An Aitken-like acceleration method applied to missing boundary data reconstruction for the Cauchy–Helmholtz problem

This Note is concerned with the severely ill-posed Cauchy–Helmholtz problem. This Cauchy problem being rephrased through an “interfacial” equation, we resort to an Aitken–Schwarz method for solving this equation. Numerical trials highlight the efficiency of the present method.     

On the limit cycles for a class of generalized Kukles differential systems

In this paper, we consider the limit cycles of a class of polynomial differential systems of the form $\dot{x}=-y, \hspace{0.2cm} \dot{y}=x-f(x)-g(x)y-h(x)y^{2}-l(x)y^{3},$ where $f(x)=\epsilon f_{1}(x)+\epsilon^{2}f_{2}(x),$ $g(x)=\epsilon g_{1}(x)+\epsilon^{2}g_{2}(x),$ $h(x)=\epsilon h_{1}(x)+\epsilon^{2}h_{2}(x)$ and $l(x)=\epsilon l_{1}(x)+\epsilon^{2}l_{2}(x)$ where $f_{k}(x),$ $g_{k}(x),$ $h_{k}(x)$ and $l_{k}(x)$ have degree $n_{1},$ $n_{2},$ $n_{3}$ and $n_{4},$ respectively for each $k=1,2,$ and $\varepsilon$ is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of the linear center $\dot{x}=-y,$ $\dot{y}=x$ using the averaging theory of first and second order.     

Influence of the solvent on the extraction of copper(II) from nitrate medium using salicylideneaniline

Different solvents including cyclohexane, dichloromethane, chloroform, toluene, 1-octanol, and methyl isobutyl ketone (MIBK) have been evaluated in extracting copper(II) from nitrate medium by salicylideneaniline. Extracted species differs from solvent to solvent: CuL₂ in cyclohexane, toluene, 1-octanol, and methyl isobutyl ketone. However, in dichloromethane or chloroform, there are two complexes of the type CuL₂ and CuL₂(HL). The extraction constants and percentage of extraction (%E) are calculated for different solvents. Solvent played an important role in recovering copper(II) from the aqueous solution, thus affecting the extraction equilibrium and extraction efficiency. The nonpolar solvent showed better performance than the polar solvent. The maximum extraction efficiency was 85.75% at pH?=?4.5, which was from cyclohexane.     

On steady motions of a rigid body bearing three-degree-of-freedom control momentum gyroscopes and their stability

Equations of motion are obtained for a rigid body bearing N three-degree-of-freedom control momentum gyroscopes in gimbals and the entire set of steady motions in a homogeneous external field is determined. The steady motion dependence on the magnitude of the system angular momentum is studied and a detailed analysis of the secular stability is performed.     

Separation of representations with quadratic overgroups

Any unitary irreducible representation π of a Lie group G defines a moment set Iπ, subset of the dual g^? of the Lie algebra of G. Unfortunately, Iπ does not characterize π. If G is exponential, there exists an overgroup G⁺ of G, built using real-analytic functions on g^?, and extensions π⁺ of any generic representation π to G⁺ such that Iπ⁺ characterizes π.In this paper, we prove that, for many different classes of group G, G admits a quadratic overgroup: such an overgroup is built with the only use of linear and quadratic functions.     

N-Octyl Quaternized P4VP Interaction With Orange Telon

The removal of orange Telon from aqueous solutions by poly(N-octyl-4-vinylpyridiniumbromide) copolymer was investigated. Batch adsorption experiments were carried out to study the effect of experimental parameters on the orange Telon adsorption equilibrium. The adsorption characteristics of copolymer to ward orange Telon in dilute aqueous solution were followed using UV-Vis spectrophotometry. Adsorption equilibrium was reached within 60 min for 0.03 g of poly(4-vinylpyridine quaternized at 58%. The kinetic of adsorption is best described by a pseudo-second-order model. Results also showed that the equilibrium modeling of orange Telon removal process was described by Langmuir isotherms. The maximum adsorption capacity determined from the Langmuir isotherm was 76.4 mg g^{? 1}. The study of the thermodynamic parameters showed that the adsorption of orange Telon on copolymer is an exothermic process and the randomness decreases at the solid-solution interface during the adsorption of dye on the copolymer.     

A tandem C-H insertion—acetal cleavage sequence: stereocontrolled synthesis of substituted tetrahydrofurans

A short sequence involving Rh(II) mediated carbene insertion followed by Lewis acid promoted reductive acetal cleavage with Et₃SiH provides a stereoselective method for the construction of 2,3,5-trisubstituted tetrahydrofuran rings.     

Missing boundary data recovering for the Helmholtz problem

This Note is dedicated to the numerical treatment of the ill-posed Cauchy–Helmholtz problem. Resorting to the domain decomposition tools, these missing boundary data are rephrased through an ‘interfacial’ equation. This equation is solved via a preconditioned Richardson algorithm with dynamic relaxation. The efficiency of the proposed method is illustrated by some numerical experiments. To cite this article: R. Ben Fatma et al., C. R. Mecanique 335 (2007).