This paper examines finite-time stability of homogeneous systems. The main result is that a homogeneous system is finite-time stable if and only if it is asymptotically stable and has a negative degree of homogeneity.

We consider the question of simultaneous extension of (pseudo)metrics defined on nonempty closed subsets of a compact metrizable space. The main result is a counterpart of the result due to Künzi and Shapiro for the case of extension operators of partial continuous functions and includes, as a special case, Banakh’s theorem on linear regular operators extending (pseudo)metrics.

We detail the spectrum of the linearized Vlasov-Poisson equation, and construct an original integro-differential operator which is related to the eigenstructure. It gives a new representation formula for the electric field, and yields new estimates for the linear Landau damping. Then we apply the technique to a problem with a dependence to the Debye length, and show weaker damping for small Deb...

Finite translation planes having a collineation group isomorphic to SL(2, 5)occur in many investigations on minimal normal non-solvable subgroups of linear translation complements. In this paper, we are looking for multiply derived translation planes of the desarguesian plane which have an inherited linear collineation group isomorphic to SL(2, 5). The Hall plane and some of the planes discover...

We consider the vector equation