The best approximation of a given function in L2L^2-norm by Lipschitz functions with gradient constraint

The starting point of this paper is the study of the asymptotic behavior, as $p\to\infty$, of the following minimization problem $$\min\left\{\frac1{p}\int|\nabla v|^{p}+\frac12\int(v-f)^2 \,, \quad \ v\in W^{1,p} (\Omega)\right\}.$$ We show that the limit problem provides the best approximation, in the $L^2$-norm, of the datum $f$ among all Lipschitz functions with Lipschitz constant less or equal than one. Moreover such approximation verifies a suitable PDE in the viscosity sense. After the analysis of the model problem above, we consider the asymptotic behavior of a related family of nonvariational equations and, finally, we also deal with some functionals involving the $(N-1)$-Hausdorff measure of the jump set of the function

Crossed-beam universal-detection reactive scattering of radical beams characterized by laser-induced-fluorescence: the case of C2 and CN

International audienceWe have generated continuous supersonic beams of dicarbon (C2) and cyano (CN) radicals by a high-pressure radio-frequency discharge beam source starting from dilute mixtures in rare gases of suitable precursor molecules. We have subsequently characterized their internal quantum state distributions by laser-induced-fluorescence (LIF) in a new crossed molecular beam-laser apparatus. We have used these supersonic beams to study the reactive scattering of C2 and CN radicals with unsaturated hydrocarbons. We report here on the C2 and CN radical beam characterization by LIF and on dynamics studies of the reactions CN + C2H2 (acetylene) and CN + CH3CCH (methylacetylene) by the crossed molecular beam scattering technique with universal mass spectrometric detection and time-of-flight analysis. The role of CN rovibrational excitation on the dynamics of the CN + C2H2 reaction is discussed with reference to previous dynamics and kinetics studies. These reactions are of interest in the chemistry of planetary atmospheres (Titan) and the interstellar medium as well as in combustion

Local regularity for fractional heat equations

We prove the maximal local regularity of weak solutions to the parabolic problem associated with the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbitrary bounded open set $\Omega\subset\mathbb{R}^N$. Proofs combine classical abstract regularity results for parabolic equations with some new local regularity results for the associated elliptic problems.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0756

Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

Habitat Suitability Modeling to Identify the Potential Nursery Grounds of the Atlantic Mackerel and Its Relation to Oceanographic Conditions in the Mediterranean Sea

Our knowledge for the distribution of Atlantic mackerel (Scomber scombrus) in the Mediterranean Sea is limited and fragmented. In the current work habitat suitability modeling was applied to summer acoustic surveys data of Atlantic mackerel juveniles derived from the north part of the Mediterranean (i.e., acoustic data from the Gulf of Lions, pelagic trawls held during acoustic surveys in Spanish Mediterranean waters, south Adriatic Sea, Strait of Sicily, and North Aegean Sea) using generalized additive models (GAMs) along with satellite environmental and bathymetry data. Bathymetry along with sea surface temperature and circulation patterns, expressed through sea level anomaly and the zonal component of the absolute geostrophic velocity, were the environmental variables best to describe nursery grounds. The selected model was used to produce maps presenting the potential nursery grounds of Atlantic mackerel throughout the Mediterranean Sea as a measure of habitat adequacy. However, the assessed potential nursery grounds were generally marked as “occasional,” implying that although there are areas presenting high probability to encounter Atlantic mackerel, this picture can largely vary from year to year stressing the high susceptibility of the species to environmental conditions. In a further step and toward a spatial management perspective, we have estimated and visualized the overlap between Atlantic mackerel and anchovy/ sardine juvenile grounds throughout the basin. Results showed that although the degree of overlapping was generally low, not exceeding 15% in general, this varied at a regional level going up to 30%. The potential of the output of this work for management purposes like the implementation of spatially-explicit management tools is discussedVersión del edito

PERENCANAAN KEBUTUHAN MATERIAL (PKM) PADA PRODUKSI KINCIR ANGIN KAPASITAS 100 WATT

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