The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

On the piezoelectricity of anionic collagen films

In this paper, we report results of a study of the physicochemical, dielectric and piezoelectric properties of anionic and native collagen films, considering the development of new biomaterials which have potential applications in coating of cardiovascular prostheses, support for cellular growth and in systems for controlled drug delivery. The piezoelectric strain tensor element d₁₄, the elastic constant s₅₅, and the dielectric permittivity ?₁₁ were measured for the anionic and native collagen films. It was observed that the collagen samples submitted to the alkaline treatment present lower thermal stability than those made from native collagen. However, the treated samples present a higher piezoelectricity compared with the native collagen. The frequency constant fL and the piezoelectric strain element d₁₄, obtained for the alkaline-treated sample (72 h), present the highest values for the samples under study (444.1 kHz m and 0.079 pC/N, respectively). We believe that the alkaline treatment led to an increase of the organization of the microscopic fiber structure of the sample, which could result in an increase of the piezoelectricity.     

Correction to: Preface

Foundations of Computational Mathematics -     

Géométrie diophantienne et variétés toriques

We present some results on projective toric varieties which are relevant in diophantine geometry. We interpret and study several invariants attached to these varieties by geometrical and combinatorial terms. We also give a Bézout theorem for Chow weights of projective varieties and an application to the theorem of successive algebraic minima. These results are extracted from the two texts of Philippon and Sombra mentioned in the references at the end of this Note (both downloadable from http://fr.arxiv.org). To cite this article: P. Philippon, M. Sombra, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

When do the Recession Cones of a Polyhedral Complex Form a Fan?

We study the problem of when the collection of the recession cones of a polyhedral complex also forms a complex. We exhibit an example showing that this is no always the case. We also show that if the support of the given polyhedral complex satisfies a Minkowski–Weyl-type condition, then the answer is positive. As a consequence, we obtain a classification theorem for proper toric schemes over a discrete valuation ring in terms of complete strongly convex rational polyhedral complexes.     

Switching and enhanced bistability in an asymmetric nonlinear directional coupler with a metamaterial channel

We numerically simulate the propagation and switching of ultra-short pulses in a metamaterial nonlinear directional asymmetric coupler where one of the guides is a conventional medium with a positive refraction index having a decreasing Kerr nonlinearity. The second guide is based in a metamaterial. A complete study of the nonlinear dynamics of ultra-short pulses propagation and switching in this new nonlinear directional coupler, including the transmission characteristics, bistability, critical power, compression factor and extinction coefficients are presented and compared to those of a conventional coupler. We conclude that the conventional coupler has higher transmission efficiency and extinction rate when compared with the metamaterial coupler. However the metamaterial coupler presents bistability which opens the possibility of such device to be used in a large variety of optical switching, storage and logical gates. We show that the input power range leading to bistability can be optimized by controlling the profile of the nonlinear refraction index of the conventional channel.     

The dielectric behavior of a thermoelectric treated B2O3-Li2O-Nb2O5 glass

A transparent glass with the composition 60B₂O₃-30Li₂O-10Nb₂O₅ (mol%) was prepared by the melt-quenching technique. Glass-ceramics, containing LiNbO₃ ferroelectric crystallites, were obtained by heat-treatment (HT) above 500 °C, with and without the presence of an external electric field. The dielectric properties of the glass and glass-ceramic were investigated, as a function of temperature (270-315 K), in the 10 mHz-32 MHz frequency range. The presence of an external electric field, during the heating process, improves the formation of LiNbO₃ crystallites. The rise of the treatment temperature and the applied field, during the heat-treatment, leads to a decrease in the dc electric conductivity (σ_dc), indicating a decrease of the charge carriers number. The dielectric permittivity (ε′) values (300 K;1 kHz) are between 16.25 and 18.83, with the exception of the 550 °C HT sample that presents a ε′ value of 11.25. An electric equivalent circuit composed by an R in parallel with a CPE element was used to adjust the dielectric data. The results reflect the important role carried out by the heat-treatment and the electric field during the HT in the electric properties of glass-ceramics.     

Soliton–like pulse dynamics in add–drop optical filters based on nonlinear fiber grating couplers

The dynamics characteristics of picosecond soliton-like pulses propagating through add–drop optical filters, based on lossless uniform and Gaussian nonlinear fiber grating couplers, are numerically investigated under different power levels. To obtain the temporal profiles, the nonlinear coupled-mode equations, that model these devices, are solved numerically. These devices can perform the extraction (drop) of an optical signal, since there is the reflection of a pulse previously switched between adjacent waveguides. The extraction efficiency, recurrently better at low power levels, is subordinated to the matching between the associated spectra of the input pulses and the hybrid devices analyzed. The switching effects, as well the gratings responsiveness, impact on the outputs profiles, since diverse temporal shapes can be obtained. The results reinforce the importance and the potential of properly engineered structures for all-optical processing requirements.     

Environmental monitoring of phenolic pollutants in water by cloud point extraction prior to micellar electrokinetic chromatography

Many aromatic compounds can be found in the environment as a result of anthropogenic activities and some of them are highly toxic. The need to determine low concentrations of pollutants requires analytical methods with high sensitivity, selectivity, and resolution for application to soil, sediment, water, and other environmental samples. Complex sample preparation involving analyte isolation and enrichment is generally necessary before the final analysis. The present paper outlines a novel, simple, low-cost, and environmentally friendly method for the simultaneous determination of p-nitrophenol (PNP), p-aminophenol (PAP), and hydroquinone (HQ) by micellar electrokinetic capillary chromatography after preconcentration by cloud point extraction. Enrichment factors of 180 to 200 were achieved. The limits of detection of the analytes for the preconcentration of 50-ml sample volume were 0.10 μg L⁻¹ for PNP, 0.20 μg L⁻¹ for PAP, and 0.16 μg L⁻¹ for HQ. The optimized procedure was applied to the determination of phenolic pollutants in natural waters from San Luis, Argentina. Figure Schematic representation of the cloud point extraction process.     

Comparisons of electrical and optical properties between graphene and silicene——A review

Two-dimensional(2D) metamaterials are considered to be of enormous relevance to the progress of all exact sciences.Since the discovery of graphene, researchers have increasingly investigated in depth the details of electrical/optical properties pertinent to other 2D metamaterials, including those relating to the silicene. In this review are included the details and comparisons of the atomic structures, energy diagram bands, substrates, charge densities, charge mobilities, conductivities,absorptions, electrical permittivities, dispersion relations of the wave vectors, and supported electromagnetic modes related to graphene and silicene. Hence, this review can help readers to acquire, recover or increase the necessary technological basis for the development of more specific studies on graphene and silicene.