arXiv subjects

Frank Wagner

Publications and source records attributed to Frank Wagner.

8 recordsLinked to original sources

arXiv2024

Irregular moons possibly injected from the outer solar system by a stellar flyby

The irregular moons orbit the giant planets on distant, inclined, and eccentric trajectories, in sharp contrast with the coplanar and quasicircular orbits of the regular moons. The origin of these irregular moons is still an open question, but these moons have a lot in common with the objects beyond Neptune (trans-Neptunian objects -- TNOs), suggestive of a common origin. Here, we show that the close flyby of a star may be the connecting element. A stellar flyby can simultaneously reproduce the complex TNO dynamics quantitatively while explaining the origin of the irregular moons and the colour distributions of both populations. This flyby would have catapulted 7.2% of the original TNO population into the region of the planets, many on retrograde orbits. Most injected TNOs would have been subsequently ejected from the solar system (85%). However, a considerable fraction would have had the potential to be captured by the planets. The exclusively distant origin of the injected TNOs may also explain the lack of very red irregular moons.

astro-ph.EP↗

arXiv2022

Some remarks on sharply 2-transitive groups and near-domains

A sharply 2-transitive permutation group of characteristic 0 whose point stabiliser has an abelian subgroup of finite index splits. More generally, a near-domain of characteristic 0 with a multiplicative subgroup of finite index avoiding all multipliers $d_{a,b}$ must be a near-field. In particular this answers question 12.48 b) of the Kourovka Notebook in characteristic 0.

math.GR↗

arXiv2017

Bad Groups

There is no bad group of Morley rank 2n+1 with an abelian Borel subgroup of Morley rank n. In particular, there is no bad group of Morley rank 3 (O. Fr{é}con).

math.LO↗

arXiv2016

Uniqueness of representation--theoretic hyperbolic Kac--Moody groups over $\Z$

For a simply laced and hyperbolic Kac--Moody group $G=G(R)$ over a commutative ring $R$ with 1, we consider a map from a finite presentation of $G(R)$ obtained by Allcock and Carbone to a representation--theoretic construction $G^λ(R)$ corresponding to an integrable representation $V^λ$ with dominant integral weight $λ$. When $R=\Z$, we prove that this map extends to a group homomorphism $ρ_{λ,\Z}: G(\Z) \to G^λ(\Z).$ We prove that the kernel $K^λ$ of the map $ρ_{\lam,\Z}: G(\Z)\to G^{\lam}(\Z)$ lies in $H(\C)$ and if the group homomorphism $φ:G(\Z)\to G(\C)$ is injective, then $K^λ\leq H(\Z)\cong(\Z/2\Z)^{rank(G)}$.

math.GR↗

arXiv1999

Improving the Efficiency of FP-LAPW Calculations

The full-potential linearized augmented-plane wave (FP-LAPW) method is well known to enable most accurate calculations of the electronic structure and magnetic properties of crystals and surfaces. The implementation of atomic forces has greatly increased it's applicability, but it is still generally believed that FP-LAPW calculations require substantial higher computational effort compared to the pseudopotential plane wave (PPW) based methods. In the present paper we analyse the FP-LAPW method from a computational point of view. Starting from an existing implementation (WIEN95 code), we identified the time consuming parts and show how some of them can be formulated more efficiently. In this context also the hardware architecture plays a crucial role. The remaining computational effort is mainly determined by the setup and diagonalization of the Hamiltonian matrix. For the latter, two different iterative schemes are compared. The speed-up gained by these optimizations is compared to the runtime of the ``original'' version of the code, and the PPW approach. We expect that the strategies described here, can also be used to speed up other computer codes, where similar tasks must be performed.

cond-mat↗

arXiv1998

Supersimple fields and division rings

It is proved that any supersimple field has trivial Brauer group, and more generally that any supersimple division ring is commutative. As prerequisites we prove several results about generic types in groups and fields whose theory is simple.

math.RA↗

arXiv1997

Quasi-o-minimal groups

The authors investigate the structure of quasi-o-minimal groups. Among other results, they show that quasi-o-minimal groups are abelian, that quasi-o-minimal densely ordered archimedian groups are divisible, and that every divisible quasi-o-minimal group is o-miminal.

math.RA↗

arXiv1997

Groups in simple theories

Groups definable in simple theories retain the chain conditions and decomposition properties known from stable groups, up to commensurability. In the small case, if a generic type of G is not foreign to some type q, there is a q-internal quotient. In the supersimple case, the Berline-Lascar decomposition works. One-based simple groups are finite-by-abelian-by-finite.

math.GR↗