Let M0 = G0/H be a (pseudo)-Riemannian homogeneous spin manifold, with reductive decomposition g0 = h + m and let S(M0) be the spin bundle defined by the spin representation Ãd : H → GLR(S) of the stabilizer H . This article studies the superizations of M0, i.e. its extensions to a homogeneous supermanifold M = G/H whose sheaf of superfunctions is isomorphic to Λ(S(M0)). Here G is the Lie super...

The goal of this article is to provide a construction of a homogeneous Lyapunov function P associated with a system of differential equations J = f(x), x ~ R ~ (n > 1), under the hypotheses: (1) f ~ C(R n, ~ ) vanishes at x = 0 and is homogeneous; (2) the zero solution of this system is locally asymptotically stable. Moreover, the Lyapunov function V(x) tends to infinity with 1[ x [I, and belon...

The motivation of this paper comes from the fact that Lp&#x2014;stability and Lp&#x2014;gain, using classical signal norms, is not well-defined for arbitrary continuous weighted homogeneous systems. However, norms it possible to show every internally stable system has a globally defined finite p sufficiently large. If approximation, Lp</i...