Search results for "Q20"
showing 10 items of 31 documents
Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality
2017
We provide a full quantitative version of the Gaussian isoperimetric inequality: the difference between the Gaussian perimeter of a given set and a half-space with the same mass controls the gap between the norms of the corresponding barycenters. In particular, it controls the Gaussian measure of the symmetric difference between the set and the half-space oriented so to have the barycenter in the same direction of the set. Our estimate is independent of the dimension, sharp on the decay rate with respect to the gap and with optimal dependence on the mass.
Biogas production from the perspective of sustainable development
2020
One of the basic aspects of sustainable development strategy involves investments in green technologies, including energy production from renewable sources. Biomass, special organic waste which belongs to “green sources” of energy can be used in the methane fermentation process of biogas production to generate heat and electricity.Biogas power plants have functioned in the Polish energy industry for many years now. On the basis of the data available from Central Statistical Office, in 2014 the ratio of biogas accounted for 7.6% of the structure of primary energy derived from renewable sources in the EU and 2.6% in Poland. An important consideration related to the production of biogas is ass…
THE 1-HARMONIC FLOW WITH VALUES IN A HYPEROCTANT OF THE N-SPHERE
2014
We prove the existence of solutions to the 1-harmonic flow — that is, the formal gradient flow of the total variation of a vector field with respect to the [math] -distance — from a domain of [math] into a hyperoctant of the [math] -dimensional unit sphere, [math] , under homogeneous Neumann boundary conditions. In particular, we characterize the lower-order term appearing in the Euler–Lagrange formulation in terms of the “geodesic representative” of a BV-director field on its jump set. Such characterization relies on a lower semicontinuity argument which leads to a nontrivial and nonconvex minimization problem: to find a shortest path between two points on [math] with respect to a metric w…
OPTIMIZATIONS FOR TENSORIAL BERNSTEIN–BASED SOLVERS BY USING POLYHEDRAL BOUNDS
2010
The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n = 6 or 7 variables. This article describes a polytope (Bernstein polytope) with a number of faces, which allows to bound a sparse, multivariate polynomial expressed in the canonical basis by solving several linear programming problems. We compare the performance of a subdivision solver using domain reductions by linear programming with a solver using a c…
Algebraic-geometric techniques for the feedback classification and robustness of the optimal control of a pair of Bloch equations with application to…
2017
The aim of this article is to classify the singular trajectories associated with the optimal control problems of a pair of controlled Bloch equations. The motivation is to analyze the robustness of the optimal solutions to the contrast and the time-minimal saturation problem, in magnetic resonance imaging, with respect to the parameters and B1-inhomogeneity. For this purpose, we use various computer algebra algorithms and methods to study solutions of polynomial systems of equations and inequalities which are used for classification issues: Gröbner basis, cylindrical algebraic decomposition of semi-algebraic sets, Thom's isotopy lemma.
$PT$-symmetry and Schrödinger operators. The double well case
2016
International audience; We study a class of $PT$-symmetric semiclassical Schrodinger operators, which are perturbations of a selfadjoint one. Here, we treat the case where the unperturbed operator has a double-well potential. In the simple well case, two of the authors have proved in [6] that, when the potential is analytic, the eigenvalues stay real for a perturbation of size $O(1)$. We show here, in the double-well case, that the eigenvalues stay real only for exponentially small perturbations, then bifurcate into the complex domain when the perturbation increases and we get precise asymptotic expansions. The proof uses complex WKB-analysis, leading to a fairly explicit quantization condi…
Self-enforcing international environmental agreements revisited
2004
In Barrett's (1994) paper on transboundary pollution abatement is shown that if the signatories of an international environmental agreement act in a Stackelberg fashion, then, depending on parameter values, a self-enforcing IEA can have any number of signatories between two and the grand coalition. Barrett obtains this result using numerical simulations and also ignoring the fact that emissions must be non-negative. Recent attempts to use analytical approaches and to explicitly recognize the non-negativity constraints have suggested that the number of signatories of a stable IEA may be very small. The way such papers have dealt with non-negativity constraints is to restrict parameter values…
Panorámica de la problemática medioambiental en el mundo y en España
2008
As energy resources become scarce and pollution increases, fundamental and often irreversible changes are affecting our global ecosystem, and these changes are already having an influence on countries’ potential for economic growth and development. In this article we examine the principal environmental problems worldwide and how such problems are affected by inequality between countries. In Spain’s case, the basic problems are greenhouse gas emissions, problems relating to water management and issues concerning territory and biodiversity. We also call for the application of economic funding mechanisms to implement environmental policies.
The Correlation Between Human Capital and Gross Added Value in the Bioeconomy Sectors at the European Union (EU) Country Level
2019
Abstract The paper aims to prove the link between human capital and gross added value in bioeconomy sectors in the EU countries. Data from EUROSTAT data base regarding employment and gross added value in 6 bioeconomy sectors were used in a cross-country regression analysis. The econometric analysis of cross-country data shows a positive correlation between human capital in bioeconomy sectors and their gross output in 2015 in 26 European countries. It is found also that the correlation is stronger in the highly developed economies as in the central-eastern countries, as well as in the European economy.
On time-harmonic Maxwell equations with nonhomogeneous conductivities : Solvability and FE-approximation
1989
The solvability of time-harmonic Maxwell equations in the 3D-case with nonhomogeneous conductivities is considered by adapting Sobolev space technique and variational formulation of the probJem in question. Moreover, a finite element approximation is presented in the 3D·case together with an error estimate in the energy norm. Some remarks are given to the 2D-problem arising from geophysics. peerReviewed