Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations

Summary. The purpose of this paper is to analyze a finite element approximation of the stationary Navier-Stokes equations that allows the use of equal velocity-pressure interpolation. The idea is to introduce as unknown of the discrete problem the projection of the pressure gradient (multiplied by suitable algorithmic parameters) onto the space of continuous vector fields. The difference between these two vectors (pressure gradient and projection) is introduced in the continuity equation. The resulting formulation is shown to be stable and optimally convergent, both in a norm associated to the problem and in the norm for both velocities and pressure. This is proved first for the Stokes problem, and then it is extended to the nonlinear case. All the analysis relies on an inf-sup condition that is much weaker than for the standard Galerkin approximation, in spite of the fact that the present method is only a minor modification of this. Received May 25, 1998 / Revised version received August 31, 1999 / Published online July 12, 2000     

Stochastic Order and Generalized Weighted Mean Invariance

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.     

Adenine versus guanine quartets in aqueous solution: dispersion-corrected DFT study on the differences in π-stacking and hydrogen-bonding behavior

We have investigated the performance of the dispersion-corrected density functionals (BLYP-D, BP86-D and PBE-D) and the widely used B3LYP functional for describing the hydrogen bonds and the stacking interactions in DNA base dimers. For the gas-phase situation, the bonding energies have been compared to the best ab initio results available in the literature. All dispersion-corrected functionals reproduce well the ab initio results, whereas B3LYP fails completely for the stacked systems. The use of the proper functional leads us to find minima for the adenine quartets, which are energetically and structurally very different from the C_4h structures, and might explain why adenine has to be sandwiched between guanine quartets to form planar adenine quartets.     

Testosterone metabolism revisited: discovery of new metabolites

The metabolism of testosterone is revisited. Four previously unreported metabolites were detected in urine after hydrolysis with KOH using a liquid chromatography–tandem mass spectrometry method and precursor ion scan mode. The metabolites were characterized by a product ion scan obtained with accurate mass measurements. Androsta-4,6-dien-3,17-dione, androsta-1,4-dien-3,17-dione, 17-hydroxy-androsta-4,6-dien-3-one and 15-androsten-3,17-dione were proposed as feasible structures for these metabolites on the basis of the mass spectrometry data. The proposed structures were confirmed by analysis of synthetic reference compounds. Only 15-androsten-3,17-dione could not be confirmed, owing to the lack of a commercially available standard. That all four compounds are testosterone metabolites was confirmed by the qualitative analysis of several urine samples collected before and after administration of testosterone undecanoate. The metabolite androsta-1,4-dien-3,17-dione has a structure analogous to that of the exogenous anabolic steroid boldenone. Specific transitions for boldenone and its metabolite 17β-hydroxy-5β-androst-1-en-3-one were also monitored. Both compounds were also detected after KOH treatment, suggesting that this metabolic pathway is involved in the endogenous detection of boldenone previously reported by several authors.     

Theoretical studies on aromaticity of selected hydroxypyrones. Part 3#. Chelatoaromaticity phenomenon in metalcomplexes of hydroxypyrones

The aim of this project is to study the aromatic properties of various forms (neutral, cationic, and anionic) of selected hydroxypyrones (pyromeconic acid, maltol, and ethylmaltol) and their metalcomplexes with aluminum, gallium, and indium ions. Aromaticity of hydroxypyrone metalcomplexes is important because it can influence the stability of such complexes, which is crucial for their applications in medicinal and environmental chemistry. Results from ten different indices of aromaticity (HOMA, NICS(0), NICS(1), NICS_scan, ASE_iso, PDI, FLU, I_ring, MCI, and KMCI) show that aromaticity in hydroxypyrones decreases in the order cations > neutral molecules > anions. Performed calculations situate the aromaticities of ligands in metalcomplexes close to their respective cations. This means that complexation causes a significant increase of the aromaticity of ligands, which stabilizes formed chelatocomplexes. On the other hand, we clearly show that rings that are involved in binding metal ions are not aromatic. Copyright © 2010 John Wiley & Sons, Ltd.     

Three‐dimensional imaging of chemical phase transformations at the nanoscale with full‐field transmission X‐ray microscopy

The ability to probe morphology and phase distribution in complex systems at multiple length scales unravels the interplay of nano‐ and micrometer‐scale factors at the origin of macroscopic behavior. While different electron‐ and X‐ray‐based imaging techniques can be combined with spectroscopy at high resolutions, owing to experimental time limitations the resulting fields of view are too small to be representative of a composite sample. Here a new X‐ray imaging set‐up is proposed, combining full‐field transmission X‐ray microscopy (TXM) with X‐ray absorption near‐edge structure (XANES) spectroscopy to follow two‐dimensional and three‐dimensional morphological and chemical changes in large volumes at high resolution (tens of nanometers). TXM XANES imaging offers chemical speciation at the nanoscale in thick samples (>20 µm) with minimal preparation requirements. Further, its high throughput allows the analysis of large areas (up to millimeters) in minutes to a few hours. Proof of concept is provided using battery electrodes, although its versatility will lead to impact in a number of diverse research fields.     

Attenuation of the depolarizing field in a thin film model relaxor

The behavior of the polarization in a microscopic statistical model for a thin film relaxor placed between two metallic electrodes is studied by numerical simulations. Depolarization fields different from zero, due to a non-perfect compensation of surface charges at the metallic electrodes, are taken into account. Different thicknesses and different values of the compositional charge disorder density for the relaxor are considered. Depolarization field is found to be extremely attenuated for large values of the number density of charge carriers in the relaxor. In such a case, field attenuation allows for the existence of a homogeneous ferroelectric ground state.     

A class of Banach spaces with no unconditional basic sequence

We give a construction of a reflexive Banach space X_ω1 with a transfinite basis of length ω₁ and with no unconditional basic sequence. In addition every bounded operator from a subspace of X_ω1 into the space X_ω1 is a sum of a simple diagonal operator and a strictly singular one. To cite this article: S.A. Argyros et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).