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In this paper we classify pairs of holomorphic foliations with a common leaf in a neighborhood of one of its points. [ABSTRACT FROM AUTHOR]

About 4 million people live on the alluvial plain of the Loire, the main river located in the centre of France. Their protection against flooding is mainly based on the construction of 650 km of old levees. During the last 100 year flood of the nineteenth century, these levees were repeatedly broken. This led to catastrophic flooding, especially in the Val d'Orléans. No new 100 year flood occurred during the twentieth and twentyfirst centuries and the likely response of these old levees to future major floods is poorly understood. Located midway along the river, the study area is 35 km long and 1-7 km wide. It is protected by 42 km of embankments that have already suffered 35 breaches. In the Val d'Orléans, 6-10 m of sandy alluvium cover a karstified limestone bedrock. Nearly 600 collapses were reported whose diameter varies from 0.50 to 18 m. 62 % occurred at <2 km from the river, that is to say, close to the levees. Statistically, 35 collapses should have occurred on the levees but only ten of them have been observed. No major consequences resulted because these collapses did not occur during a flood event. The question that arises here is to estimate the potential role of karst in levees breaches occurring during flooding. However, most of these collapses appeared in the nineteenth and early twentieth centuries and the role of karst was not looked at. The risk scenario is as follows: the Loire flooding causes karst flooding (because kasrtic channels are connected to the river), which induces or reactivates collapses. For the 'karst collapse' hazard, some predisposing factors can be listed: density of ancient collapses, thickness and nature of the alluvium, hydroclimatic conditions (frost, snow, heavy rain, floods, low water period etc.). This paper examines this issue and seeks to determine the potential role of karst in the levee breaches. The intensity and probability of this hazard is then characterised. Several mechanisms of levee instability, potentially due to karst, are reviewed. If a causal link between flood, karst and collapse is established, it will enable us to monitor the risk of breaches during the next major flood. [ABSTRACT FROM AUTHOR]

Teacher attrition: state of knowledge - At a time when a number of countries are concerned about teacher shortages, the question arises why so many teachers are leaving the profession. This review of the literature, based on the analysis of 69 scientific papers (containing either empirical data or rigorous theoretical analysis) specifically aims to provide answers to this question by identifying the factors involved in teacher attrition. The listed factors are divided into three categories (factors related to teaching tasks, to the teacher or to the social environment), and then examined in the conclusion. [ABSTRACT FROM AUTHOR]

This paper deals with codimension one (may be singular) foliations on compact Kälher manifoldswhose conormal bundle is assumed to be pseudo-effective. Using currents with minimal singularities, we show that one can endow the space of leaves with a metric of constant non positive curvature wich may degenerate on a 'rigidly' embedded invariant hypersurface. [ABSTRACT FROM AUTHOR]

Augustin-Louis Cauchy published most of his arithmetical research between 1829 and 1840. These are however only mentioned in some number theory history centered on reciprocity laws or on theory of algebraic numbers. They are described as containing some results similar to those of Gauss, Jacobi and Dirichlet but in a incomplete and disorganized way. The objective of this paper is to present an analysis of Cauchy's arithmetical texts published between 1829 and 1840 to show that they contain a rather consistent set of results related to quadratic forms 4pu = x2 + ny2, where p is a prime and n a divisor of p-1. We will also discuss the particular form of this body of texts and the strategy we used to find the guidelines of the work of Cauchy.

IsomonodromicdeformationsofFuchsianequationsoforder2onRiemann sphere are parameterized by the solutions of Garnier system. The purpose of this paper is to construct algebraic solutions exotic, i.e. corresponding to deformations of Fuchsian equation with Zariski dense monodromy. Specifically, we classify all the algebraic solutions (complete) exotic constructed by the method of pull-back of Doran-Kitaev: they are deduced from the data isomonodromic deformations pulling back a Fuchsian equation E given by a family of branched coverings ϕ. We first introduce the structures and associated orbifoldes underlying Fuchsian equation. This allows us to have are fined version of the Riemann Hurwitz formula that allows us quickly to show that E must be hypergeometric. Then we come to limit the degree of ϕ and exponents, and finally to Painlevé VI. We explicitly construct one of these solutions. [ABSTRACT FROM AUTHOR]

