The first coefficients of the asymptotic expansion of the Bergman kernel of the spin^c Dirac operator

We establish the existence of the asymptotic expansion of the Bergman kernel associated to the spin-c Dirac operators acting on high tensor powers of line bundles with non-degenerate mixed curvature (negative and positive eigenvalues) by extending the paper " On the asymptotic expansion of Bergman kernel " (math.DG/0404494) of Dai-Liu-Ma. We compute the second coefficient b_1 in the asymptotic expansion using the method of our paper "Generalized Bergman kernels on symplectic manifolds" (math.DG/0411559).Comment: 21 pages, to appear in Internat. J. Math. Precisions added in the abstrac

Selection of dune shapes and velocities. Part 2: A two-dimensional modelling

We present in this paper a simplification of the dune model proposed by Sauermann et al. which keeps the basic mechanisms but allows analytical and parametric studies. Two kinds of purely propagative two dimensional solutions are exhibited: dunes and domes, which, by contrast to the former, do not show avalanche slip face. Their shape and velocity can be predicted as a function of their size. We recover in particular that dune profiles are not scale invariant (small dunes are flatter than the large ones), and that the inverse of the velocity grows almost linearly with the dune size. We furthermore get the existence of a critical mass below which no stable dune exists. However, the linear stability analysis of a flat sand sheet shows that it is unstable at large wavelengths and suggests a mechanism of dune initiation.Comment: submitted to Eur. Phys. J. B, 13 pages, 17 figure

Equivalence between spectral properties of graphs with and without loops

In this paper we introduce a spectra preserving relation between graphs with loops and graphs without loops. This relation is achieved in two steps. First, by generalizing spectra results got on (m, k)-stars to a wider class of graphs, the (m, k, s)-stars with or without loops. Second, by defining a covering space of graphs with loops that allows to remove the presence of loops by increasing the graph dimension. The equivalence of the two class of graphs allows to study graph with loops as simple graph without loosing information

Selection of dune shapes and velocities. Part 1: Dynamics of sand, wind and barchans

Almost fifty years of investigations of barchan dunes morphology and dynamics is reviewed, with emphasis on the physical understanding of these objects. The characteristics measured on the field (shape, size, velocity) and the physical problems they rise are presented. Then, we review the dynamical mechanisms explaining the formation and the propagation of dunes. In particular a complete and original approach of the sand transport over a flat sand bed is proposed and discussed. We conclude on open problems by outlining future research directions.Comment: submitted to Eur. Phys. J. B, 20 pages, 20 figure

Structure of the interleukin-2 tyrosine kinase Src homology 2 domain; comparison between X-ray and NMR-derived structures

The crystal structure of the interleukin-2 tyrosine kinase Src homology domain (Itk SH2) is described and it is found that unlike in studies of this domain using NMR spectroscopy, cis-trans-prolyl isomerization is not readily detected in the crystal structure. Based on similarities between the Itk SH2 crystal form and the cis form of the Itk SH2 NMR structure, it is concluded that it is likely that the prolyl imide bond at least in part adopts the cis conformation in the crystal form. However, the lack of high-resolution data and the dynamic nature of the proline-containing loop mean that the precise imide-bond conformation cannot be determined and prolyl cis-trans isomerization in the crystal cannot be ruled out. Given the preponderance of structures that have been solved by X-ray crystallography in the Protein Data Bank, this result supports the notion that prolyl isomerization in folded proteins has been underestimated among known structures. Interestingly, while the precise status of the proline residue is ambiguous, Itk SH2 crystallizes as a domain-swapped dimer. The domain-swapped structure of Itk SH2 is similar to the domain-swapped SH2 domains of Grb2 and Nck, with domain swapping occurring at the β-meander region of all three SH2 domains. Thus, for Itk SH2 structural analysis by NMR spectroscopy and X-ray crystallography revealed very different structural features: proline isomerization versus domain-swapped dimerization, respectively