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.     

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.     

A helical array of pendant fullerenes on a helical poly(phenylacetylene) induced by non-covalent chiral interactions

Novel [60]fullerene-based poly(phenylacetylene)s prepared by the copolymerization of achiral phenylacetylenes bearing a C(60) or crown ether pendant form a one-handed helix upon complexation with L- and D-alanine, yielding a helical array of the pendant fullerenes with a predominant screw-sense along the polymer backbone.     

Synthesis of Optically Active Vasicinone Based on Intramolecular Aza-Wittig Reaction and Asymmetric Oxidation(1)

Both optical isomers of a quinazoline alkaloid, vasicinone, were synthesized by two different methods. The first method used (3S)-3-hydroxy-gamma-lactam as a chiral synthon, which was, after O-TBDMS protection, o-azidobenzoylated followed by treatment with tri-n-butylphosphine to afford (S)-(-)-vasicinone via the tandem Staudinger/intramolecualr aza-Wittig reaction. The second method utilized asymmetric oxygenation of deoxyvasicinone with (1S)-(+)- or (1R)-(-)-(10-camphorsulfonyl)oxaziridine (the Davis reagent), respectively. The aza-enolate anion of deoxyvasicinone was treated with (S)-(+)-reagent to afford (R)-(+)-vasicinone in 71% ee, while the reaction with (R)-(-)-reagent gave (S)-(-)-vasicinone in 62% ee. The optical purity was analyzed by HPLC on specially modified cellulose as a stationary phase. These results provided a facile method to prepare both optical isomers of vasicinone and confirmed the recently reversed stereochemistry of natural (-)-vasicinone.     

Macromolecular chirality induction on optically inactive poly(4-carboxyphenyl isocyanide) with chiral amines: a dynamic conformational transition of poly(phenyl isocyanide) derivatives

Optically active polyisocyanides (poly(iminomethylenes)) have been prepared with much interest in developing new functional materials. Polyisocyanides have been considered to have a stable 4(1) helical conformation even in solution when they have a bulky side group. However, the conformational characteristics of poly(phenyl isocyanide) (PPI) derivatives are still under debate. We now report that an optically inactive PPI derivative, poly(4-carboxyphenyl isocyanide) (poly-1), shows optical activity in the polymer backbone induced by external, chiral stimuli through acid-base interactions under thermodynamic control and exhibits induced circular dichroism (ICD) in the UV-visible region in DMSO. The ICD intensities of the poly-1-chiral amine complexes in DMSO gradually increased with time, and, in one case, the value reached 3 times that of the original value after 2 months at 30 degrees C. The conformational changes also occurred very slowly for poly-1 alone and its ethyl ester with time on the basis of (1)H NMR spectroscopic analysis. These results indicate that PPIs bearing a less bulky substituent may not have a 4(1) helical conformation but have a different type of prochiral conformation, for instance, an s-trans (zigzag) structure which may transform to a dynamic, one-handed helical conformation when the PPIs have a functional group capable of interacting with chiral compounds. The mechanism of helicity induction on poly-1 through a dynamic conformational transition is discussed on the basis of the above results together with molecular dynamic simulation results for PPI.