Minima of initial segments of infinite sequences of reals

Suppose that 〈x_k〉_k∈? is a countable sequence of real numbers. Working in the usual subsystems for reverse mathematics, RCA₀ suffices to prove the existence of a sequence of reals 〈u_k〉_k∈? such that for each k, u_k is the minimum of {x₀, x₁, …, x_k}. However, if we wish to prove the existence of a sequence of integer indices of minima of initial segments of 〈x_k〉_k∈?, the stronger subsystem WKL₀ is required. Following the presentation of these reverse mathematics results, we will derive computability theoretic corollaries and use them to illustrate a distinction between computable analysis and constructive analysis. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rearrangement in the mass spectrometer via a 3,3,1-bicyclic reaction path

The fragmentation of some azoacylals showed a 3,3,1 bicyclic rearrangement which could be demonstrated by a deuterium labelling study.     

Superconductors containing impurities with crystal-field split energy levels

We investigate theoretically the problem of a superconducting matrix containing paramagnetic rare earth impurities with crystal-field split energy levels. There are two competing mechanisms which change the superconducting transition temperatureT _c. One is inelastic charge scattering of conduction electrons from the aspherical part of the 4f charge distribution, which leads to an increase inT _c similar to that of optical phonons. The other and often predominant mechanism comes from the exchange interaction, which depressesT _c and can be very effective even among non-magnetic levels via off-diagonal matrix elements. Crystalline fields serve to alter the effectiveness of the two kinds of scattering depending upon the symmetry character of the low-lying levels, and in favorable cases one may study separately the effects of the two types of scattering by adding different impurities to a given host. We find that crystal-field levels at energies quite high compared tok _B·T_c can still have an important effect onT _c. It is shown that the crystalline-field splitting should be directly observable as structure in the tunneling characteristics.     

Application of the INDO-MO method to the calculation of hyperfine splitting constants for styrene radical anions

The results of INDO-MO calculations of hyperfine splitting constants for the radical-anions of a series of styrene derivatives are presented. The calculations reproduce the general features of the observed e.s.r. spectra but the detailed agreement is less good than that of previously reported McLachlan calculations.     

Configuration crossover in 4f substances under pressure

It is well established that in 4f substances the application of pressure tends to reduce the number of 4f electrons, so that if a configuration 4fⁿ is initially stable there may be a crossover to 4f^n?1 as the stable configuration at high pressures. We develop a simple theory of this configuration crossover, with particular emphasis on the questions of whether the crossover occurs discontinuously and whether a fractional-valence thermodynamic state, in which the individual 4f ions undergo rapid interconfiguration fluctuations, is stable near the crossover. The theory yields the 4f occupancy, which implies the main contribution to the Mössbauer isomer shift, and the pressure-volume relation. Model calculations are given for Ce metal and for the Sm monochalcogenides.     

Orbital angular momentum of 3d impurities in metals

It is shown that 3d impurities often have a significant orbital moment due to the high symmetry of the crystalline electric field in typical metallic hosts. The EPR behavior which has been observed for such impurities is clarified and further predictions are made. The configurations of 3d impurities in noble metals are established: for example, Fe has 6 3d electrons andS=2. A spin-orbit splitting of about 0.02 eV is expected for Fe impurities, which may be observable by inelastic neutron scattering. The influence of orbital angular momentum on the Kondo effect is briefly discussed.     

Excited states of HCl

Ab initio CI calculations are presented for potential curves for the valence states of HCl, for the vertical electronic spectrum and for the potential curve for the B ¹Σ⁺ state. The valence ¹Π, ³Π and ³Σ⁺ states are found to be repulsive. Calculated vertical excitation energies are in good agreement with experiment. The B ¹Σ⁺ curve is predicted to have a double minimum.     

Late-Stage Functionalization by Chan–Lam Amination: Rapid Access to Potent and Selective Integrin Inhibitors

A late-stage functionalization of the aromatic ring in amino acid derivatives is described. The key step is a copper-catalysed diversification of a boronate ester by amination (Chan–Lam reaction) that can be carried out on a complex β-aryl-β-amino acid scaffold. This not only considerably extends the substrate scope of amination partners, but also delivers an array of potent and selective integrin inhibitors as potential treatment agents of idiopathic pulmonary fibrosis (IPF). This versatile chemical strategy, which is amenable to high-throughput-array protocols, allows the installation of pharmaceutically valuable heteroaromatic fragments at a late stage by direct coupling to NH heterocycles, leading to compounds with drug-like attributes. It thus constitutes a useful addition to the medicinal chemist's repertoire.     

Charge-transfer transitions in the vacuum-ultraviolet of protein circular dichroism spectra

Circular dichroism (CD) is widely used in the structural characterization and secondary structure determination of proteins. The vacuum UV region (below 190 nm), where charge-transfer transitions have an influence on the CD spectra, can be accessed using synchrotron radiation circular dichroism (SRCD) spectroscopy. Recently, charge-transfer transitions in a conformationally diverse set of dipeptides have been characterized ab initio using complete active space self-consistent field calculations, and the relevant charge distributions have been parametrized for use in the matrix method for calculations of protein CD. Here, we present calculations of the vacuum UV CD spectra of 71 proteins, for which experimental SRCD spectra and X-ray crystal structures are available. The theoretical spectra are calculated considering charge-transfer and side chain transitions. This significantly improves the agreement with experiment, raising the Spearman correlation coefficient between the calculated and the experimental intensity at 175 nm from 0.12 to 0.79. The influence of the conformation on charge-transfer transitions is analyzed in detail, showing that the n --> pi* charge-transfer transitions are most important in alpha-helical proteins, whereas in beta strand proteins the pi --> pi* charge-transfer transition along the chain in the amino- to carboxy-end direction is most dominant.