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We show that for the family of complex reflection groups G = G(m, p,2) appearing in the Shephard–Todd classification, the endomorphism ring of the reduced hyperplane arrangement A(G) is a non-commutative resolution for the coordinate ring of the discriminant Δ of G. This furthers the work of Buchweitz, Faber and Ingalls who showed that this result holds for any true reflection group. In particular, we construct a matrix factorization for Δ from A(G) and decompose it using data from the irreducible representations of G. For G(m, p,2) we give a full decomposition of this matrix factorization, including for each irreducible representation a corresponding maximal Cohen–Macaulay module. The decomposition concludes that the endomorphism ring of the reduced hyperplane arrangement A(G) will be a non-commutative resolution. For the groups G(m,1,2), the coordinate rings of their respective discriminants are all isomorphic to each other. We also calculate and compare the Lusztig algebra for these groups. [ABSTRACT FROM AUTHOR]

The Caribbean is highly vulnerable to coastal hazards. Based on their short recurrence intervals over the intra-American seas, high-category tropical cyclones and their associated effects of elevated storm surge, heavy wave impacts, mudslides and floods represent the most serious threat. Given the abundance of historical accounts and trigger mechanisms (strike-slip motion and oblique collision at the northern and southern Caribbean plate boundaries, submarine and coastal landslides, volcanism), tsunamis must be considered as well. This paper presents interdisciplinary multi-proxy investigations of sediment cores (grain size distribution, carbonate content, loss-on-ignition, magnetic susceptibility, microfauna, macrofauna) from Washington-Slagbaai National Park, NW Bonaire (Leeward Antilles). No historical tsunami is recorded for this island. However, an allochthonous marine layer found in all cores at Boka Bartol reveals several sedimentary criteria typically linked with tsunami deposits. Calibrated C data from these cores point to a palaeotsunami with a maximum age of 3,300 years. Alternative explanations for the creation of this layer, such as inland flooding during tropical cyclones, cannot entirely be ruled out, though in recent times even the strongest of these events on Bonaire did not deposit significant amounts of sediment onshore. The setting of Boka Bartol changed from an open mangrove-fringed embayment into a poly- to hyperhaline lagoon due to the establishment or closure of a barrier of coral rubble during or subsequent to the inferred event. The timing of the event is supported by further sedimentary evidence from other lagoonal and alluvial archives on Bonaire. [ABSTRACT FROM AUTHOR]

Working with a large temporal dataset spanning several decades often represents a challenging task, especially when the record is heterogeneous and incomplete. The use of statistical laws could potentially overcome these problems. Here we apply Benford's Law (also called the 'First-Digit Law') to the traveled distances of tropical cyclones since 1842. The record of tropical cyclones has been extensively impacted by improvements in detection capabilities over the past decades. We have found that, while the first-digit distribution for the entire record follows Benford's Law prediction, specific changes such as satellite detection have had serious impacts on the dataset. The least-square misfit measure is used as a proxy to observe temporal variations, allowing us to assess data quality and homogeneity over the entire record, and at the same time over specific periods. Such information is crucial when running climatic models and Benford's Law could potentially be used to overcome and correct for data heterogeneity and/or to select the most appropriate part of the record for detailed studies. [ABSTRACT FROM AUTHOR]

The article focuses on the life and death of the corals and coral reefs in the Philipines following the super typhoon Haiyan in November 2013. Topics discussed include the damage caused by the typhoon, damaged subtidal reef area, massive poritids and faviids, and the sediment dynamics. The damage to the Sagay Marine Reserve of the country is also noted.