Timelike Minimal Surfaces via Loop Groups

This work consists of two parts. In Part I, we shall give a systematic study of Lorentz conformal structure from structural viewpoints. We study manifolds with split-complex structure. We apply general results on split-complex structure for the study of Lorentz surfaces.In Part II, we study the conformal realization of Lorentz surfaces in the Minkowski 3-space via conformal minimal immersions. We apply loop group theoretic Weierstrass-type representation of timelike constant mean curvature for timelike minimal surfaces. Classical integral representation formula for timelike minimal surfaces will be recovered from loop group theoretic viewpoint.     

Explicit 2-Factorisations of the Odd Graph

In this note we show how 1-factors in the middle two layers of the discrete cube can be used to construct 2-factors in the Odd graph (the Kneser graph of (k − 1)-sets from a (2k − 1)-set). In particular, we use the lexical matchings of Kierstead and Trotter, and the modular matchings of Duffus, Kierstead and Snevily, to give explicit constructions of two different 2-factorisations of the Odd graph. This revised version was published online in September 2006 with corrections to the Cover Date.     

A Characterisation of Posets that Are nearly Antichains

We present a characterisation of posets of size n with linear discrepancy n − 2. These are the posets that are “furthest” from a linear order without being an antichain. This revised version was published online in September 2006 with corrections to the Cover Date.     

Modelling of an underground waste disposal site by upscaling

In this paper, we study the global behaviour of an underground waste disposal in order to have an accurate upscaled model suitable for the computations involved in safety assessment processes. We start from a detailed model describing the transport of pollutant leaking from a high number of units. Using the method of homogenization, going to the limit, we obtain first a macroscopic model where the sources are now appearing globally. Then we compute a first‐order matched asymptotic expansion and we give the error estimates for this approximation. Copyright © 2004 John Wiley & Sons, Ltd.     

The long‐time behaviour of the thermoconvective flow in a porous medium

For the Boussinesq approximation of the equations of coupled heat and fluid flow in a porous medium we show that the corresponding system of partial differential equations possesses a global attractor. We give lower and upper bounds of the Hausdorff dimension of the attractor depending on a physical parameter of the system, namely the Rayleigh number of the flow. Numerical experiments confirm the theoretical findings and raise new questions on the structure of the solutions of the system. Copyright © 2004 John Wiley & Sons, Ltd.     

Some non‐standard problems in viscous flow

Energy bounds are derived for Dirichlet type boundary value problems for the Navier–Stokes and Stokes equations when a combination of the solution values initially and at a later time is prescribed. The bounds are obtained by means of a differential inequality and imply uniqueness and continuous data dependence of the solutions for a range of values of the parameter in the non‐standard auxiliary condition. Copyright © 2004 John Wiley & Sons, Ltd.     

Diffusion in poro‐plastic media

A model is developed for the flow of a slightly compressible fluid through a saturated inelastic porous medium. The initial‐boundary‐value problem is a system that consists of the diffusion equation for the fluid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto‐visco‐plastic type. The variational form of this problem in Hilbert space is a non‐linear evolution equation for which the existence and uniqueness of a global strong solution is proved by means of monotonicity methods. Various degenerate situations are permitted, such as incompressible fluid, negligible porosity, or a quasi‐static momentum equation. The essential sufficient conditions for the well‐posedness of the system consist of an ellipticity condition on the term for diffusion of fluid and either a viscous or a hardening assumption in the constitutive relation for the porous solid. Copyright © 2004 John Wiley & Sons, Ltd.     

Anionically Substituted 1,1′,1″‐Methylidynetris[1H‐pyrazole] Ligands for the Formation of Neutral Lanthanide Complexes in Water: Synthesis,Characterization, and Photophysical Properties

The six‐step synthesis of the new podand‐type ligand 6,6′,6″‐[methylidenetri(1H‐pyrazole‐1,3‐diyl)]tris[pyridine‐2‐carboxylic acid] (LH₃) is described. Reaction of LH₃ with LnCl₃ ?6 H₂O (Ln=Eu, Gd, Tb) in MeOH resulted in the isolation of [LnL]?HCl complexes characterized by elemental analysis, mass and IR spectroscopy. Photophysical studies of the Eu and Tb complexes in aqueous solutions revealed the characteristic luminescence features of the metal atoms, indicative of an efficient ligand‐to‐metal energy‐transfer process. Determination of the luminescence quantum yields in H₂O showed the Tb complex to be highly luminescent (?=15%), while, for the Eu complex, the quantum efficiency was only 2%. Excited‐state‐lifetime measurements in H₂O and D₂O evidenced the presence of ca. three H₂O molecules in the first coordination sphere of the complexes. Investigation of the Gd complex allowed the determination of the ligand‐centered triplet state and showed the ligand to be well suited for energy transfer to the metal. The luminescence properties of the complexes are described, and the properties of the ligand as a suitable complexation pocket is questioned.     

An improved synthesis of rhinocerotinoic acid

The stereoselective synthesis of E-rhinocerotinoic acid has been achieved in five steps from (−)-sclareol in an overall yield of 32%. This constitutes a significant improvement on the previous synthesis of this anti-inflammatory compound.