Numerical blow‐up for the porous medium equation with a source

We study numerical approximations of positive solutions of the porous medium equation with a nonlinear source, where m > 1, p > 0 and L > 0 are parameters. We describe in terms of p, m, and L when solutions of a semidiscretization in space exist globally in time and when they blow up in a finite time. We also find the blow‐up rates and the blow‐up sets, proving that there is no regional blow‐up for the numerical scheme. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004     

On the dynamics of generic non-Abelian free actions

We investigate some global generic properties of the dynamics associated to non-Abelian free actions in certain special cases. The main properties considered in this paper are related to the existence of dense orbits, to ergodicity and to topological rigidity. We first deal with them in the case of conservative homeomorphisms of a manifold and C ¹-diffeomorphisms of a surface. Groups of analytic diffeomorphisms of a manifold which, in addition, contain a Morse-Smale element and possess a generating set close to the identity are considered as well. From our discussion we also derive the existence of a rigidity phenomenon for groups of skew-products which is opposed to the phenomenon present in Furstenbergs celebrated example of a minimal diffeomorphism that is not ergodic (cf. [Ma]).     

Domination by Positive Narrow Operators

We prove that each positive operator from a Köthe function-space E() to a Banach lattice F with a narrow majorant is itself narrow provided the norm on F is order continuous. We also prove that every l ²-strictly singular regular operator from L ^p[0,1], 1p < , to a Banach lattice F is narrow, provided F has an order continuous norm.     

A cross-correlation velocimetry technique for breakup of an annular liquid sheet

A novel experimental technique for studying the stability of the breakup of a two-phase flow is presented. High-speed backlit photography is used to capture realisations of the unstable mixing layer, and the edge velocity is derived in order to measure the effects of parameters such as gas/liquid momentum ratio, Reynolds and Weber Number. This has traditionally been an edge detection problem that introduces additional uncertainty. Here, a cross-correlation solution is presented, which overcomes the limitations of threshold techniques. Practical application is demonstrated for an atomising annular liquid sheet under several conditions. Sensitivity due to edge blurring and noise is quantified by artificial analysis. Sensitivity analysis shows accuracy and precision to permit sub-pixel precise velocity and stability measurements up to 0.6 sheet thicknesses from the nozzle exit at the conditions studied.     

Determination of β-glucosidase activity in soils with a bioanalytical sensor modified with multiwalled carbon nanotubes

Soil microorganisms and enzymes are the primary mediators of soil biological processes, including organic matter degradation, mineralization, and nutrient recycling. They play an important role in maintaining soil ecosystem quality and functional diversity. Moreover, enzyme activities can provide an indication of quantitative changes in soil organic matter. β-Glucosidase (β-Glu) activity has been found to be sensitive to soil management and has been proposed as a soil quality indicator because it provides an early indication of changes in organic matter status and its turnover. The aims of the present study were to test and use a simple and convenient procedure for the assay of β-Glu activity in agricultural soil. The method described here is based on the enzymatic degradation of cellobiose by β-Glu present in the soil sample and the subsequent determination of glucose produced by the enzymatic reaction using screen-printed carbon electrodes modified with multiwalled carbon nanotubes (SPCE-CNT) equipped with coimmobilized glucose oxidase and horseradish peroxidase enzymes. The potential applied to the SPCE-CNT detection was −0.15 V versus a Ag/AgCl pseudo-reference electrode. A linear calibration curve was obtained in the range 2.7–11.3 mM with a correlation coefficient. In the present study, an easy and effective SPCE-CNT-modified electrode allowed an improved amperometric response to be achieved and this is attributed to the increased surface area upon electrode modification.     

Simultaneous analysis of multiple PCR amplicons enhances capillary SSCP discrimination of MHC alleles

Major histocompatibility complex (MHC) genotyping still remains one of the most challenging issues for evolutionary ecologists. To date, none of the proposed methods have proven to be perfect, and all provide both important pros and cons. Although denaturing capillary electrophoresis has become a popular alternative, allele identification commonly relies upon conformational polymorphisms of two single‐stranded DNA molecules at the most. Using the MHC class II (β chain, exon 2) of the black kite (Aves: Accipitridae) as our model system, we show that the simultaneous analysis of overlapping PCR amplicons from the same target region substantially enhances allele discrimination. To cover this aim, we designed a multiplex PCR capable to generate four differentially sized and labeled amplicons from the same allele. Informative peaks to assist allele calling then fourfold those generated by the analysis of single PCR amplicons. Our approach proved successful to differentiate all the alleles (N=13) isolated from eight unrelated birds at a single optimal run temperature and electrophoretic conditions. In particular, we emphasize that this approach may constitute a straightforward and cost‐effective alternative for the genotyping of single or duplicated MHC genes displaying low to moderate sets of divergent alleles.     

Bounded rank-one perturbations in sampling theory

Sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points. In this paper we derive an orthogonal sampling theory and associated Lagrange interpolation formulae from a family of bounded rank-one perturbations of a self-adjoint operator that has only discrete spectrum of multiplicity one.     

Tetramethyl­ammonium 2,5‐dinitro­phenolate monohydrate

The crystal structure of the title compound, C₄H₁₂N⁺·C₆H₃N₂O·H₂O, is built up from tetramethyl­ammonium cations, 2,5‐dinitro­phenolate anions and water molecules. The nitro groups are almost coplanar with the aryl ring, which exhibits significant distortion from an ideal hexagonal form. The X‐ray geometry of the tetramethyl­ammonium cation shows slight distortion from the tetrahedral symmetry predicted by molecular orbital calculations. The O—H⋯O hydrogen‐bonded water and 2,5‐dinitro­phenolate units are related by an inversion center and form dimers. The 2,5‐dinitro­phenolate anions, related by an inversion center and translation, are stacked to form a column along the [100] direction.     

Efficient functionalization of quinolizinium cations with organotrifluoroborates in water

An efficient functionalization of the quinolizinium system is reported. The reaction of the four isomeric bromoquinolizinium salts with different organotrifluoroborates afforded alkyl-, vinyl-, aryl-, and heteroaryl quinolizinium derivatives in moderate or good yields. Reactions are carried out in water using a counterion exchange for the isolation of the cationic-coupled compounds.