Remisporine B, a novel dimeric chromenone derived from spontaneous Diels-Alder reaction of remisporine A

A novel cyclopentachromenone, remisporine A, has been isolated from liquid culture of the marine fungus Remispora maritima. Remisporine A is not stable under normal conditions and autocatalytically dimerizes to give rise to a stereospecific product remisporine B via Diels-Alder reaction. The structure of remisporine B was elucidated by spectroscopic analyses including 2D-NMR and HRMS data.     

Radical cyclization; towards the syntheses of tetranor metabolites of 15-F2t-isoprostane

Radical cyclization of acyclic 1-substituted-2,4-dihydroxylated 5-hexenyl radicals produced functionalized cyclopentane derivatives. These cyclopentanic precursors after different protection/deprotection reactions followed by Wittig and Horner-Wadsworth-Emmons coupling reactions led to the main urinary tetranor metabolites of 15-F_2t-isoprostane (8-epi-PGF_2α).     

Sur une loi de conservation issue de la géologie

In this Note, we are interested in the theoretical analysis of a geological stratigraphic model, taking into account a limited weathering condition. Firstly, we present the physical model and the mathematical formulation, which lead to an original conservation law. Then, the definition of a solution and some mathematical tools in order to resolve the problem are given. At last, we treat the 1-D case and we present some open problems. To cite this article: G. Vallet, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Perfluorinated anion exchange membranes: Preparation and preliminary tests of dialysis

Using the preirradiation technique a kinetic study of the grafting of the 4-vinyl pyridine (V₄P) and an aliphatic ammonium monomer (ALAM) onto the copolymer film of ethylene–tetrafluoroethylene (ETFE) has been performed. The influence of dose, temperature, and concentration of monomer, reticular agent, and inhibitor were investigated. The results are discussed on the basis of the interactions between monomer diffusibility and viscosity of the medium. The characteristics of some membranes were determined. Their applicability to the recovery of acid by dialysis is demonstrated.     

The Khler-Einstein metric for some Hartogs domains over symmetric domains

We study the complete Kahler-Einstein metric of a Hartogs domainΩbuilt on an irreducible bounded symmetric domainΩ, using a power Nμof the generic norm ofΩ.The generating function of the Kahler-Einstein metric satisfies a complex Monge-Ampere equation with a boundary condition. The domainΩis in general not homogeneous, but it has a subgroup of automorphisms, the orbits of which are parameterized by X∈[0,1[. This allows us to reduce the Monge-Ampere equation to an ordinary differential equation with a limit condition. This equation can be explicitly solved for a special valueμ0 ofμ.. We work out the details for the two exceptional symmetric domains. The special valueμ0 seems also to be significant for the properties of other invariant metrics like the Bergman metric; a conjecture is stated, which is proved for the exceptional domains.     

Fractionalization of the complex-valued Brownian motion of order n using Riemann–Liouville derivative. Applications to mathematical finance and stochastic mechanics

The (complex-valued) Brownian motion of order n is defined as the limit of a random walk on the complex roots of the unity. Real-valued fractional noises are obtained as fractional derivatives of the Gaussian white noise (or order two). Here one combines these two approaches and one considers the new class of fractional noises obtained as fractional derivative of the complex-valued Brownian motion of order n. The key of the approach is the relation between differential and fractional differential provided by the fractional Taylor’s series of analytic function , where E is the Mittag–Leffler function on the one hand, and the generalized Maruyama’s notation, on the other hand. Some questions are revisited such as the definition of fractional Brownian motion as integral w.r.t. (dt), and the exponential growth equation driven by fractional Brownian motion, to which a new solution is proposed. As a first illustrative example of application, in mathematical finance, one proposes a new approach to the optimal management of a stochastic portfolio of fractional order via the Lagrange variational technique applied to the state moment dynamical equations. In the second example, one deals with non-random Lagrangian mechanics of fractional order. The last example proposes a new approach to fractional stochastic mechanics, and the solution so obtained gives rise to the question as to whether physical systems would not have their own internal random times.