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Conditions aux limites approchées pour les couches minces périodiques

Habib Ammari, Chiraz Latiri-Grouz (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Nous écrivons et nous justifions des conditions aux limites approchées pour des couches minces périodiques recouvrant un objet parfaitement conducteur en polarisation transverse électrique et transverse magnétique.

Conditions ensuring T-1(Y) ⊂ Y.

Dagmar Medková (2005)

Extracta Mathematicae

The following theorem is the main result of the paper: Let X be a complex Banach space and T belong to L(X). Suppose that 0 lies at the unbounded component of the set of those l such that lI - T is a Fredholm operator. Let Y be a dense subspace of the dual space X' and S be a closed operator from Y to X such that T'(Y) is contained in Y and TSy = ST'y for every y belonging to Y. Then for every vector x belonging to X', T'x belongs to Y if and only if x belongs to Y.

Conditions for periodic vibrations in a symmetric n-string

Claude Gauthier (2008)

Open Mathematics

A symmetric N-string is a network of N ≥ 2 sections of string tied together at one common mobile extremity. In their equilibrium position, the sections of string form N angles of 2π/N at their junction point. Considering the initial and boundary value problem for small-amplitude oscillations perpendicular to the plane of the N-string at rest, we obtain conditions under which the solution will be periodic with an integral period.

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