Théorèmes d'existence pour les modifications analytiques

Sans résumé     

Uniqueness for Quasi-variational Inequalities

This paper presents a uniqueness result for a quasi-variational inequality QVI(1) that, in contrast to existing results, does not require the projection mapping on a variable closed and convex set to be a contraction. Our basic idea is to find a simple QVI(0), for example a variational inequality, for which we can show the existence of a unique solution. Further, exploiting some nonsingularity condition, we will guarantee the existence of a continuous solution path from the unique solution of QVI(0) to a solution of QVI(1). Finally, we can show that the existence of a second different solution of QVI(1) contradicts the nonsingularity condition. Moreover, we present some matrix-based sufficient conditions for our nonsingularity assumption, and we discuss these assumptions in the context of generalized Nash equilibrium problems with quadratic cost and affine linear constraint functions.     

Singlet Oxygen Photo‐Oxygenation in Water/Pluronic F‐127 Hydrogels: Increased Reaction Efficiency Coupled with a Switch in Regioselectivity

Pluronic F‐127 hydrogels are highly efficient microenvironments for photochemical reactions, as demonstrated for singlet oxygen reactions of monoalkenes. Nonpolar substrates are localized in the nanosized polymer compartment, which can be visualized by neutron scattering. The efficiency of ¹O₂ reactions is strongly increased for tiglate derivatives and the regioselectivity of the ene reaction of trisubstituted alkenes is completely switched in comparison with solution phase and inverted in comparison with intrazeolite photo‐oxygenations.     

Binary Zinc Azides

Pure, solvent‐free Zn(N₃)₂ was prepared by reaction of diethyl zinc and hydrazoic acid in aprotic solvents. The single‐crystal structure determination, along with the comprehensive characterization of α‐Zn(N₃)₂ and two metastable polymorphs, could be achieved for the first time. Since these data disagree in large parts with the known, previously reported values, all previous syntheses of Zn(N₃)₂, and for comparison Zn(N₃)₂?2.5 H₂O and Zn(OH)N₃ were reinvestigated, indicating that some of the earlier work has to be revised.