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We try to identify -- in a learning situation -- clues related to the emergence of invariants related to three concepts of the field of physical sciences (mass, moment of a force, chemical element). We seek and analyze within the didactic interactions (more particularly the exchanges of representations between actors), the relevance of the indices, pathways that characterize and give meaning to the construction of the concepts. [ABSTRACT FROM AUTHOR]

The dynamic relationship between invariant and scientific concept is apt in the case of the concepts within physical science (physics).It is relevant as much for the understanding as for the construct of the concept itself and can thus become the very core of the learning process. Furthermore it represents a cross-disciplinary approach and as such should be part of the training of teachers. [ABSTRACT FROM AUTHOR]

Résumé: The remarkable consequences of the Yukawa particle, theoretically proposed in 1935, are reviewed. The production, the decay and the intrinsic structure of the Yukawa particle opened new frontiers with laws and regularities which brought us to the discovery of subnuclear physics and now to the Quark-Gluon-Coloured-World (QGCW). [Copyright &y& Elsevier]

The modelling of homogeneous turbulent flows with mean rotatio, considered in a previous Note, is handled under the form M*=M[b,y,Q*] in terms of componental and dimensional anisotropies, and of the symmetrized stropholysis. A systematic technique of expansion is proposed. The necessary realisability conditions are then applied. It is shown that there exists no realisable functional M which would be isotropic with respect to its arguments. To cite this article: J. Piquet, C. R. Mecanique 331 (2003). [Copyright &y& Elsevier]

The anthropogenic emissions of greenhouse gases should result in a marked warming of the Planet. Although quantitatively uncertain, this message is well apprehended by the society. Development of more investigations upon future climate and sources of energy should help to limit the extensiveness of this risk. To cite this article: C. Lorius, C. R. Geoscience 335 (2003). [Copyright &y& Elsevier]

If the physical sciences were the cradle of modelling approaches, now almost all disciplines are concerned by this methodology. First based on mathematical language, the modelling formalisms become more and more diverse. Computer sciences contribute widely to the extension of the methodology at two levels : the first to make easier the use of mathematical models, the second to develop new formalisms, such as cellular automata or neural networks. The fields of basic and applied research on the environment and related technological developments give good examples of applications of this methodology, from global modelling at the planet level, for example for the study of climate changes, to local and specialised models, for example in population dynamics or water transfers in soils. Models are also developed to reach various goals : in basic research, to understand how environmental systems work, in technological development, to design adapted techniques, and in decision making process, as an argument, among others, to elaborate a decision. The recent expansion of modelling, to almost all disciplines implied in environmental research, makes it also a tool in interdisciplinary dialog. The model becomes a link between disciplines, for example between natural and social sciences, by combining dynamics of ecological and social systems. But the use of models is not exempt of hazards. Used in bad conditions, off its limits of validity, or running with a deficient simulator, it may lead to incorrect results. It may also be a screen to hide an insufficient knowledge. It such cases, it can be a wrong decisive argument in decision process or to lead to a bad technical device or protocol. Anyway, built and used carefully it is a precious and efficient tool. So, the state of the art and actual methodological problems and applications in environmental basic and technical research are presented. The foreseeable advances and endeavours are also envisaged. The text is essentially illustrated by examples developed by scientists and engineers of the Cemagref. Finally, the environment is an example of a complex system. Modelling is a good tool for complexity analysis and methodological advances in environmental research would be useful for other systems which are qualified “complex”, and then have a larger range of application than studies on environment. [Copyright &y& Elsevier]

Les Sphériques ont été écrites par Ménélaos sous la forme d’un traité d’apparence purement mathématique. Cependant, la matière qui y est développée dans les deuxième et troisième livres est étroitement liée à des problèmes rencontrés en astronomie: calcul des coordonnées équatoriales du Soleil, établissement de tables d’ascensions, étude du mouvement du Soleil dans la sphère oblique, levers simultanés. Ce lien, qui demeure implicite dans le texte, a été mis en évidence par deux mathématiciens et astronomes arabo-musulmans, qui ont exposé la signification astronomique de certains théorèmes des Sphériques. Nous présenterons, commenterons et complèterons cette explicitation en classant les théorèmes concernés en trois groupes: sens de variation de certaines grandeurs sur la sphère, propositions de trigonométrie sphérique et applications, sens de variation de rapports entre certaines grandeurs sur la sphère. The Spherics were written by Menelaos in the form of a purely mathematical treatise. However, the material developed in the second and third book is closely linked to problems met in astronomy: computation of equatorial coordinates of the Sun, setting up of rising-time tables, study of the motion of the Sun in the sphaera obliqua, simultaneous risings. This link, which remains implicit in the text, was clearly displayed by two arabo-islamic mathematicians and astronomers, who expounded the astronomical meaning of some theorems of the Spherics. We describe, comment and complement their explanations, by classifying the implications of the theorems in three groups: direction of variation of some quantities on the sphere, spherical trigonometry and applications, direction of variation of ratios of some quantities on the sphere. [ABSTRACT FROM AUTHOR]