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Nonmetrizable topological dynamical characterization of central sets

Hong-Ting ShiHong-Wei Yang — 1996

Fundamenta Mathematicae

Without the restriction of metrizability, topological dynamical systems ( X , T s s G ) are defined and uniform recurrence and proximality are studied. Some well known results are generalized and some new results are obtained. In particular, a topological dynamical characterization of central sets in an arbitrary semigroup (G,+) is given and shown to be equivalent to the usual algebraic characterization.

Shape Hessian for generalized Oseen flow by differentiability of a minimax: A Lagrangian approach

Zhiming GaoYichen MaHong Wei Zhuang — 2007

Czechoslovak Mathematical Journal

The goal of this paper is to compute the shape Hessian for a generalized Oseen problem with nonhomogeneous Dirichlet boundary condition by the velocity method. The incompressibility will be treated by penalty approach. The structure of the shape gradient and shape Hessian with respect to the shape of the variable domain for a given cost functional are established by an application of the Lagrangian method with function space embedding technique.

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