On an explicit finite difference method for fractional diffusion equations

A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick's law. In this paper we combine the forward time centered space (FTCS) method, well known for the numerical integration of ordinary diffusion equations, with the Grunwald-Letnikov definition of the fractional derivative operator to obtain an explicit fractional FTCS scheme for solving the fractional diffusion equation. The resulting method is amenable to a stability analysis a la von Neumann. We show that the analytical stability bounds are in excellent agreement with numerical tests. Comparison between exact analytical solutions and numerical predictions are made.Comment: 22 pages, 6 figure

Towards new schemes: A Lie-group approach of the CBKDV and its derived equations

The aim of this paper is to propose methods that enable us to build new numerical schemes, which preserve the Lie symmetries of the original differential equations. To this purpose, the compound Burgers-Korteweg-de Vries (\textit{CBKDV}) equation is considered. The particular case of the Burgers equation is taken as a numerical example, and the resulting semi-invariant scheme is exposed

Do Fixed-Term Contracts Increase the Long-Term Employment Opportunities of the Unemployed?

The paper investigates whether (unsubsidised) fixed-term contracts (FTCs) are a means of integration for the unemployed in the West German labour market. This is done by analysing whether entering into an FTC improves the employment opportunities of an unemployed person in terms of the probability of subsequent permanent contracts and subsequent periods of employment and unemployment. The empirical analysis is based on propensity score matching methods, obtaining the effects of FTCs by comparing the future situation of (?treated?) unemployed entering into FTCs after a particular unemployment duration with a suitable control group of ?non-treated? individuals. In principal different counterfactual situations for treated persons entering into FTCs after a certain number of month of unemployment are reasonable. A first counterfactual is never to enter into an FTC. A second counterfactual is not to take up an FTC job in this month but possibly in a later month. These two possible counterfactuals imply different definitions for the group of non-treated individuals and impose different policy questions. Both definitions are analysed in the paper. The propensity score is estimated by a discrete hazard rate model, which seems to be an appropriate way of taking into account the potential endogenous effect of the unemployment duration on the selection into the type of contract. Further insights are gained by comparing the determinants of the transition to FTC and permanent contract jobs. There is some evidence that FTCs may serve as ?stepping stones? towards permanent employment for the unemployed. However, the hypothesis that FTCs lead to dual labour markets cannot be rejected. --Fixed-term Contracts,Propensity Score Matching,Hazard Rate Model,Unemployment Duration,Stepping Stones,Dual Labour Markets

Software dependability techniques validated via fault injection experiments

The present paper proposes a C/C++ source-to-source compiler able to increase the dependability properties of a given application. The adopted strategy is based on two main techniques: variable duplication/triplication and control flow checking. The validation of these techniques is based on the emulation of fault appearance by software fault injection. The chosen test case is a client-server application in charge of calculating and drawing a Mandelbrot fracta

Aggregate Employment Dynamics and (Partial) Labour Market Reforms

European labour markets have undergone several important innovations over the last three decades. Most countries have reformed their labour markets since the mid-1990s, with the liberalization of fixed-term contracts and temporary work agencies being the common elements to such reforms. This paper investigates the existence of a change in the dynamic behaviour of the aggregate employment for major European Union countries - France, Germany, Italy, and Spain. According to our results, partial labour market reforms have made the response of the aggregate employment to output shocks larger and quite comparable to that found for the UK - the most flexible labour market in Europe since the Thatcher reforms.labour market deregulation; dynamic responses

The Political Economy of Two-tier Reforms of Employment Protection in Europe

Reforms of employment protection (EPL) in Europe eased the recourse to temporary forms of employment while not reducing the strictness of EPL of permanent jobs (with the exception of Spain). Since 1990, such two-tier reforms have been implemented in Belgium, Denmark, Germany, Greece, Italy, the Netherlands and Sweden. The paper seeks to show why two-tier reforms of EPL have taken place in some countries and have failed on other occasions. This isdone by having a loser look at the history of national reform processes. In addition the paper seeks to determine whether two-tier reforms later led to EPL reforms for permanent jobs.employment protection, two-tier reforms, political economy

Finite-Volume Two-Pion Amplitudes in the I=0 Channel

We perform a calculation in one-loop chiral perturbation theory of the two-pion matrix elements and correlation functions of an I=0 scalar operator, in finite and infinite volumes for both full and quenched QCD. We show that major difficulties arise in the quenched theory due to the lack of unitarity. Similar problems are expected for quenched lattice calculations of $K \to \pi \pi$ amplitudes with $\Delta I=1/2$. Our results raise the important question of whether it is consistent to study $K\to\pi\pi$ amplitudes beyond leading order in chiral perturbation theory in quenched or partially quenched QCD.Comment: Version to appear on Phys. Lett. B, with only very minor and stylistic change

Trust In Fairtrade: The 'Feel-Good' Effect

Fairtrade is nurtured with stories aimed at making consumers feel good by buying Fairtrade products. This ‘feel-good’ factor may vary when it is found that, the proportional division of the benefits between producer and other potential gainers is biased towards the distributors. There is, therefore, an incentive to verify whether the trust accorded to Fairtrade is justified. If trust and therefore the feel-good factor are undermined or enhanced as a result of the validation of the stories, then the whole Fairtrade movement could potentially crumble or burgeon. Drawing on elements in Glaeser (2005)’s model, this paper analyses the factors behind the recent expansion of Fairtrade.Fairtrade

Validation of a software dependability tool via fault injection experiments

Presents the validation of the strategies employed in the RECCO tool to analyze a C/C++ software; the RECCO compiler scans C/C++ source code to extract information about the significance of the variables that populate the program and the code structure itself. Experimental results gathered on an Open Source Router are used to compare and correlate two sets of critical variables, one obtained by fault injection experiments, and the other applying the RECCO tool, respectively. Then the two sets are analyzed, compared, and correlated to prove the effectiveness of RECCO's methodology