ar X iv : m at h / 04 10 28 4 v 1 [ m at h . C A ] 1 2 O ct 2 00 4 A bisection algorithm for the numerical Mountain Pass

ar X iv : m at h / 04 10 61 1 v 1 [ m at h . A G ] 2 8 O ct 2 00 4 ON RATIONAL CUSPIDAL PROJECTIVE PLANE CURVES

ar X iv : h ep - t h / 04 10 18 8 v 1 18 O ct 2 00 4 Spacetime quantization induced by axial currents

ar X iv : m at h / 04 10 57 8 v 1 [ m at h . C V ] 2 7 O ct 2 00 4 OPTIMAL CONTROL IN BOMBIERI ’ S AND TAMMI ’ S CONJECTURES

Let S stand for the usual class of univalent regular functions in the unit disk U = {z : |z| < 1} normalized by f(z) = z + a2z + . . . in U , and let S be its subclass defined by restricting |f(z)| < M in U , M ≥ 1. We consider two classical problems: Bombieri’s coefficient problem for the class S and the sharp estimate of the fourth coefficient of a function from S . Using Löwner’s parametric ...

ar X iv : m at h / 04 10 21 7 v 1 [ m at h . C O ] 8 O ct 2 00 4 Joints in graphs

In 1969 Erd˝ os proved that if r ≥ 2 and n > n0 (r) , every graph G of order n and e (G) > tr (n) has an edge that is contained in at least n r−1 / (10r) 6r (r + 1)-cliques. In this note we improve this bound to n r−1 /r r+5. We also prove a corresponding stability result.

ar X iv : m at h / 04 10 34 7 v 1 [ m at h . C O ] 1 5 O ct 2 00 4 COMPLETING A k − 1 ASSIGNMENT

We consider the distribution of the value of the optimal k-assignment in an m× n-matrix, where the entries are independent exponential random variables with arbitrary rates. We give closed formulas for both the Laplace transform of this random variable and for its expected value under the condition that there is a zero-cost k − 1-assignment.