… :g<x> + g’(><)u (1.5) where x are local coordinates of a smooth ndimensional manifold M,
uER"‘, g0 and the m columns g/' of g are smooth vector fields on M (smooth means either …

… We show that a stronger form of the Bott Vanishing Theory must hold if a locally (f,g)-invariant
distribution can be rendered "input-insensitive" by feedback, yielding topological …

… Definition 1.3 A distribution A is locally {f,g}-invariant at … local {f,g}-invarlance and {f,g}-invariance
is contained in Hirschorn [8]. The present definitions have been extended to this case ~-f…

… For this we study the various fibres of the mapping 'rI and in each case we check that a
GL2(k)-invariant distribution on that fibre is invariant under the involution. We will denote by Fx …

… We claim that it can not be extended to an F*-invariant distribution on F. … In chapter I (sections
1-4) we study invariant distributions. Section 1 contains a … Y is a locally closed subset of X …

… optimal strategies in a distributed array. In this regard, we show in Section VA that a natural
distributed architecture can be provided, where local controllers observe the local state and …

… The distributions IM (7r, X, f) may be viewed as the obstruction to this. In ?4 we shall study …
of IM (y, f). We shall define new invariant distributions CIM (y, f) and CIm (nr, X, f) by improving …

… intersection of locally (ady, g) invariant distributions need not be invariant in the same sense.
However the sum of locally (ady, g) invariant distributions is again locally (ads, g) invariant. …

… Invariant Learning method (GIL) to learn invariant and OOD generalized graph representations
under distribution shifts… To the best of our knowledge, we are the first to study invariant …

… \(G\) and \(H\) are connected. Then the integrability condition of the invariant distributions
is … such that any Carnot–Carathéodory metric corresponding to this distribution is locally bi-…