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.     

A Novel Tetranuclear Organotin(IV) Carboxylate with Chain Structure: Synthesis,Crystal Structure,and Characterizations

A new tetranuclear organotin carboxylate {[(n‐Bu₂SnO)₂L]₂}_n (complex 1 ) was synthesized by the reaction of di‐n‐butyltin oxide with (p‐carboxymethoxy‐phenoxy) acetic acid (LH₂) and characterized by elemental analyses: IR, UV–visible, ¹H, ¹³C, ¹¹⁹Sn NMR spectroscopy and single crystal X‐ray study. X‐ray crystallography diffraction data revealed that the complex 1 was polymeric fashion with a chain structure containing a ladder‐like tetranuclear organo‐oxotin cluster. In the complex 1 , the ligand LH₂ is coordinated to the central tin(IV) atoms via the carboxylato‐O atoms. The tetranuclear tin system is formed by the bridges through the carbonyl oxygen atom of the carboxylate moieties and making the tin atom of pentacoordinated in distorted trigonal bipyramidal geometry. Single crystal X‐ray data indicate that the complex 1 crystallized in the cubic system with the space group C₂/c.     

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.     

Application of Homotopy Perturbation Method and Variational Iteration Method to Nonlinear Oscillator Differential Equations

In this paper, homotopy perturbation method (HPM) and variational iteration method (VIM) are applied to solve nonlinear oscillator differential equations. Illustrative examples reveal that these methods are very effective and convenient for solving nonlinear differential equations. Moreover, the methods do not require linearization or small perturbation. Comparisons are also made between the exact solutions and the results of the homotopy perturbation method and variational iteration method in order to prove the precision of the results obtained from both methods mentioned.     

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.     

On the analytical solution for MHD natural convection flow and heat generation fluid in porous medium

Homotopy analysis method (HAM) is employed to investigate the momentum, heat and mass transfer characteristics of MHD natural convection flow and heat generation fluid driven by a continuously moving permeable surface immersed in a fluid saturated porous medium. The solution is found to be dependent on several governing parameters, including the magnetic field strength parameter, Prandtl number, Darcy number, the dimensionless inertia coefficient, the dimensionless heat generation/absorption coefficient and the dimensionless suction/blowing coefficient. A parametric study of all governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Representative results are presented for velocity and temperature distributions as well as the local friction coefficient and local Nusselt number. Finally, a proper discussion is derived on the obtained results and some remarkable conclusions are mentioned.     

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.