Some extremal functions in Fourier analysis, III

We obtain the best approximation in $L^1(\R)$, by entire functions of exponential type, for a class of even functions that includes $e^{-\lambda|x|}$, where $\lambda >0$, $\log |x|$ and $|x|^{\alpha}$, where $-1 < \alpha < 1$. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded degree.Comment: 26 pages. Submitte

Bio+mine project: empowering the community to develop a site-specific system for the rehabilitation of a legacy mine

The rehabilitation of legacy mines continues to be a big challenge because of the difficulties in returning them to safe and stable conditions and ensuring that the mined-out areas become productive to support the economic activity of the host community. Previous efforts are often focused on purely technical and environmental aspects, leading to resistance from the local community due to their exclusion from the rehabilitation process. To address the issues associated with legacy mines and lack of participation of the community, we have developed a project, Biodiversity Positive Mining For The Net Zero Challenge (Bio + Mine), focusing on the abandoned Sto. Niño copper mine (Benguet, Philippines). The mine was closed in 1982 without a plan involving local stakeholders and leaving a significant ongoing negative legacy. Using the social-ecological-technological system framework, we will explore the intersections of the structure and functions of socio-economicdemographic, ecological, and technological data useful in devising a more inclusive mitigation strategy for the reconstruction of the supporting ecosystem. We aim to develop a site-specific system, underpinned by the local community's knowledge and practices, that can be a model for wider implementation in other legacy and active mines worldwide

Nearshore tsunami amplitudes across the Maldives archipelago due to worst-case seismic scenarios in the Indian Ocean

The Maldives face the threat of tsunamis from a multitude of sources. However, the limited availability of critical data, such as bathymetry (a recurrent problem for many island nations), has meant that the impact of these threats has not been studied at an island scale. Conducting studies of tsunami propagation at the island scale but across multiple atolls is also a challenging task due to the large domain and high resolution required for modelling. Here we use a high-resolution bathymetry dataset of the Maldives archipelago, as well as corresponding high numerical model resolution, to carry out a scenario-based tsunami hazard assessment for the entire Maldives archipelago to investigate the potential impact of plausible far-field tsunamis across the Indian Ocean at the nearshore island scales across the atolls. The results indicate that the bathymetry of the atolls, which are characterized by very steep boundaries offshore, is extremely efficient in absorbing and redirecting incoming tsunami waves. Results also highlight the importance that local effects have in modulating tsunami amplitude nearshore, including the location of the atoll in question, the location of a given island within the atoll, and the distance of that island to the reef, as well as a variety of other factors. We also find that the refraction and diffraction of tsunami waves within individual atolls contribute to the maximum tsunami amplitude patterns observed across the islands in the atolls. The findings from this study contribute to a better understanding of tsunamis across complex atoll systems and will help decision and policy makers in the Maldives assess the potential impact of tsunamis across individual islands. An online tool is provided which presents users with a simple interface, allowing the wider community to browse the simulation results presented here and assess the potential impact of tsunamis at the local scale.</p

Retraction: Morley et al. A Database for the Extraction, Trade, and Use of Sand and Gravel. Resources 2022, 11, 38

The published article [...

A Database for the Extraction, Trade, and Use of Sand and Gravel

Increasing demand for sand and gravel globally is leading to social, environmental, and political issues that are becoming more widely recognised. Lack of data and poor accessibility of the few available data contribute to exacerbating these issues and impair evidence-based management efforts. This article presents a database framework designed to describe stocks and flows data for sand and gravel from different sources. The classification system underlying the database builds on the Universal Materials Information System (UMIS) nomenclature, which is used to construct hierarchical order in the data. The common classification system is used to structure sand and gravel data records into a database formatted in the same manner as the Yale Stocks and Flow Database (YSTAFDB), a common data format. To illustrate how the database is built and used, a case study using UK data is presented. The UK is chosen owing to its relatively better access to data compared to other locations. Quantitative analyses of the UK data highlight possible risks in the supply chain of these materials for the UK. Results show that indigenous extraction only contributes 11% to UK sand and gravel production, with trade accounting for the rest of the inputs, of which 50% is reliant on only one nation

Retraction: Morley et al. A Database for the Extraction, Trade, and Use of Sand and Gravel. <i>Resources</i> 2022, <i>11</i>, 38

The published article [...