Galois module structure of unramified covers

We use the theory of n-cubic structures to study the Galois module structure of the coherent cohomology groups of unramified Galois covers of varieties over the integers. Assuming that all the Sylow subgroups of the covering group are abelian, we show that the invariant that measures the obstruction to the existence of a “virtual normal integral basis” is annihilated by a product of certain Bernoulli numbers with orders of even K-groups of Z. We also show that the existence of such a basis is closely connected to the truth of the Kummer-Vandiver conjecture for the prime divisors of the degree of the cover. Partially supported by NSF grants # DMS05-01049 and # DMS01-11298 (via the Institute for Advanced Study).     

A bundle-type algorithm for routing in telecommunication data networks

To optimize the quality of service through a telecommunication network, we propose an algorithm based on Lagrangian relaxation. The bundle-type dual algorithm is adapted to the present situation, where the dual function is the sum of a polyhedral function (coming from shortest path problems) and of a smooth function (coming from the congestion function).     

Contrasting chemoselectivities in the ultrasound and microwave assisted bromination reactions of substituted alkylaromatics with N-bromosuccinimide

Ultrasound and microwave assisted bromination reactions of various alkylaryls with N-bromosuccinimide, either neat or in water, shows diverse chemoselectivity. Thus, ring substitution occurs in water with ultrasound, whereas with microwaves both side-chain α-bromination and ring substitution occur. With neat reactants, side-chain α-bromination predominates for microwave assisted reactions. In the presence of water the chemoselectivity with microwave-promoted bromination is similar to that observed using classical methods.     

Magnetic anisotropy axis reorientation at ultrathin FePt films

Ultrathin FePt films (thickness between 1 nm and 5 nm) were studied for non‐volatile memories applications. The films were magnetron sputtered on monocrystalline MgO?001? substrates at 500 °C. The films are polycrystalline, except the 1 nm thick film which is not continuous. It is shown that films with thickness higher than 2.7 nm have L1₀ structure and perpendicular magnetic anisotropy, while a transition to in‐plane anisotropy occurs for thinner films. The out‐of‐plane coercivity drops from 16 kOe at the thicker film to 0.5 kOe at the thinner one.

Hysteresis cycles of FePt films as a function of film thickness.     

Hořava–Lifshitz cosmology

The cosmological equations suggested by the non-relativistic renormalizable gravitational theory proposed by Hořava are considered. It is pointed out that the early universe cosmology has features that may give an alternative to inflation and the theory may be able to escape singularities.     

Laminar axisymmetric flow of a weakly compressible viscoelastic fluid

The combined effects of weak compressibility and viscoelasticity in steady, isothermal, laminar axisymmetric Poiseuille flow are investigated. Viscoelasticity is taken into account by employing the Oldroyd-B constitutive model. The fluid is assumed to be weakly compressible with a density that varies linearly with pressure. The flow problem is solved using a regular perturbation scheme in terms of the dimensionless isothermal compressibility parameter. The sequence of partial differential equations resulting from the perturbation procedure is solved analytically up to second order. The two-dimensional solution reveals the effects of compressibility and the other dimensionless numbers and parameters in the flow. Expressions for the average pressure drop, the volumetric flow rate, the total axial stress, as well as for the skin friction factor are also derived and discussed. The validity of other techniques used to obtain approximate solutions of weakly compressible flows is also discussed in conjunction with the present results.     

One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal

We demonstrate theoretically the existence of one-way electromagnetic modes in a waveguide formed between a semi-infinite photonic crystal structure and a semi-infinite metal region under a static magnetic field. Such a waveguide provides a frequency range where only one propagating direction is allowed. In this frequency range, disorder-induced scattering is completely suppressed. Such a waveguide also modifies the basic properties of waveguide-cavity interaction.     

Effect of biochar on the mobility and photodegradation of metribuzin and metabolites in soil‒biochar thin-layer chromatography plates

Biochars obtained by biomass pyrolysis have been proposed as a soil amendment to improve soil properties and fertility as well as to retain pesticides and other environmental contaminants. The present study investigates the degradation of metribuzin herbicide and its metabolites deamino- (DA), deaminodiketo- (DADK) and diketo- (DK) metribuzin under simulated solar light and dark conditions as well as their mobility using TLC plates coated with soil and soil?biochar mixtures at 1% and 5% w/w ratio. Biochar was characterised by X-Ray diffraction, porosimetry, scanning electron microscopy and Fourier transform infrared spectroscopy. Degradation under light conditions followed biphasic kinetics, with bi-exponential model fitted better for the soil substrate, while the Gustafson–Holden model was found more appropriate to describe degradation kinetics in 1% soil/biochar mixture. In soil, DA presented the lowest degradation rate (DT₅₀:440.9 h), followed by metribuzin (DT₅₀:208.0 h), DADK (DT₅₀:110.8 h) and DK (DT₅₀:106.5 h). The addition of biochar reduced drastically the degradation or even inhibited the photolytic process for the studied reaction period. The mobility retention factor (Rf) in soil ranged from 0.49 for metribuzin to 0.63 for DADK. The addition of biochar practically immobilises the compounds in the surface layer as Rf ranged from 0.14 to 0.10 for metribuzin and from 0.23 to 0.16 for DADK in soil/biochar mixtures 1% and 5%, respectively. In conclusion, the addition of biochar reduced dramatically the photodegradation rates as well as the mobility of metribuzin and its metabolites due to increased adsorption.     

Illustrating the power of singlet oxygen chemistry in a synthetic context: biomimetic syntheses of litseaverticillols A-G, I and J and the structural reassignment of litseaverticillol E

Biomimetic syntheses of the litseaverticillols A-G, I and J are reported herein. The syntheses rely heavily on the application of two different modes of reaction for photochemically generated singlet oxygen, namely, the [4+2] cycloaddition of singlet oxygen (1O2) with furans and the ene reaction of 1O2 with double bonds. The highlight of these syntheses is a one-pot cascade sequence, involving five synthetic operations initiated by a [4+2] reaction, to form the fully functionalised litseaverticillol core. A series of regioselective ene reactions are then used to appositely functionalise the side chains. The synthesis of litseaverticillol E (both its originally proposed and its actual structures) allows a structural reassignment of this natural product.