TL;DR: In this article, a new model of two-phase flow coupling with structure based on an improved Riemann solver is described for the water entry problems with the effect of air.
TL;DR: In this article, Gherardelli and Andreotti showed that a quasi-abelian variety X = Cn / Γ has an ample Riemann form of kind k, where k ≤ 2k ≤ n − m ≤ n - m.
Abstract: Gherardelli and Andreotti defined a quasi-abelian variety of kind k. However, this definition is somewhat vague and we do not know the real meaning of the ‘kind’. We give an example of a quasi-abelian variety which is of kind k › 0 but not of kind 0, in the sense of Gherardelli and Andreotti. We prove that if a quasi-abelian variety X = Cn / Γ has an ample Riemann form of kind k, then it has an ample Riemann form of kind k' for any k' with 2k ≤ 2k' ≤ n - m, where rank Γ = n + m. Next we consider the pair (X , L) of a quasi-abelian variety X and a positive line bundle L on it. We characterize an extendable line bundle L to a compactification $\\overline X$ of X.
TL;DR: In this article, the authors review fundamental equations of geometrical invariants on a Finsler manifold and their applications and give some related open problems, as well as discuss recent developments in finsler geometry.