A chain graph (CG) is a graph admitting both directed and undirected edges with forbidden directed cycles. It generalizes both the concept of undirected graph (UG) and the concept of directed acyclic graph (DAG). CGs can be used eeciently to store graphoids, that is, independency knowledge of the form \X is independent of Y given Z" obeying a set of ve properties (axioms). Two equivalent criter...

In a study of Riemannian manifolds admitting conformal transformation, the Riemannian and Ricci curvatures play an important role for characterizations and classify such a manifold. In this note, we summarize known results about Riemannian manifold admitting conformal transformations and related topics.

We give new homotopy theoretic criteria for deciding when a fibration with homotopy finite fibers admits a reduction to a fiber bundle with compact topological manifold fibers. The criteria lead to an unexpected result about homeomorphism groups of manifolds. A tool used in the proof is a surjective splitting of the assembly map for Waldhausen’s functor A(X). We also give concrete examples of f...

For a connected reductive group G and a finite–dimensional G–module V , we study the invariant Hilbert scheme that parameterizes closed G–stable subschemes of V affording a fixed, multiplicity–finite representation of G in their coordinate ring. We construct an action on this invariant Hilbert scheme of a maximal torus T of G, together with an open T–stable subscheme admitting a good quotient. ...