On Dumont's polynomials

We derive two generating functions and an explicit formula for the polynomials {H_n(x)} studied by Dumont.     

Absence of Positive Eigenvalues for the Linearized Elasticity System

In this paper, we prove that the linearized elasticity system has no eigenvalues in two geometric situations: the whole space and a local perturbation of the half-space. We consider the Lamé coefficients and the density varying in an unbounded part of the domain. For the whole space, we use the operations curl and div to reduce our system to a scalar problem and use a limiting absorption principle for the reduced scalar equation given by the partial Fourier transform. For the perturbed half-space, this decompositions being no longer valid, we give an other method based on a pseudo-decomposition using the operations div and curl in the horizontal direction. In contrast to the whole space case, the reduced problems depend strongly on the dual Fourier variable which do not enable us to use same techniques. To study these reduced problems, we use the analytic theory of linear operators.     

STM-based molecular detection of "catch-and-release" of protons for bipyridine bound to phenylene-ethynylene thiol

The protonation/deprotonation response of a novel bipyridine containing (phenylene-ethynylene) thiol adsorbed to a Au surface was investigated with scanning tunneling microscopy (STM), showing reversible changes in the average heights (approximately 50 spots) and the height distribution arising from protonation/deprotonation.     

Unsupervised Bayesian image segmentation using orthogonal series

This paper deals with the problem of unsupervised image segmentation which consists in first mixture identification phase and second a Bayesian decision phase. During the mixture identification phase, the conditional probability density function (pdf) and the a priori class probabilities must be estimated. The most difficult part is the estimation of the number of pixel classes or in other words the estimation of the number of density mixture components. To resolve this problem, we propose here a Stochastic and Nonparametric Expectation-Maximization (SNEM) algorithm. The algorithm finds the most likely number of classes, their associated model parameters and generates a segmentation of the image by classifying the pixels into these classes. The non-parametric aspect comes from the use of the orthogonal series estimator. Experimental results are promising, we have obtained accurate results on a variety of real images.     

Energy decay for the elastic wave equation with a local time-dependent nonlinear damping

In this paper, we shall investigate the decay property of the solutions to the initial-boundary value problem for the elastic wave equation with a local time-dependent nonlinear damping. We give some decay rate of the energy when the damping term is effective only in a neighborhood of a suitable subset of the boundary. The results obtained in this paper extend, in particular, the known results for the scalar wave equation.     

Testability of parity checkers

Checkers are used in digital circuits to detect both intermittent and stuck-at faults. The most common error detectors are parity checkers. Such circuits are themselves subject to failures. The use of parity trees is outlined, and techniques for testing them are surveyed. The effect of the checker's structure on its testability is discussed. Several fault models are considered: single stuck-at, multiple stuck-at, and bridging faults. The effectiveness of single stuck-at fault test sets in detecting multiple stuck-at and bridging faults is described. Upper bounds for the double fault coverage of the minimal single fault test are given for different tree structures. The testabilities of some selected checkers are examined to illustrate the concepts developed. A built-in self-test is proposed     

Hysteresis suppression for primary and subharmonic 3:1 resonances using fast excitation

Nonlinear Dynamics - We analyze the effect of a fast harmonic excitation on hysteresis and on entrainment area in a forced van der Pol–Duffing oscillator near the primary and the 3:1...     

Elaboration and characterisation of a plasticized cellulose triacetate membrane containing trioctylphosphine oxyde (TOPO): Application to the transport of uranium and molybdenum ions

A cellulose triacetate (CTA) membrane containing trioctylphosphine oxyde (TOPO) as carrier and 2-nitrophenyloctyl ether (NPOE) as a plasticizer was prepared. The membrane CTA + NPOE + TOPO was characterised using chemical techniques as well as Fourier Transform InfraRed (FTIR) spectroscopy, X-ray diffraction and Scanning Electron Microscopy (SEM). The CTA membrane is characterised by well-defined pores; these pores are completely filled with the NPOE and carrier. Surfaces of membranes with TOPO are smooth. The systems constituted by the mixture of CTA + NPOE, CTA + NPOE + TOPO do not give any diffraction. This can be due to the absence of crystallization within the membrane. On the other hand, this result should be attributable to the amorphous state of the structure, which permits us to eliminate the mechanism of transfer of the ions by electron jump. A comparative study of transport across a polymer inclusion membrane (PIM) and a supported liquid membrane (SLM) containing the same carrier in chloroform has shown that uranium or molybdenum transport efficiency was increased using PIM instead of SLM. PIM showed higher stability than SLM, the flux of transport remain constant in the former case after 2 weeks.     

Wideband chaos generation using a delayed oscillator and a two-dimensional nonlinearity induced by a quadrature phase-shift-keying electro-optic modulator

We present a new optoelectronic architecture intended for chaotic optical intensity generation. The principle relies on an electro-optic nonlinear delay dynamics, where the nonlinearity originates from an integrated four-wave optical interferometer, involving two independent electro-optic modulation inputs. Consequently, the setup involves both two-dimensional nonlinearity and dual-delay feedback dynamics, which results in enhanced chaos complexity of particular interest in chaos encryption schemes. The generated chaos observed with large feedback gains has a bandwidth ranging from 30 kHz to 13 GHz and is confirmed by numerical simulations of the proposed dynamical model and bifurcation diagram calculation.