A generalisation of de la Vallée-Poussin procedure to multivariate approximations

Advances in Computational Mathematics - Persistence diagrams are one of the main tools in the field of Topological Data Analysis (TDA). They contain fruitful information about the shape of data....     

The Hausdorff dimension of graphs of Weierstrass functions

The Weierstrass nowhere differentiable function, and functions constructed from similar infinite series, have been studied often as examples of functions whose graph is a fractal. Though there is a simple formula for the Hausdorff dimension of the graph which is widely accepted, it has not been rigorously proved to hold. We prove that if arbitrary phases are included in each term of the summation for the Weierstrass function, the Hausdorff dimension of the graph of the function has the conjectured value for almost every sequence of phases. The argument extends to a much wider class of Weierstrass-like functions.

     

Simulation du drapé des tissus par maillages adaptatifsAdaptive meshing for cloth draping

Numerical simulation methods regarding fabric and cloth draping are generally based on mechanical models. These models are usually applied to uniform grids representing the true geometry of the fabric. Fabrics being a very flexible material, wrinkles appear on its surface when submitted to free or constrained motion. The main problem of the simulation is to represent realistically cloth surface motion. This is strongly dependent on the surface discretization. We present a new cloth animation scheme based on adaptive surface discretization. It can be seen as a multi-grid method which allows us to obtain realistic simulations. We propose also a new mechanical model well suited to our adaptive meshing strategy. A numerical example is given to show the efficiency of the method. To cite this article: J. Villard et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 561–566.     

Isolation and On‐Line LC/CD Analysis of 3,8″‐Linked Biflavonoids from Gnidia involucrata

Investigation of the methanol extract of the roots of Gnidia involucrata (Thymelaeaceae) led to the isolation and characterization of two new 3,8″‐biflavonoid diastereoisomers, named GB‐4 ( 6a ) and GB‐4a ( 6b ). Their absolute configurations were determined in mixture by on‐line LC/CD measurements, which also allowed the revision of absolute configurations of the biflavanoids GB‐1 and GB‐2, and the configurational assignment of GB‐3.     

Heat-treatment studies of molybdenum oxide-monohydrate

The dehydration of molybdic acid, MoO₃---H₂O, was studied by thermal analysis, X-ray diffractometry and FTIR spectroscopy. The results show that an intermediate phase, MoO₃-2/3H₂O is formed at 216 °C and the monoclinic form of MoO₃ is grown above 350 °C. The mechanism of dehydration and structural rearrangement were confirmed by the features of the infrared spectra showing formation of corner-shared MoO₆ octahedra.     

Motivic Serre invariants of curves

In this article, we generalize the theory of motivic integration on formal schemes topologically of finite type and the notion of motivic Serre invariant, to a relative point of view. We compute the relative motivic Serre invariant for curves defined over the field of fractions of a complete discrete valuation ring R of equicharacteristic zero. One aim of this study is to understand the behavior of motivic Serre invariants under ramified extension of the ring R. Thanks to our constructions, we obtain, in particular, an expression for the generating power series, whose coefficients are the motivic Serre invariant associated to a curve, computed on a tower of ramified extensions of R. We give an interpretation of this series in terms of the motivic zeta function of Denef and Loeser.     

Realization of 2-solvable nilpotent groups as groups of classes of homotopy self-equivalences

Let X be a 1-connected CW-complex of finite type and ε_?(X) be the group of homotopy classes of self-equivalences of X which induce the identity on homotopy groups. In this paper, we prove that every finitely generated 2-solvable rational nilpotent group is realizable as ε_?(X) where X is the rationalization of a 1-connected CW-complex of finite type.     

Error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method

In this paper we derive a priori and a posteriori error estimates for cell centered finite volume approximations of nonlinear conservation laws on polygonal bounded domains. Numerical experiments show the applicability of the a posteriori result for the derivation of local adaptive solution strategies.