Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics

It is shown that, depending upon the orientation of the end tangents t₀,t₁ relative to the end point displacement vector p=p₁–p₀, the problem of G¹ Hermite interpolation by PH cubic segments may admit zero, one, or two distinct solutions. For cases where two interpolants exist, the bending energy may be used to select among them. In cases where no solution exists, we determine the minimal adjustment of one end tangent that permits a spatial PH cubic Hermite interpolant. The problem of assigning tangents to a sequence of points p₀,...,p_n in R³, compatible with a G¹ piecewise-PH-cubic spline interpolating those points, is also briefly addressed. The performance of these methods, in terms of overall smoothness and shape-preservation properties of the resulting curves, is illustrated by a selection of computed examples.     

Finite volume schemes for the approximation via characteristics of linear convection equations with irregular data

We consider the approximation by multidimensional finite volume schemes of the transport of an initial measure by a Lipschitz flow. We first consider a scheme defined via characteristics, and we prove the convergence to the continuous solution, as the time step and the ratio of the space step to the time step tend to zero. We then consider a second finite volume scheme, obtained from the first one by addition of some uniform numerical viscosity. We prove that this scheme converges to the continuous solution, as the space step tends to zero, whereas the ratio of the space step to the time step remains bounded by below and by above, and under assumption of uniform regularity of the mesh. This is obtained via an improved discrete Sobolev inequality and a sharp weak BV estimate, under some additional assumptions on the transport flow. Examples show the optimality of these assumptions.     

Novel stereocontrolled addition of allylmetal reagents to alpha-imino esters: efficient synthesis of chiral tetrahydroquinoline derivatives

To prepare in multigram scale new antagonists of the glycine binding site associated to the NMDA receptor, an efficient distereoselective route was set up. The addition of suitable allyltin reagents to chiral N-aryl alpha-imino esters (R-(+)-tert-butyl lactate used as chiral auxiliary), gave the corresponding alpha amino acid-type derivative in high chemical yield and optical purity. This allylation reaction represents a novel example of efficient long-range stereodifferentiation process. In the last part of the synthesis, a regioselective Heck-type cyclization reaction enabled preparation of the target tetrasubstituted exocycle and trisubtituted endocycle double bond derivatives.     

A vanishing diffusion process in unsaturated soils

A model for simulating water flow and air flow in unsaturated soils is presented herein. Drainage from a one-dimensional soil column is specifically investigated. A mathematical analysis of the equations reveals that, due to a vanishing diffusion process, the gradient of the water degree of saturation is infinite at the water table. Moreover, this discontinuity propagates at a velocity that satisfies a local non-linear equation involving only the properties of the material. A numerical simulation of this problem serves to confirm the results obtained.     

Theoretical study of electromagnetic scattering by metal nanoparticles

Progress in near-field optical spectroscopy research on metal nanoparticles demands a better understanding of the role of particle-particle and tip-sample interactions. In this perspective, we investigate theoretically, at a very moderate level of sophistication, the optical behavior of simple silver nanoparticle aggregates, in terms of a formalism involving a multipolar expansion of the fields involved, along with a simplified model for the optical behavior of nanostructures previously developed. In particular, the tip-sample interaction is taken into account roughly, treating the tip as an additional, single particle, characterized by proper dielectric behavior.     

Sol-Gel Synthesis of Transparent Alumina Gel and Pure Gamma Alumina by Urea Hydrolysis of Aluminum Nitrate

-Alumina was synthesized by a sol-gel method with the aluminum ion hydrolysis control performed by urea. The initial saturated Al³⁺/urea solution presented urea coordinated with the aluminum ion, as shown in the ¹³C NMR and ²⁷Al NMR spectra and longitudinal relaxation times, T ₁, from the latter. The substitution of water molecules in the Al³⁺ coordination shell by urea controlled the hydrolysis process and provided an extensive nucleation during the initial steps of the aluminum hydroxide formation due to urea thermolysis at 90°C. The resulting sol, composed of Al(OH)₃ nanoparticles, coalesced and became a transparent gel permeated by a solution of urea and the polycation ion [Al₁₃O₄(OH)₂₄(H₂O)₁₂]⁷⁺. The freshly prepared gel was transformed, under heating at 300°C, directly to -alumina, characterized by FTIR, ²⁷Al-MAS-NMR and S_BET techniques, without - or -phases, as a consequence of the high degree of homogeneity of the -alumina precursor.     

Regioselective cis-trans isomerization of arachidonic double bonds by thiyl radicals: the influence of phospholipid supramolecular organization

Trans unsaturated fatty acids in humans may be originated by two different contributions. The exogenous track is due to dietary supplementation of trans fats and the endogenous path deals with free-radical-catalyzed cis-trans isomerization of fatty acids. Arachidonic acid residue (5c,8c,11c,14c-20:4), which has only two out of the four double bonds deriving from the diet, was used to differentiate the two paths and to assess the importance of a radical reaction. A detailed study on the formation of trans phospholipids catalyzed by the HOCH2CH2S* radical was carried out on L-alpha-phosphatidylcholine from egg lecithin and 1-stearoyl-2-arachidonoyl-L-alpha-phosphatidylcholine (SAPC) in homogeneous solution or in large unilamellar vesicles (LUVET). Thiyl radicals were generated from the corresponding thiol by either gamma-irradiation or UV photolysis, and the reaction course was followed by GC, Ag/TLC, and 13C NMR analyses. The isomerization was found to be independent of cis double bond location (random process) in i-PrOH solution. In the case of vesicles, the supramolecular organization of lipids produced a dramatic change of the isomerization outcome: (i) in egg lecithin, the reactivity of arachidonate moieties is higher than that of oleate and linoleate residues, (ii) in the linoleate residues of egg lecithin, the 9t,12c-18:2 isomer prevailed on the 9c,12t-18:2 isomer (3:1 ratio), and (iii) a regioselective isomerization of SAPC arachidonate residues occurred in the 5 and 8 positions. This effect of "positional preference" indicates that thiyl radicals entering the hydrophobic region of the membrane bilayer start to isomerize polyunsaturated fatty acid residues having the double bonds nearest to the membrane surfaces. We propose that arachidonic acid and its trans isomers can function as biomarkers in membranes for distinguishing the two trans fatty acid-forming pathways.