Une caractérisation des fonctions holomorphes injectives en analyse ultramétriqueA characterization of injective holomorphic functions in ultrametric analysis

We prove that a non constant holomorphic function f defined over an analytic subspace of $\text{C}{}_{\mathrm{p}}$ is injective if and only if

$\text{f(x)?f(y)}\text{x?y}{}^2\text{=}\text{f′(x)·f′(y)}\text{,}\text{for every distinct}\text{x}\text{and}\text{y.}$

This characterization proves the analogue, for holomorphic functions, of a conjecture of A. Escassut and M.C. Sarmant. On the other hand we give a counter-example to this conjecture, that concerns bi-analytic elements. To cite this article: J. Rivera-Letelier, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 441–446.     

Parallel kinetic resolution of racemic mixtures: a new strategy for the preparation of enantiopure compounds?

Kinetic resolution of racemic mixtures is a well-established methodology for the preparation of optically active compounds. However, excellent enantioselectivities are required to obtain them in enantiopure form, due to the decrease in ee when conversion values are close to 50%. To overcome this limitation, a parallel (asymmetric) reaction can remove the disfavored enantiomer. In this review, several examples of this strategy showing its wide range of applicability are described, as well as their mathematical treatment and some new applications in combinatorial chemistry.     

Magnetism in polyoxometalates: anisotropic exchange interactions in the Co3II moiety of [Co3W(D2O)2(ZnW9O34)2](12-)--A magnetic and inelastic neutron scattering study

The ground-state properties of a Co3II moiety encapsulated in a polyoxometalate anion were investigated by combining measurements of specific heat, magnetic susceptibility, and low-temperature magnetization with a detailed inelastic neutron scattering (INS) study on a fully deuterated polycrystalline sample of Na12[Co3W(D2O)2(ZnW9O34)2].40D2O (Co3). The ferromagnetic Co3O14 cluster core consists of three octahedrally oxo-coordinated CoII ions. According to the single-ion anisotropy and spin-orbit coupling of the octahedral CoII ions, the appropriate exchange Hamiltonian to describe the ground-state properties of the Co3 spin cluster is anisotropic and is expressed as H = -2 sigma a = x,y,z (Ja12 S1a S2a + Ja23 S2a S3a), where Ja are the components of the exchange interactions between the CoII ions. To reproduce the INS data, different orientations of the two anisotropic J tensors must be considered, and the following conditions had to be introduced: Jx12 = Jy23, Jy12 = Jx23, Jz12 = Jz23. This result was correlated with the molecular symmetry of the complex. The following set of parameters was obtained: Jx12 = Jy23 = 1.37, Jy12 = Jx23 = 0.218, and Jz12 = Jz23 = 1.24 meV. This set also reproduces in a satisfactory manner the specific heat, susceptibility, and magnetization properties of Co3.     

Validation of a gas chromatographic method for determination of fatty alcohols in 10 mg film-coated tablets of policosanol

A gas chromatographic method using a packed column and 1-eicosanol as an internal standard was validated for the determination of the fatty alcohols that compose policosanol in 10 mg film-coated tablets. The alcohols were determined as trimethylsilyl derivatives, prepared with N-methyl-N-trimethylsilyltrifluoroacetamide. The method can detect degradation products with high retention times, without interfering with the peaks of the active principle. Good linearity (correlation coefficient = 0.9992) and accuracy (mean recovery -100.27 +/- 1.66%) were proven over a range of 25-200% of the nominal concentration. Within- and between-day precision at the nominal 100% value met the acceptance criteria (<2%). Ruggedness was examined through an intralaboratory experimental study in which 6 operational changes were made; the changes were found to have no effect on quantitation, repeatability, resolution, and relative retention time. The method is suitable for the quality control process and stability studies of these tablets.     

