Analytic extension of differentiable functions defined in closed sets by means of continuous linear operators

In this paper we solve the following problem posed by Schmets and Valdivia: Under which conditions does there exist an extension operator from the space of the Whitney jets on a closed set to so that the extended functions are real analytic outside ?

     

PI by NMR: Probing CH–π Interactions in Protein–Ligand Complexes by NMR Spectroscopy

While CH–π interactions with target proteins are crucial determinants for the affinity of arguably every drug molecule, no method exists to directly measure the strength of individual CH–π interactions in drug–protein complexes. Herein, we present a fast and reliable methodology called PI (π interactions) by NMR, which can differentiate the strength of protein–ligand CH–π interactions in solution. By combining selective amino-acid side-chain labeling with ¹H-¹³C NMR, we are able to identify specific protein protons of side-chains engaged in CH–π interactions with aromatic ring systems of a ligand, based solely on ¹H chemical-shift values of the interacting protein aromatic ring protons. The information encoded in the chemical shifts induced by such interactions serves as a proxy for the strength of each individual CH–π interaction. PI by NMR changes the paradigm by which chemists can optimize the potency of drug candidates: direct determination of individual π interactions rather than averaged measures of all interactions.     

A Reactive Molecular Dynamics Study of Chlorinated Organic Compounds. Part I: Force Field Development

This work presents a novel parametrization for the ReaxFF formalism as a means to investigate reaction processes of chlorinated organic compounds. Force field parameters cover the chemical elements C, H, O, Cl and were obtained using a novel optimization approach involving relaxed potential energy surface scans as training targets. The resulting ReaxFF parametrization shows good transferability, as demonstrated on two independent ab initio validation sets. While this first part of our two-paper series focuses on force field parametrization, we apply our parameters to the simulation of chlorinated dibenzofuran formation and decomposition processes in Part II.     

Holditch-Sätze für Regelflächen bzw. sphärische Kurven

In this paper we present some results (similar to the Holditch theorem) about the total torsion and total curvature of closed ruled surfaces resp. the area and length of closed spherical curves.