Short normal paths and spectral variation

Short Normal Paths and Spectral Variation1

We introduce the notion of a "short normal path" between matrices S and T, that is, a continuous path from S to T consisting of normal matrices and having the same length as the straight line path from S to T. By this means we prove that for certain normal matrices S and T the eigenvalues of S and T may be paired in such a way that the maximum distance (in the complex plane) between the pairs i...

Spectral Variation, Normal Matrices, and Finsler Geometry

Short and Smooth Polygonal Paths

Automatic graph drawers need to compute paths among vertices of a simple polygon which besides remaining in the interior need to exhibit certain aesthetic properties. Some of these require the incorporation of some information about the polygonal shape without being too far from the actual shortest path. We present an algorithm to compute a locally convex region that “contains” the shortest Euc...

Short P-R Syndrome with Normal QRS and Paroxysmal Tachycardia

Syndrome de P -R court et QRS normal avec les crises de tachycardie Paroxystique ou le syndrome de (Lown-Ganong-Levine). Dans une enqete epidemiologique sur les ma­ladies cardiovasculaires chez deux populations rurales de Roudsar et Azarbaidjan oriental nous avons retrouve 6 cas de P -R court avec QRS normal. Dans cet article nous avons brievement passe en revue les vois de conduction auriculov...

Short Paths in Expander Graphs

Graph expansion has proved to be a powerful general tool for analyzing the behavior of routing algorithms and the inter{connection networks on which they run. We develop new routing algorithms and structural results for bounded{degree expander graphs. Our results are uniied by the fact that they are all based upon, and extend, a body of work asserting that expanders are rich in short, disjoint ...