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Multiplicative Cauchy functional equation and the equation of ratios on the Lorentz cone

Jacek Wesołowski (2007)

Studia Mathematica

It is proved that the solution of the multiplicative Cauchy functional equation on the Lorentz cone of dimension greater than two is a power function of the determinant. The equation is solved in full generality, i.e. no smoothness assumptions on the unknown function are imposed. Also the functional equation of ratios, of a similar nature, is solved in full generality.

Multiplicity of a foliation on projective spaces along an integral curve.

Julio García (1993)

Revista Matemática de la Universidad Complutense de Madrid

We compute the global multiplicity of a 1-dimensional foliation along an integral curve in projective spaces. We give a bound in the way of Poincaré problem for a complete intersection curves. In the projective plane, this bound give us a bound of the degree of non irreducible integral curves in function of the degree of the foliation.

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