Analysis of Wave Propagation in 1D Inhomogeneous Media

In this paper, we consider the one-dimensional inhomogeneous wave equation with particular focus on its spectral asymptotic properties and its numerical resolution. In the first part of the paper, we analyze the asymptotic nodal point distribution of high-frequency eigenfunctions, which, in turn, gives further information about the asymptotic behavior of eigenvalues and eigenfunctions. We then turn to the behavior of eigenfunctions in the high- and low-frequency limit. In the latter case, we derive a homogenization limit, whereas in the first we show that a sort of self-homogenization occurs at high frequencies. We also remark on the structure of the solution operator and its relation to desired properties of any numerical approximation. We subsequently shift our focus to the latter and present a Galerkin scheme based on a spectral integral representation of the propagator in combination with Gaussian quadrature in the spectral variable with a frequency-dependent measure. The proposed scheme yields accurate resolution of both high- and low-frequency components of the solution and as a result proves to be more accurate than available schemes at large time steps for both smooth and nonsmooth speeds of propagation.     

Overview of policies,standards and certifications supporting the European bio-based economy

With the Lisbon agenda, the EU recognizes the important role of an economy driven by innovation in tackling contemporary societal challenges. This transition to innovative and sustainable modes of production and consumption is being shaped by policy efforts and policy instruments, including regulations, certifications, standards and sustainability assessment tools. In this paper, we present an overview of the different public policies and policy measures behind the establishment of a European sustainable bio-based economy. The aim of the paper is to describe the evolution of the policies and policy instruments that affect the establishment of a sustainable and innovative bio-based economy, in order to understand its limits, contradictions and existing gaps.     

Formation of the iron-oxo hydroxylating species in the catalytic cycle of aromatic amino acid hydroxylases

The first part of the catalytic cycle of the pterin‐dependent, dioxygen‐using nonheme‐iron aromatic amino acid hydroxylases, leading to the Fe^IV?O hydroxylating intermediate, has been investigated by means of density functional theory. The starting structure in the present investigation is the water‐free Fe? O₂ complex cluster model that represents the catalytically competent form of the enzymes. A model for this structure was obtained in a previous study of water‐ligand dissociation from the hexacoordinate model complex of the X‐ray crystal structure of the catalytic domain of phenylalanine hydroxylase in complex with the cofactor (6R)‐L ‐erythro‐5,6,7,8‐tetrahydrobiopterin (BH₄) (PAH‐Fe^II‐BH₄). The O? O bond rupture and two‐electron oxidation of the cofactor are found to take place via a Fe‐O‐O‐BH₄ bridge structure that is formed in consecutive radical reactions involving a superoxide ion, O₂^?. The overall effective free‐energy barrier to formation of the Fe^IV?O species is calculated to be 13.9 kcal mol^?1, less than 2 kcal mol^?1 lower than that derived from experiment. The rate‐limiting step is associated with a one‐electron transfer from the cofactor to dioxygen, whereas the spin inversion needed to arrive at the quintet state in which the O? O bond cleavage is finalized, essentially proceeds without activation.     

2,3‐Diaryl‐3‐hydroxy­propionic acid inter­mediates in the synthesis of threo forms of 1,2‐diaryl‐1,3‐propane­diols

Racemic threo‐3‐hydroxy‐2,3‐diphenyl­propionic acid, C₁₅H₁₄O₃, (I), crystallizes from ethyl acetate as a conglomerate of separate (+)‐ and (−)‐crystals. The geometries of (I) and its methyl ester are compared. Reduction of (I) gives threo‐1,2‐diphenyl‐1,3‐propane­diol. The synthesis of threo forms of 1,2‐diaryl‐1,3‐propane­diols via 2,3‐diaryl‐3‐hydroxy­propionic acids is discussed.     

Liquid-phase microextraction utilising plant oils as intermediate extraction medium--towards elimination of synthetic organic solvents in sample preparation

Hollow fibre based liquid-phase microextraction (LPME) using fatty oils and essential oils as the organic phase was evaluated to develop sample preparation technology eliminating the use of hazardous organic solvents. Basic drugs were extracted from different aqueous samples (0.2 to 1 mL) through approximately 15 microL of either almond oil, arachis oil, olive oil, soy-bean oil, anise oil, fennel oil, lavender oil, or peppermint oil (organic phase) immobilised within the pores of a polypropylene hollow fibre and into 20 microL of 10 mM HCOOH (acceptor phase) present inside the lumen of the hollow fibre. The extraction performance of the essential oils was comparable with the solvents normally used in LPME (dihexyl ether, n-octanol, and dodecyl acetate) in terms of extraction recovery and extraction speed. Whereas all essential oils tested were compatible with human urine, only anise oil was successful for plasma. The fatty oils provided lower recoveries than the essential oils due to higher viscosity, but all the fatty oils were compatible both with urine and plasma samples. In spite of the multi-component nature of the oils tested, they were not found to seriously contaminate the acceptor phases during extraction. In conclusion, fatty oils and essential oils may serve as alternative organic phase in LPME, eliminating the use of hazardous organic solvents.     

Note on the spectrum of the Hodge-Laplacian for k-forms on minimal Legendre submanifolds in S^{2n+1}

Given a minimal Legendre immersion L in and we prove that is an eigenvalue of the Hodge-Laplacian acting on k and (k-1)-forms on L. In particular we show that the eigenspaces Eig and Eig are at least of dimension Received: 10 February 2000 / Accepted: 23 January 2001 / Published online: 4 May 2001