We prove that positive solutions of the fractional Lane-Emden equation with homogeneous Dirichlet boundary conditions satisfy pointwise estimates in terms of the best constant in Poincaré's inequality on all open sets, and are isolated in $L^1$ on smooth bounded ones, whence we deduce the isolation of the first non-local semilinear eigenvalue .

Age of infection epidemic models [1, 3], based on non-linear integro-dierential equations, naturally describe the evolution of diseases whose infectivity depends on the time since becoming infected. Here we consider a multi-group age of infection model [2] and we extend the investigations in [4], [5] and [6] to provide numerical solutions that retain the main properties of the continuous system. In particular, we use Direct Quadrature methods and prove that the numerical solution is positive and bounded.

Image resizing is a basic tool in image processing, and in literature, we have many methods based on different approaches, which are often specialized in only upscaling or downscaling. In this paper, independently of the (reduced or enlarged) size we aim to get, we approach the problem at a continuous scale where the underlying function representing the image is globally approximated by its Lagrange-Chebyshev I kind interpolation polynomial corresponding to suitable (tensor product) grids of first kind Chebyshev zeros.

The aim of the Connected Maximum Lifetime Problem is to define a schedule for the activation intervals of the sensors deployed inside a region of interest, such that at all times the activated sensors can monitor a set of interesting target locations and route the collected information to a central base station, while maximizing the total amount of time over which the sensor network can be operational. Complete or partial coverage of the targets are taken into account.

This paper provides a unified point of view on fractional perimeters and Riesz potentials. Denoting byH? - for ? 2 .0; 1/ - the ?-fractional perimeter and by J ? - for ? 2 .(d; 0)- the ?-Riesz energies acting on characteristic functions, we prove that both functionals can be seen as limits of renormalized self-attractive energies as well as limits of repulsive interactions between a set and its complement. We also show that the functionals H? and J ? , up to a suitable additive renormalization diverging when ? ? 0, belong to a continuous one-parameter family of functionals, which for ?

We consider a simple exchangeable model, which accounts for heterogeneity and dependence. Based on this model, we show how, and in which sense, situations of negative aging arise in a natural way from conditions of heterogeneity among items.

In this paper we take into account three different spanning tree problems with degree-dependent objective functions. The main application of these problems is in the field of optical network design. In particular, we propose the classical Minimum Leaves Spanning Tree problem as a relevant problem in this field and show its relations with the Minimum Branch Vertices and the Minimum Degree Sum Problems. We present a unified memetic algorithm for the three problems and show its effectiveness on a wide range of test instances. © 2013 Elsevier B.V. All rights reserved.

Given a graph G with a label (color) assigned to each edge (not necessarily properly) we look for an hamiltonian cycle of G with the minimum number of different colors. The problem has several applications in telecommunication networks, electric networks, multimodal transportation networks, among others, where one aims to ensure connectivity or other properties by means of limited number of different connections. We analyze the complexity of the problem on special graph classes and propose, for the general case, heuristic resolution algorithms.

We aim to maximize the operational time of a network of sensors, which are used to monitor a predefined set of target locations. The classical approach proposed in the literature consists in individuating subsets of sensors (covers) that can individually monitor the targets, and in assigning appropriate activation times to each cover. Indeed, since sensors may belong to multiple covers, it is important to make sure that their overall battery capacities are not violated.

A product quadrature rule, based on the filtered de la Vallée Poussin polynomial approximation, is proposed for evaluating the finite weighted Hilbert transform in [-1,1]. Convergence results are stated in weighted uniform norm for functions belonging to suitable Besov type subspaces. Several numerical tests are provided, also comparing the rule with other formulas known in literature.