Calculus of functors and model categories

The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure [B. Chorny, W.G. Dwyer, Homotopy theory of small diagrams over large categories, preprint, 2005]. In this paper we construct various localizations of the projective model structure and also give a variant for functors from simplicial sets to spectra. We apply these model categories in the study of calculus of functors, namely for a classification of polynomial and homogeneous functors. In the n-homogeneous model structure, the nth derivative is a Quillen functor to the category of spectra with Σn-action. After taking into account only finitary functors—which may be done in two different ways—the above Quillen map becomes a Quillen equivalence. This improves the classification of finitary homogeneous functors by T.G. Goodwillie [T.G. Goodwillie, Calculus. III. Taylor series, Geom. Topol. 7 (2003) 645-711 (electronic)].     

GC Method for Determining Polyadipate Plasticizers in Foods: Transesterification to Dibutyl Adipate, Conversion to Migrating Polyadipate

The determination of the migration of polyadipates (plasticizers in PVC) into foods or food simulants for compliance testing involves three principal steps. (1) Adipate from the polyadipate material in the food or simulant is measured through transesterification to the butyl esters directly in the homogenated food, which presupposes tight control of the kinetics. Butyl esters are more easily extracted, and the butanol used for transesterification also serves as principal extraction solvent. (2) To check compliance with the specific migration limit, adipate is determined in the material of a molecular mass below 1,000 Da, which involves preparative preseparation by size exclusion chromatography followed by transesterification. (3) The migrated polyadipate material is calculated from the adipate measured by a conversion factor determined from the qualitative and quantitative analysis of the polyadipate components <1,000 Da.     

über Katalysatoren- und Fermentmodelle (1)

Ohne Zusammenfassung Die Arbeit wurde aus Mitteln des Marshall-Planes (ERP-Mittel) und mit Spenden aus dem „Fonds Chemie“ ausgeführt. Wir sprechen den zust?ndigen Stellen für die Gew?hrung der Beihilfe unseren verbindlichsten Dank aus. Der Deutschen Forschungsgemeinschaft danken wir für die überlassung einer Ultrazentrifuge, den Behring-Werken für die uns zur Verfügung gestellten Serumalbumin- und -globulin-Pr?parate.     

2,2-Dioxo-1H-thieno[3,4-c][1,2]thiazines. Synthesis and some reactions of a new heterocycle

The first synthesis of substituted 2,2-dioxo-1-phenyl-1H-thieno[3,4-c][1,2]thiazines 2 and some of their reactions are achieved. Compounds 2 were prepared from the 3,5-dimethyl-1,1-dioxo-1,2-thiazine-4-carbaldehydes 1 by reaction with sulfur and triethyl amine in dimethylformamide under mild conditions. They were characterized spectroscopically and by X-ray structure analysis. The formylation, chlorination and oxidation of 2 are reported.