/arxiv@algebrach_bot

Robin Lang. On the eigenvalues of quantum graph Laplacians with large complex   $δ$ couplings. We study the location of the spectrum of the Laplacian on compact metric graphs with complex Robin-type vertex conditions, also known as $\delta$ conditions, on some or all of the graph vertices. We classify the eigenvalue asymptotics as the complex Robin parameter(s) diverge to $\infty$ in $\mathbb{C}$: for each vertex $v$ with a Robin parameter $\alpha \in \mathbb{C}$ for which $\mathrm{\Re}\,\alpha \to -\infty$ sufficiently quickly, there exists exactly one divergent eigenvalue, which behaves like $-\alpha^2/\mathrm{deg}\,v^2$, while all other eigenvalues stay near the spectrum of the Laplacian with a Dirichlet condition at $v$; if $\mathrm{Re}\,\alpha$ remains bounded from below, then all eigenvalues stay near the Dirichlet spectrum. Our proof is based on an analysis of the corresponding Dirichlet-to-Neumann matrices (Titchmarsh--Weyl M-functions). We also use sharp trace-type inequalities to prove estimates on the numerical range and hence on the spectrum of the operator, which allow us to control both the real and imaginary parts of the eigenvalues in terms of the real and imaginary parts of the Robin parameter(s).

— 2001.10244v2.pdf, 0.48 Мб

/arxiv@algebrach_bot

Alexander Schmeding. Convergence of Lie group integrators. We relate two notions of local error for integration schemes on Riemannian homogeneous spaces, and show how to derive global error estimates from such local bounds. In doing so, we prove for the first time that the Lie-Butcher theory of Lie group integrators leads to global error estimates.

— 1807.11829v2.pdf, 0.25 Мб

это правда или нет?

Вголос

Этапы жизни человека
1) рождение
2) три поноса
3) смерт

А где send?

nudes

Ну типа нудес не имеют смысла без сенд

Поч

зависит от нудес, присылай -- решим

Какие тебе нудсы дед

Настины

Что он там не видел?

Хз, насколько у него зрение плохое