Mesure invariante pour l’équation stochastique d’un modéle de compétition limitée entre des espéces avec une diffusion spatiale

On considére l’équation stochastique decrivant un systéme den espéces avec une perturbation stochastique du type environnemental et une diffusion dans un territoire de chaque espéce. On suppose la compétition avec un effet limité entre le espéces différentes, tandis que l’effet logistique pour chaque espéce est supposé quadratique. Sous une condition convenable pour les coefficients, on démontre l’existence d’une mesure invariante pour cette équation stochastique, oú la densité de population de chaque espéce est presque surement positive.      

Systematic enantiomeric separation of [60]fullerene bisadducts possessing an inherent chiral addition pattern

The optical resolution of trans-2 and trans-3 [60]fullerene bisadducts with an inherent chiral addition pattern, modified by Bingel reaction, cycloaddition by benzyne, Prato reaction, and cycloaddition by o-quinodimethane, was systematically investigated by using chiral HPLC columns (Chiralcel OD and Chiralpak AD). The chiroptical properties of enantiomers separated were also examined.     

Chiral amplification in macromolecular helicity assisted by noncovalent interaction with achiral amines and memory of the helical chirality

Poly[(4-carboxyphenyl)acetylene] (poly-1) exhibits an intense induced circular dichroism (ICD) in the UV-visible region upon complexation with excess (R)-1-(1-naphthyl)ethylamine ((R)-2), owing to the formation of a predominantly single-handed helical conformation of the polymer backbone. In the presence of a small amount of (R)-2, poly-1 showed a very weak ICD due to the lack of a single-handed helical conformation. However, we have found that the co-addition of the excess bulky, achiral 1-naphthylmethylamine (5) with a small amount of (R)-2 caused a dramatic increase in the ICD magnitude, comparable to the full ICD induced by excess (R)-2. This indicates that an almost single-handed helix can be induced on poly-1 upon complexation with a small amount of (R)-2 assisted by achiral 5. Furthermore, the induced single-handed helical poly-1 could be successfully memorized by the replacement of (R)-2 and 5 with achiral 2-aminoethanol or n-butylamine.     

Structures and ligand exchange of N-confused porphyrin dimer complexes with group 12 metals

N-confused 5,20-diphenylporphyrin (NCDPP, 1) formed 2:2 dimer complexes with group 12 metals both in the solid state and in solution. X-ray single-crystal analyses of the Zn(II) and Cd(II) complexes (7, 8) revealed that each metal ion is coordinated with three inner core nitrogens and a peripheral nitrogen of the other NCDPP in the pair. In the (1)H NMR spectra of 7, 8, and the Hg(II) complex (9), the outer alpha-H signals of the confused pyrrole ring appeared in the upfield region at 2.57, 3.44, and 3.60 ppm, respectively, due to the ring current effect by the coordinated porphyrins. In the case of the Cd(II) and Hg(II) complexes (8, 9), additional magnetic couplings with the metal nuclei of the partner rings were observed. The equilibrium constants (K) of the monomer exchange reaction at 25 degrees C were determined to be 2.5, 1.3, and 0.6 for the (Zn-Cd), (Cd-Hg), and (Zn-Hg) heterodimer complexes, respectively, from the (1)H NMR spectra of a solution containing two different dimers. Furthermore, a metal-transfer reaction from a Zn(II) NCP dimer complex to the free base porphyrin was demonstrated.     

Structural analysis of amylose tris(3,5-dimethylphenylcarbamate) by NMR relevant to its chiral recognition mechanism in HPLC

The structural analysis of amylose tris(3,5-dimethylphenylcarbamate) (ADMPC) was performed by NMR spectroscopy using a sample with a lower degree of polymerization in order to understand the chiral recognition mechanism when it was used as a chiral stationary phase (CSP) in high-performance liquid chromatography (HPLC). ADMPC exhibited chiral discrimination for many enantiomers, including 1-(9-anthryl)-2,2,2-trifluoroethanol (1) and 1,1'-bi-2-naphthol (2) in both NMR and HPLC. A good agreement was observed between the HPLC and NMR results when chloroform was employed as the common solvent. The structure of ADMPC in solution was investigated by NMR using the 2D NOESY technique coupled with computer modeling, and a left-handed 4/3 helical structure was obtained as the most probable one. The binding geometry between ADMPC and the enantiomers of 1 was also investigated by (1)H NMR titration. On the basis of these results combined with molecular modeling, a rational model to explain the chiral discrimination mechanism of 1 on ADMPC was proposed.     

Equazioni monodimensionali di un gas viscoso barotropico con una perturbazione poco regolare

The equations for a barotropic viscous gas in one space dimensiondν=(μ(?ν_ε)_ε?p _ε)dt+dG,? _t +?²ν_ε=0,p=?^γ with a perturbationdG are considered under the assumption thatG is only a function of bounded variation inL ²(Θ) orH ₀ ¹ (Θ) (Θ=]0, α[) and the esistence and the uniqueness of the global solution in a class of solutions of «strong type» as well as in a class of solutions of «weak type» are proved. This result constitutes a generalization of the result of Kazhikhov [8] and that of Shelukhin [10] and contains preliminary considerations for the corrisponding stochastic equations.