Hoffman’s Error Bounds and Uniform Lipschitz Continuity of Best l(p) -Approximations

In a central paper on smoothness of best approximation in 1968 R. Holmes and B. Kripke proved among others that on ℝn, endowed with the lρ-norm, 1\u3c p \u3c ∞, the metric projection onto a given linear subspace is Lipschitz continuous where the Lipschitz constant depended on the parameter p. Using Hoffman’s Error Bounds as a principal tool we prove uniform Lipschitz continuity of best lρ -ap- proximations. As a consequence, we reprove and prove, respectively, Lipschitz. continuity of the strict best approximation (sba, p = ∞ and of the natural best approximation (nba, p = 1

Preparation and characterisation of carbon-free Cu(111) films on sapphire for graphene synthesis

This work presents an investigation of carbon formed on polycrystalline Cu(111) thin films prepared by ion beam sputtering at room temperature on c-plane Al2O3 after thermal treatment in a temperature range between 300 and 1020°C. The crystallinity of the Cu films was studied by XRD and RBS/channeling and the surface was characterised by Raman spectroscopy, XPS and AFM for each annealing temperature. RBS measurements revealed the diffusion of the Cu into the Al2O3 substrate at high temperatures of > 700°C. Furthermore, a cleaning procedure using UV ozone treatment is presented to remove the carbon from the surface which yields essentially carbon-free Cu films that open the possibility to synthesize graphene of well-controlled thickness (layer number)

Bi12Rh3Cu2I5: A 3D Weak Topological Insulator with Monolayer Spacers and Independent Transport Channels

Topological insulators (TIs) are semiconductors with protected electronic surface states that allow dissipation-free transport. TIs are envisioned as ideal materials for spintronics and quantum computing. In Bi14Rh3I9, the first weak 3D TI, topology presumably arises from stacking of the intermetallic [(Bi4Rh)3I]2+ layers, which are predicted to be 2D TIs and to possess protected edge-states, separated by topologically trivial [Bi2I8]2− octahedra chains. In the new layered salt Bi12Rh3Cu2I5, the same intermetallic layers are separated by planar, i.e., only one atom thick, [Cu2I4]2− anions. Density functional theory (DFT)-based calculations show that the compound is a weak 3D TI, characterized by (Formula presented.), and that the topological gap is generated by strong spin–orbit coupling (E g,calc. ∼ 10 meV). According to a bonding analysis, the copper cations prevent strong coupling between the TI layers. The calculated surface spectral function for a finite-slab geometry shows distinct characteristics for the two terminations of the main crystal faces ⟨001⟩, viz., [(Bi4Rh)3I]2+ and [Cu2I4]2−. Photoelectron spectroscopy data confirm the calculated band structure. In situ four-point probe measurements indicate a highly anisotropic bulk semiconductor (E g,exp. = 28 meV) with path-independent metallic conductivity restricted to the surface as well as temperature-independent conductivity below 60 K

First-principles design of a single-atom–alloy propane dehydrogenation catalyst

The complexity of heterogeneous catalysts means that a priori design of new catalytic materials is difficult, but the well-defined nature of single-atom–alloy catalysts has made it feasible to perform unambiguous theoretical modeling and precise surface science experiments. Herein we report the theory-led discovery of a rhodium-copper (RhCu) single-atom–alloy catalyst for propane dehydrogenation to propene. Although Rh is not generally considered for alkane dehydrogenation, first-principles calculations revealed that Rh atoms disperse in Cu and exhibit low carbon-hydrogen bond activation barriers. Surface science experiments confirmed these predictions, and together these results informed the design of a highly active, selective, and coke-resistant RhCu nanoparticle catalyst that enables low-temperature nonoxidative propane dehydrogenation

