On the Dynamics of Inverse Magnetic Billiards

Consider a strictly convex set $\Omega$ in the plane, and a homogeneous, stationary magnetic field orthogonal to the plane whose strength is $B$ on the complement of $\Omega$ and $0$ inside $\Omega$. The trajectories of a charged particle in this setting are straight lines concatenated with circular arcs of Larmor radius $\mu$. We examine the dynamics of such a particle and call this inverse magnetic billiards. Comparisons are made to standard Birkhoff billiards and magnetic billiards, as some theorems regarding inverse magnetic billiards are consistent with each of these billiard variants while others are not.Comment: 22 pages, 10 figure

Periodic Trajectories and Topology of the Integrable Boltzmann System

We consider the Boltzmann system corresponding to the motion of a billiard with a linear boundary under the influence of a gravitational field. We derive analytic conditions of Cayley's type for periodicity of its trajectories and provide geometric descriptions of caustics. The topology of the phase space is discussed using Fomenko graphs.Comment: 18 pages, 14 figure

Import, Export and Turnover in Morocco

International trade is commonly view as an useful tool to remove market distortions, to promote competition among firms and hence increase welfare. However, trade openness is not costless and unavoidably creates gainers and losers (Wood (1995, 1998)). Hence, a complete evaluation of the gain from trade should consider both efficiency benefits and adjustment costs. Indeed, to enjoy of the gain from trade liberalisation, some adjustment processes are required. Increasing trade will induce reallocation of resources from less efficient firms to more productive one, with a final positive effect on growth and uncertain consequences for the labour market. With increasing competition, the less efficient firms will exit from the market and the others should increase their productivity to strengthen their position. The first attempts to analyse the impact of trade on labour market focused on the net change in wage and employment levels (Bottini (2005) and Hoeckman and Winters (2005) for a review of the literature). However, further analysis have highlighted that looking at total levels of employment is likely to conceal important dynamics in the labour market and in the economic analysis (Davis and Haltiwanger, 1996). Indeed net change in total employment is derived by adding up new places available through the entry of new firms and expansion of existing firms and employment losses over shrinking and exiting establishments. Studying the link between trade liberalisation and job dynamics is hence a way to examine how increasing trade impacts on job turnover and input reallocation. Furthermore, it is important to detangle the effect of trade on labour market by dealing separately with import and export flows. The available literature shows that trade liberalisation will lead to labour reallocation, with jobs moving away from import-competing industries toward export industries (Davidson and Matusz (2001)). Intuitively, import and export flows have an opposite impact on labour market. Increasing import competition worsen market condition for domestic firms and causes firms exit and downsizing with a final negative effect on employment. On the other side, increasing exports creates more opportunities for domestic firms, induces sector expansion and creation of new jobs. Finally, trade liberalisation. has been also blamed for a “race to the bottom” in the labour market in the form of lower compliance with labour market standards, more extensive use of part-time and temporary labour, and a decrease in the job quality for the neo-employed (Goldberg and Pavcnik, 2004). Hence, it would be interesting to investigate whether trade liberalisation impact in a different way on temporary and permanent workers. The purpose of this paper is to study how import and export flows impact on job reallocation in the Moroccan economy

Costs of trade and self-selection into exporting and importing: the case of Turkish manufacturing firms

This paper focuses on self-selection into trade by exporting and importing firms, and on the presence of differential variable and sunk costs between exporters and importers across different categories of imports. We use a rich and recent dataset for Turkish manufacturing firms for the period 2003-10.This allows us to provide a comprehensive analysis of firm heterogeneity and the connection between firm-level performance and international trade. We provide evidence on the remarkable heterogeneity across firms where only-importers (importers) perform better than only-exporters (exporters). We detect a self-selection effect for both importing and exporting firms with a stronger effect for importers. The results suggest that the nature of sunk costs varies between importing and exporting activities with importers facing higher sunk costs. Tari§s represent a potentially important source of variation in the variable costs of trading. When taking the tariffs faced by firms into account, we find that the self-selection effect associated with sunk costs is still present but greatly reduced with a smaller reduction for importers compared to exporters

A preliminary study of air-pollution measurement by active remote-sensing techniques

Air pollutants are identified, and the needs for their measurement from satellites and aircraft are discussed. An assessment is made of the properties of these pollutants and of the normal atmosphere, including interactions with light of various wavelengths and the resulting effects on transmission and scattering of optical signals. The possible methods for active remote measurement are described; the relative performance capabilities of double-ended and single-ended systems are compared qualitatively; and the capabilities of the several single-ended or backscattering techniques are compared quantitatively. The differential-absorption lidar (DIAL) technique is shown to be superior to the other backscattering techniques. The lidar system parameters and their relationships to the environmental factors and the properties of pollutants are examined in detail. A computer program that models both the atmosphere (including pollutants) and the lidar system is described. The performance capabilities of present and future lidar components are assessed, and projections are made of prospective measurement capabilities for future lidar systems. Following a discussion of some important operational factors that affect both the design and measurement capabilities of airborne and satellite-based lidar systems, the extensive analytical results obtained through more than 1000 individual cases analyzed with the aid of the computer program are summarized and discussed. The conclusions are presented. Recommendations are also made for additional studies to investigate cases that could not be explored adequately during this study

Blueprint for UK to leave EU shows just how hard it would be

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The impact of preferences on developing countries’ exports to the European Union: bilateral gravity modelling at the product level

Unilateral preferences aim at increasing exports from developing countries via reductions on applied tariffs and the incentives created by the preference margin. After decades of existence the evidence as to the extent to which preferential schemes have been genuinely effective in increasing exports is mixed. This paper evaluates the impact of the European Union’s (EU) unilateral preferential regimes on the exports of developing countries using a bilateral gravity model at the product level. We use a unique dataset that allows us to determine the actual tariff rate paid by each export flow at the product level (Combined Nomenclature CN-10 digits) to the EU and the preferential regime of entry. This allows us to accurately specify the impact of each trade regime and to properly address the issue of utilisation and non-utilisation of trade preferences. The most important findings of the paper are that unilateral preferences have been effective in increasing exports to the EU both as a result of the direct effect of lower tariffs and positive preference margin, and because of secondary effects associated with the preference regimes; although the outcome of these secondary effects depends on the margin of trade considered