On the index of a holomorphic vector field tangent to a singular variety

In this article we define and compute an index for a holomorphic vector field on a (possibly singular) subvariety of a complex manifold, provided the subvariety is a local complete intersection. This index reduces to the usual Poincaré-Hopf index in case the subvariety is smooth, and is equal more generally to the index defined in [GSV] and [SS].     

An adaptive discretization of shallow‐water equations based on discontinuous Galerkin methods

In this paper, we present a discontinuous Galerkin formulation of the shallow‐water equations. An orthogonal basis is used for the spatial discretization and an explicit Runge–Kutta scheme is used for time discretization. Some results of second‐order anisotropic adaptive calculations are presented for dam breaking problems. The adaptive procedure uses an error indicator that concentrates the computational effort near discontinuities like hydraulic jumps. Copyright © 2006 John Wiley & Sons, Ltd.     

The electric quadrupole interaction of the 134 keV state of197Hg in the metal hosts Cd,Zn, Sn and Ti studied by e−-γ TDPAC measurements

The electric quadrupole coupling constants of the lowest excited 5/2^? state in¹⁹⁷Hg have been measured by the e^?-γ TDPAC method for the hosts Ti and Sn at room temperature and for Zn and Cd at various temperatures. The observed temperature dependences are approximately the same as those known for other impurities in the same host lattices. They are well described by a simpleT ^3/2 relation.     

First-order kinetic approximation for a reactive gas mixture

A multicomponent reacting gas with an arbitrary number of chemical species and one reversible reaction is studied at a kinetic level in the frame of discrete velocity models of the Boltzmann equation, with the main objective of deriving the reactive Navier Stokes equations of the model, and characterizing the dissipative terms related to shear viscosity, thermal conductivity and thermal diffusion. The closure of the system formed by conservation and chemical rate equations is based on a first-order Chapman-Enskog method, to be applied in the strong reaction regime, and on a convenient representation of the density vector space in terms of the macroscopic variables. A mathematical procedure is proposed which leads to identification of the transport coefficients, and may be applied to a quite large variety of reactive gas flows. Moreover, it allows characterization of the functional form of the transport coefficients in dependence on the local gas concentrations, once the model is specified.Received: 4 October 2004, Accepted: 3 December 2004, Published online: 18 March 2005PACS: 51.10. + y, 51.20. + d, 47.70.Fw Correspondence to: A.J. Soares     

Homoclinic phenomena in the gravitational collapse

A class of Bianchi IX cosmological models is shown to have chaotic gravitational collapse, due to Poincaré's homoclinic phenomena. We can program such models so that for any given positive integer N (N=∞ included) the universe undergoes N non-periodic oscillations (each oscillation requiring a long time) before collapsing. For N=∞ the universe undergoes periodic oscillations.     

Phthalocyanine-modulated isomerization behaviour of an azo-based photoswitch

A photoswitchable azobenzene-phthalocyanine-azobenzene triad has been synthesized and its electrochemical properties determined. Energy transfer among the subunits allows for modification of the E-Z ratio by selective excitation of the phthalocyanine moiety.     

Characterization of nanostructured HfO2 films using Perturbed Angular Correlation (PAC) technique

The hyperfine field at ¹⁸¹Ta lattice sites in nanostructured HfO₂ thin films was studied by the Perturbed Angular Correlation (PAC) technique. Thin oxide films were deposited by Electron Beam Evaporation on a silicon substrate. The thickness of the films was ~100 nm and ~250 nm. Radioactive ¹⁸¹Hf nuclei were produced by neutron activation of the film samples in the Brazilian Research Reactor (IPEN IEA-R1) by the reaction ¹⁸⁰Hf(n,γ)¹⁸¹Hf. PAC measurements were carried out after annealing at 1473 K. The PAC technique allows the determination of the electric field gradient (EFG) at the probe sites.     

Conformational and orientational guidance of the analgesic dipeptide kyotorphin induced by lipidic membranes: putative correlation toward receptor docking

The analgesic dipeptide kyotorphin (L-Tyr-L-Arg) and an acylated kyotorphin derivative were studied by a combination of theoretical (molecular dynamics simulation and quantum mechanics methods) and experimental (fluorescence and infrared spectroscopies) approaches both in solution and in model systems of membranes. At biological pH the peptides have a neutral net charge. Nevertheless, their phenolic rings interact with phospholipid molecules (partition coefficient varies from 6 x 10(2) to 2 x 10(4), depending on the lipid and pH used) despite being exposed to the aqueous bulk medium. The lowest energy transition dipole moment is displaced from the normal to the lipid bilayer by 20 degrees on average. The observed extensive interaction, pK(a), precise location, and well-defined orientation in membranes combined with the ability to discriminate rigid raftlike membrane domains suggest that kyotorphin meets the structural constraints needed for receptor-ligand interaction. The acylated kyotorphin derivative mimics kyotorphin properties and represents a promising way for entrapment in a drug carrier and transport across the blood-brain barrier.     

Optical activity and damage recovery of erbium implanted strontium titanate

Single crystalline SrTiO 3 samples were implanted with Er ions of 150 v keV at room temperature with fluences of 5 ‐ 10 14 and 5 ‐ 10 15 . Annealing treatments were carried out both in reducing and oxidising atmospheres to recover the implantation damage. Infrared 1.54 v m Er 3+ luminescence between the two lowest spin-orbit levels 4 I 13/2 M 4 I 15/2 as well as emission from higher excited states 4 S 3/2 M 4 I 15/2 , 4 F 9/2 M 4 I 15/2 and 4 S 3/2 M 4 I 13/2 were observed in the implanted samples with highest fluence, annealed either in air or in vacuum. Multiple site location of Er 3+ ion is discussed and compared with RBS/C and emission channelling results that indicate that Er goes to Sr and Ti sites.