Search results for "Polygon"

Hölder stability for Serrin’s overdetermined problem

2015

In a bounded domain \(\varOmega \), we consider a positive solution of the problem \(\Delta u+f(u)=0\) in \(\varOmega \), \(u=0\) on \(\partial \varOmega \), where \(f:\mathbb {R}\rightarrow \mathbb {R}\) is a locally Lipschitz continuous function. Under sufficient conditions on \(\varOmega \) (for instance, if \(\varOmega \) is convex), we show that \(\partial \varOmega \) is contained in a spherical annulus of radii \(r_i 0\) and \(\tau \in (0,1]\). Here, \([u_\nu ]_{\partial \varOmega }\) is the Lipschitz seminorm on \(\partial \varOmega \) of the normal derivative of u. This result improves to Holder stability the logarithmic estimate obtained in Aftalion et al. (Adv Differ Equ 4:907–93…

Reliable polygonal approximations of imaged real objects through dominant point detection

1998

Abstract The problem of dominant point detection is posed, taking into account what usually happens in practice. The algorithms found in the literature often prove their performance with laboratory contours, but the shapes in real images present noise, quantization, and high inter and intra-shape variability. These effects are analyzed and solutions to them are proposed. We will also focus on the conditions for an efficient (few points) and precise (low error) dominant point extraction that preserves the original shape. A measurement of the committed error (optimization error, E 0 ) that takes into account both aspects is defined for studying this feature.

Solving the length constrained K-drones rural postman problem

2021

[EN] In this paper we address the Length Constrained K-Drones Rural Postman Problem (LC K-DRPP). This is a continuous optimization problem where a fleet of homogeneous drones have to jointly service (traverse) a set of (curved or straight) lines of a network. Unlike the vehicles in classical arc routing problems, a drone can enter a line through any of its points, service a portion of that line, exit through another of its points, then travel directly to any point on another line, and so on. Moreover, since the range of the drones is restricted, the length of each route is limited by a maximum distance. Some applications for drone arc routing problems include inspection of pipelines, railwa…

Optimal Guard Placement Problem Under L-Visibility

2006

Two points a and b in the presence of polygonal obstacles are L-visible if the length of the shortest path avoiding obstacles is no more than L. For a given convex polygon Q, Gewali et al [4]. addressed the guard placement problem on the exterior boundary that will cover the maximum area exterior to the polygon under L-visibility. They proposed a linear time algorithm for some given value of L. When the length L is greater than half of the perimeter, they declared that problem as open. Here we address that open problem and present an algorithm whose time complexity is linear in number of vertices of the polygon.

Refitting Solutions Promoted by $$\ell _{12}$$ Sparse Analysis Regularizations with Block Penalties

2019

International audience; In inverse problems, the use of an l(12) analysis regularizer induces a bias in the estimated solution. We propose a general refitting framework for removing this artifact while keeping information of interest contained in the biased solution. This is done through the use of refitting block penalties that only act on the co-support of the estimation. Based on an analysis of related works in the literature, we propose a new penalty that is well suited for refitting purposes. We also present an efficient algorithmic method to obtain the refitted solution along with the original (biased) solution for any convex refitting block penalty. Experiments illustrate the good be…

Effect of raster resolution and polygon-conversion algorithm on landslide susceptibility mapping

2016

The choice of the proper resolution in landslide susceptibility mapping is a worth considering issue. If, on the one hand, a coarse spatial resolution may describe the terrain morphologic properties with low accuracy, on the other hand, at very fine resolutions, some of the DEM-derived morphometric factors may hold an excess of details. Moreover, the landslide inventory maps are represented throughout geospatial vector data structure, therefore a conversion procedure vector-to-raster is required.This work investigates the effects of raster resolution on the susceptibility mapping in conjunction with the use of different algorithms of vector-raster conversion. The Artificial Neural Network t…

Temperature interpolation by local information ; the example of France

2010

International audience; Methods of interpolation, whether based on regressions or on kriging, are global methods in which all the available data for a given study area are used. But the quality of results is affected when the study area is spatially very heterogeneous. To overcome this difficulty, a method of local interpolation is proposed and tested here with temperature in France. Starting from a set of weather stations spread across the country and digitized as 250 m-sided cells, the method consists in modelling local spatial variations in temperature by considering each point of the grid and the n weather stations that are its nearest neighbours. The procedure entails a series of steps…

The Monotone Area-preserving Flux-Form Advection Algorithm: Reducing the Time-splitting Error in Two-Dimensional Flow Fields

1993

Influence of gas environment on the dynamics of wetting transition of laser-textured stainless steel meshes

2021

We analyze the role of surrounding gas and aging in ambient air in the wettability behavior of laser-processed stainless steel meshes. Laser texturing of meshes was carried out in the presence of different gases (N2, O2, CO2, Ar, and SF6) in ambient atmospheric air and under different vacuum conditions. The influence of each gas on the evolution of the wettability properties after aging in ambient air is analyzed. The effects of low-pressure and vacuum aging allowed transforming the initial superhydrophilic characteristics of the laser-structured meshes to an almost superhydrophobic state.

Representable and Continuous Functionals on Banach Quasi *-Algebras

2017

In the study of locally convex quasi *-algebras an important role is played by representable linear functionals; i.e., functionals which allow a GNS-construction. This paper is mainly devoted to the study of the continuity of representable functionals in Banach and Hilbert quasi *-algebras. Some other concepts related to representable functionals (full-representability, *-semisimplicity, etc) are revisited in these special cases. In particular, in the case of Hilbert quasi *-algebras, which are shown to be fully representable, the existence of a 1-1 correspondence between positive, bounded elements (defined in an appropriate way) and continuous representable functionals is proved.