Given a coherent ideal sheaf J we construct locally a vector-valued residue current R whose annihilator is precisely the given sheaf. In case J is a complete intersection, R is just the classical Coleff-Herrera product. By means of these currents we can extend various results, previously known for a complete intersection, to general ideal sheaves. Combining with integral formulas we obtain a residue version of the Ehrenpreis-Palamodov fundamental principle. © 2007 Elsevier Masson SAS RÉSUMÉ.-Soit J un faisceau cohérent d'idéaux. Nous construisons localement un courant résiduel R à valeurs vectorielles dont l'annihilateur est J. Au cas où J serait une intersection complète, R est simplement le produit classique de Coleff-Herrera. Ces courants permettent d'étendre au cas général des résultats divers, déjà connus dans le cas d'une intersection complète. En utilisant ces courants résiduels et des formules intégrales, nous obtenons ainsi une version résiduelle du Principe Fondamental d'Ehrenpreis-Palamodov.

Let X be a complex space of pure dimension. We introduce fine sheaves A X q of (0, q)-currents, which coincides with the sheaves of smooth forms on the regular part of X, so that the associated Dolbeault complex yields a resolution of the structure sheaf O X . Our construction is based on intrinsic and quite explicit semi-global Koppelman formulas.

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Multiangle light scattering (MALS) is a well-established technique used to determine the size of macromolecules and particles. In this study, different extrapolation procedures used in MALS were investigated with regard to accuracy and robustness in the obtained molar mass and rms radius. Three different mathematical transformations of the light scattering function referred to as the Debye, Zimm, and Berry methods for constructing the Debye plot were investigated for two idealized polymer shapes, homogeneous spheres and random coils, with radii from 25 to 250 nm. The effect of the angular interval used for the extrapolation was investigated, as was the robustness of the different transformations toward errors in the measured light scattering intensity at low angles. For an rms radius less than 50 nm, the relative error in molar mass due to extrapolation was less than 1% independent of the method used. For larger radii, the error increased and the extrapolation procedure became more critical. For random coil polymers, the Berry method was superior in terms of accuracy and robustness. For spheres, the Debye method was superior. The Zimm method was inferior to the others. The different extrapolation methods were evaluated and compared on experimental data from a size exclusion chromatography-MALS analysis of an ultrahigh molar mass poly(ethylene oxide) (PEO). The PEO data qualitatively verified the calculations and stressed the importance of optimizing the extrapolation procedure after careful evaluation of the experimental data. A discussion of how to detect erroneous data in an experimental Debye plot is given.