parameter space has no topological or other structure here; it is merely a set indexing the possible distributions. Hence, the formulation is not restricted to those problems known in the statistical literature as parametric problems. In nonstatistical contexts, the distribution does not depend on an unknown parameter. All such problems may be included in the formulation by the device of choosing the parameter space to consist of only one point, corresponding to the given distribution