Adsorption of n-alkanes on plasma-oxidized high-strength carbon fibers

The objective of this work was to characterize the degree of heterogeneity brought about by oxygen plasma treatment of carbon fibers by studying its effects on the adsorption of n-alkanes. Untreated and unsized high-strength carbon fibers were subjected to oxygen plasma treatments with different degrees of severity. A sample of the same material oxidized following a standard industrial method was also studied for comparison. Adsorption of C5-C10n-alkanes at 303-353 K was measured by inverse gas chromatography (IGC). Elution peaks were symmetrical for the fresh and industrially oxidized samples; however, a large extent of asymmetry was observed for the plasma-treated fibers. Differences in surface heterogeneity were quantified in terms of several adsorption thermodynamic magnitudes. Differential heats of adsorption exhibited values similar to those corresponding to the probe-basal plane interaction. The dispersive component of the surface tension of the solids increased clearly upon plasma oxidation, the increase being systematic according to the severity of plasma treatment. It can be concluded that plasma oxidation generates high-surface-energy sites responsible for trapping of n-alkane molecules, this effect being more marked as the chain length increases. The possibility of this effect being associated to creation of micropores was ruled out on the basis of volumetric CO2 adsorption experiments and IGC measurements at finite dilution. Scanning tunneling microscopy observations allowed us to establish a possible connection between fiber surface nanostructure and IGC results. The sites accessible to n-alkane molecules in the industrially oxidized sample seem to be highly disordered, thus leading to a weaker interaction with the adsorbate.     

Preparation of enantiopure ketones and alcohols containing a quaternary stereocenter through parallel kinetic resolution of beta-keto nitriles

Racemic 1-methyl-2-oxocycloalkanecarbonitriles have been subjected to bioreduction by the fungus Mortierella isabellina NRRL 1757 through a parallel kinetic-resolution process. The u and l alcohols thus obtained (up to >99% ee) were easily separated and oxidized to the R and S ketones, respectively. The process can be then repeated so that both enantiomers of the ketone and two epimers of the alcohol can be obtained in their enantiopure forms.     

Novel acid-catalyzed rearrangement of tetrahydro-1,2,3,4-tetrazines: unexpected formation of glycosazones

The present contribution discloses a simple and unexpected acid-catalyzed cleavage of tetrahydrotetrazines leading to 1,2-bis(hydrazones). Incorporation of a chiral fragment derived from carbohydrates enables the rapid preparation of glycosazones, a family of compounds employed by Emil Fischer to elucidate the configuration of sugars. In addition, a mechanistic proposal accounts for experimental observations.     

Highly emissive,nine-coordinate enantiopure lanthanide complexes incorporating tetraazatriphenylenes as probes for DNA

The interaction of q = 0 delta- and lambda-Tb and Eu complexes with poly(dAdT), poly(dGdC) and calf-thymus DNA has been examined by absorption, emission and chiroptical spectroscopy and is sensitive to complex helicity, base-pair type and the nature of the lanthanide excited state.     

Minimalist peptidomimetic cyclophanes as strong organogelators

L-Valine containing cyclophanes have been shown to gelate organic solvents leading to soft materials with a clear expression of their chirality at the supramolecular level.     

Theory of Extended Solutions¶for Fast-Diffusion Equations¶in Optimal Classes of Data.¶Radiation from Singularities

This paper is devoted to constructing a general theory of nonnegative solutions for the equation called “the fast-diffusion equation” in the literature. We consider the Cauchy problem taking initial data in the set ?⁺ of all nonnegative Borel measures, which forces us to work with singular solutions which are not locally bounded, not even locally integrable. A satisfactory theory can be formulated in this generality in the range 1 > m > m _c = max {(N? 2)/N,0}, in which the limits of classical solutions are also continuous in ? ^N as extended functions with values in ?₊∪{∞}. We introduce a precise class of extended continuous solutions ? _c and prove (i) that the initial-value problem is well posed in this class, (ii) that every solution u(x,t) in ? _c has an initial trace in ?⁺, and (iii) that the solutions in ? _c are limits of classical solutions. Our results settle the well-posedness of two other related problems. On the one hand, they solve the initial-and-boundary-value problem in ?× (0,∞) in the class of large solutions which take the value u=∞ on the lateral boundary x∈??, t>0. Well-posedness is established for this problem for m _c < m > 1 when ? is any open subset of ? ^N and the restriction of the initial data to ? is any locally finite nonnegative measure in ?. On the other hand, by using the special solutions which have the separate-variables form, our results apply to the elliptic problem Δf=f ^q posed in any open set ?. For 1 > q > N/(N? 2)₊ this problem is well posed in the class of large solutions which tend to infinity on the boundary in a strong sense. As is well known, initial data with such a generality are not allowed for m≧ 1. On the other hand, the present theory fails in several aspects in the subcritical range 0> m≦m _c , where the limits of smooth solutions need not be extended-continuously.