Certaines classes de distributions quasi-analytiques au sens de S. Bernstein
Problems of making inferences about abrupt changes in the mechanism underlying a sequence of observations are considered in both retrospective and on-line contexts. Among the topics considered are the Lindisfarne scribes problem; switching straight lines; manoeuvering targets, and shifts of level or slope in linear time series models. Summary analyses of data obtained in studies of schizophrenic and kidney transplant patients are presented.
The authors generalize a construction of Connes by defining for an -bundle over smooth manifold and a reduced cyclic cohomology class a sequence of de Rham cohomology classes . Here is a convenient algebra, defined by the authors, and is a locally trivial bundle with standard fibre a right finitely generated projective -module and bounded -modules homomorphisms as transition functions.
The discourse begins with a definition of a Lie algebroid which is a vector bundle over a manifold with an -Lie algebra structure on the smooth section module and a bundle morphism which induces a Lie algebra morphism on the smooth section modules. If has constant rank, the Lie algebroid is called regular. (A monograph on the theory of Lie groupoids and Lie algebroids is published by K. Mackenzie [Lie groupoids and Lie algebroids in differential geometry (1987; Zbl 0683.53029)].) A principal...
Summary: Arrays of numbers may be written not only on a line (= ``a vector'') or in the plain (= ``a matrix'') but also on a circle (= ``a circular vector''), on a torus (= ``a toroidal matrix'') etc. In the latter case, the immanent index-rotation ambiguity converts the standard ``scalar'' product into a binary operation with several interesting properties.