On Strictly Convex Subsets in Negatively Curved Manifolds

In a complete simply connected Riemannian manifold X of pinched negative curvature, we give a sharp criterion for a subset C to be the ??-neighbourhood of some convex subset of X, in terms of the extrinsic curvatures of the boundary of C.     

Determination of parabens in wastewater samples via robot-assisted dynamic single-drop microextraction and liquid chromatography–tandem mass spectrometry

Dynamic single-drop microextraction (SDME) was automatized employing an Arduino-based lab-made Cartesian robot and implemented to determine parabens in wastewater samples in combination with liquid chromatography–tandem mass spectrometry. A dedicated Arduino sketch controls the auto-performance of all the stages of the SDME process, including syringe filling, drop exposition, solvent recycling, and extract collection. Univariate and multivariate experiments investigated the main variables affecting the SDME performance, including robot-dependent and additional operational parameters. Under selected conditions, limit of detections were established at 0.3 µg/L for all the analytes, and the method provided linear responses in the range between 0.6 and 10 µg/L, with adequate reproducibility, measured as intraday relative standard deviations (RSDs) between 5.54% and 17.94%, (n = 6), and inter-days RSDs between 8.97% and 16.49% (n = 9). The robot-assisted technique eased the control of dynamic SDME, making the process more feasible, robust, and reliable so that the developed setup demonstrated to be a competitive strategy for the automated extraction of organic pollutants from water samples.     

Domain decomposition methods for the study of the particular behavior of a very thin long structure

The homogenization process of the Poisson equations in a thin structure leads to partial differential equation systems on different subdomains. As a result, it produces artificial interfaces and particular transmission conditions. © 1996 John Wiley & Sons, Inc.     

Adsorption equilibria of binary ethylmercaptan/hydrocarbon mixtures on a NaX zeolite

We present here coadsorption data of ethylmercaptan with n-heptane or toluene on NaX at 298 K in the aim to use this adsorbent for removing mercaptans from natural gas. Results show that NaX has an adsorption affinity for sulphur compound strong enough to perform a deep desulphurization. NaX adsorbs preferentially ethylmercaptan over a large domain of pore filling. A displacement of n-heptane by ethylmercaptan is even observed. However, toluene becomes preferentially adsorbed at high filling. The dependence of filling and composition on selectivities and failed prediction of coadsorption equilibria by the IAS Theory indicate that the adsorbed mixture behaves as a non-ideal solution. Calorimetric measurements of coadsorption heats show that the coadsorption process is not governed by enthalpic effects but by entropic effects consecutive to steric hindrance of molecules in confined spaces.     

Relative influence of two small parameters in non uniformly elliptic homogenization problems

We study three elliptic problems depending on two small parameters (? = homogenization parameter and δ = perturbation parameter which causes non uniform ellipticity). In each case, the homogenized operator corresponding to the second order operator is independent of the way (?, δ) → (0, 0), but the convergence results and the limit solution do depend on the relative size of ? and δ; the relevant parameter is δ?^?2.     

On the exterior algebra method applied to restricted set addition

In 1994 Dias da Silva and Hamidoune solved a long-standing open problem of Erd?s and Heilbronn using the structure of cyclic spaces for derivatives on Grassmannians and the representation theory of symmetric groups. They proved that for any subset A$A$ of the p$p$-element group Z/pZ$\mathbb{Z}/p\mathbb{Z}$ (where p$p$ is a prime), at least min{p,m|A|−m²+1}$min\{p,m\left|A\right|-m^2+1\}$ different elements of the group can be written as the sum of m$m$ different elements of A$A$. In this note we present an easily accessible simplified version of their proof for the case m=2$m=2$, and explain how the method can be applied to obtain the corresponding inverse theorem.     

Generalized Darboux transformation and parameter-dependent rogue wave solutions to a nonlinear Schrödinger system

Objectives of the paper are (1) to design two new real and complex no equilibrium point hyperchaotic systems, (2) to design synchronisation technique for the new systems using the contraction theory and (3) to validate the results by using circuit realisation. First a new no equilibrium point hyperchaotic system is developed using a 3-D generalised Lorenz system; then using the new system a new complex no equilibrium point hyperchaotic system is reported. Both the new systems have hidden chaotic attractors. Various dynamical behaviours are observed in the new systems like chaotic, periodic, quasi-periodic and hyperchaotic. Both the systems have inverse crisis route to chaos with the variation of parameter a and crisis route to chaos with the variation of parameters \(b,\ c\) and d. These phenomena along with hidden attractors in a complex hyperchaotic system are not seen in the literature. Synchronisation between the identical new hyperchaotic systems is achieved using the contraction theory. Further the synchronisation between the identical new complex hyperchaotic systems is achieved using adaptive contraction theory. The proposed synchronisation strategies are validated using the MATLAB simulation and circuit implementation results. Further, an application of the proposed system is shown by transmitting and receiving an audio signal.     

Analysis of Path Integrals at Low Temperature: Box Formula,Occupation Time and Ergodic Approximation

We study the low temperature behavior of path integrals for a simple one-dimensional model. Starting from the Feynman–Kac formula, we derive a new functional representation of the density matrix at finite temperature, in terms of the occupation times for Brownian motions constrained to stay within boxes with finite sizes. From that representation, we infer a kind of ergodic approximation, which only involves double ordinary integrals. As shown by its applications to different potentials, the ergodic approximation turns out to be quite efficient, especially in the low-temperature regime where other usual approximations fail.     

Constructions arborescentes d'immeubles

 We prove that, contrarily to the case of spherical and euclidean buidings, the set of (isomorphism classes of) locally finite 3-dimensional hyperbolic buildings is uncountable. The proof uses on one hand a classification of 3-dimensional Coxeter polytops satisfying some local properties of irreducibility and symmetry, and on another hand, an arborescent construction of buildings for splitable Coxeter systems. Received: 20 September 2001 / Revised version: 22 May 2002 / Published online: 2 December 2002 Mathematics Subject Classification (2000): 51E24, 51M10, 51F15     

Un Groupe Hyperbolique Est Determine Par Son Bord

We construct on the boundary of a hyperbolic group (in Gromov'ssense) a natural visual measure and a natural crossratio. Weprove that the I-quasiconformal homeomorphisms (in Pansu's sense)between the boundaries of hyperbolic groups are the quasimöbiusmaps (that is, the bijections that almost preserve the crossratios),and that they are the extensions of the quasi-isometries betweenthe groups. We define a barycentre for every probability measureon the boundary without atom, extending the Douady-Earle construction.