A new reduced gradient method for solving linearly constrained multiobjective optimization problems

In this paper, we consider the linearly constrained multiobjective minimization, and we propose a new reduced gradient method for solving this problem. Our approach solves iteratively a convex quadratic optimization subproblem to calculate a suitable descent direction for all the objective functions, and then use a bisection algorithm to find an optimal stepsize along this direction. We prove, under natural assumptions, that the proposed algorithm is well-defined and converges globally to Pareto critical points of the problem. Finally, this algorithm is implemented in the MATLAB environment and comparative results of numerical experiments are reported.     

Optimizing biological wastewater treatment

Ricerche di Matematica - In this paper we propose a non linear mathematical model describing the process of biodegradation of organic pollutants by means of fungi, and using glucose to sustain its...     

Water behavior revisited at the air/ionic solution and silica/ionic solution interfaces. Extension to coadsorption of ions and organic molecules

This paper reports on investigations about the adsorption at the air-water surface, and for the sake of comparison at the silica-solution interface, of two 1-2 electrolytes, Pb(NO(3))(2) and PbCl(2), at first alone and then from a mixture with carbofuran or with benzene; all of them were at concentrations below 10(-2) M. The limited domain, where the Debye and Hückel formalism for solutions and the Wagner-Onsager-Samaras (WOS) model for surfaces are correct, is then respected. This study was aimed at trying to identify the part played in the surface by the different particles of the system components and in particular the role of water. When aqueous solutions of nonorganic salts are dilute enough, their surface tensions are known to be salt concentration-independent; however, the zero value of the resulting relative adsorption has never been the subject of analysis about water behavior. By combining experimental relative adsorptions and Gibbs excesses calculated from the WOS theory, we will show that, in well-known solutions such as KCl ones, where the negative excess in salt can be very precisely modeled by the WOS theory, the resulting water excess Gamma(W) is negative. The same result can be obtained by taking into account the Ray-Jones effect. This observation drove us to wonder about the results of a similar analysis done on solutions of unsymmetrical electrolytes and on mixtures of salt and organic molecules. Experiments showed that, for all of the systems, Gamma(W) was negative. For a given salt, Gamma(W) was more negative in the presence of organic molecules, and carbofuran was a more efficient water repellent than benzene; water repulsion was greater with nitrates than with chlorides. From these data, it seems that water was repelled toward the solution bulk, whereas ions probably took place between the bulk and a layer of organic molecules. These observations called for a more detailed modeling.     

Perturbation theory for convolution semigroups

We deal with convolution semigroups (not necessarily symmetric) in Lp(RN) and provide a general perturbation theory of their generators by indefinite singular potentials. Such semigroups arise in the theory of Lévy processes and cover many examples such as Gaussian semigroups, α-stable semigroups, relativistic Schrödinger semigroups, etc. We give new generation theorems and Feynman-Kac formulas. In particular, by using weak compactness methods in L¹, we enlarge the extended Kato class potentials used in the theory of Markov processes. In L² setting, Dirichlet form-perturbation theory is finely related to L¹-theory and the extended Kato class measures is also enlarged. Finally, various perturbation problems for subordinate semigroups are considered.     

Relaxed Dirichlet problem and shape optimization within the linear elasticity framework

This work is mainly motivated by the study of shape optimization problems within the linear elastic framework and posed in general variable subdomains of a domain of or 3. We precisely study the sets of measures which can be obtained through the relaxed optimization process. The case of an homogeneous and isotropic elastic material is specially emphasized.     

Inversion transformation of Stokes flows bounded by parallel planes

The positive inversion transformation applied to a two-dimensional Stokes flow around bodies leads alike to a Stokes flow. This fact can be exploited to find new two-dimensional Stokes flow solutions around inverse bodies. Some features of this method, such as the relations between the reference and inverse fluid velocity fields, are presented followed by an application to examples of cellular flow between two parallel plates induced by rotating or translating cylinder. Thus hydrodynamic characteristics of flow around circular bodies obtained by inversion of the plates are straightforward deduced. Typical fluid flow patterns around two circular cylinders in contact placed in the centre of a rotating or a translating circular cylinder are thus illustrated.     

Thermal and structural properties of sodium,potassium and carbonate doped strontium hydroxyfluorapatite

Ion-doping in hydroxyapatite bioceramics has attracted a lot of interest particularly for biomedical applications in repairing and replacing failure parts of musculoskeletal systems. Thus the multiple doping aims to mimic and resemble the chemical composition of the bone mineral component. Herein strontium hydroxyapatites bioceramics containing sodium Na⁺ and potassium K⁺ as cationic substituent and carbonate CO₃^2? and fluoride as anionic substituent were synthesized and characterized by several analysis techniques. Therefore the chemical assays indicated that obtained compounds were less stoichiometric comparably to bone tissues. The X-ray diffraction diagrams and the infrared spectra revealed that pure phases of hydroxyfluorapatite containg the cited ions were obtained. The triple insertion of sodium, potassium and carbonate into the apatite structure leaded to the B-type carbonate apatite. The FE-SEM micrographs of the powders were formed by agglomerates. Moreover, the particles' morphology strongly depends on the ions nature and amount. The D-GTA curves indicated that the heating of the powders from the room temperature to 1000 °C didn't affect the structural and thermal stability of the materials apart from a partial decomposition of the apatite inducing the formation of the β-tristrontium phosphate phase and enhancing the biomaterial character of the materials.     

Un modèle viscoélastique de remodelage osseux : approche unidimensionnelleA viscoelastic model of bone remodeling: unidimensional approach

A bone remodeling model taking into account the viscoelastic properties of the material is proposed. The nonlinear equations governing the evolution of the bone apparent density are solved by a finite difference method in the unidimensional case of a n-unit elements model. The results show the effects of the viscous damping on the structure for a controlled mechanical loading. To cite this article: S. Baïotto, M. Zidi, C. R. Mecanique 332 (2004).