Approximate resolution of linear systems of differential equations with varying coefficients is
a recurrent problem, shared by a number of scientific and engineering areas, ranging from …

A left pre-Lie algebra over a field k is a k-vector space A with a bilinear binary composition▷
that satisfies the left pre-Lie identity (a▷ b)▷ ca▷(b▷ c)=(b▷ a)▷ c− b▷(a▷ c), for a, b, c …

Hopf algebra structures on rooted trees are by now a well-studied object, especially in the
context of combinatorics. In this work we consider a Hopf algebra H by introducing a …

The Magnus series is an infinite series which arises in the study of linear ordinary differential
equations. If the series converges, then the matrix exponential of the sum equals the …

Abstract Pre-Lie (or Vinberg) algebras arise from flat and torsion-free connections on
differential manifolds. These algebras have been extensively studied in recent years, both …

In this paper we show how higher-order averaging can be used to remedy serious technical
issues with the direct application of the averaging theorem. While doing so, we reconcile two …

In nonlinear control, it is helpful to choose a formalism well suited to computations involving
solutions of controlled differential equations, exponentials of vector fields, and Lie brackets …

We define combinatorial representations of finite skew braces and use this idea to produce a
database of skew braces of small size. This database is then used to explore different …

Relations between moments and cumulants play a central role in both classical and non-
commutative probability theory. The latter allows for several distinct families of cumulants …

After providing a short review on the recently introduced notion of post-group by Bai, Guo,
Sheng and Tang, we exhibit post-group counterparts of important post-Lie algebras in the …