New perturbation theorems are proved for simultaneous bases of singular subspaces of real matrices. These results improve the absolute bounds previously obtained in [6] for general (complex) matrices. Unlike previous results, which are valid only for the Frobenius norm, the new bounds, as well as those in [6] for complex matrices, are extended to any unitarily invariant matrix norm. The bounds ...

This study investigates science teachers' understanding and teaching of complex systems. The field of complex systems is the study of how parts of a system give rise to its collective behaviors. Since the 1990s, scientific and educational agencies have advocated the importance of complex systems in science education. Despite this call for instructional emphasis in complex systems, recent studie...

Let X be a complex projective surface with arbitrary singularities. We construct a generalized Abel–Jacobi map A0(X) → J 2(X) and show that it is an isomorphism on torsion subgroups. Here A0(X) is the appropriate Chow group of smooth 0-cycles of degree 0 on X, and J 2(X) is the intermediate Jacobian associated with the mixed Hodge structure on H 3(X). Our result generalizes a theorem of Roitman...

We study the behavior of the Gauss-Bonnet integrand on the level sets of a holomorphic function in a neighborhood of an isolated critical point. This is a survey of some older results of Griffiths, Langevin, Lê and Teissier. It is a blend of classical integral geometry and complex Morse theory (a.k.a Picard-Lefschetz theory). Motivation Consider the family of plane complex curves Ct = { (x, y))...