Borders, translation and politics of difference: the hermeneutic task of comparative education - Governments are making increasing use of international comparisons as a tool to run and reform education systems, through the establishment of competency norms and assessment standards. In light of this trend, this paper wishes not only to reiterate the crucial distinction, made by Max Weber as early as 1922, between scientific research and political action, but also to recall the principles of separation and mediation from which the comparative approach in education derives. The concepts that comprise a language, that are disseminated and become established in a social world, are borne of history, of dynamic uses, and are culturally rooted. By neglecting this social and cultural provenance of words there is a danger that one can end up with a comparability based on functional equivalencies alone; although there are strong pressures in this direction, it is probably the surest way, in the words of Marcel Détienne, of 'comparing the incomparable'. The purely instrumental rationality that favours the spread of such frameworks or interpretative models appears indifferent to questions of meaning and culture, apart from being irrational on an axiological level, if we follow Weber. Strangeness or even 'otherness' tends to be erased. One wonders therefore what issues are raised for the comparativist when the illusion of spontaneity in translation is reduced to a functional equivalence. In keeping with the researcher's responsibility to mediate, he/she must promote clarification and mutual understanding (inspired by C. Taylor), replacing the standardisation of words with a critical illumination of the semiotic variations generated by their use. [ABSTRACT FROM AUTHOR]

Mutualism is a biological association for a mutual benefit between two different species. In this paper, firstly, we examine the history and signification of mutualism in relation to symbiosis. Then, we consider the link between concepts and models of mutualism. Models of mutualism depend on different concepts we use: If mutualism is situated at populations' level, it will be expressed by Lotka-Volterra models, concerning exclusively populations' size. If mutualism is considered as a resources' exchange or a biological market increasing the fitness of these organisms, it will be described at an individual level by a cost-benefit model. Our analysis will be limited to the history and epistemology of Lotka-Volterra models and we hypothesize that these models are adapted at first to translate dynamic evolutions of mutualism. They render stability or variations of size and assume that there are clear distinctions and a state of equilibrium between populations of different species. Italian mathematician.Vito Volterra demonstrated that biological associations consist in a constant relation between some species. In 1931 and 1935, Volterra described the general form of antagonistic or mutualistic biological associations by the same differential equations. We recognize that these equations have been more used to model competition or prey-predator interactions, but a simple sign change allows describing mutualism. The epistemological problem is the following: Volterra's equations help us to conceptualize a global phenomenon. However, mutualistic interactions may have stronger effects away from equilibrium and these effects may be better understood at individual level. We conclude that, between 1985 and 2000, some researchers carried on working and converting Lotka-Volterra models but this description appeared as insufficient. So, other researchers adopted an economical viewpoint, considering mutualism as a biological market. [ABSTRACT FROM AUTHOR]

At the beginning of the 1890s, Schwarz and Peano (independently of each other) showed that Serret’s definition of the area of a surface was flawed. This paper first aims at describing the various methods that the mathematicians have used for correcting Serret’s reasoning; its second goal is to compare and to present more in detail two solutions: Lebesgue’s notorious construction and Peano’s definition. [ABSTRACT FROM AUTHOR]

This paper reflects on the teaching of mathematics in Quebec, pointing to some of its successes and some of its difficulties. Prospects for the future are examined at a moment when a new curriculum in mathematics education, centred on the development of competencies, has been put in place in primary schools and is being introduced in high schools. This article focuses not only on the prescriptions and content of this curriculum but also on the representations of mathematics built by teachers and their students and more globally by the population. This portrait permits us to understand certain tendencies, present in Quebec but also in other countries in the world, particularly a tendency to lower the demands made of mathematics students. The analysis also suggests some strategies for resisting these tendencies so as to have a positivie effect. [ABSTRACT FROM AUTHOR]

