This paper describes certain facet classes for the planar subgraph polytope. These facets are extensions of Kuratowski facets and are of the form 2x(U)+x(E(G)\U) ≤ 2|U |+|E(G)\U | −2 where the edge set U varies and can be empty. Two of the new types of facets complete the class of extended subdivision facets, explored by Jünger and Mutzel. In addition, the other types of facets consist of a new...

In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach ...

Given a complex matrix H, we consider the decomposition H = QRP∗, where R is upper triangular and Q and P have orthonormal columns. Special instances of this decomposition include the singular value decomposition (SVD) and the Schur decomposition where R is an upper triangular matrix with the eigenvalues of H on the diagonal. We show that any diagonal for R can be achieved that satisfies Weyl’s...