Showing papers by "Wolfgang K. Schief published in 2016"
TL;DR: In this paper, the geometric and algebraic structure of fundamental line complexes and the underlying privileged discrete integrable system for the minors of a matrix which constitute associated Plucker coordinates are investigated.
Abstract: In the spirit of Klein's Erlangen Program, we investigate the geometric and algebraic structure of fundamental line complexes and the underlying privileged discrete integrable system for the minors of a matrix which constitute associated Plucker coordinates. Particular emphasis is put on the restriction to Lie circle geometry which is intimately related to the master dCKP equation of discrete integrable systems theory. The geometric interpretation, construction and integrability of fundamental line complexes in Mobius, Laguerre and hyperbolic geometry are discussed in detail. In the process, we encounter various avatars of classical and novel incidence theorems and associated cross- and multi-ratio identities for particular hypercomplex numbers. This leads to a discrete integrable equation which, in the context of Mobius geometry, governs novel doubly hexagonal circle patterns.
15 citations
TL;DR: In this paper, a hybrid Ermakov-Painleve II system is introduced and those with underlying integrable structure delimited, and the Backlund transformation is applied iteratively in this connection.
Abstract: Novel hybrid Ermakov–Painleve II systems are introduced and those with underlying integrable structure delimited. The Ermakov invariant is used to construct an algorithmic solution procedure which involves both the isolation of positive solutions $$\varSigma$$
of Painleve XXXIV and the integration of $$\varSigma ^{-1}$$
. The Backlund transformation admitted by Painleve II is applied iteratively in this connection.
13 citations
TL;DR: In this paper, the authors developed a ROM simulation algorithm that generates multivariate samples with exact means, covariances, and multivariate skewness, which can be used for risk management of financial institutions.
Abstract: We develop a ROM simulation algorithm that generates multivariate samples with exact means, covariances, and multivariate skewness. If required for financial applications, absence of arbitrage can be ensured. We use the Kollo measure of multivariate skewness, which is more informative than the Mardia skewness previously used in this context. Potential applications include the simulation of risk factors for the risk management of financial institutions.
1 citations