Micro and nanoparticles in biosensing systems for food safety and environmental monitoring. An example of converging technologies

We report on the integration of micro and nanostructured materials in biosensing devices to obtain analytical nano-bio-systems with improved performance. The simplest case of electrochemical biosensing presented here is based on graphite microparticles to obtain a graphite-epoxy composite. The integration of the bioreceptor within the composite provides an analytical biosystem with improved performances for biosensing. The further addition of gold nanoparticles results in an analytical nano-bio-system which allows an improved strategy for the immobilization of the bioreceptor. And finally, the integration of magnetic beads to graphite-epoxy composite magneto electrodes provides further advantages in terms of separation of the analyte from complex matrix and enhanced biological reactions, resulting in analytical magneto-nano-bio-systems. The application of these systems mainly in food safety and environmental monitoring are reported. The benefits of the integration of these materials to obtain improved analytical systems are discussed and represent an example of converging technologies.     

The Dirichlet problem associated to the relativistic heat equation

We prove existence and uniqueness of entropy solutions for the nonhomogeneous Dirichlet problem associated to the relativistic heat equation.     

New results on restriction of Fourier multipliers

We develop an extension of the Transference methods introduced by R. Coifman and G. Weiss and apply it to study the problem of the restriction of Fourier multipliers between rearrangement invariant spaces, obtaining natural extensions of the classical de Leeuw’s result and its further extension to maximal Fourier multipliers due to C. Kenig and P. Tomas.     

Exploring the structural and electronic properties of nitrogen-containing exohydrogenated carbon nanotubes: a quantum chemistry study

Saturated nanotubes consisting of 2–10 and 20 layers of cyclic units of six-membered rings, each one having a pyrimidine-like framework (i.e., –C–C–C–N–C–N–), were studied by quantum chemistry methods using Density Functional Theory (DFT) at the B3LYP/6-31G* level of theory. Four different nanotube (NT) configurations were theoretically studied in this work. They were formed by covalently arranging each layer over the other, with uniform relative rotations of 0°, 60°, 120°, and 180° with respect to each of the layers. Different structures can be created by modulating the relative rotation as layers are added to the main nanostructure. NTs with a relative rotation of 60° showed both greater stabilities and highest potential for catalytic activity. All of them showed band gaps of around 0.2 eV. Charges and other properties can be controlled by appropriate layer arrangement. The studied families of NTs have a very small diameter and could find potential applications in chemistry, physics, and medicine.     

Left K-Completeness in Quasi-Metric Spaces

Regular left K-sequentially complete quasi-metric spaces are characterized. We deduce that these spaces are complete Aronszajn and that every metrizable space admitting a left K-sequentially complete quasi-metric is completely metrizable. We also characterize quasi-metric spaces having a quasi-metric left K-sequential completion in terms of certain bases of countable order.     

A formula with some applications to the theory of Lyapunov exponents

We prove an elementary formula about the average expansion of certain products of 2 by 2 matrices. This permits us to quickly re-obtain an inequality by M. Herman and a theorem by Dedieu and Shub, both concerning Lyapunov exponents. Indeed, we show that equality holds in Herman’s result. Finally, we give a result about the growth of the spectral radius of products. Financial support from Pronex-Dynamical Systems, CNP_q 001/2000 and from Faperj is gratefully acknowledged.     

Wijsman and Hit-and-Miss Topologies of Quasi-Metric Spaces

The relationship between the Wijsman topology and (proximal) hit-and-miss topologies is studied in the realm of quasi-metric spaces. We establish the equivalence between these hypertopologies in terms of Urysohn families of sets. Our results generalize well-known theorems and provide easier proofs. In particular, we prove that for a quasi-pseudo-metrizable space (X,T) the Vietoris topology on the set P ₀(X) of all nonempty subsets of X is the supremum of all Wijsman topologies associated with quasi-pseudo-metrics compatible with T. We also show that for a quasi-pseudo-metric space (X,d) the Hausdorff extended quasi-pseudo-metric is compatible with the Wijsman topology on P ₀(X) if and only if d ^–1 is hereditarily precompact.     

Textile/Metal–Organic‐Framework Composites as Self‐Detoxifying Filters for Chemical‐Warfare Agents

The current technology of air‐filtration materials for protection against highly toxic chemicals, that is, chemical‐warfare agents, is mainly based on the broad and effective adsorptive properties of hydrophobic activated carbons. However, adsorption does not prevent these materials from behaving as secondary emitters once they are contaminated. Thus, the development of efficient self‐cleaning filters is of high interest. Herein, we report how we can take advantage of the improved phosphotriesterase catalytic activity of lithium alkoxide doped zirconium(IV) metal–organic framework (MOF) materials to develop advanced self‐detoxifying adsorbents of chemical‐warfare agents containing hydrolysable P? F, P? O, and C? Cl bonds. Moreover, we also show that it is possible to integrate these materials onto textiles, thereby combining air‐permeation properties of the textiles with the self‐detoxifying properties of the MOF material.