We examine the simultaneous embedding with fixed edges problem for two planar graphs G1 and G2 with the focus on their intersection S = G1∩G2. In particular, we will present the complete set of intersection graphs S that guarantee a simultaneous embedding with fixed edges for (G1, G2). More formally, we define the subset ISEFE of all planar graphs as follows: A graph S lies in ISEFE if every pa...

The Newton-Schulz iteration is a quadratically convergent, inversion-free method for computing the sign function of a matrix. It is advantageous over other methods for high-performance computing because it is rich in matrix-matrix multiplications. In this paper we propose a variant for Hermitian matrices that improves the initially slow convergence of the iteration. The main idea is to scale th...

E is a theorem prover for full first-order logic with equality. It reduces first-order problems to clause normal form and employs a saturation algorithm based on the equational superposition calculus. E is built on shared terms with cached rewriting, and employs several innovations for efficient clause indexing. Major strengths of the system are automatic problem analysis and highly flexible se...

In this paper we discuss a technique for calculating moments of polydisperse materials in terms of concentration readings along the cell. The proposed method minimizes dependence on data from the en'd points ·where they may be unreliable'. An analysis is given of the errors involved in the use of the proposed method when the underlying molecular weight distribution is the Schulz distribution or...