In the last years, there has been a large number of papers discussing possible extensions of the Einstein-Hilbert Lagrangian for gravity : L = R , where R is the scalar space-time curvature. There has been mainly 2 kinds of theories discussed, the so-called f (R) theories, where f is a function of the scalar curva- ture [1], and theories based on quadratic terms built on the curvature tensor [2], more or less like the Lagrangian of gauge fields, or even more **general** ones [3] including torsion. The existence of torsion has also often been discussed with possible effects for the early universe [4].

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Available online 23 February 2018
a b s t r a c t
This paper proposes an erfc potential to incorporate in a symmetric metric. One key feature of this model is that it relies on the existence of an intrinsic physical constant r , a star-specific proper length that scales all its surroundings. Based thereon, the new metric is used to study the space–time geometry of a static symmetric massive object, as seen from its interior. The analytical solutions to the Einstein equation are presented, highlighting the absence of singularities and discontinuities in such a model. The geodesics are derived in their second- and first-order differential formats. Recalling the slight impact of the new model on the classical **general** **relativity** **tests** in the solar system, a number of facts and open problems are briefly revisited on the basis of a heuristic definition of r . A special attention is given to gravitational col- lapses and non-singular black holes.

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The current knowledge of Mercury’s orbit has mainly been gained by direct radar ranging obtained from the 60s to 1998 and by five Mercury flybys made with Mariner 10 in the 70s, and with MESSENGER made in 2008 and 2009. On March 18, 2011, MESSENGER became the first spacecraft to orbit Mercury. The radioscience observations acquired during the orbital phase of MESSENGER drastically improved our knowledge of the orbit of Mercury. An accurate MESSENGER orbit is obtained by fitting one-and-half years of tracking data using GINS orbit determination software. The systematic error in the Earth-Mercury geometric positions, also called range bias, obtained from GINS are then used to fit the INPOP dynamical modeling of the planet motions. An improved ephemeris of the planets is then obtained, INPOP13a, and used to perform **general** **relativity** **tests** of the parametrized post-Newtonian (PPN) formalism. Our estimations of PPN parameters (γ and β) are more stringent than previous results.

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This test is similar in spirit to the χ 2 GW search statistic
[2,61] , which divides the model waveform into frequency bands and checks to see that the SNR accumulates as
expected across those bands. Large matched-filter SNR values which are accompanied by a large χ 2 statistic are very likely due either to noise glitches or to a mismatch between the signal and the model matched-filter waveform. Conversely, reduced- χ 2 values near unity indicate that the data are consistent with waveform plus the expected detector noise. Thus, large χ 2 values are a warning that some parts of the waveform are a much worse fit than others, and thus the candidates may result from instrument glitches that are very loud, but they do not resemble binary-inspiral signals. However, χ 2 **tests** are performed by comparing the data with a single theoretical waveform, while in this case we allow the inspiral and postinspiral partial waveforms to select different physical parameters. Thus, this test should be sensitive to subtler deviations from the predictions of GR. In Fig. 4 we summarize our findings. The top panel shows the posterior distributions of M f and a f estimated from the inspiral and postinspiral signals, and from the entire inspiral-merger-ringdown waveform. The plot con- firms the expected behavior: the inspiral and postinspiral 90% confidence regions (defined by the isoprobability contours that enclose 90% of the posterior) have a significant region of overlap. As a sanity check (which, strictly speaking, is not part of the test of GR that is being performed), we also produced the 90% confidence region computed with the full inspiral-merger-ringdown wave- form; it lies comfortably within this overlap. We have verified that these conclusions are not affected by the specific formula [40,59,62] used to predict M f and a f , or by the choice of f end insp GW within 50 Hz.

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by a consistent point estimate. Such a procedure can be interpreted as a parametric bootstrap test based on the percentile method [see Efron and Tibshirani (1993, Chapter 16) and Hall (1992)]. The term “parametric” may however be misleading here, because such MC **tests** can be applied as well to nonparametric (distribution-free) test statistics. We give **general** conditions under which a Monte Carlo test obtained after replacing an unknown nuisance parameter yield an asymptotically valid test in cases where the limit distribution of the test statistic involves nuisance parameters. Following the **general** spirit of Monte Carlo testing and in contrast with typical bootstrap arguments, the proofs take the number of Monte Carlo simulations as fixed (possibly very small, such as 19 to obtain a test with level 0.05). As in standard bootstrap arguments, the conditions considered involve a smooth (continuous) dependence of the asymptotic distribution upon the nuisance parameters. It is, however, important to note that these conditions are more restrictive and more difficult to check than those under which CSEMMC procedures would be applicable. We conclude in Section 7.

