Note: Axiomatic Derivation of the Doppler Factor and Related Relativistic Laws

The formula for the relativistic Doppler effect is investigated in the context of two compelling invariance axioms. The axioms are expressed in terms of an abstract operation generalizing the relativistic addition of velocities. We prove the following results. (1) If the standard representation for the operation is not assumed a priori, then each of the two axioms is consistent with both the relativistic Doppler effect formula and the Lorentz-Fitzgerald Contraction. (2) If the standard representation for the operation is assumed, then the two axioms are equivalent to each other and to the relativistic Doppler effect formula. Thus, the axioms are inconsistent with the Lorentz-FitzGerald Contraction in this case. (3) If the Lorentz-FitzGerald Contraction is assumed, then the two axioms are equivalent to each other and to a different mathematical representation for the operation which applies in the case of perpendicular motions. The relativistic Doppler effect is derived up to one positive exponent parameter (replacing the square root). We prove these facts under regularity and other reasonable background conditions.Comment: 12 page

Knowledge Spaces and Learning Spaces

How to design automated procedures which (i) accurately assess the knowledge of a student, and (ii) efficiently provide advices for further study? To produce well-founded answers, Knowledge Space Theory relies on a combinatorial viewpoint on the assessment of knowledge, and thus departs from common, numerical evaluation. Its assessment procedures fundamentally differ from other current ones (such as those of S.A.T. and A.C.T.). They are adaptative (taking into account the possible correctness of previous answers from the student) and they produce an outcome which is far more informative than a crude numerical mark. This chapter recapitulates the main concepts underlying Knowledge Space Theory and its special case, Learning Space Theory. We begin by describing the combinatorial core of the theory, in the form of two basic axioms and the main ensuing results (most of which we give without proofs). In practical applications, learning spaces are huge combinatorial structures which may be difficult to manage. We outline methods providing efficient and comprehensive summaries of such large structures. We then describe the probabilistic part of the theory, especially the Markovian type processes which are instrumental in uncovering the knowledge states of individuals. In the guise of the ALEKS system, which includes a teaching component, these methods have been used by millions of students in schools and colleges, and by home schooled students. We summarize some of the results of these applications

Relation between the weak itinerant magnetism in A2A_2Ni7_7 compounds (AA = Y, La) and their stacked crystal structures

The weak itinerant magnetic properties of $A_2$Ni$_7$ compounds with $A$ = {Y, La} have been investigated using electronic band structure calculations in the relation with their polymorphic crystal structures. These compounds crystallizes in two structures resulting from the stacking of two and three blocks of [$A_2$Ni$_4$ + 2 $A$Ni$_5$] units for hexagonal $2H$-La$_2$Ni$_7$ (Ce$_2$Ni$_7$ type) and rhombohedral $3R$-Y$_2$Ni$_7$ (Gd$_2$Co$_7$ type) respectively. Experimentally, $2H$-La$_2$Ni$_7$ is a weak itinerant antiferromagnet whereas $3R$-Y$_2$Ni$_7$ is a weak itinerant ferromagnet. From the present first principles calculation within non-spin polarized state, both compounds present an electronic density of state with a sharp and narrow peak centered at the Fermi level corresponding to flat bands from $3d$-Ni. This induces a magnetic instability and both compounds are more stable in a ferromagnetic (FM) order compared to a paramagnetic state ($\Delta E \simeq$ -35 meV/f.u.). The magnetic moment of each of the five Ni sites varies with their positions relative to the [$A_2$Ni$_4$] and [$A$Ni$_5$] units: they are minimum in the [$A_2$Ni$_4$] unit and maximum at the interface between two [$A$Ni$_5$] units. For $2H$-La$_2$Ni$_7$, an antiferromagnetic (AFM) structure has been proposed and found with an energy comparable to that of the FM state. This AFM structure is described by two FM unit blocks of opposite Ni spin sign separated by a non-magnetic layer at z = 0 and $\frac12$. The Ni ($2a$) atoms belonging to this intermediate layer are located in the [La$_2$Ni$_4$] unit and are at a center of symmetry of the hexagonal cell ($P6_3/mmc$) where the resultant molecular field is cancelled. Further non-collinear spin calculations have been performed to determine the Ni moment orientations which are found preferentially parallel to the $c$ axis for both FM and AFM structures.Comment: 19 pages, 7 figures, 2 table

