On boundaries of Levi-flat hypersurfaces in Cn

Let S be a smooth 2-codimensional real compact submanifold of ${\mathbb{C}}^n$, $n>2$. We address the problem of finding a compact hypersurface M, with boundary S, such that $M?S$ is Levi-flat. We prove the following theorem. Assume that (i) S is nonminimal at every CR point, (ii) every complex point of S is flat and elliptic and there exists at least one such point, (iii) S does not contain complex submanifolds of dimension $n?2$. Then there exists a Levi-flat $(2n?1)$-subvariety $\stackrel{?}{M}?\mathbb{C}\times {\mathbb{C}}^n$ with negligible singularities and boundary $\stackrel{?}{S}$ (in the sense of currents) such that the natural projection $\pi :\mathbb{C}\times {\mathbb{C}}^n\to {\mathbb{C}}^n$ restricts to a CR diffeomorphism between S and $\stackrel{?}{S}$. To cite this article: P. Dolbeault et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Diffusion constant of Ga adatom on GaAs (001) surface: Molecular dynamics calculations

A valence force field to reproduce both the phonon dispersion curves of crystalline GaAs and first principle derived interaction energies of Ga adatom on GaAs (001) surface has been optimized. Calculations of diffusion constant of isolated Ga atoms on the GaAs surface have been performed by molecular dynamics classical trajectory simulations.     

On Some Cohomological Properties of Almost Complex Manifolds

We study a special type of almost complex structures, called pure and full and introduced by T.J. Li and W. Zhang (, 2007), in relation to symplectic structures and Hard Lefschetz condition. We provide sufficient conditions to the existence of the above type of almost complex structures on compact quotients of Lie groups by discrete subgroups. We obtain families of pure and full almost complex structures on compact nilmanifolds and solvmanifolds. Some of these families are parametrized by real 2-forms which are anti-invariant with respect to the almost complex structures.     

On the \partial\overline{\partial}-Lemma and Bott-Chern cohomology

On a compact complex manifold X, we prove a Frölicher-type inequality for Bott-Chern cohomology and we show that the equality holds if and only if X satisfies the $\partial\overline{\partial}$ -Lemma.     

Phytochemical profiles,antioxidant and anti-acetylcholinesterasic activities of the leaf extracts of Rhamnus lycioides subsp. oleoides (L.) Jahand. & Maire in different solvents

In this work, the extracts obtained with different solvents from the leaves of Rhamnus lycioides subsp. oleoides (L.) Jahand. & Maire were studied for their phytochemical profile and then for their antioxidant and acetylcholinesterase inhibitory activities. The phytochemical profiles of the extracts in n-hexane, dichloromethane, ethyl acetate, methanol, anthraquinone rich and water, showed the presence of different compounds belonging to several classes of natural products such as flavonoids, anthraquinones, saccharides and fatty acids. For what concerns the biological tests, the ethyl acetate, methanol and anthraquinone rich extracts showed the highest activities in both assays due to the high amount of compounds possessing those properties such as flavonoids and anthraquinones. By consequence, these specific extracts of the species may be considered to be potential sources of natural antioxidant and anti-acetylcholinesterasic compounds.     

Geometric properties of solutions of the levi-equation

Sunto Data un'ipersuperficie reale M di C² si definisce la curvatura di Levi k di M. Se M è un grafico x₄=u(x₁, x₂, x₃) allora u è soluzione di un'equasione quasi-lineare ellittica degenere L(k; u)=0, l'equazione di Levi. Net presente lavoro si stabiliseono alcune proprietà geometriche delle solusioni dell'equazione L(k; u)=0.

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Supported by M.P.I.