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I NTRODUCCIÓN **GENERAL**
Presentamos en este volumen algunos de los trabajos preparados para el simposio Dinámica de las lenguas en contacto organizado en el marco del 51 Congreso Internacional de Americanistas celebrado en Santiago de Chile del 14 al 18 de julio de 2003. Este simposio reunió a 19 investigadores que laboran en 16 instituciones de siete países de Norte, Centro y Sur América y Europa. A lo largo del simposio, los aportes y las preguntas relacionadas con los cambios estructurales de las lenguas que se encuentran en una situación de contacto confrontaban o interpelaban las teórias desarolladas en sus estudios por Weinreich (1953) Thomason y Kaufman (1988), Thomason (2001), Field (2002) y Winford (2003) para citar únicamente algunos. Por lo tanto, en esta introducción nos proponemos hacer una presentación analítica de los trabajos enfocando algunas problemáticas en particular.

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The role of an irreducibility assumption is to guarantee that the non-emptiness of one δ i ( ) p implies the non-emptiness of all. The **general** idea is to assume that, in some sense to be specified, it is always possible for any non-empty and proper group of consumers to benefit from the resources of the group of the other consumers. Various irreducibility assumptions have been proposed by Gale in the context of linear exchange economies, McKenzie, Debreu, Arrow-Hahn, Bergstrom and many others. To enter in the technical subtleties of the different formulations would exceed the objectives of this survey.

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equivalent to the likelihood ratio, Wald, and Lagrange multiplier. tests for H*[r]

In this paper, we perform a test of SR using a net- work of distant optical lattice clocks located in France, Germany and the UK. By exploiting the difference be- tween the velocities of each clock in the inertial geocen- tric frame, due to their different positions on the surface of the Earth, we are able to improve upon previous **tests** of time dilation. The connection between these clocks, achieved with phase-compensated optical fibers, allows

Dans le futur nous pourrons appliquer des techniques de rafﬁnement Bensalem et al. (2007) ou de sélection Lahami et al. (2015) pour simpliﬁer l’étape de génération de **tests** en terme de temps de calcul et espace de stockage. Nous pourrons également appliquer des techniques de placement des testeurs Krichen et al. (2018b) ; Maâlej et al. (2018) ; Lahami et al. (2012) utili- sés aﬁn de tenir compte des ressources disponibles au niveau des diffèrents nœuds du syste ` me. Il est envisageable aussi d’adopter le standard de test TTCN3 Lahami et al. (2012) et d’utiliser des services cloud pour la génération et l’exécution des **tests** Lahami et al. (2019) ; Lahami et al. (2018). Finalement, il est également possible de considérer des aspects de securité Kri- chen et al. (2020) et de les combiner avec des aspects de conformité.

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by a consistent point estimate. Such a procedure can be interpreted as a parametric bootstrap test based on the percentile method [see Efron and Tibshirani (1993, Chapter 16) and Hall (1992)]. The term “parametric” may however be misleading here, because such MC **tests** can be applied as well to nonparametric (distribution-free) test statistics. We give **general** conditions under which a Monte Carlo test obtained after replacing an unknown nuisance parameter yield an asymptotically valid test in cases where the limit distribution of the test statistic involves nuisance parameters. Following the **general** spirit of Monte Carlo testing and in contrast with typical bootstrap arguments, the proofs take the number of Monte Carlo simulations as ﬁxed (possibly very small, such as 19 to obtain a test with level 0.05). As in standard bootstrap arguments, the conditions considered involve a smooth (continuous) dependence of the asymptotic distribution upon the nuisance parameters. It is, however, important to note that these conditions are more restrictive and more difﬁcult to check than those under which CSEMMC procedures would be applicable. We conclude in Section 7.

