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.     

Decomposition algorithms for the tree edit distance problem

We study the behavior of dynamic programming methods for the tree edit distance problem, such as [P. Klein, Computing the edit-distance between unrooted ordered trees, in: Proceedings of 6th European Symposium on Algorithms, 1998, p. 91–102; K. Zhang, D. Shasha, SIAM J. Comput. 18 (6) (1989) 1245–1262]. We show that those two algorithms may be described as decomposition strategies. We introduce the general framework of cover strategies, and we provide an exact characterization of the complexity of cover strategies. This analysis allows us to define a new tree edit distance algorithm, that is optimal for cover strategies.     

New example of a non-heme mononuclear iron(IV) oxo complex. Spectroscopic data and oxidation activity

The green complex S=1 [(TPEN)FeO]2+ [TPEN=N,N,N',N'-tetrakis(2-pyridylmethyl)ethane-1,2-diamine] has been obtained by treating the [(TPEN)Fe]2+ precursor with meta-chloroperoxybenzoic acid (m-CPBA). This high-valent complex belongs to the emerging family of synthetic models of Fe(IV)=O intermediates invoked during the catalytic cycle of biological systems. This complex exhibits spectroscopic characteristics that are similar to those of other models reported recently with a similar amine/pyridine environment. Thanks to its relative stability, vibrational data in solution have been obtained by Fourier transform infrared. A comparison of the Fe=O and Fe=(18)O wavenumbers reveals that the Fe-oxo vibration is not a pure one. The ability of the green complex to oxidize small organic molecules has been studied. Mixtures of oxygenated products derived from two- or four-electron oxidations are obtained. The reactivity of this [FeO]2+ complex is then not straightforward, and different mechanisms may be involved.     

Gas-phase ion/molecule reactions between dimethoxyphosphonium ions and aromatic hydrocarbons

Ion/molecule reactions between O=P(OCH(3))(2)(+) phosphonium ions and six aromatic hydrocarbons (benzene, toluene, 1,2,4-trimethylbenzene, naphthalene, acenaphthylene and fluorene) were performed in a quadrupole ion trap mass spectrometer. The O=P(OCH(3))(2)(+) phosphonium ions, formed by electron impact from neutral trimethyl phosphite, were found to react with aromatic hydrocarbons (ArHs) to give (i) an adduct [ArH, O=P(OCH(3))(2)](+) and (ii) for ArHs which have an ionization energy below or equal to 8.14 eV, a radical cation ArH(+ *) by charge transfer reaction. Collision-induced dissociation experiments, which produce fragment ions other than the O=P(OCH(3))(2)(+) ions, indicate that the adduct ions are covalent species. Isotope-labeled ArHs were used to elucidate fragmentation mechanisms. The charge transfer reactions were investigated using density functional theory at the B3LYP/6-311 + G(3df,2p)//B3LYP/6-31G(d,p) level of theory. The potential energy surface obtained from B3LYP/6-31G(d,p) calculations for the reaction between O=P(OCH(3))(2)(+) and benzene is described.     

Preparative and electrochemical investigations on the electron sponge behavior of cobalt telluride clusters: CO substitution in [Co11Te7(CO)10]n- ions (n=1, 2) by PMe2Ph and crystal structure of [Co11Te7(CO)5(PMe2Ph)5

The reaction of the cluster salts [Cp(2*) Nb(CO)(2)](n)[Co(11)Te(7)(CO)(10)] (Cp*=C(5)Me(5); n=1, 2) with excess PMe(2)Ph gave the neutral, dark brown clusters [Co(11)Te(7)(CO)(6)(PMe(2)Ph)(4)] (5) and [Co(11)Te(7)(CO)(5)(PMe(2)Ph)(5)] (6) with 147 metal valence electrons. The new compounds were characterized by IR spectroscopy, elemental analyses, and mass spectrometry. The molecular structure of 6 was determined by X-ray crystallography. Like its precursor anion, it consists of a pentagonal-prismatic [Co(11)Te(7)] core, but with a ligand sphere composed of five CO and five PMe(2)Ph ligands. Detailed electrochemical studies of both reactions reveal that a stepwise substitution of CO ligands in the initial cluster anions takes place leading to intermediate [Co(11)Te(7)(CO)(10-m)(PMe(2)Ph)(m)](n-) ions (m=1-5; n=1, 2). Each of these intermediates is distinguished by at least one oxidation and two reduction waves, giving rise to a total of 21 redox couples and 27 electroactive species. The electron sponge character of the new compounds is particularly pronounced in 5, which exhibits charges n between +1 and -4 corresponding to metal valence electron counts of between 146 and 151.     

Electrophoretic separations of twelve phenothiazines and N-demethyl derivatives by using capillary zone electrophoresis and micellar electrokinetic chromatography with non ionic surfactant

We focused our work on the separation of phenothiazines that are important drugs used for the treatment of psychic diseases. For a better understanding of the metabolism of these solutes, we wanted to separate not only a mixture of 12 phenothiazines but also a mixture containing phenothiazines and their N-demethyl metabolites by capillary electrophoresis. Separations in capillary zone electrophoresis were performed using 3 x 10(-2) mol/L H3PO4 (pH 2.5) but the obtained resolutions were not entirely satisfactory especially with regard to phenothiazine -N-demethyl derivative pairs. To improve the obtained results, we have performed separations by using micellar electrokinetic chromatography. In this approach, we used a running electrolyte containing 3 x 10(-2) mol/L H3PO4 electrolyte (pH 2.5) and octaethylene glycol monododecyl ether (C12E8) as neutral surfactant. By introducing 2 x 10(-3) mol/L C12E8 in the electrolyte, 11 out of 12 phenothiazines have been baseline separated. With respect to the separation of a mixture containing 3 phenothiazines and their 3 demethyl derivatives, we obtained an excellent separation by using a running electrolyte prepared with 7.5 x 10(-4) mol/L C12E8 and 3 x 10(-2) mol/L H3PO4.     

Molecular orbital studies on the conformation of GABA (γ-aminobutyric acid)

In distinction to Extended Hückel Theory which predicts as the most stable conformation of free zwitterionic GABA a totally extended form, PCILO and SCF ab initio studies show that the intrinsically preferred conformation of the isolated molecule is a highly folded one, resulting from strong interactions between the two charged ends. Computations are also carried out for hydrated GABA in the supermolecule approach allowing moreover for the flexibility of binding of some of the water molecules of the first hydration shell. They predict the coexistence in solution of a large number of conformations showing different degrees of folding (or extension), a result confirmed by recent NMR studies. This and a number of similar results show that we have to adapt our thinking on the role of conformations in pharmacological activity to this situation, which was frequently obscured by the more abundant results of X-ray crystallography yielding a single conformation.