Open Sets Avoiding Integral Distances

We study open point sets in Euclidean spaces $\mathbb{R }^d$ R d without a pair of points an integral distance apart. By a result of Furstenberg, Katznelson, and Weiss such sets must be of Lebesgue upper density $0$ 0 . We are interested in how large such sets can be in $d$ d -dimensional volume. We determine the exact values for the maximum volumes of the sets in terms of the number of their connected components and dimension. Here techniques from diophantine approximation, algebra and the theory of convex bodies come into play. Our problem can be viewed as a counterpart to known problems on sets with pairwise rational or integral distances. It possibly opens a new research direction with strong links to topology and measure theory.     

Evidence for an isomeric 3/2- state in 53Co

The fragmentation of a 550MeV/u primary beam of ⁵⁸Ni on a ⁹Be target has been used to measure time- and energy-correlated γ decays following the implantation of event-by-event discriminated secondary fragments into a ⁹Be stopper plate. A new isomeric γ decay with T _1/2 = 14( ) ns and E _γ = 646.2(2) keV is observed and attributed to the decay of the yrast 3/2^- state in ⁵³ ₂₇Co₂₆ . This short-lived isomeric state has been populated by means of nuclear reactions during the stopping process of the secondary fragments. The experimental findings are discussed in the framework of large-scale spherical shell model calculations in conjunction with isospin symmetry-breaking residual interactions for the A = 53 , T _z = ±1/2 mirror nuclei ⁵³Co and ⁵³Fe .     

Evolution of Oxygen–Metal Electron Transfer and Metal Electronic States During Manganese Oxide Catalyzed Water Oxidation Revealed with In Situ Soft X‐Ray Spectroscopy

Manganese oxide (MnO_x) electrocatalysts are examined herein by in situ soft X‐ray absorption spectroscopy (XAS) and resonant inelastic X‐ray scattering (RIXS) during the oxidation of water buffered by borate (pH 9.2) at potentials from 0.75 to 2.25 V vs. the reversible hydrogen electrode. Correlation of L‐edge XAS data with previous mechanistic studies indicates Mn^IV is the highest oxidation state involved in the catalytic mechanism. MnO_x is transformed into birnessite at 1.45 V and does not undergo further structural phase changes. At potentials beyond this transformation, RIXS spectra show progressive enhancement of charge transfer transitions from oxygen to manganese. Theoretical analysis of these data indicates increased hybridization of the Mn?O orbitals and withdrawal of electron density from the O ligand shell. In situ XAS experiments at the O K‐edge provide complementary evidence for such a transition. This step is crucial for the formation of O₂ from water.     

Total Synthesis and Structural Revision of the Antibiotic Tetrapeptide GE81112A

The total synthesis of the naturally occurring antibiotic GE81112A, a densely functionalized tetrapeptide, is reported. Comparison of spectral data with those of the natural product and the lack of biological activity of the synthesized compound led us to revise the published configuration of the 3‐hydroxypipecolic acid moiety. This hypothesis was fully validated by the synthesis of the corresponding epimer.     

Particle Formation from Single Droplets of Aqueous Solutions of Lead Nitrate

The thermal evolution of droplets of aqueous solution of lead nitrate was studied in a drop-tube furnace, which simulates typical conditions for material synthesis, through spray pyrolysis, and for the thermal destruction of liquid-containing waste. The processes of droplet evaporation, precursor precipitation within the droplet and thermolysis of the precipitated particles were followed by means of the spectral analysis of the ultraviolet light scattered by the aerosol produced during the heating of aqueous droplets (100 μm) of lead nitrate, with different salt concentrations, from ambient temperature up to 1200 K. Dimensions and physico-chemical properties of the droplets/particles were obtained in situ by means of ultraviolet spectra of light scattering (UVSLS) and compared with scanning electron microscopy (SEM) of the sampled material. A plasma generated in the air by an optical breakdown induced by a Nd:YAG laser was employed as the light source in the wavelength range 200–400 nm, thus allowing an exceptionally high photon flux in the ultraviolet region where intense and species-specific interactions with metal species take place. The spray drying process was followed by measuring the light transmitted by the droplets in the backward region. As the drying process progresses, the surface concentration reaches a saturation value and solute is deposited as a solid phase forming a surface crust, which grows steadily. At this point in the process of droplet drying, information was retrieved from the light reflected by the particle interface. Two spectral scattering behaviors were detected at temperatures above the salt precipitation within the droplet. On the basis of Mie calculations and SEM measurements, these behaviors were attributed to lead nitrate particles with typical diameters of the residual droplets (about 50 μm) and to micrometer-sized lead oxide particles. The effect of salt concentration on the drying process and the thermolysis of lead nitrate to oxide was investigated by changing the salt concentration from very dilute conditions up to almost the saturation concentration.     

