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.     

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.     

Adaptive fuzzy control‐based projective synchronization of uncertain nonaffine chaotic systems

This article aims to introduce a projective synchronization approach based on adaptive fuzzy control for a class of perturbed uncertain multivariable nonaffine chaotic systems. The fuzzy‐logic systems are employed to approximate online the uncertain functions. A Lyapunov approach is used to design the parameter adaptation laws and to demonstrate the boundedness of all signals of the closed‐loop system as well as the convergence of the synchronization errors to bounded residual sets. Finally, numerical simulation results are presented to verify the feasibility and effectiveness of the proposed synchronization system based on fuzzy adaptive controller. © 2014 Wiley Periodicals, Inc. Complexity 21: 180–192, 2015     

The asymptotic properties of the motions of satellites in a central field due to internal dissipation

A satellite in the form of a system of bodies that does not have the property of a gyrostat in the general case is considered. An algorithm for determining all the equilibrium configurations of the system that correspond to steady motions in a central gravitational field and an algorithm for analysing their stability are given. A method based on Routh's first theorem is used to investigate the asymptotic stability of the steady motions in the unconstrained problem. Three effects caused by internal dissipation are established in a model example: stabilization of the satellites in a neighbourhood of rotations about a normal to the orbital plane, which is codirectional with the axis of the largest moment of inertia, evolution of elliptic orbits into circular orbits, and capture of the satellites in resonant oscillatory modes of motion.     

The properties of the steady motions of a body carrying a system of two-degree-of-freedom powered gyroscopes

The steady motions of a rigid body carrying several two-degree-of-freedom powered gyroscopes in a uniform external field are investigated. It is shown that when the installation scheme of the gyroscopes in the carrying body is collinear, the problem of determining the steady motions of the system and analysing their secular stability reduces for the most part to the previously solved, similar problem for a system with one gyroscope. It is established that when there is dissipation in the axes of the gyroscope frames, the system tends asymptotically to a state of rest if the absolute value of the total angular momentum of the system lies in the segment of possible absolute values of the angular momentum of the gyroscope rotors. The results of an analysis of the steady motions of a system carrying two gyroscopes with a non-collinear installation scheme are presented.     

Synthesis,anticancer screening,and in silico ADME prediction of novel 2-pyridones as Pim inhibitors

A novel series of 26 substituted N-(2-ethylphenyl)-2-oxo-pyridine-3-carbonitriles have been designed and synthesized via one-pot synthesis of various aromatic aldehydes, different aromatic acetophenones, and 2-cyano-N-(2-ethylphenyl)acetamide 1 . Moreover, cytotoxicity of the target compounds was evaluated by NCI, which selected 14 compounds for one-dose screening. Among them, compound 21 was selected for five-dose screening, which confirmed its potency against most of cancer cell lines. This compound elicited selectivity profile against human cell line WI-38. Cell cycle analysis was carried out, revealed that compound 21 is an apoptosis inducer causing cell cycle arrest at G2/M. Further exploration on the mode of action by evaluating its effect against Pim-1, Pim-2, and Pim-3 demonstrated its inhibitory effect on Pim-1 and Pim-3 rather than Pim-2. Molecular docking showed that compound 21 binds with high affinity to the active site of Pim-1 enzyme through three hydrogen bonds and two arene-H bonds.     

The solvolysis oftrans-[Co(4-Mepy)4Cl2]ClO4 in water-methanol mixtures

Summary The solvolysis of thetrans-[Co(4-Mepy)₄Cl₂]ClO₄ complex was studied in 0 to 70% v/v H₂O: MeOH mixtures at 40, 45, 50 and 55 °C. The high negative S^* values found for the complex cation under investigation, relative to that oftrans- [Co(py)₄Cl₂]⁺ reported in the literature, were attributed to the substituent methyl groups. The free energies of transfer of both the ground and the transition states were calculated from which the dominant effect of the solvent on the transition state is apparent.     

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.     

Solvent effects on the initial and transition states upon solvolysis oftrans-dichlorotetra(4-ethylpyridine)cobalt(III) perchlorate in water+methanol mixtures

Summary The solvolysis of trans-[Co(4-Etpy)₄Cl₂]⁺ (1) (Etpy=ethylpyridine) was investigated in water and in a wide range of water+methanol mixtures. The effect of temperature on the solvolysis was considered and the thermodynamic parameters of activation were calculated. The free energies of transfer of (1) in the initial state were calculated from the solubility of the complex [Co(4-Etpy)₄Cl₂]₂[ReCl₆]. The free energy of transfer of the cation (1) in the transition state was calculated using a free energy cycle. The effect of the solvent structure on (1) is dominant in the transition state, where –G _t ^o (1) transition >–G _t ^o (1) initial. Comparison of the present thermodynamic data with those obtained previously fortrans-[Co(4-Mepy)₄Cl₂]⁺, (2), andtrans-[Co(py₄Cl₂]⁺, (3) in the same solvent mixture, shows that the stability increases in the order: (1), (2)<(3) at low mole fraction of the co-solvent, contrary to expectation, while at high mole fraction the order of increasing stability is: (1)<(3)<(2). The results were interpreted on non-electrostatic grounds.     

Missing boundary data reconstruction by the factorization method

We consider the data completion problem for the Laplace equation in a cylindrical domain. The Neumann and Dirichlet boundary conditions are given on one face of the cylinder while there is no condition on the other face. This Cauchy problem has been known since Hadamard (1953) to be ill-posed. Here it is set as an optimal control problem with a regularized cost function. We use the factorization method for elliptic boundary value problems. For each set of Cauchy data, to obtain the estimate of the missing data one has to solve a parabolic Cauchy problem in the cylinder and a linear equation. The operator appearing in these problems satisfy a Riccati equation that does not depend on the data. To cite this article: A. Ben Abda et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).