Regularity, Local and Microlocal Analysis in Theories of Generalized Functions

We introduce a general context involving a presheaf A and a subpresheaf B of A. We show that all previously considered cases of local analysis of generalized functions (defined from duality or algebraic techniques) can be interpretated as the B-local analysis of sections of A. But the microlocal analysis of the sections of sheaves or presheaves under consideration is dissociated into a "frequential microlocal analysis " and into a "microlocal asymptotic analysis". The frequential microlocal analysis based on the Fourier transform leads to the study of propagation of singularities under only linear (including pseudodifferential) operators in the theories described here, but has been extended to some non linear cases in classical theories involving Sobolev techniques. The microlocal asymptotic analysis can inherit from the algebraic structure of B some good properties with respect to nonlinear operations

An Analytical Prediction of the Bifurcation Scheme of a Clarinet-Like Instrument: Effects of Resonator Losses

The understanding of the relationship between excitation parameters andoscillation regimes is a classical topic concerning bowed stringinstruments. The paper aims to study the case of reed woodwinds and attemptsto find consequences on the ease of playing.In the minimum model of clarinet-like instruments, three parameters areconsidered: i) the mouth pressure, ii) the reed opening at rest, iii) thelength of the resonator \ assumed to be cylindrical. Recently asupplementary parameter was added: the loss parameter of the resonator(using the \textquotedblleft Raman model\textquotedblright, that considersresonator losses to be independent of frequency). This allowed explainingthe extinction of sound when the mouth pressure becomes very large. Thepresent paper presents an extension of the paper by Dalmont et al (JASA,2005), searching for a diagram of oscillation regimes with respect to thereed opening and the loss parameter. An alternative method is used, whichallows easier generalization and simplifies the calculation. The emphasis is done on the emergencebifurcation: for very strong losses, it can be inverse, similarly to theextinction one for weak losses. The main part of the calculations areanalytical, giving clear dependence of the parameters. An attempt to deducemusical consequences for the player is given

Integer-ambiguity resolution in astronomy and geodesy

Recent theoretical developments in astronomical aperture synthesis have revealed the existence of integer-ambiguity problems. Those problems, which appear in the self-calibration procedures of radio imaging, have been shown to be similar to the nearest-lattice point (NLP) problems encountered in high-precision geodetic positioning, and in global navigation satellite systems. In this paper, we analyse the theoretical aspects of the matter and propose new methods for solving those NLP problems. The related optimization aspects concern both the preconditioning stage, and the discrete-search stage in which the integer ambiguities are finally fixed. Our algorithms, which are described in an explicit manner, can easily be implemented. They lead to substantial gains in the processing time of both stages. Their efficiency was shown via intensive numerical tests.Comment: 12 pages. Soumis et accept\'e pour publication dans "Astronomische Nachrichten

Pointvalue characterizations in multi-parameter algebras

We extend classical results from the Colombeau algebra, concerning point-value characterizations of generalized functions, to the more general case of multi-parameter (C,E,P)–algebras. Our investigations include considerations about different definitions of subspaces related to tempered generalized functions.Algebra of generalized functions, pointvalue characterization, tempered generalized functions

Fair Wages in a New Keynesian Model of the Business Cycle

We build a New Keynesian model of the business cycle with sticky prices and real wage rigidities motivated by efficiency wages of the gift exchange variety. Compared to a standard sticky price model, our Fair Wage model provides an explanation for structural unemployment and generates more plausible labor market dynamics - notably accounting for the low correlation between wages and employment. The fair wage induced real wage rigidity also significantly reduces the elasticity of marginal cost with respect to output. The smoother dynamics of real marginal cost increase both amplification and persistence of output responses to monetary shocks, thus remedying the well-known lack of internal propagation of standard sticky price models. We take these improvements as a strong endorsement of the addition of real wage rigidities to nominal price rigidities and conclude that the fair wage extension of this paper constitutes a promising platform for an enriched New Keynesian synthesis.Efficiency wages, business cycles, sticky prices, persistence

Weathering the storm- Fair weather versus stormy-weather governance in the euro area

Jean Pisani-Ferry and André Sapir believe that the euro has proved attractive as a fair-weather currency for countries and investors well beyond its borders. But it still remains to be seen if its governance is strong enough for it to succeed as a stormy-weather currency. The authors already detect, howevever, that the crisis shows the euro-area governance system lacks some crucial properties: speed of reaction, policy discretion and centralised decision-making.

The Business Cycle Implications of Reciprocity in Labor Relations

We develop a reciprocity-based model of wage determination and incorporate it into a moder dynamic general equilibrium framework. We estimate the model and find that, among potential determinants of wage policy, rent-sharing (between workers and firms) and a measure of wage entitlement are critical to fit the dynamic responses of hours, wages and inflation to various exogenous shocks. Aggregate employment conditions (measuring workers' outside option), on the other hand, are found to play only a negligible role in wage setting. These results are broadly consistent with micro-studies on reciprocity in labor relations but contrast with traditional efficiency wage models which emphasize aggregate labor market variables as the main determinant of wage setting. Overall, the empirical fit of the estimated model is at least as good as the fit of models postulating nominal wage contracts. In particular, the reciprocity model is more successful in generating the sharp and significant fall of inflation and nominal wage growth in response to a neutral technology shock.Efficiency wages, Reciprocity, Estimated DSGE models

The Business Cycle Implications of Reciprocity in Labor Relations

We develop a reciprocity-based model of wage determination and incorporate it into a modern dynamic general equilibrium framework. We estimate the model and find that, among potential determinants of wages, rent-sharing (between workers and firms) and wage entitlement (based on wages earned in the past) are important to fit the dynamic responses of output, wages and inflation to various exogenous shocks. Aggregate employment conditions (measuring workers' outside option), on the other hand, are found to play only a negligible role for wage setting. These results are broadly consistent with micro-studies on reciprocity in labor relations but contrast with traditional efficiency wage models which emphasize aggregate labor market variables as the main determinant of wage setting.Efficiency Wages, Reciprocity, Estimated DSGE Models