Tootfinder

Rota-Baxter operators on compact simple Lie groups and algebras
Saveliy V. Skresanov
https://arxiv.org/abs/2506.14324 https://arxiv.o…

Rota-Baxter operators on compact simple Lie groups and algebras
A Rota-Baxter operator on a Lie group $ G $ is a smooth map $ B : G \to G $ such that $ B(g)B(h) = B(gB(g)hB(g)^{-1}) $ for all $ g, h \in G $. This concept was introduced in 2021 by Guo, Lang and Sheng as a Lie group analogue of Rota-Baxter operators of weight 1 on Lie algebras. We show that the only Rota-Baxter operators on compact simple Lie groups are the trivial map and the inverse map. A similar description for Rota-Baxter operators of weight 1 on compact simple Lie algebras is provided.

Tram Positioning with Map-Enabled GNSS Data Reconciliation
Jakub Ka\v{s}par, V\'it Fanta, Vladim\'ir Havlena
https://arxiv.org/abs/2506.08032 https…

Tram Positioning with Map-Enabled GNSS Data Reconciliation
This paper presents an approach to tackle the problem of tram localization through utilizing a custom processing of Global Navigation Satellite System (GNSS) observables and the track map. The method is motivated by suboptimal performance in dense urban environments where the direct line of sight to GNSS satellites is often obscured which leads to multipath propagation of GNSS signals. The presented concept is based upon the iterated extended Kalman filter (IEKF) and has linear complexity (with…

Finite-time scaling on low-dimensional map bifurcations
Daniel A. Martin, Qian-Yuan Tang, Dante R. Chialvo
https://arxiv.org/abs/2505.24673 https://…

Finite-time scaling on low-dimensional map bifurcations
Recent work has introduced the concept of finite-time scaling to characterize bifurcation diagrams at finite times in deterministic discrete dynamical systems, drawing an analogy with finite-size scaling used to study critical behavior in finite systems. In this work, we extend the finite-time scaling approach in several key directions. First, we present numerical results for 1D maps exhibiting period-doubling bifurcations and discontinuous transitions, analyzing selected paradigmatic examples.…