1,183 research outputs found
Bailouts in a common market: a strategic approach
Governments in the EU grant Rescue and Restructure Subsidies to bail out ailing firms. In an international asymmetric Cournot duopoly we study effects of such subsidies on market structure and welfare. We adopt a common market setting, where consumers from the two countries form one market. We show that the subsidy is positive also when it fails to prevent the exit. The reason is a strategic effect, which forces the more efficient firm to make additional cost-reducing effort. When the exit is prevented, allocative and productive efficiencies are lower and the only gaining player is the rescued firm
Mathematical Model of Easter Island Society Collapse
In this paper we consider a mathematical model for the evolution and collapse
of the Easter Island society, starting from the fifth century until the last
period of the society collapse (fifteen century). Based on historical reports,
the available primary sources consisted almost exclusively on the trees. We
describe the inhabitants and the resources as an isolated system and both
considered as dynamic variables. A mathematical analysis about why the
structure of the Easter Island community collapse is performed. In particular,
we analyze the critical values of the fundamental parameters driving the
interaction humans-environment and consequently leading to the collapse. The
technological parameter, quantifying the exploitation of the resources, is
calculated and applied to the case of other extinguished civilization (Cop\'an
Maya) confirming, with a sufficiently precise estimation, the consistency of
the adopted model.Comment: 9 pages, 1 figure, final version published on EuroPhysics Letter
Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization
In this article, we study an analog of the Bj\"orling problem for isothermic
surfaces (that are more general than minimal surfaces): given a real analytic
curve in , and two analytic non-vanishing orthogonal
vector fields and along , find an isothermic surface that is
tangent to and that has and as principal directions of
curvature. We prove that solutions to that problem can be obtained by
constructing a family of discrete isothermic surfaces (in the sense of Bobenko
and Pinkall) from data that is sampled along , and passing to the limit
of vanishing mesh size. The proof relies on a rephrasing of the
Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its
discretization which is induced from the geometry of discrete isothermic
surfaces. The discrete-to-continuous limit is carried out for the Christoffel
and the Darboux transformations as well.Comment: 29 pages, some figure
Scattering from Singular Potentials in Quantum Mechanics
In non-relativistic quantum mechanics, singular potentials in problems with
spherical symmetry lead to a Schrodinger equation for stationary states with
non-Fuchsian singularities both as r tends to zero and as r tends to infinity.
In the sixties, an analytic approach was developed for the investigation of
scattering from such potentials, with emphasis on the polydromy of the wave
function in the r variable. The present paper extends those early results to an
arbitrary number of spatial dimensions. The Hill-type equation which leads, in
principle, to the evaluation of the polydromy parameter, is obtained from the
Hill equation for a two-dimensional problem by means of a simple change of
variables. The asymptotic forms of the wave function as r tends to zero and as
r tends to infinity are also derived. The Darboux technique of intertwining
operators is then applied to obtain an algorithm that makes it possible to
solve the Schrodinger equation with a singular potential containing many
negative powers of r, if the exact solution with even just one term is already
known.Comment: 19 pages, plain Tex. In this revised version, the analysis of Eq.
(5.29) has been amended, and an appendix has been added for completenes
Critical gaps in nanoplastics research and their connection to risk assessment
Reports of plastics, at higher levels than previously thought, in the water that we drink and the air that we breathe, are generating considerable interest and concern. Plastics have been recorded in almost every environment in the world with estimates on the order of trillions of microplastic pieces. Yet, this may very well be an underestimate of plastic pollution as a whole. Once microplastics (<5Â mm) break down in the environment, they nominally enter the nanoscale (<1,000Â nm), where they cannot be seen by the naked eye or even with the use of a typical laboratory microscope. Thus far, research has focused on plastics in the macro- (>25Â mm) and micro-size ranges, which are easier to detect and identify, leaving large knowledge gaps in our understanding of nanoplastic debris. Our ability to ask and answer questions relating to the transport, fate, and potential toxicity of these particles is disadvantaged by the detection and identification limits of current technology. Furthermore, laboratory exposures have been substantially constrained to the study of commercially available nanoplastics; i.e., polystyrene spheres, which do not adequately reflect the composition of environmental plastic debris. While a great deal of plastic-focused research has been published in recent years, the pattern of the work does not answer a number of key factors vital to calculating risk that takes into account the smallest plastic particles; namely, sources, fate and transport, exposure measures, toxicity and effects. These data are critical to inform regulatory decision making and to implement adaptive management strategies that mitigate risk to human health and the environment. This paper reviews the current state-of-the-science on nanoplastic research, highlighting areas where data are needed to establish robust risk assessments that take into account plastics pollution. Where nanoplastic-specific data are not available, suggested substitutions are indicated
The New Political Economy of EU State Aid Policy
Despite its importance and singularity, the EU’s state aid policy has attracted less scholarly attention than other elements of EU competition policy. Introducing the themes addressed by the special issue, this article briefly reviews the development of EU policy and highlights why the control of state aid matters. The Commission’s response to the current economic crisis notably in banking and the car industry is a key concern, but the interests of the special issue go far beyond. They include: the role of the European Commission in the development of EU policy, the politics of state aid, and a clash between models of capitalism. The special issue also examines the impact of EU policy. It investigates how EU state aid decisions affect not only industrial policy at the national level (and therefore at the EU level), but the welfare state and territorial relations within federal member states, the external implications of EU action and the strategies pursued by the Commission to limit any potential disadvantage to European firms, and the conflict between the EU’s expanding legal order and national
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