This paper focus on solving the problem of optimizing students' orientation. After four years spent in secondary school, pupils take exams and are assigned to the high school. The main difficulty of Education Department Inspection (EDI) of Dakar lies in the allocation of pupils in the suburbs. In this paper we propose an allocation model using the p-median problem. The model takes into account the distance of the standards imposed by international organizations between pupil's home and school. The p-median problem is a location-allocation problem that takes into account the average (total) distance between demand points (pupil's home) and facility (pupil's school). The p-median problem is used to determine the best location to place a limited number of schools. The model has been enhanced and applied to a wide range of school location problems in suburbs. After collecting necessary numerical data to each EDI, a formulation is presented and computational results are carried out.

The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.

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In this paper, we are interested in the inverse problem of the determination of the unknown part ∂ Ω , Γ 0 of the boundary of a uniformly Lipschitzian domain Ω included in ℝ N from the measurement of the normal derivative ∂ n v on suitable part Γ 0 of its boundary, where v is the solution of the wave equation ∂ t t v x , t − Δ v x , t + p x v x = 0 in Ω × 0 , T and given Dirichlet boundary data. We use shape optimization tools to retrieve the boundary part Γ of ∂ Ω . From necessary conditions, we estimate a Lagrange multiplier k Ω which appears by derivation with respect to the domain. By maximum principle theory for hyperbolic equations and under geometrical assumptions, we prove a uniqueness result of our inverse problem. The Lipschitz stability is established by increasing of the energy of the system. Some numerical simulations are made to illustrate the optimal shape.