Computation of the invariant measure for a Lévy driven SDE: Rate of convergence

We study the rate of convergence of some recursive procedures based on some “exact” or “approximate” Euler schemes which converge to the invariant measure of an ergodic SDE driven by a Lévy process. The main interest of this work is to compare the rates induced by “exact” and “approximate” Euler schemes. In our main result, we show that replacing the small jumps by a Brownian component in the approximate case preserves the rate induced by the exact Euler scheme for a large class of Lévy processes.     

Measurement of Total and Unbound Mycophenolic Acid and Its Glucuronide by LC Coupled with MS. Application to a Pharmacokinetic Study of Mycophenolate Mofetil in Patients with Autoimmune Diseases

Liquid chromatography coupled with mass spectrometry for the determination of total and unbound mycophenolic acid and its major metabolite in human plasma has been developed. Sample preparations were based on a fully automated solid-phase extraction process and ultrafiltration. Mass spectrometric data were acquired in a single-ion monitoring method. The analytes and nevirapine (internal standard) were well separated in an isocratic mode over 8 min. Validation study exhibited excellent linearity, with intra- and inter-day precision and accuracy of less than 12%. The assay was successfully applied to the pharmacokinetic study of mycophenolic acid in patients with autoimmune diseases.     

A vibrational study of the nature of hydroxyl groups chemical bonding in two aluminium hydroxides

Lengths, strengths and valences of OH bonds in the two aluminium hydroxides gibbsite and bayerite were determined on the basis of vibrational spectral data. The uncoupled OD stretching modes in the range 2400–2800 cm⁻¹ were recorded by means of infrared diffuse reflectance, thereby avoiding effects of surface, vibrational coupling or particle shape. The assignment of the corresponding Raman spectra resulted in the determination of harmonic wavenumbers, force constants and anharmonicity coefficients of bulk OH groups in the two minerals. OH bond lengths deduced from these data varied from 0.964 Å to 0.975 Å in gibbsite and 0.962 Å to 0.973 Å in bayerite. These lengths appear to correspond to weak H-bonds contrary to previously recognized data from X-ray diffraction and neutron diffraction studies. Finally, bond valences were calculated on the basis of these new bond lengths and discussed as a function of crystallographic structures and the nature of hydrogen bonding in these two structures.     

A heuristic for the multi-period petrol station replenishment problem

In the multi-period petrol station replenishment problem (MPSRP) the aim is to optimize the delivery of several petroleum products to a set of petrol stations over a given planning horizon. One must determine, for each day of the planning horizon, how much of each product should be delivered to each station, how to load these products into vehicle compartments, and how to plan vehicle routes. The objective is to maximize the total profit equal to the revenue, minus the sum of routing costs and of regular and overtime costs. This article describes a heuristic for the MPSRP. It contains a route construction and truck loading procedures, a route packing procedure, and two procedures enabling the anticipation or the postponement of deliveries. The heuristic was extensively tested on randomly generated data and compared to a previously published algorithm. Computational results confirm the efficiency of the proposed methodology.     

Turbulent Energy Scale-Budget Equations for nearly Homogeneous Sheared Turbulence

For moderate Reynolds numbers, the isotropic relation between second-order and third-order moments for velocity increments (Kolmogorov's equation) is not respected, reflecting a non-negligible correlation between the scales responsible for the injection, transfer and dissipation of the turbulent energy. For (shearless) grid turbulence, there is only one dominant large-scale phenomenon, which is the non-stationarity of statistical moments resulting from the decay of energy downstream of the grid. In this case, the extension of Kolmogorov's analysis, as carried out by Danaila, Anselmet, Zhou and Antonia, J. Fluid Mech. 391, 1999 359-369) is quite straightforward. For shear flows, several large-scale phenomena generally coexist with similar amplitudes. This is particularly the case for wall-bounded flows, where turbulent diffusion and shear effects can present comparable amplitudes. The objective of this work is to quantify, in a fully developed turbulent channel flow and far from the wall, the influence of these two effects on the scale-by-scale energy budget equation. A generalized Kolmogorov equation is derived. Relatively good agreement between the new equation and hot-wire measurements is obtained in the outer region (40 < x ⁺ ₃ < 150) of the channel flow, for which the turbulent Reynolds number is R _λ≈ 36.     

