Shannon sampling II: Connections to learning theory

We continue our study [S. Smale, D.X. Zhou, Shannon sampling and function reconstruction from point values, Bull. Amer. Math. Soc. 41 (2004) 279–305] of Shannon sampling and function reconstruction. In this paper, the error analysis is improved. Then we show how our approach can be applied to learning theory: a functional analysis framework is presented; dimension independent probability estimates are given not only for the error in the L² spaces, but also for the error in the reproducing kernel Hilbert space where the learning algorithm is performed. Covering number arguments are replaced by estimates of integral operators.     

Selbstheilende Polymere

Even though the field of self‐healing is rarely known so far – self healing materials are already present at our market. Nevertheless just due to modern scientific concepts we are now able to understand the basic mechanistic steps in a more detailed way. Further progress on this field will open access to materials with a wide range of adjustable properties. Therefore, applications of such self healing materials are not limited – assuming the market‐price is competitive and the elongated lifetime delivers an appropriate advantage. Already demonstrated for concrete and clear coatings for cars, the investigations done so far have generated materials with improved properties and prolonged durability.     

Optimization of the electrodeposition process of high-performance bismuth antimony telluride compounds for thermoelectric applications

High-quality films of bismuth antimony telluride were synthesized by electrodeposition from nitric acid electroplating baths. The influence of a surfactant, sodium ligninsulfonate, on the structure, morphology, stoichiometry, and homogeneity of the deposited films has been investigated. It was found that addition of this particular surfactant significantly improved the microstructural properties as well as homogeneity of the films with a significant improvement in the thermoelectric properties over those deposited in the absence of surfactant. A detailed microprobe analysis of the deposited films yielded a stoichiometric composition of Bi(0.35)Sb(1.33)Te(3) for the films electrodeposited in the absence of surfactant and a stoichiometry of Bi(0.32)Sb(1.33)Te(3) for films deposited in the presence of surfactant.     

On the origin of altered diastereomeric ratios for anionic versus neutral reaction conditions in the oxy-Cope/ene reaction: an interplay of experiment and computational modeling

We report herein a detailed investigation into the reaction mechanism for a sequential oxy-Cope/ene reaction under anionic conditions. With DFT calculations and ab initio molecular dynamics simulations, the observed diastereoselectivity is shown to be the result of an isomerization of the enolate olefin, which would evidently not occur under neutral conditions. The potential energy surface was thoroughly mapped out for the reaction pathways and the proposed mechanism confirmed the different product distributions observed under neutral and anionic oxy-Cope conditions. In addition, other possible pathways are shown to be higher in energy and experimental evidence is given that supports the olefin-isomerization pathway.     

Analysis of the reactivities of protein C-H bonds to H atom abstraction by OH radical

Ab initio and density functional theory calculations are used to monitor the process wherein a OH· radical is allowed to approach the various CH groups of a Leu dipeptide, with its CH(2)CH(CH(3))(2) side chain. After forming an encounter complex, the OH· abstracts the pertinent H atom, and the resulting HOH is then dissociated from the complex. The energy barriers for H· abstraction from the β, γ, and δ CH groups are all less than 8 kcal/mol, but a significantly higher barrier is computed for the C(α)H removal. This higher barrier is the result of the strong H-bonds formed in the encounter complex between the OH· and the NH and C═O groups of the peptide units that surround the C(α) atom. This low-energy complex represents a kinetic trap which raises the energy needed to surmount the ensuing H· transfer barrier.     

Hawking radiation, Unruh radiation, and the equivalence principle

We compare the response function of an Unruh-DeWitt detector for different space-times and different vacua and show that there is a detailed violation of the equivalence principle. In particular comparing the response of an accelerating detector to a detector at rest in a Schwarzschild space-time we find that both detectors register thermal radiation, but for a given, equivalent acceleration the fixed detector in the Schwarzschild space-time measures a higher temperature. This allows one to locally distinguish the two cases. As one approaches the horizon the two temperatures have the same limit so that the equivalence principle is restored at the horizon.