Schwarz lê Brecht

Lê Numbers of Arrangements and Matroid Identities

We present several new polynomial identities associated with matroids and geometric lattices, and relate them to formulas for the characteristic polynomial and the Tutte polynomial. The identities imply a formula for the L^ e numbers of complex hyperplane arrangements.

Overlapping Schwarz

Rotational Perturbations in Neveu-Schwarz–Neveu-Schwarz String Cosmology

First order rotational perturbations of the flat Friedmann-Robertson-Walker (FRW) metric are considered in the framework of four dimensional Neveu-Schwarz–Neveu-Schwarz (NS-NS) string cosmological models coupled with dilaton and axion fields. The decay rate of rotation depends mainly upon the dilaton field potential U . The equation for rotation imposes strong limitations upon the functional fo...

Anisotropic four-dimensional Neveu-Schwarz–Neveu-Schwarz string cosmology

An anisotropic ~Bianchi type I! cosmology is considered in the four-dimensional Neveu-Schwarz–NeveuSchwarz ~NS–NS! sector of low-energy effective string theory coupled to a dilaton and an axionlike H field within a de Sitter–Einstein frame background. The general solution of the gravitational field equations can be expressed in an exact parametric form in both Einstein and string frames. The st...

Schwarz boundary problem on a triangle

In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...