Generalised sk-Spline Interpolation on Compact Abelian Groups

The notion of sk-spline is generalised to arbitrary compact Abelian groups. A class of conditionally positive definite kernels on the group is identified, and a subclass corresponding to the generalised sk-spline is used for constructing interpolants, on scattered data, to continuous functions on the group. The special case ofd-dimensional torus is considered and convergence rates are proved when the kernel is a product of one-dimensional kernels, and the data are gridded.     

Impact of thioesterase activity on tylosin biosynthesis in Streptomyces fradiae.

BACKGROUND: The polyketide lactone, tylactone, is produced in Streptomyces fradiae by the TylG complex of five multifunctional proteins. As with other type I polyketide synthases, the enzyme catalysing the final elongation step (TylGV) possesses an integral thioesterase domain that is believed to be responsible for chain termination and ring closure to form tylactone, which is then glycosylated to yield tylosin. In common with other macrolide producers, S. fradiae also possesses an additional thioesterase gene (orf5) located within the cluster of antibiotic biosynthetic genes. The function of the Orf5 protein is addressed here. RESULTS: Disruption of orf5 reduced antibiotic accumulation in S. fradiae by at least 85%. Under such circumstances, the strain accumulated desmycosin (demycarosyl-tylosin) due to a downstream polar effect on the expression of orf6, which encodes a mycarose biosynthetic enzyme. High levels of desmycosin production were restored in the disrupted strain by complementation with intact orf5, or with the corresponding thioesterase gene, nbmB, from S. narbonensis, but not with DNA encoding the integral thioesterase domain of TylGV. CONCLUSIONS: Polyketide metabolism in S. fradiae is strongly dependent on the thioesterase activity encoded by orf5 (tylO). It is proposed that the TylG complex might operate with a significant error frequency and be prone to blockage with aberrant polyketides. A putative editing activity associated with TylO might be essential to unblock the polyketide synthase complex and thereby promote antibiotic accumulation.     

First μ+SR studies on thin films with a new beam of low energy positive muons at energies below 20 keV

At the Paul Scherrer Institute slow positive muons (μ⁺) with nearly 100% polarization and an energy of about 10 eV are generated by moderation of an intense secondary beam of surface muons in an appropriate condensed gas layer. These epithermal muons are used as a source of a tertiary beam of tunable energy between 10 eV and 20 keV. The range of these muons in solids is up to 100 nm which allows the extension of the μ⁺SR techniques (muon spin rotation, relaxation, resonance) to the study of thin films. A basic requirement for the proper interpretation of μ⁺SR results on thin films and multi-layers is the knowledge of the depth distribution of muons in matter. To date, no data are available concerning this topic. Therefore, we investigated the penetration depth of μ⁺ with energies between 8 keV and 16 keV in Cu/SiO₂ samples. The experimental data are in agreement with simulated predictions. Additionally, we present two examples of first applications of low energy μ⁺ in μ⁺SR investigations. We measured the magnetic field distribution inside a 500-nm thin High-T_C superconductor (YBa₂Cu₃O_7-δ), as well as the depth dependence of the field distribution near the surface. In another experiment a 500-nm thin sample of Fe-nanoclusters (diameter 2.4(4) nm), embedded in an Ag matrix with a volume concentration of 0.1%, was investigated with transverse field μ⁺SR. This revised version was published online in August 2006 with corrections to the Cover Date.     

Polycrystal constraint and grain subdivision

Typically, intergranular constraint relations of various sorts are introduced to improve the accuracy of prediction of texture evolution and macroscale stress–strain behavior of metallic polycrystals within the context of simple polycrystal averaging schemes. This paper examines the capability of a 3-D polycrystal plasticity theory (Kocks, U.F., Kallend, J.S., Wank, H.-R., Rollett, A.D. and Wright, S.I. (1994), popLA, Preferred Orientation Package—Los Alamos. LANL LA-CC-89-18), based on the Taylor assumption of uniform deformation among grains, to predict texture evolution and stress–strain behavior for complex finite deformation loading paths of OFHC Cu. Compression, shear and sequences of deformation path are considered. It is shown that the evolution of texture is too rapid and that the intensity of peaks is more pronounced than for experimentally measured pole figures. Comparisons of both stress–strain behavior and texture evolution are made with experiments, with and without the inclusion of latent hardening effects. It is argued that grain subdivision processes accommodate intergranular kinematical constraints, leading to the notion of a generalized Taylor constraint that considers the distribution of subgrain orientations. The subdivision process is assumed to follow the experimentally observed refinement of low energy dislocation structures associated with geometrically necessary dislocations. A modification of the kinematical structure of crystal plasticity is proposed based on generation of geometrically necessary dislocations that accommodate a fraction of the plastic stretch and rotation at the scale of a grain.     

