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Copyright of ERA Forum is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of ERA Forum is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of ERA Forum is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Mathematische Annalen is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of ERA Forum is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of International Review of Education / Internationale Zeitschrift für Erziehungswissenschaft is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Israel Journal of Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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

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The article focuses on the presentation of arithmetic fractions in the work of Italian mathematician Leonardo Fibonacci. Topics discussed include Fibonacci's work in arithmetic and practical and abstract problems in geometry; calculations based on the use of the Hindu-Arabic numerals and positional decimal system by Fibonacci; and the relationship between mathematicians and mathematical works of Islamic countries and Fibonacci.

Copyright of Czechoslovak Mathematical Journal is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Mathematische Zeitschrift is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

Copyright of ERA Forum is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of International Review of Education / Internationale Zeitschrift für Erziehungswissenschaft is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Lettre de Medecine Physique et de Readaptation is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

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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.

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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]

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Copyright of Recherche Transports Sécurité is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Recherche Transports Sécurité is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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Copyright of Mathematische Annalen is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Recherche Transports Sécurité is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Recherche Transports Sécurité is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Recherche Transports Sécurité is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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Let F be a field of characteristic not 2. In this article, we treat the quadratic forms of Im( W( F) → W( F( φ))) which are indecomposable, i.e., those which are not isometric to a sum of two nonzero forms of this image, where W( F) is the Witt ring of F-quadratic forms, and F( φ) is the function field of the affine quadric given by φ. This is related to the descent problems studied in [, ]. More precisely, we will focus on indecomposable quadratic forms of minimal dimension, which we detail for φ of dimension less than or equal to 8. We also include other related results. [ABSTRACT FROM AUTHOR]

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