Weather Observations of Remote Polar Areas Using an AWS Onboard a Unique Zero-Emissions Polar Vehicle

The Antarctic Plateau is one of the land areas with the largest gaps in surface weather observations on Earth, gaps that are usually filled with simulations provided by climate models. However, these simulated values must be ground-validated, which is particularly difficult and costly in remote polar regions. We designed and developed a Mobile Automatic Weather Station (M-AWS) which, on board a zero-emissions polar vehicle, recorded a large set of ground measurements that could be used to evaluate numerical weather simulations in an inexpensive way during the Year of Polar Prediction Southern Hemisphere Special Observing Period (YOPP). The M-AWS registered several weather variables over a transect of 2538 km in the East Antarctic Plateau. These meteorological data were also used by other scientific projects that were part of the expedition and for improving weather forecasting during the mission. The innovative design of the M-AWS overcame the main challenges imposed by the harsh conditions of a voyage in one of the world’s most extreme regions.

Second-order dynamical systems with penalty terms associated to monotone inclusions

In this paper, we investigate in a Hilbert space setting a second-order dynamical system of the form [Formula: see text] where [Formula: see text]image[Formula: see text] is a maximal monotone operator, [Formula: see text] is the resolvent operator of [Formula: see text] and [Formula: see text] are cocoercive operators, and [Formula: see text], and [Formula: see text] are step size, penalization and, respectively, damping functions, all depending on time. We show the existence and uniqueness of strong global solutions in the framework of the Cauchy–Lipschitz–Picard Theorem and prove ergodic asymptotic convergence for the generated trajectories to a zero of the operator [Formula: see text] where [Formula: see text] and [Formula: see text] denotes the normal cone operator of [Formula: see text]. To this end, we use Lyapunov analysis combined with the celebrated Opial Lemma in its ergodic continuous version. Furthermore, we show strong convergence for trajectories to the unique zero of [Formula: see text], provided that [Formula: see text] is a strongly monotone operator.

Numbers with simply normal β-expansions

In [6] the first author proved that for any β ∈ (1, βKL) everyx∈ (0, 1/(β − 1)) has a simply normal β-expansion, where βKL≈ 1.78723 is the Komornik–Loreti constant. This result is complemented by an observation made in [22], where it was shown that whenever β ∈ (βT, 2] there exists anx∈ (0, 1/(β − 1)) with a unique β-expansion, and this expansion is not simply normal. Here βT≈ 1.80194 is the unique zero in (1, 2] of the polynomialx3−x2− 2x+ 1. This leaves a gap in our understanding within the interval [βKL, βT]. In this paper we fill this gap and prove that for any β ∈ (1, βT], everyx∈ (0, 1/(β − 1)) has a simply normal β-expansion. For completion, we provide a proof that for any β ∈ (1, 2), Lebesgue almost everyxhas a simply normal β-expansion. We also give examples ofxwith multiple β-expansions, none of which are simply normal.Our proofs rely on ideas from combinatorics on words and dynamical systems.

Random affine code tree fractals: Hausdorff and affinity dimensions and pressure

We prove that for random affine code tree fractals the affinity dimension is almost surely equal to the unique zero of the pressure function. As a consequence, we show that the Hausdorff, packing and box counting dimensions of such systems are equal to the zero of the pressure. In particular, we do not presume the validity of the Falconer–Sloan condition or any other additional assumptions which have been essential in all the previously known results.