Non-archimedean Yomdin-Gromov parametrizations and points of bounded height

We prove an analogue of the Yomdin-Gromov Lemma for $p$-adic definable sets and more broadly in a non-archimedean, definable context. This analogue keeps track of piecewise approximation by Taylor polynomials, a nontrivial aspect in the totally disconnected case. We apply this result to bound the number of rational points of bounded height on the transcendental part of $p$-adic subanalytic sets, and to bound the dimension of the set of complex polynomials of bounded degree lying on an algebraic variety defined over $\mathbb{C} ((t))$, in analogy to results by Pila and Wilkie, resp. by Bombieri and Pila. Along the way we prove, for definable functions in a general context of non-archimedean geometry, that local Lipschitz continuity implies piecewise global Lipschitz continuity.Comment: 54 pages; revised, section 5.6 adde

The Marseille Schmidt survey for active star-forming galaxies. I. Data on 92 emission line objects in two fields

We present data from a moderately deep spectroscopic Schmidt survey (Blim=17.5) of ``active galaxies'' selected by the presence of emission lines in their spectra and/or their UV excess. The redshift, magnitudes, color and diameter reduction methods have been discussed in a previous paper. Here we explain the emission line equivalent width determination method. 92 emission line objects have been found in two adjacent fields (approximately 50deg^2) in the direction of the south extension of the Virgo cluster. We give a catalog containing positions, photographic R and B magnitudes, U-R colors, effective diameters, redshifts, equivalent widths and intensity ratios of the [OIII]4959,5007, Hbeta and [OII] 3727 emission lines. On these fields, we evaluate the completeness limit of the survey at a pseudo B magnitude value of 15.7.Comment: tar gzipped file 7 AA latex2e pages(including 7 figures) + 1 tex table (2 pages) + 5 pages (color ps) charts will appear in A&A, available also at http://hasso.mpia-hd.mpg.de/Surace/surace.html#article

Adaptive estimation of the hazard rate with multiplicative censoring

We propose an adaptive estimation procedure of the hazard rate of a random variable X in the multiplicative censoring model, Y = XU , with U ∼ U([0, 1]) independent of X. The variable X is not directly observed: an estimator is built from a sample {Y1, ..., Yn} of copies of Y. It is obtained by minimisation of a contrast function over a class of general nested function spaces which can be generated e.g. by splines functions. The dimension of the space is selected by a penalised contrast criterion. The final estimator is proved to achieve the best bias-variance compromise and to reach the same convergence rate as the oracle estimator under conditions on the maximal dimension. The good behavior of the resulting estimator is illustrated over a simulation study

Fluctuations in the Irreversible Decay of Turbulent Energy

A fluctuation law of the energy in freely-decaying, homogeneous and isotropic turbulence is derived within standard closure hypotheses for 3D incompressible flow. In particular, a fluctuation-dissipation relation is derived which relates the strength of a stochastic backscatter term in the energy decay equation to the mean of the energy dissipation rate. The theory is based on the so-called ``effective action'' of the energy history and illustrates a Rayleigh-Ritz method recently developed to evaluate the effective action approximately within probability density-function (PDF) closures. These effective actions generalize the Onsager-Machlup action of nonequilibrium statistical mechanics to turbulent flow. They yield detailed, concrete predictions for fluctuations, such as multi-time correlation functions of arbitrary order, which cannot be obtained by direct PDF methods. They also characterize the mean histories by a variational principle.Comment: 26 pages, Latex Version 2.09, plus seceq.sty, a stylefile for sequential numbering of equations by section. This version includes new discussion of the physical interpretation of the formal Rayleigh-Ritz approximation. The title is also change

The Crab pulsar light curve in the soft gamma ray range: FIGARO II results

The FIGARO II experiment (a large area, balloon borne, crystal scintillator detector working from 0.15 to 4.3 MeV) observed the Crab pulsar on 1990 Jul. 9 for about seven hours. The study of the pulse profile confirms some structures detected with a low significance during the shorter observation of 1986, and adds new important elements to the picture. In particular, between the two main peaks, two secondary peaks appear centered at phase values 0.1 and 0.3, in the energy range 0.38 to 0.49 MeV; in the same energy range, a spectral feature at 0.44 MeV, interpreted as a redshifted positron annihilation line, was observed during the same balloon flight in the phase interval including the second main peak and the neighboring secondary peak. If the phase interval considered is extended to include also the other secondary peak, the significance of the spectral line appears to increase