Synthesis and characterization of A4[Re6Q8L6]@SiO2 red-emitting silica nanoparticles based on Re6 metal atom clusters (A = Cs or K, Q = S or Se, and L = OH or CN)

Metal atom clusters constitute very promising candidates as luminophores for applications in biotechnology because they are nanosized entities offering robust luminescence in the near-infrared field (NIR). However, they cannot be used as prepared for biological applications because of potential toxic effects and quenching of the clusters' luminescence in aqueous media, and they therefore need to be dispersed in a biocompatible matrix. We describe herein the encapsulation of octahedral rhenium clusters, denoted as A(4)[Re(6)Q(8)L(6)] (A = Cs or K, Q = S or Se, and L = OH or CN), in silica nanoparticles by a water-in-oil microemulsion process, paying particular attention to the clusters' stability. The obtained A(4)[Re(6)Q(8)L(6)]@SiO(2) nanoparticles are 30 nm in size with good monodispersity and a perfectly spherical shape, as shown by scanning electron microscopy (SEM). The presence of cluster units inside the silica matrix was evidenced by scanning transmission electron microscopy in annular dark-field mode (ADF-STEM). From the point of view of their optical properties, the A(4)[Re(6)Q(8)L(6)]@SiO(2) nanoparticles show red and NIR emission under UV excitation, even when dispersed in water. The evolution of the structural and luminescence properties of clusters before and after encapsulation was followed by Raman and photoluminescence spectroscopy.     

On the reactivity of isoindolo[2,1-a]quinazoline-5-ones

Base- and acid-catalyzed nucleophilic addition of 11H-isoindolo[2,1-a]quinazoline-5-one to aromatic aldehydes and maleimides was investigated. The aldol adducts and condensation products were obtained stereoselectively. Main diastereomers of the Michael adducts were isolated in 74-89% yield, and converted by N-methylation to new stable α-substituted isoindole derivatives, for which 6-methylisoindolo[2,1-a]]quinazoline-5-one stands as the unsubstituted reference. The stability of the latter was monitored in moist aerated CDCl₃ solution, and one of the oxidative hydrolysis product was characterized by X-ray diffraction analysis as the corresponding N-arylphthalimide. The reactivity of the unsubstituted 6-methylisoindolo[2,1-a]]quinazoline-5-one was also investigated with acetylenic Michael acceptors. Fully conjugated isoindole derivatives possessing an original pull-push-pull structure were obtained. The conformations and molecular orbitals of the dibenzoylacetylene adduct were studied at the DFT level of theory. Its static quadratic hyperpolarizabilty β₀ was also calculated at the ZINDO level.     

Full-dimensional quantum dynamics of vibrationally highly excited NHD2

We report on full-dimensional vibrational quantum dynamics of the highly excited ammonia isotopologue NHD(2) using a newly developed potential energy surface and the MCTDH program package. The calculations allow to realistically simulate an infrared laser induced stereomutation reaction at the pyramidal nitrogen atom in the femtosecond time domain. Our results allow for a thorough qualitative and quantitative understanding of infrared photoinduced stereomutation kinetics, the underlying quantum dynamics, and the reaction mechanisms. Comparison is made with a previous, reduced dimensionality study of the same reaction [R. Marquardt, M. Quack, I. Thanopulos, and D. Luckhaus, J. Chem. Phys. 118, 643 (2003)], and it is shown that slight variances of reduced spaces lead to significantly different kinetics. Because the quantum dynamics depends subtly on variances of reduced spaces, reduced dimensionality treatments are not reliable even for qualitative predictions of the stereomutation kinetics. The first direct comparison between the Multiconfigurational Time Dependent Hartree [M. H. Beck, A. Ja?ckle, G. A. Worth et al., Phys. Rep. 324, 1 (2000)] and Unimolecular Reactions Induced by Monochromatic Infrared Radiation [M. Quack and E. Sutcliffe, QCPE Bulletin 6, 98 (1986)] program packages on a specific, four dimensional quantum dynamical problem allows for their full validation in the present work.     

The magic effect of endocyclic but non-sterically hindering biisoquinoline chelates: From fast-moving molecular shuttles to [3]rotaxanes

The use of 8,8′-diaryl-substituted 3,3′-biisoquinolines allows the construction of new multi-component assemblies that are inaccessible with the 2,9-diaryl-substituted 1,10-phenanthroline ligands previously developed by the Sauvage group. This is due to the sterically non-hindering nature of the new chelates, which makes three-component entanglements around octahedral metal centres such as iron(II), cobalt(II) and ruthenium(II) readily possible. Among the newly synthesized molecular assemblies are [3]rotaxanes and [3]pseudorotaxanes in which two molecular strings pass through a single macrocycle, as well as molecular shuttles that exhibit greatly improved shuttling kinetics when compared to previously investigated molecular machines that are based on copper(I)/copper(II) redox chemistry.