In many countries, school curricula are now structured on a principle called the shifting of competencies. This paper illustrates one possible by-product of this shifting of competencies, observed in Belgium but probably true in other countries, regardless of the specific nature of this reform. This consists in some misuse of the concept of problem situation as diametrically opposed to the concept of adidactical situation. [ABSTRACT FROM AUTHOR]

After a short presentation of historical and sociocultural elements, common to different educational systems in countries from the Maghreb, the paper centres on the essential developments that have led to new reforms in these countries. In conclusion, a brief presentation of the orientations of these reforms, with some remarks on their application in practice, is developed. [ABSTRACT FROM AUTHOR]

In French secondary education, the place of arithmetic—the arena of numbers par excellence—has varied greatly, both qualitatively and quantitatively, over the history of the curriculum. After spending years in mothballs, it reappeared in 1998 in the curriculum for the terminale (18 years-old, Grade 12) science course and in the enseignement de spécialité (enriched education with three possible concentrations) and has, since then, also figured in the courses of the troisième (15 years-old. Grade 9) and the seconde (16 years-old, Grade 10). In pan, its reintroduction was a reflection of the concept that arithmetic could foster work on mathematical reasoning. Curricular developments of this kind inevitably bring into play questions of teaching methods. To be specific. Does the type of arithmetic covered in the current terminale curriculum genuinely encourage this type of work, and. if so. what are its specific characteristics? For more than 20 years, a significant amount of education research has taken up questions related to mathematical reasoning and proof—in other words, mathematical rationality. On [he whole, the present study is positioned within this body of research, but at the same time, it adopts as its point of approach the examination of a specific field—namely, arithmetic conceived of as number theory. In contrast to what has occurred in the case of geometry, for obvious cultural reasons, the potentialities offered by this field of learning and the teaching of mathematical rationality seem, in my view, to have been less systematically explored, particularly at the relatively advanced level analyzed here. The answers to the questions posed above are thus far from being self-evident. This is why in this study, the choice has been made to intertwine analyses hearing on epistemology and on teaching methods. The purpose of the epistemological analysis is to provide a basis for studying the characteristics of modes of reasoning that bring into play the arithmetical concepts at stake at this level. The present analysis then goes on to discuss such concepts in terms of a reasoning in arithmetic, so as to fully distinguish it from the arithmetical type of reasoning identified in research on algebra and especially on the arithmetic-algebra transition (Schmidt. 2002). In cases of reasoning in arithmetic, algebraic symbolism functions as a tool that has presumably been mastered with sufficient proficiency by termintate science students. The epistemological analysis is based on the study of historical and present-day arithmetical proofs. Thus, the first part of this article offers an historical demonstration as a means of introducing a tool generated by this same demonstration—that is, on the one hand, a process of differentiation between two, so-called organizing and operative dimensions of reasoning and. on the other, the identification of both components' characteristics. This differentiation and these characteristics served, to evaluate, from the outset, the potentialities of this field for the teaching and learning of mathematical reasoning. The objective of the methods-related analysis was to study the ecology of the potentialities revealed by the epistemological analysis in the curricular context considered here. This particular analysis was conducted along various main threads of inquiry. However, the present article only takes up an analysis of the reasoning of students confronted with arithmetical problem solving. As mathematical reasoning depends not only on the field involved but also on the context within which it is produced, two types of corpora were analyzed: (1) student test paper from a baccalauréat (secondary school graduation certificate) training examination, and (2) the process adopted by a group of students in a classroom situation to produce an arithmetical proof. These two examples serve to demonstrate the relevance, in terms of teaching methods, of the analytical tool resulting from the epistemological research. [ABSTRACT FROM AUTHOR]

