Caratheodory interpolation kernels

Kernels over the unit disk for which a version of Carathéodory interpolation is true are characterized in a simple computationally verifiable manner.     

Preservice Elementary Teachers' Use of Mathematics in a Project‐Based Science Approach

The use of a project‐based science (PBS) approach to teaching encourages students to integrate mathematics and science in meaningful ways as they create projects. As a beginning study of how students use mathematics in such an approach, an analysis of 23 projects developed by preservice elementary teachers enrolled in an elementary science course was conducted. Findings showed that students made a number of different types of mathematical errors and underutilized data representation and summary forms. Implications included the importance of developing methods for supporting the use of mathematical tools in utilizing a project‐based approach and considering ways that such tools mediate scientific thinking.     

Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains

In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets. Finally, we prove the existence of a pullback attractor for a non-autonomous 2D Navier–Stokes model in an unbounded domain, a case in which the theory of uniform attractors does not work since the non-autonomous term is quite general. To cite this article: T. Caraballo et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Optimal control of unsteady compressible viscous flows

The control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical flow control systems. However, most of the prior work in this area has focused on incompressible flow which precludes many of the important physical flow phenomena that must be controlled in practice including the coupling of fluid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two‐dimensional compressible Navier–Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter‐rotating viscous vortices above an infinite wall which, due to the self‐induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall‐normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the influence of control regularization for each case. Copyright © 2002 John Wiley & Sons, Ltd.     

Identification by high-performance liquid chromatography of tyrosine ammonia-lyase activity in purified fractions of Phaseolus vulgaris phenylalanine ammonia-lyase.

Activities of phenylalanine ammonia-lyase (PAL) and tyrosine ammonia-lyase (TAL) were assessed at each stage of a three-step purification of PAL. Assays were performed by high-performance liquid chromatographic (HPLC) separation and ultraviolet detection of reaction products. Use of HPLC permitted assay of low activities of PAL and TAL for periods up to approximately four and two days, respectively. HPLC also facilitated the accurate quantitation of the product of the TAL reaction, trans-p-coumaric acid, which was observed to isomerize readily under experimental conditions. PAL and TAL were associated throughout the purification procedure, with TAL activity at 0.6-1.3% of PAL activity. It was concluded that, contrary to previous reports, TAL and PAL activities are mediated by the same enzyme, or else by chromatographically very similar enzymes.     

Azine bridged silver coordination polymers: Powder X-ray diffraction route to crystal structure determination of silver benzotriazole

In continuation of our interest in solid-state structures of silver complexes of photographic importance, the structure for silver benzotriazole (AgBZT), has now been obtained. The preferred method for solving crystal structures is via single-crystal X-ray diffraction (XRD). However, for some materials, growing single crystals of appropriate size and quality is often difficult or even impossible. AgBZT is an example of such a silver complex with poor solubility. The usual routes to preparing single crystals using recrystallization from a cooperating solvent resulted in polycrystalline powder samples. We propose a crystal structure for AgBZT, solved from synchrotron X-ray powder diffraction data, using a direct-space Monte Carlo simulated annealing approach. AgBZT crystals are monoclinic, (P2₁/c), with unit cell dimensions, a=14.8052(3) Å, b=3.7498(4) Å, c=12.3495(12) Å, and β=114.200(6)°. The AgBZT complex is constructed from all three of the Benzotriazole (BZT) nitrogens bonding to a separate silver atom. As a consequence of this bonding mode, the structure is a highly cross-linked, coordination polymer.     

On a symmetry of turbulence

This paper presents results on symmetries of the spectrum of singularities for random cascades found in the statistical theory of turbulence. It is shown that empirical dimension curves possess a natural symmetry whose presence restricts the class of allowable probability distributions of the cascade generator in a simple manner. In particular, necessary and sufficient conditions on the probability distribution of the generator are obtained for symmetry of the singularity spectrum within a large class of cascade models.     

In vivo tibial lead measurement to assess the health hazard of Venezuelan workers

Gamma-ray induced X-ray emission (GIXE) technique for elemental lead in-vivo tibial measurement using a large volume hyper pure germanium detector is presented with the most convenient source-sample-detector geometry. The system operates advantageously when several parameters are considered for a lower dead time operation. The detection limit (DL) is better that 3.5 μg/g of Ca. Results of in-vivo average tibial lead concentration for some of the monitored groups are: control 7 μg of lead per g of Ca; gasoline filling attendants 6 μg/g of Ca; custom office workers near the DL; industrial workers range from DL up to 84±3 μg/g of Ca, suggesting that lead accumulation in the bone does not represent a major health risk This revised version was published online in August 2006 with corrections to the Cover Date.