Oscillating waves and optimal smoothing effect for one-dimensional nonlinear scalar conservation laws

Lions, Perthame, Tadmor conjectured in 1994 an optimal smoothing effect for entropy solutions of nonlinear scalar conservations laws . In this short paper we will restrict our attention to the simpler one-dimensional case. First, supercritical geometric optics lead to sequences of $C^\infty$ solutions uniformly bounded in the Sobolev space conjectured. Second we give continuous solutions which belong exactly to the suitable Sobolev space. In order to do so we give two new definitions of nonlinear flux and we introduce fractional $BV$ spaces

Construction of sheaves on the subanalytic site

On a real analytic manifold M, we construct the linear subanalytic Grothendieck topology Msal together with the natural morphism of sites $\rho$ from Msa to Msal, where Msa is the usual subanalytic site. Our first result is that the derived direct image functor by $\rho$ admits a right adjoint, allowing us to associate functorially a sheaf (in the derived sense) on Msa to a presheaf on Msa satisfying suitable properties, this sheaf having the same sections that the presheaf on any open set with Lipschitz boundary. We apply this construction to various presheaves on real manifolds, such as the presheaves of functions with temperate growth of a given order at the boundary or with Gevrey growth at the boundary. On a complex manifold endowed with the subanalytic topology, the Dolbeault complexes associated with these new sheaves allow us to obtain various sheaves of holomorphic functions with growth. As an application, we can endow functorially regular holonomic D-modules with a filtration, in the derived sense.Comment: v 5: Chapter 5 has been expanded and other minor correction

Is Short-Time Work a Good Method to Keep Unemployment Down?

Short-time work compensation aims at reducing lay-offs by allowing employers to temporarily reduce hours worked while compensating workers for the induced loss of income. These programs are now widespread in the OECD countries, notably following the 2008-2009 crisis. This paper discusses the efficiency of this type of policy and investigates its impact on unemployment and employment. There is some evidence that short-time compensation programs stabilize permanent employment and reduce unemployment during downturns. All in all, it seems that short-time work programs used in the recent downturn had significant beneficial effects. This suggests that countries which do not have short-time compensation programs could benefit from their introduction. But short-time compensation programs can also induce inefficient reductions in working hours and reduce the prospects of outsiders if used too intensively. Thus, the design of short-time compensation programs should include an experience-rating component.short-time work, unemployment, employment

The Detaxation of Overtime Hours: Lessons from the French Experiment

In October 2007 France introduced an exemption on the income tax and social security contributions that applied to wages received for hours worked overtime. The goal of the policy was to increase the number of hours worked. This article shows that this reform has had no significant impact on hours worked. Conversely, it has had a positive impact on the overtime hours declared by highly qualified wage-earners, who have opportunities to manipulate the overtime hours they declare in order to optimize their tax situation, since the hours they work are difficult to verify.tax exemption, overtime hours, working time

A Cache Management Strategy to Replace Wear Leveling Techniques for Embedded Flash Memory

Prices of NAND flash memories are falling drastically due to market growth and fabrication process mastering while research efforts from a technological point of view in terms of endurance and density are very active. NAND flash memories are becoming the most important storage media in mobile computing and tend to be less confined to this area. The major constraint of such a technology is the limited number of possible erase operations per block which tend to quickly provoke memory wear out. To cope with this issue, state-of-the-art solutions implement wear leveling policies to level the wear out of the memory and so increase its lifetime. These policies are integrated into the Flash Translation Layer (FTL) and greatly contribute in decreasing the write performance. In this paper, we propose to reduce the flash memory wear out problem and improve its performance by absorbing the erase operations throughout a dual cache system replacing FTL wear leveling and garbage collection services. We justify this idea by proposing a first performance evaluation of an exclusively cache based system for embedded flash memories. Unlike wear leveling schemes, the proposed cache solution reduces the total number of erase operations reported on the media by absorbing them in the cache for workloads expressing a minimal global sequential rate.Comment: Ce papier a obtenu le "Best Paper Award" dans le "Computer System track" nombre de page: 8; International Symposium on Performance Evaluation of Computer & Telecommunication Systems, La Haye : Netherlands (2011