The convenient setting for quasianalytic Denjoy-Carleman differentiable mappings

For quasianalytic Denjoy-Carleman differentiable function classes CQ where the weight sequence Q=(Qk) is log-convex, stable under derivations, of moderate growth and also an L-intersection (see (1.6)), we prove the following: The category of CQ-mappings is cartesian closed in the sense that CQ(E,CQ(F,G))≅CQ(E×F,G) for convenient vector spaces. Applications to manifolds of mappings are given: The group of CQ-diffeomorphisms is a regular CQ-Lie group but not better.     

On Mincʼs sheltered middle path

This paper shows that a construction, which was introduced by Piotr Minc in connection with a problem that came from Helly type theorems and that allows to replace three PL-arcs with a “sheltered middle path”, can in the case of general (non-PL) paths result in the topologist?s sine curve.     

Molecular Dynamics Simulation of Ester‐Linked Hen Egg White Lysozyme Reveals the Effect of Missing Backbone Hydrogen Bond Donors on the Protein Structure

The three‐dimensional structure of a protein is stabilized by a number of different atomic interactions. One of these is hydrogen bonding. Its influence on the spatial structure of the hen egg white lysozyme is investigated by replacing peptide bonds (except those of the two proline residues) by ester bonds. Molecular dynamics simulations of native and ester‐linked lysozyme are compared with the native crystal structure and with NOE distance bounds derived from solution NMR experiments. The ester‐linked protein shows a slight compaction while losing its native structure. However, it does not unfold completely. The structure remains compact due to its hydrophobic core and a changed network of hydrogen bonds involving side chains.     

An adaptive algorithm for simulation of stochastic reaction–diffusion processes

We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction–diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie’s stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the timesteps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.     

Cyclization of Propargylic Amides: Mild Access to Oxazole Derivatives

The substrate scope, the mechanistic aspects of the gold‐catalyzed oxazole synthesis, and substrates with different aliphatic, aromatic, and functional groups in the side chain were investigated. Even molecules with several propargyl amide groups could easily be converted, delivering di‐ and trioxazoles with interesting optical properties. Furthermore, the scope of the gold(I)‐catalyzed alkylidene synthesis was investigated. Further functionalizations of these isolable intermediates of the oxazole synthesis were developed and chelate ligands can be obtained. The use of Barluenga’s reagent offers a new and mild access to the synthetically valuable iodoalkylideneoxazoles from propargylic amides, this reagent being superior to other sources of halogens.