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Endomorphisms of symbolic algebraic varieties

Misha Gromov (1999)

Journal of the European Mathematical Society

The theorem of Ax says that any regular selfmapping of a complex algebraic variety is either surjective or non-injective; this property is called surjunctivity and investigated in the present paper in the category of proregular mappings of proalgebraic spaces. We show that such maps are surjunctive if they commute with sufficiently large automorphism groups. Of particular interest is the case of proalgebraic varieties over infinite graphs. The paper intends to bring out relations between model theory,...

Energy decay rates for solutions of Maxwell's system with a memory boundary condition

Serge Nicaise, Cristina Pignotti (2007)

Collectanea Mathematica

We consider the stabilization of Maxwell's equations with space variable coefficients in a bounded region with a smooth boundary, subject to dissipative boundary conditions of memory type on the boundary. Under suitable conditions on the domain and on the permeability and permittivity coefficients, we prove the exponential/polynomial decay of the energy. Our result is mainly based on the use of the multipliers method and the introduction of a suitable Lyapounov functional.

Enumeration of real conics and maximal configurations

Erwan Brugallé, Nicolas Puignau (2013)

Journal of the European Mathematical Society

We use floor decompositions of tropical curves to prove that any enumerative problem concerning conics passing through projective-linear subspaces in P n is maximal. That is, there exist generic configurations of real linear spaces such that all complex conics passing through these constraints are actually real.

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