A PDE based and interpolation-free framework for modeling the sifting process in a continuous domain

The empirical mode decomposition (EMD) is a powerful tool in signal processing. Despite its algorithmic origin making its theoretical analysis and formulation very difficult, a few recent works has contributed to its theoretical framework. Herein, the former local mean is formulated in a more convenient way by introducing operators to calculate local upper and lower envelopes. This enables the use of differential calculus and other classical calculations on the new local mean. Based on its more accurate formulation, a partial differential equation (PDE) consistency result is provided to approximate the sifting process iterations, without any envelope interpolation. In addition, a new stopping criterion based on the introduced local mean is proposed. This new criterion is a local measure and resolves the null integral conservative property of the previous derived PDE, which made any signal having a null integral be a PDE-based mode. Moreover, the δ inner model parameter is now linked to the signal intrinsic properties, providing to the latter a physical meaning and making the proposed model keep the auto-adaptive property of the EMD. New decomposition modes are now analytically and fully characterized, and also interpolation free. Finally, properties of the interpolation free PDE model are presented. Results obtained with our proposed approach by explicit computations thanks to the eigendecomposition of the Laplacian operator, and also by numerical resolution of the derived PDE, show noticeable improvements for both stationary and non stationary signals, in comparison to the former EMD algorithm.     

Experimental investigations and thermodynamic description of the PbO−Bi2O3 system

In the present work, the experimental characterization of the pseudo-binary PbO–Bi₂O₃ cut has been performed by differential thermal analysis (DTA), isothermal annealing, powder X-ray diffraction analysis (XRD), scanning electron microscopy (SEM), and electron probe microanalysis (EPMA). A thermodynamic assessment according to the Calphad method was also performed based on the present results as well as previous experimental data using the ThermoCalc software.     

Rational synthesis of chiral layered magnets by functionalization of metal simple hydroxides with chiral and non-chiral Ni(II) Schiff base complexes

Synthesis of new heterometallic layered magnets with controlled chirality have been achieved by insertion of chiral and non-chiral salen-type Ni(II) complexes into copper and cobalt layered simple hydroxides.     

Preparation and property assessment of neat lignocellulose nanofibrils (LCNF) and their composite films

Lignocellulose nanofibrils (LCNF) were produced from thermo-mechanical pulp (TMP) using a micro-grinder and were characterized with respect to fiber diameter and thermal stability. The initial water content in the TMP affected the defibrillation process and longer grinding time was necessary for the air-dried TMP, resulting in LCNF with higher fibril diameter. As compared to the reference cellulose nanofibrils (CNF) produced through a refining process, LCNF was less thermally stable and started to degrade at a temperature that was 30 °C lower than that of CNF. LCNF obtained from the never-dried TMP was combined with various additives (10 wt%) to produce composite films. The neat LCNF and composite films did not reach the mechanical properties of the neat CNF film that was evaluated as reference. However, the addition of poly(vinyl alcohol) (PVA) at 10 wt% on a dry basis did cause a 46 and 25% increase in tensile strength and elastic modulus, respectively. Other additives including cellulose nanocrystals, bentonite and CNF were also found to increase to some extent the Young’s modulus and ductility of the LCNF composite films whereas the addition of talc did not improve the film performance. Water absorption of neat LCNF films was lower than the reference CNF and was negatively affected by the addition of PVA.     

Doubly‐Charged Xe Ions Evidenced by Time Resolved RPA Measurement in the Far Field Plume of a Low‐Power HET

A low power Hall Effect Thruster (HET), based on a permanent magnet circuit, was investigated in the GREMI laboratory facility. The thruster operated in the working range between 50 and 300 W and the previously measured thrust is between 4 and 16 mN for an anodic efficiency respectively between 15% and 27%. The pulsed character of the thruster current is an important feature of this HET. The ion current's bursts are recorded at 30 and 70 cm from the exit plane in the thruster plume and are time‐resolved, which lead to a preliminary analysis of the time of flight (TOF) phenomena. This paper presents a detailed study of these bursts of ion current in the plume. The total ion current is shown to be a superposition of 2 distinct contributions of charged species. In complement, a controlled single current interruption in stable anodic current condition leads to exactly the same features than in oscillating mode. This crucial verification garantees the validity of the time of flight origine of the two distinct contributions. Then, the slower one is the more intense and is proportional to the ion Xe+ current whereas the faster one could be attributed either to doubly‐charged Xe⁺⁺ or to superfast Xe⁺. The work presents a way to determine unambiguously the nature of the fast contribution by recording the Retardated Potential Analyser (RPA) signals at various repelling grid potentials with respect to time. The energy distribution of the 2 wellseparated contributions are reconstructed and confirms the contribution of doubly‐charged xenon ions (Xe⁺⁺) in the plume. This way of RPA collecting data and interpretation presents the main advantage tobe an easy way for the identification of the nature of the charged species in the plume. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exponential Behavior of Solutions to Stochastic Integrodifferential Equations with Distributed Delays

In this work, we study the existence, uniqueness, and exponential asymptotic behavior of mild solutions to stochastic integrodifferential delay evolution equations. We assume that the non-delay part generates a C₀-semigroup.     

Consistency of a nonparametric conditional quantile estimator for random fields

Given a stationary multidimensional spatial process (Z _i = (X _i , Y _i ) ∈ ℝ ^d × ℝ, i ∈ ℤ ^N ), we investigate a kernel estimate of the spatial conditional quantile function of the response variable Y _i given the explicative variable X _i . Almost complete convergence and consistency in L ^2r norm (r ∈ ℕ*) of the kernel estimate are obtained when the sample considered is an α-mixing sequence.     

Singular homogenization with stationary in time and periodic in space coefficients

We study the homogenization problem for a random parabolic operator with coefficients rapidly oscillating in both the space and time variables and with a large highly oscillating nonlinear potential, in a general stationary and mixing random media, which is periodic in space. It is shown that a solution of the corresponding Cauchy problem converges in law to a solution of a limit stochastic PDE.     

Degré d'une solution algébrique d'un tissu sur le plan projectif complexe

Let γ be an algebraic solution of a non-dicritical d-web in the complex projective plane. We give a formula relating global data (degree of the solution and of the web) to local data (some indices supported on the union of the singular set of γ with the intersection of the curve with the discriminant of the web).