Realization of an OpenMath Server for REDUCE

Various approaches and standards for transferring mathematical objects between different computer programs in multimedia environment in the framework of the OpenMath project are described. The use of these standards might revolutionize the exchange of mathematical information caused by the development of computer algebra tools and telecommunication possibilities. The standards make it possible to create databases and easily save and use mathematical objects obtained in different applications, e.g., to exchange the data obtained in different computer algebra systems and place information on the Internet. Bibliography: 9 titles.     

Pourquoi, pour qui enseigner les mathématiques? Une mise en perspective historique de l’évolution des programmes de mathématiques dans la société française au XXe siècle

Evolutions of mathematical curricula in French society have been marked by the successive answers intitutions have given to the following question since one century: Why and whom teaching mathematics? Here I present two of these, one given in 1908 and one in 1967. Each symbolises a breaking period of reforms in secondary mathematics teaching in France. We will see in the two first part of this paper that they belong to two different worlds, with social, institutional, ideological and mathematical specific features. In the third part, I’ll focus on geometry, showing the effects of the different answers concerning the public and the aims of mathematical teaching.     

Closure laws for a two-fluid two-pressure modelLois de fermeture pour un modèle à deux pressions d'écoulement diphasique

Closure laws for interfacial pressure and interfacial velocity are proposed within the frame work of two-pressure two-phase flow models. These enable us to ensure positivity of void fractions, mass fractions and internal energies when investigating field by field waves in the Riemann problem. To cite this article: F. Coquel et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 927–932.     

Towards a characterization of generalized twisted field planes

In this work we study semifield planes of orderq ⁿ(q=p ^r ,p prime) with a collineation whose order is ap-primitive divisor ofq ⁿ–1.Research supported in part by NSF Grant No. DMS-9107372Research supported in part by NSF grants RII-9014056, component IV of the EPSCoR of Puerto Rico grant and ARO grant for Cornell MSI.     

An aqueous route to organically functionalized silica diatom skeletons

Diatomaceous earth was functionalized by grafting organotrialkoxysilane precursors onto the surface of the porous silica cell walls of this biomineral. Vinyl- and mercapto-containing structures were prepared in aqueous media without disruption of the diatomic architecture. Successful grafting of the organic moieties was confirmed using solid state ²⁹Si MAS NMR spectroscopy, and the presence of the intact diatom framework by scanning electron microscopy. The sorption properties of mercaptopropyl-functionalized diatoms towards heavy metals was studied by measuring the accessibility and diffusion rates of mercury(II) species to the binding sites (-SH) by the means of electrochemical methods.     

Dendrimers and combinatorial chemistry—tools for fluorescent enhancement in protease assays

FRET based systems are some of the best methods available to detect and monitor proteolytic activity. To enhance fluorescent signals and hence assay sensitivity, two different systems were developed using two different dendrimeric constructs. In the first case, a triple branched dendrimer bearing three dansyl groups was used to enhance assay sensitivity and showed a significant enhancement of fluorescence following enzymatic cleavage. In another example, a tris-fluorescein probe, that undergoes self-quenching, was utilized in a combinatorial library synthesis to map the substrate specificity of proteases.     

Construction of nonanuclear supramolecular structures from simple modular units

A porphyrazine based supramolecule with a nonanuclear structure has been prepared by the ready coordination of pyridine donor sites in octakis(4-pyridoxyethylthio)porphyrazinatomagnesium with vanadyl bis(acetylacetonate) and characterized by EPR spectroscopy.     

Un modèle mathématique de cyclone

The source waves are some particular solutions to genuinely non linear hyperbolic systems with a source term, whose propagation velocity is a constant determined by the roots of this source term. We propose a system of 2 equations on a 2 dimension space, which model the velocity field of the atmosphere near the ground. The source term is made of three parts: a given pressure gradient, a friction or aspiration effect and the Coriolis force. In the case where these parameters are constant, we build a solution which is a constant outside a circular crown. The internal circle represents the eye's wall of the hurricane and corresponds to a share shock wave. The external circle is a set generating the bifurcation which actually models the hurricane. To cite this article: A.-Y. LeRoux et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Contractibility of Efficient Frontier of Simply Shaded Sets

In finite dimensional Euclidean space, we prove the contractibility of the efficient frontier of simply shaded sets. This work extends the result of Peleg [7], which confirms the contractibility of the efficient frontier in the convex case.     

Fracture strength of class II slot cavities restored with polymerizable restorative materials

This study compared the fracture strength of Class II slot cavities restored with polymerizable restorative materials. Sixty, caries-free, posterior teeth were divided into five groups of 12 teeth. The Class II slot cavities were prepared. The teeth were restored with two packable composites (Filtek P60, Surefil), a microhybrid composite (Filtek Z250)and two ormocer (Definite, Admira). The restorations were then subjected to fracture resistance tests. The marginal ridges of the restorations were loaded at an angle of 13.5° to the long axis of the tooth in an Universal Testing Machine until failure. Analysis of mean forces indicated that, Filtek P60, Surefil and Filtek Z250 exhibited better performance than Definite and Admira. The tested resin composites differed in their mechanical properties. This study suggested that fracture behavior were highly influenced by the filler system. Overall, Filtek P60, Surefil, Filtek Z250, demonstrated good fracture resistance. Copyright © 2003 John Wiley & Sons, Ltd.