Ultrathin 2 nm gold as ideal impedance-matched absorber for infrared light

Thermal detectors are a cornerstone of infrared (IR) and terahertz (THz) technology due to their broad spectral range. These detectors call for suitable broad spectral absorbers with minimalthermal mass. Often this is realized by plasmonic absorbers, which ensure a high absorptivity butonly for a narrow spectral band. Alternativly, a common approach is based on impedance-matching the sheet resistance of a thin metallic film to half the free-space impedance. Thereby, it is possible to achieve a wavelength-independent absorptivity of up to 50 %, depending on the dielectric properties of the underlying substrate. However, existing absorber films typicallyrequire a thickness of the order of tens of nanometers, such as titanium nitride (14 nm), whichcan significantly deteriorate the response of a thermal transducers. Here, we present the application of ultrathin gold (2 nm) on top of a 1.2 nm copper oxide seed layer as an effective IR absorber. An almost wavelength-independent and long-time stable absorptivity of 47(3) %, ranging from 2 $\mu$m to 20 $\mu$m, could be obtained and is further discussed. The presented gold thin-film represents analmost ideal impedance-matched IR absorber that allows a significant improvement of state-of-the-art thermal detector technology

A substrate mimic allows high-throughput assay of the FabA protein and consequently the identification of a novel inhibitor of <i>Pseudomonas aeruginosa</i> FabA

The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement n° 223461, Senior Investigator Award WT100209MA (JHN), Swedish Science Council (GS), Wellcome Trust Strategic grant 100476/Z/12/Z (DWG) and National Institutes of Health R01GM095970 (MB). JHN & ADS are Royal Society Wolfson Merit Award holders.Eukaryotes and prokaryotes possess fatty acid synthase (FAS) biosynthetic pathway(s) that comprise iterative chain elongation, reduction, and dehydration reactions. The bacterial FASII pathway differs significantly from human FAS pathways and is a long-standing target for antibiotic development against Gram-negative bacteria due to differences from the human FAS, and several existing antibacterial agents are known to inhibit FASII enzymes. N-acetylcysteamine (NAC) fatty acid thioesters have been used as mimics of the natural acyl carrier protein (ACP) pathway intermediates to assay FASII enzymes, and we now report an assay of FabV from Pseudomonas aeruginosa using (E)-2-decenoyl-NAC. In addition, we have converted an existing UV absorbance assay for FabA, the bifunctional dehydration/epimerization enzyme and key target in the FAS II pathway, into a high throughput enzyme coupled fluorescence assay that has been employed to screen a library of diverse small molecules. With this approach, N-(4-chlorobenzyl)-3-(2-furyl)-1H-1,2,4-triazol-5-amine (N42FTA) was found to competitively inhibit (pIC50 = 5.7 ± 0.2) the processing of 3-hydroxydecanoyl-NAC by P. aeruginosa FabA. N42FTA was shown to be potent in blocking crosslinking of E. coli ACP and FabA, a direct mimic of the biological process. The co-complex structure of N42FTA with P. aeruginosa FabA protein rationalizes affinity and suggests future design opportunities. Employing NAC fatty acid mimics to developing further high throughput assays for individual enzymes in the FASII pathway should aid in the discovery of new antimicrobials.Publisher PDFPeer reviewe

Modulating endothelial adhesion and migration impacts stem cell therapies efficacy

Background: Limited knowledge of stem cell therapies‘ mechanisms of action hampers their sustainable implementation into the clinic. Specifically, the interactions of transplanted stem cells with the host vasculature and its implications for their therapeutic efficacy are not elucidated. We tested whether adhesion receptors and chemokine receptors on stem cells can be functionally modulated, and consequently if such modulation may substantially affect therapeutically relevant stem cell interactions with the host endothelium. Methods: We investigated the effects of cationic molecule polyethylenimine (PEI) treatment with or without nanoparticles on the functions of adhesion receptors and chemokine receptors of human bone marrow-derived Mesenchymal Stem Cells (MSC). Analyses included MSC functions in vitro, as well as homing and therapeutic efficacy in rodent models of central nervous system´s pathologies in vivo. Findings: PEI treatment did not affect viability, immunomodulation or differentiation potential of MSC, but increased the CCR4 expression and functionally blocked their adhesion receptors, thus decreasing their adhesion capacity in vitro. Intravenously applied in a rat model of brain injury, the homing rate of PEI-MSC in the brain was highly increased with decreased numbers of adherent PEI-MSC in the lung vasculature. Moreover, in comparison to untreated MSC, PEI-MSC featured increased tumour directed migration in a mouse glioblastoma model, and superior therapeutic efficacy in a murine model of stroke. Interpretation: Balanced stem cell adhesion and migration in different parts of the vasculature and tissues together with the local microenvironment impacts their therapeutic efficacy. Funding: Robert Bosch Stiftung, IZEPHA grant, EU grant 7 FP Healt