Rational functions orthogonal on the unit circle with prescribed poles lying outside the unit circle are studied. We use the potential theory to discuss the zeros distribution for the orthogonal rational functions.

In the first paper with the same title the authors were able to determine all partially oriented flag manifolds that are stably parallelizable or parallelizable, apart from four infinite families that were undecided. Here, using more delicate techniques (mainly K-theory),we settle these previously undecided families and show that none of the manifolds in them is stably parallelizable, apart from one 30-dimensional manifold which still remains undecided.

Non-hermitian solutions of algebraic matrix Riccati equations (of the continuous and discrete types) are studied. Existence is proved of non-hermitian solutions with given upper bounds of the ranks of the skew-hermitian parts, under the sign controllability hypothesis.

LetM(X, Y) denote the space of all continuous functions between X and Y and Mƒ(X, Y) the path component corresponding to a given map ƒ : X → Y. When X and Y are classical flag manifolds, we prove the components of M(X, Y) corresponding to “simple” maps ƒ are classified up to rational homotopy type by the dimension of the kernel of ƒ in degree two cohomology. In fact, these components are themselves all products of flag manifolds and odd spheres.