Remarques sur l'expression de la généralité en mathématiques

International audienceThis paper gives a condition of the expression of generality in mathematics from the application of Löwenheim-Skolem theorem to Zermelo's axioms. It gives an example of an "expression problem" from Gauss's Disquisitiones Arithmeticae and caracterizes the used of sets in it.L'article dégage une condition de l'expression de la généralité en mathématiques à partir de l'application du théorème de Löwenheim-Skolem aux axiomes de Zermelo. Il donne un exemple de "problème d'expression" à partir des Disquisitiones Arithmeticae de Gauss, dégageant ainsi une condition du recours aux ensembles

The Ectoparasites of Some of the Rodents in the Vicinity of Brookings, South Dakota

The animals known as rodents furnish very satisfactory material for the study of parasite infestations. Because parasites of rodents as well as the rodents themselves are unusually interesting, many examinations have been made, by students, of the parasites and their hosts. These investigations have, no doubt, been facilitated by the small size, abundance, and comparative ease with which these rodents can be captured. Rodents are economically important in that they themselves are injurious in doing damage to fields, crops, and forests and are responsible for looses running into the thousands of dollars annually. Also many rodents harbor parasites which are and have been responsible for the spread of infectious diseases through bacteria and fungi

Libration driven multipolar instabilities

We consider rotating flows in non-axisymmetric enclosures that are driven by libration, i.e. by a small periodic modulation of the rotation rate. Thanks to its simplicity, this model is relevant to various contexts, from industrial containers (with small oscillations of the rotation rate) to fluid layers of terrestial planets (with length-of-day variations). Assuming a multipolar $n$-fold boundary deformation, we first obtain the two-dimensional basic flow. We then perform a short-wavelength local stability analysis of the basic flow, showing that an instability may occur in three dimensions. We christen it the Libration Driven Multipolar Instability (LDMI). The growth rates of the LDMI are computed by a Floquet analysis in a systematic way, and compared to analytical expressions obtained by perturbation methods. We then focus on the simplest geometry allowing the LDMI, a librating deformed cylinder. To take into account viscous and confinement effects, we perform a global stability analysis, which shows that the LDMI results from a parametric resonance of inertial modes. Performing numerical simulations of this librating cylinder, we confirm that the basic flow is indeed established and report the first numerical evidence of the LDMI. Numerical results, in excellent agreement with the stability results, are used to explore the non-linear regime of the instability (amplitude and viscous dissipation of the driven flow). We finally provide an example of LDMI in a deformed spherical container to show that the instability mechanism is generic. Our results show that the previously studied libration driven elliptical instability simply corresponds to the particular case $n=2$ of a wider class of instabilities. Summarizing, this work shows that any oscillating non-axisymmetric container in rotation may excite intermittent, space-filling LDMI flows, and this instability should thus be easy to observe experimentally

Libration-driven multipolar instabilities

We consider rotating flows in non-axisymmetric enclosures that are driven by libration, i.e. by a small periodic modulation of the rotation rate. Thanks to its simplicity, this model is relevant to various contexts, from industrial containers (with small oscillations of the rotation rate) to fluid layers of terrestrial planets (with length-of-day variations). Assuming a multipolar $n$ -fold boundary deformation, we first obtain the two-dimensional basic flow. We then perform a short-wavelength local stability analysis of the basic flow, showing that an instability may occur in three dimensions. We christen it the libration-driven multipolar instability (LDMI). The growth rates of the LDMI are computed by a Floquet analysis in a systematic way, and compared to analytical expressions obtained by perturbation methods. We then focus on the simplest geometry allowing the LDMI, a librating deformed cylinder. To take into account viscous and confinement effects, we perform a global stability analysis, which shows that the LDMI results from a parametric resonance of inertial modes. Performing numerical simulations of this librating cylinder, we confirm that the basic flow is indeed established and report the first numerical evidence of the LDMI. Numerical results, in excellent agreement with the stability results, are used to explore the nonlinear regime of the instability (amplitude and viscous dissipation of the driven flow). We finally provide an example of LDMI in a deformed spherical container to show that the instability mechanism is generic. Our results show that the previously studied libration-driven elliptical instability simply corresponds to the particular case $n= 2$ of a wider class of instabilities. Summarizing, this work shows that any oscillating non-axisymmetric container in rotation may excite intermittent, space-filling LDMI flows, and this instability should thus be easy to observe experimentall

Archeologische onderzoek Oostakker R4 Eksaarderijweg

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La fonction inaugurale de La Géométrie de Descartes

International audienceThis paper introduces the notions of inaugural texts and inaugural statements and applied them to La Géometrie of Descartes. Some consequences of the existence of this kind of texts and statements are given for mathematics and their history.Cet article introduit les notions de textes et d'énoncés inauguraux et les applique à La Géométrie de Descartes. Quelques conséquences sur les mathématiques et leur histoire sont ensuite tirées de l'existence de tels textes et de tels énoncés