Abstract:
Using a standard 'forward-backward' translation procedure, the English language versions of the two instruments (i.e. the 12-item General Health Questionnaire and the Subjective Vitality Scale) were translated into French. A sample of adults aged 58–72 years then completed both questionnaires. Internal consistency was assessed by Cronbach's alpha coefficient. The factor structures of the two instruments were extracted by confirmatory factor analysis (CFA). Finally, the relationship between the two instruments was assessed by correlation analysis.In all, 217 elderly adults participated in the study. The mean age of the respondents was 61.7 (SD = 6.2) years. The mean GHQ-12 score was 17.4 (SD = 8.0), and analysis showed satisfactory internal consistency (Cronbach's alpha coefficient = 0.78). The mean VS score was 22.4 (SD = 7.4) and its internal consistency was found to be good (Cronbach's alpha coefficient = 0.83). While CFA showed that the VS was uni-dimensional, analysis for the GHQ-12 demonstrated a good fit not only to the two-factor model (positive vs. negative items) but also to a three-factor model. As expected, there was a strong and significant negative correlation between the GHQ-12 and the VS (r = -0.71, P < 0.001).The results showed that the French versions of the 12-item General Health Questionnaire (GHQ-12) and the Subjective Vitality Scale (VS) are reliable measures of psychological distress and vitality. They also confirm a significant negative correlation between these two instruments, lending support to their convergent validity in an elderly French population. The findings indicate that both measures have good structural characteristics.The General Health Questionnaire (GHQ) was developed in England as a screening instrument to identify psychological distress in primary care settings [1]. It was originally designed as a 60-item instrument but several shortened versions are currently available, including the GHQ-30, the GHQ-28, the GHQ-20 and the GH

We consider a destination
country with an aversion toward legal and illegal migration. Candidate migrants
differ in terms of skills level and the legal migrants pay income taxes. There
is a positive probability to become clandestine once a candidate migrant is
rejected. We show that the government will give the priority to candidate
migrants with high skills. We derive the optimal quotas of the legal
immigration and show that the number of legal migrants increases as soon as the
probability of entering into the destination country illegally becomes larger.

Abstract:
Associators were introduced by Drinfel'd in as a monodromy representation of a KZ equation. Associators can be briefly described as formal series in two non-commutative variables satisfying three quations. These three equations yield a large number of algebraic relations between the coefficients of the series, a situation which is particularly interesting in the case of the original Drinfel'd associator, whose coefficients are multiple zetas values. In the first part of this paper, we work out these algebraic relations among multiple zeta values by direct use of the defining relations of associators. While well-known for the first two relations, the algebraic relations we obtain for the third (pentagonal) relation, which are algorithmically explicit although we do not have a closed formula, do not seem to have been previously written down. The second part of the paper shows that if one has an explicit basis for the bar-construction of the moduli space of genus zero Riemann surfaces with 5 marked points at one's disposal, then the task of writing down the algebraic relations corresponding to the pentagon relation becomes significantly easier and more economical compared to the direct calculation above. We also discuss the explicit basis described by Brown and Gangl, which is dual to the basis of the enveloping algebra of the braids Lie algebra.

Abstract:
In this paper, the author constructs a family of algebraic cycles in Bloch's cubical cycle complex over the projective line minus three points which are expected to correspond to multiple polylogarithms in one variable. Elements in this family are in particular equidimensional over the projective line minus three points. In weight greater or equal to $2$, they are naturaly extended as equidimensional cycle over the affine line. This allows to consider their fibers at the point 1 and this is one of the main differences with Gangl, Goncharov and Levin work where generic arguments are imposed for cycles corresponding to multiple polylogarithms in many variables. Considering the fiber at 1 make it possible to think of these cycles as corresponding multiple zeta values. After the introduction, the author recalls some properties of Bloch's cycle complex, presents the strategy and enlightens the difficulties on a few examples. Then a large section is devoted to the combinatorial situation which is related to the combinatoric of trivalent trees and to a differential on trees already introduced by Gangl Goncharov and Levin. In the last section, two families of cycles are constructed as solution to a "differential system" in Bloch cycle complex. One of this families contains only cycles with empty fiber at 0 and should correspond to multiple polylogarithms while the other contains only cycles empty at 1. The use of two such families is required in order to work with equidimimensional cycles and to insure the admissibility condition.

Abstract:
In a previous work, the author have built two families of distinguished algebraic cycles in Bloch-Kriz cubical cycle complex over the projective line minus three points. The goal of this paper is to show how these cycles induce well-defined elements in the $\HH^0$ of the bar construction of the cycle complex and thus generated comodules over this $\HH^0$, that is a mixed Tate motives as in Bloch and Kriz construction. In addition, it is shown that out of the two families only ones is needed at the bar construction level. As a consequence, the author obtains that one of the family gives a basis of the tannakian coLie coalgebra of mixed Tate motives over $\ps$ relatively to the tannakian coLie coalgebra of mixed Tate motives over $\Sp(\Q)$. This in turns provides a new formula for Goncharov motivic coproduct, which arise explicitly as the coaction dual to Ihara action by special derivations.

Abstract:
This paper proves a "new" family of functional equations (Eqn) for Rogers dilogarithm. These equations rely on the combinatorics of dihedral coordinates on moduli spaces of curves of genus 0, M 0,n. For n = 4 we find back the duality relation while n = 5 gives back the 5 terms relation. It is then proved that the whole family reduces to the 5 terms relation. In the author's knownledge, it is the first time that an infinite family of functional equations for the dilogarithm with an increasing number of variables (n -- 3 for (Eqn)) is reduced to the 5 terms relation.

Abstract:
In a recent work, the author has constructed two families of algebraic cycles in Bloch cycle algebra over the prjective line minus 3 points that are expected to correspond to multiple polylogarithms in one variable and have a good specialization at 1 related to multiple zeta values. This is a short presentation, by the way of toy examples in low weight (5), of this contruc- tion and could serve as an introduction to the general setting. Working in low weight also makes it possible to push ("by hand") the construction further. In particular, we will not only detail the construction of the cycle but we will also associate to these cycles explicit elements in the bar construction over the cycle algebra and make as explicit as possible the "bottow-left" coefficient of the Hodge realization periods matrix. That is, in a few relevant cases we will associated to each cycles an integral showing how the specialization at 1 is related to multiple zeta values. We will be particularly interested in a new weight 3 example .

Abstract:
Upper bounds for rates of convergence of posterior distributions associated to Gaussian process priors are obtained by van der Vaart and van Zanten in [14] and expressed in terms of a concentration function involving the Reproducing Kernel Hilbert Space of the Gaussian prior. Here lower-bound counterparts are obtained. As a corollary, we obtain the precise rate of convergence of posteriors for Gaussian priors in various settings. Additionally, we extend the upper-bound results of [14] about Riemann-Liouville priors to a continuous family of parameters.

Abstract:
The goal of this article is to give an elementary proof of the double shuffle relations directly for the Goncharov and Manin motivic multiple zeta values. The shuffle relation is straightforward, but for the stuffle we use a modification of a method first introduced by P. Cartier for the purpose of proving stuffle for the real multiple zeta values via integrals and blow-up sequences.

Abstract:
The aim of this paper is to give a result concerning the stability properties of the solutions of magnetohydrodynamics equations at small but finite Reynolds numbers. These solutions are found using the alpha-effect: this method gives us solutions which are highly oscillating spatially on the scale of the underlying flow but are growing on a larger scale depending on a parameter epsilon. We prove nonlinear stability and instability results for a dense subset of initial velocity field of the flow at given Reynolds number.