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Poincaré’s silence with respect to Einstein’s theory has been the subject of much historical speculation, and will not concern us here. Instead, let us ask why no one else in France saw fit to mention Einstein’s theory in print before 1911. And to begin with, let us investigate why one person in particular, Paul Langevin, did not mention Einstein’s theory in print before 1911. Recall that in 1905 Langevin proposed an electron theory similar in some respects to that of Alfred Heinrich Bucherer, featuring an electron model of constant volume, and velocity-dependent shape, and that Poincaré showed Langevin’s theory to be incompatible with **relativity**. Langevin acknowledged Poincaré’s judgment of his theory, but did not give it up until the experimental results presented by A.H. Bucherer in September 1908 persuaded him to do so. 38 To put it briefly, until the fall of 1908 there were several plausible alternatives available to **relativity** theory, some of which enjoyed, like Abraham’s rigid-electron theory, better empirical support in some **tests** than did the theory of **relativity**. 39

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Accordingly, beyond the documented testimonies (e.g. on censorship) supplied by literary history, the history of publishing, law history etc., a tighter understanding[r]

La question 4 de la présente recherche s'intéresse particulièrement à la validité convergente des **tests** de créativité. Rappelons que la question 4 se lit comme suit: les **tests** de créativité lorsque soumis à une analyse factorielle font-ils émerger un facteur commun assez important expliquant la majeure partie de la variance des **tests** de créativité? Lorsque nous som- mes en présence de **tests** qui ont la prétention de mesurer un même construit ou d'être reliés à un même construit, nous devrions exiger, si l'on soumet ces **tests** à une analyse factorielle, un premier facteur important qui ex- plique plus de la moitiée de la variance totale et ceci représente une exi- gence minimale à notre avis. En effet, lorsque des items ou des **tests** con- vergent vers la mesure d'un même trait l'analyse factorielle en composan- tes principales fait émerger un premier facteur important qui explique une grande partie de la variance totale. Pour donner un exemple, Bernier (1979) a obtenu un premier facteur expliquant 78% de la variance totale à partir de 23 variables reliées à l'évaluation des cours. Cela signifie clairement que les variables utilisées par Bernier convergent vers la mesure d'un mê- me trait, soit la satisfaction à l'égard d'un cours. Or si les quatre **tests** de créativité convergent vers la mesure d'un même trait, soit la créativité, nous devrions obtenir un premier facteur important. Plus ce premier facteur sera important plus les **tests** de créativité en question seront considérés comme converaeant vers la mesure de la créativité. Bref, 1'analvse en compo-

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1. To grant to the Director **General**-elect, Dr. Chelston W.D. Brathwaite, **General** Power of Attorney for a period of four years, beginning January 15, 2002, so that he may faithfully fulfill the responsibilities of Director **General** conferred upon him under Article 20 of the Convention and Chapter II of the Rules of Procedure of the **General** Directorate.

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Because of the importance of wood in the Canadian economy, research on exterior coatings for this substrate has always been a n important part of the work of th[r]

Despite the **general** rule of cross resistance between quinolones, garenoxacin, a new non-fluorinated quinolone, retains most of its activity against strains harboring QRDR mutations, in species such as Streptococcus pneumoniae and Helicobacter pylori [28–31]. This characteristic, combined with a lower rate of resistant mutant and favorable PK-PD parameters contribute to its higher activity against strains harboring DNA gyrase mutations compared to other quinolones. We previously demonstrated that garenoxacin has the same inhibitory activity against purified M. leprae DNA gyrase carrying mutation implicated in quinolone resistance than against the wild-type enzyme [15]. Although less active than moxifloxacin against wild-type strains [32], garenoxacin is as active as moxifloxacin against the GyrA A91V mutant. Garenox- acin is currently under development in several countries [33].

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consider other kinds of assumptions on the transition density. We shall assume that s belongs to classes of functions satisfying structural assumptions and for which faster rates of convergence can be achieved. This approach was developed by Juditsky et al. (2009) (in the Gaussian white noise model) and by Baraud and Birg´e (2011) (in more statistical settings) to avoid the curse of dimensionality. More precisely, Baraud and Birg´e (2011) showed that these rates can be deduced from a **general** model selection theorem, which strengthen its theoretical interest. This strategy was used in Chapter 2 to establish risk bounds over many classes of functions for Poisson processes with covariates. In this chapter, we shall use these assumptions to obtain faster rates of convergence for autoregressive Markov chains (whose conditional variance may not be constant).

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