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Modeling and computing of mutual inductance between solid conductors or coils of rectangular cross section carrying uniform current and parallelepiped magnets of rigid polarization have been made. For this purpose, the integral approach using a quasi-static Green's functions is used. The inductance is calculated between the total volume of a conductor and the equivalent current surfaces densities described by the Amperian model of permanent magnets. The analytical results are obtained after five integrations. It is to be noted that the formulas developed in this paper are more general that the ones established in the literature and can be used for optimization purposes. In addition, this paper is carried out without using any simplifying assumptions. Consequently, these expressions are accurate whatever the magnet dimensions are. This analytical formulation compared with finite element method one is suitable for the design of unconventional magnetic couplings, magnetically planar actuator, electric machines, wigglers, and so on.Index Terms-Conductor, interaction energy, mutual inductance, permanent magnet (PM).

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We consider the integro-dierential equation describing the coagulation processus of water drops falling in the air in a three-dimensional domain with presence of a horizontal wind. Under suitable hypothesis and some conditions we prove the existence of the stationary solution and then the global solution using the techniques developed in [10] and [2].

In the present paper, we apply the Galerkin method using Chebyshev wavelets to approximate the exact solution for a second order Fredholm integro-differential equation with initial conditions. This numerical method gives us a nonlinear algebraic system that would be solved using the Picard successive approximations technique. Furthermore, we show the validity and the ability of the proposed method through some illustrative examples.