The motivation of this work comes from the study of lattices in real simple Lie groups. The famous Margulis’s superrigidity theorem claims that finite dimensional reductive representations of any lattice of a real simple Lie group of real rank ≥2 are superrigid. As a corollary such a lattice is arithmetic. These results extend to the real rank one case for lattices in Sp(n,1) and F4(-20) by the work of Corlette and Gromov-Schoen. On the other hand Mostow and Deligne-Mostow exhibited arithmetic lattices with non-superrigid representations as well as non-arithmetic lattices in the unitary group PU(2,1). A natural question is then to find simple sufficient conditions for superrigidity or arithmeticity of lattices in PU(2,1). Rogawski conjectured the following: let Γ be a torsion-free cocompact lattice in PU(2,1) such that the hyperbolic quotient M=Γ\B2ℂ verifies the cohomogical conditions b1(M)=0 and H1,1(M,ℂ)∩H2(M,ℚ)≃ℚ. Then Γ is arithmetic. In this paper we consider a smooth complex projective surface M verifying the above cohomological assumptions and study Zariski-dense representations of the fundamental group π1(M) in a simple k-group H of k-rank ≤2 (where k denotes a local field). Our main result states that there are strong restrictions on such representations, especially when k is non-archimedean (Theorem 5). We then consider some cocompact lattices in PU(2,1) of special geometric interest: recall that a “fake P2ℂ” is a smooth complex surface (distinct from P2ℂ) having the same Betti numbers as P2ℂ. “Fake P2ℂ” exist by a result of Mumford and are complex hyperbolic quotients Γ\H2ℂ by Yau’s proof of the Calabi conjecture. They obviously verify the hypotheses of Rogawski’s conjecture. In this case we prove that every Zariski-dense representation of Γ in PGL(3) is superrigid in the sense of Margulis (Theorem 3). As a corollary every “fake P2ℂ” is an arithmetic quotient of the ball B2ℂ. [ABSTRACT FROM AUTHOR]

This paper compares anti-hookworm campaigns conducted in the early twentieth century in France, Germany, Brazil and West India. The populations that suffer from hookworm are not identical in the North and in the South. In tropical and semi-tropical regions hookworm is mainly found among poor peasants and is related to lack of hygiene, while in temperate climates hookworm was a professional disease of miners, a highly organized professional segment. Nevertheless, major disparities in the pattern of hookworm control did not reflect the North-South divide, but a difference between campaigns. These aimed at the eradication of hookworm infection (Germany and West-India) and at alleviating the effects of this infection on populations (France and Brazil). Maps that represented the prevalence of hookworm mirrored the aims of the sanitary campaign in which they were used: eradication of parasitic worms versus the reduction of the handicap induced by these worms. In public health as well, representing is intervening. And vice versa: patterns of intervention shape representations. [ABSTRACT FROM AUTHOR]

Abstract--This paper presents some of the elements which have been typical of music in different contexts and cultures, and describes an approach to musical phenomena which relates them to the intercultural and interdisciplinary dimension of lifelong education (music considered as a cultural good, an expression form, a field of creativity, an artistic production and an aesthetic experience). From the educational point of view, the aim is to form ?multi-musical? individuals. In this framework are set the problem of musical identity and the need to spell out that identity in relation to stereotypes (popular music, classical music, folk music, etc.) and the differing shades of diversity. Particular attention needs to be given to the question of the universals seen in the psychology of music and the configuration of musical phenomena as structures which are organized hierarchically in several dimensions. In short, music in all its forms can help to form a dynamic, pluralist identity in the European context. [ABSTRACT FROM AUTHOR]

This paper presents the preliminary results of a recent study comparing the perindopril/indapamide combination treatment with sequential and step by step strategies. The 9-month randomised double-blind study included 533 patients.Patients were shown to have better blood pressure control without adverse effects following treatment with the perindopril/indapamide combination than with the sequential strategy of atenolol (50 mg) then losartan (50 mg) then amlodipine (5 mg) or with the step-by-step strategy of valsartan (40 mg then 80 mg, then 80 mg plus hydrochlorothiazide 12.5 mg). In addition, the perindopril/indapamide combination was shown to induce significantly greater control of systolic blood pressure levels with comparable effects on diastolic blood pressure. [ABSTRACT FROM AUTHOR]