Directed evolution of high-affinity antibody mimics using mRNA display

We constructed a library of >10(12) unique, covalently coupled mRNA-protein molecules by randomizing three exposed loops of an immunoglobulin-like protein, the tenth fibronectin type III domain (10Fn3). The antibody mimics that bound TNF-alpha were isolated from the library using mRNA display. Ten rounds of selection produced 10Fn3 variants that bound TNF-alpha with dissociation constants (K(d)) between 1 and 24 nM. After affinity maturation, the lowest K(d) measured was 20 pM. Selected antibody mimics were shown to capture TNF-alpha when immobilized in a protein microarray. 10Fn3-based scaffold libraries and mRNA-display allow the isolation of high-affinity, specific antigen binding proteins; potential applications of such binding proteins include diagnostic protein microarrays and protein therapeutics.     

Water oxidation catalysed by manganese compounds: from complexes to 'biomimetic rocks'

One of the most fundamental processes of the natural photosynthetic reaction sequence is the light-driven oxidation of water to molecular oxygen. In vivo, this reaction takes place in the large protein ensemble Photosystem II, where a μ-oxido-Mn(4)Ca- cluster, the oxygen-evolving-complex (OEC), has been identified as the catalytic site for the four-electron/four-proton redox reaction of water oxidation. This Perspective presents recent progress for three strategies which have been followed to prepare functional synthetic analogues of the OEC: (1) the synthesis of dinuclear manganese complexes designed to act as water-oxidation catalysts in homogeneous solution, (2) heterogeneous catalysts in the form of clay hybrids of such Mn(2)-complexes and (3) the preparation of manganese oxide particles of different compositions and morphologies. We discuss the key observations from the studies of such synthetic manganese systems in order to shed light upon the catalytic mechanism of natural water oxidation. Additionally, it is shown how research in this field has recently been motivated more and more by the prospect of finding efficient, robust and affordable catalysts for light-driven water oxidation, a key reaction of artificial photosynthesis. As manganese is an abundant and non-toxic element, manganese compounds are very promising candidates for the extraction of reduction equivalents from water. These electrons could consecutively be fed into the synthesis of "solar fuels" such as hydrogen or methanol.     

True reference nanosensor realized with silicon nanowires

Conventional gate oxide layers (e.g., SiO(2), Al(2)O(3), or HfO(2)) in silicon field-effect transistors (FETs) provide highly active surfaces, which can be exploited for electronic pH sensing. Recently, great progress has been achieved in pH sensing using compact integrateable nanowire FETs. However, it has turned out to be much harder to realize a true reference electrode, which--while sensing the electrostatic potential--does not respond to the proton concentration. In this work, we demonstrate a highly effective reference sensor, a so-called reference FET, whose proton sensitivity is suppressed by as much as 2 orders of magnitude. To do so, the Al(2)O(3) surface of a nanowire FET was passivated with a self-assembled monolayer of silanes with a long alkyl chain. We have found that a full passivation can be achieved only after an extended period of self-assembling lasting several days at 80 °C. We use this slow process to measure the number of active proton binding sites as a function of time by a quantitative comparison of the measured nonlinear pH-sensitivities to a theoretical model (site-binding model). Furthermore, we have found that a partially passivated surface can sense small changes in the number of active binding sites reaching a detection limit of δN(s) ≈ 170 μm(-2) Hz(-1/2) at 10 Hz and pH 3.     

Magnetic circular dichroism spectrum of the molybdenum(V) complex [Mo(O)Cl3dppe]: C-term signs and intensities for multideterminant excited doublet states

The molybdenum(V) complex [Mo(O)Cl(3)dppe] [dppe = 1,2-bis(diphenylphosphino)ethane] is considered as a model system for a combined study of the electronic structure using UV/vis absorption and magnetic circular dichroism (MCD) spectroscopy. In order to determine the signs and MCD C-term intensities of the chlorido → molybdenum charge-transfer transitions, it is necessary to take the splitting of the excited doublet states into sing-doublet and trip-doublet states into account. While transitions to the sing-doublet states are electric-dipole-allowed, those to the trip-doublet states are electric-dipole-forbidden. As spin-orbit coupling within the manifold of sing-doublet states vanishes, configuration interaction between the sing-doublet and trip-doublet states is required to generate the MCD C-term intensity. The most prominent feature in the MCD spectrum of [Mo(O)Cl(3)dppe] is a "double pseudo-A term", which consists of two corresponding pseudo-A terms centered at 27000 and 32500 cm(-1). These are assigned to the ligand-to-metal charge-transfer transitions from the p(π) orbitals of the equatorial chlorido ligands to the Mo d(yz) and d(xz) orbitals. On the basis of the theoretical expressions developed by Neese and Solomon (Inorg. Chem. 1999, 38, 1847-1865), a general treatment of the MCD C-term intensity of these transitions is presented that explicitly considers the multideterminant character of the excited states. The individual MCD signs are determined from the corresponding transition densities derived from the calculated molecular orbitals of the title complex (BP86/LANL2DZ).