Solving stochastic differential equations with Cartan's exterior differential systems

The aim of this work is to use systematically the symmetries of the (one dimensional) bacward heat equation with potentiel in order to solve certain one dimensional It\^o's stochastic differential equations. The special form of the drift (suggested by quantum mechanical considerations) gives, indeed, access to an algebrico-geometric method due, in essence, to E.Cartan, and called the Method of Isovectors. A V singular at the origin, as well as a one-factor affine model relevant to stochastic finance, are considered as illustrations of the method

Short Note on the Unemployment Rate of the “French overseas regionsâ€

This article analyzes the hysteresis hypothesis in the unemployment rates of the four “French overseas regions†(Guadeloupe, Martinique, Guyana, Reunion) [FORs] over the period 1993-2008. We use standard univariate and panel unit root tests, among them Choi (2006) and Lopez (2009) that account for cross-sectional dependence and have improved performance when the number of countries and the time dimension of the data are limited. Our results cannot reject the null hypothesis of a unit root and so find evidence supporting hysteresis in the unemployment rates for the FORs.Hysteresis, Unemployment, Panel unit root test, cross-section dependence, convergence

A reliable system for the transformation of cantaloupe charentais melon (Cucumis melo L. var. cantalupensis) leading to a majority of diploid regenerants

An efficient system of transformation leading to a majority of transformed diploid plants from leaf explants of Cucumis melo L. var. Cantalupensis (cv. Védrantais) was developed. Several regeneration protocols using cotyledon or leaf explants were analysed with particular emphasis on the regeneration efficiency and the ploidy level of the regenerated melon plants. The use of leaf explants excised from 10 day-old seedlings, cultured in Murashige and Skoog's medium supplemented with 1 mM 6-benzylaminopurine (BAP) and 1 mM 6-(g,g-dimethylallylamino)-purine (2iP), resulted in a high regeneration frequency (73%). In these conditions, more than 84% of the regenerated plants were found to be diploid. Addition of an Agrobacterium-mediated transformation step did not significantly change the percentage (81.8%) of diploid plants regenerated. This protocol was successfully used to produce diploid transgenic melon plants expressing the antisense ACC oxidase gene, encoding ACC oxidase which catalyses the last step of ethylene biosynthesis. Ethylene production and ACC oxidase activity of the leaf explants from transgenic plants was reduced by more than 80% as compared to the control untransformed tissues. This transformation/ regeneration method could be routinely used for the introduction of other genes of interest in melon

Propositions méthodologiques pour l'étude des feux agro-sylvo-pastoraux en montagne pyrénéenne. Evaluation qualitative et quantitative des résidus d'incendies à partir des analyses pédo-anthracologiques

International audienceNous proposons dans cet article une réflexion méthodologique autour de la représentativité qualitative et quantitative des charbons dans les sols provenant de pratiques pastorales et agricoles du feu dans les Pyrénées. Nous exposons ici une méthode d’étude des charbons provenant des feux actuels et récents dans le but d’établir un référentiel permettant de clarifier la lecture des diagrammes anthracologiques. Aucun résultat n’est présenté ici car les analyses sont en cours, mais notre démarche vise à montrer l’importance de la connaissance des pratiques de feux pour mieux comprendre la représentation de leurs vestiges carbonés. Il est essentiel de partir de ce que l’on peut vérifier aujourd’hui afin d’interpréter les données paléo-environnementales. Chaque site d’étude, la forêt d’Antenac (Luchon, Haute-Garonne) et le Pays de Sault (Aude, Ariège), ont été sélectionnés en fonction des fréquences de feux connues pour le premier, et des travaux éco-historiques fournissant des cartes détaillées sur les formations forestières, les landes et les défrichements depuis la Réformation de 1669 jusqu’à l’actuel, pour le second. Chaque site a été traité selon un protocole expérimental spécifique présenté dans cet article

gouvernement a raison d'alléger l'impôt.

Cette publication n'a pas de résumé