Enantioselective synthesis of 2-hydroxy-1-indanone,a key precursor of enantiomerically pure 1-amino-2-indanol

Enantiomerically pure (R)- or (S)-2-hydroxy-1-indanone was synthesized by enzymatic kinetic resolution of racemic 2-acetoxy-1-indanone through hydrolysis or transesterification.     

The structure of diphosphine radical cations

When R₂NNR₂ molecules lose an electron to give (R₂NNR₂)^+· radical cations, the whole unit becomes planar, with a(π₁)²(π₂)¹ configuration. However, because R₃P molecules are far more strongly pyramidal than R₃N molecules, this flattening on electron loss is less, and phosphorous centred radical cations do not achieve planarity. This is clearly so for (R₂PPR₂)⁺ centres, whose liquid and solid state spectra analysed herein in terms of two equivalent ³¹P hyperfine couplings, show ca. 9% 3s character. This indicates considerable bending at each phosphorous centre. Furthermore, the form of the spectra, with no x — y splitting of the ‘perpendicular’ lines, suggests that each ³¹P coupling shares a common axis. This means that a trans conformation is required, as expected because this relieves steric strain and favours “π” type orbital overlap.     

Hot versus cold neutron stars

Hot neutron stars at birth are compared with usual cold neutron stars and discussed concerning the energy release and the spin-up in the cooling stage. It is remarked that new constraints are imposed on the critical mass and the maximum rotation rate of cold neutron stars by the consideration of their hot stage.     

On stability of the elliptical “orbits” of diamagnetic positronium

The stability of the elliptical orbits of diamagnetic positronium is studied and it is found to depend only on the eccentricity ε and the combination of parameters λ = B²r_0c³ (where B is the magnetic field strength and r_0c the conserved guiding center). For small and large values of λ the orbits remain stable while at approximately λ = 1 unstable behavior appears when the eccentricity becomes larger than ε = 0.25.     

Semi-passivity and synchronization of diffusively coupled neuronal oscillators

We discuss synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling, i.e. linearly coupled via gap junctions. In particular, we present sufficient conditions for synchronization in these networks using the theory of semi-passive and passive systems. We show that the conductance based neuronal models of Hodgkin-Huxley, Morris-Lecar, and the popular reduced models of FitzHugh-Nagumo and Hindmarsh-Rose all satisfy a semi-passivity property, i.e. that is the state trajectories of such a model remain oscillatory but bounded provided that the supplied (electrical) energy is bounded. As a result, for a wide range of coupling configurations, networks of these oscillators are guaranteed to possess ultimately bounded solutions. Moreover, we demonstrate that when the coupling is strong enough the oscillators become synchronized. Our theoretical conclusions are confirmed by computer simulations with coupled Hindmarsh-Rose and Morris-Lecar oscillators. Finally we discuss possible “instabilities” in networks of oscillators induced by the diffusive coupling.     

Modelling transient heat conduction in solids at multiple length and time scales: A coupled non-equilibrium molecular dynamics/continuum approach

A method for controlling the thermal boundary conditions of non-equilibrium molecular dynamics simulations is presented. The method is simple to implement into a conventional molecular dynamics code and independent of the atomistic model employed. It works by regulating the temperature in a thermostatted boundary region by feedback control to achieve the desired temperature at the edge of an inner region where the true atomistic dynamics are retained. This is necessary to avoid intrinsic boundary effects in non-equilibrium molecular dynamics simulations. Three thermostats are investigated: the global deterministic Nosé–Hoover thermostat and two local stochastic thermostats, Langevin and stadium damping. The latter thermostat is introduced to avoid the adverse reflection of phonons that occurs at an abrupt interface. The method is then extended to allow atomistic/continuum models to be thermally coupled concurrently for the analysis of large steady state and transient heat conduction problems. The effectiveness of the algorithm is demonstrated for the example of heat flow down a three-dimensional atomistic rod of uniform cross-section subjected to a variety of boundary conditions.