Let R be a standard graded polynomial ring over a field k. The paper focuses on homogeneous ideals J⊂R of codimension 2 generated by three forms of the same degree d≥2 that are almost Cohen–Macaulay, i.e., of homological dimension 2. Based on the structure of the minimal graded free resolution of J and numerical data inspired by the corresponding shifts, one introduces the notion of a level matrix associated with these data. The main result provides a complete characterization of an almost Cohen–Macaulay 3-generated ideal J of codimension 2 in terms of the existence of a related level matrix for which J arises as the ideal of its maximal minors that fix a submatrix. One provides algebraic and geometric examples illustrating the results.
In this article, we study the set of potential functions on noncompact quasi-Einstein manifolds. We show that the space of all positive potential functions on a three-dimensional noncompact quasi-Einstein manifold has dimension at most two, and that equality holds if and only if the manifold is isometric to a product B×R, where B is a λ-Einstein surface or one of the examples obtained by L. Bérard Bergery and described in Besse's book [6, Section 9.118]. Moreover, we prove that any asymptotically flat n-dimensional quasi-Einstein manifold with λ=0 is necessarily Ricci-flat.
Visible and near-infrared diffuse reflectance spectroscopy (vis-NIR) and X-ray fluorescence spectroscopy (XRF) are promising alternatives for rapid, reagent-free soil analysis that can help scale up soil organic carbon (SOC) monitoring for soil health and carbon credit reporting. We investigated whether combining laboratory-based vis-NIR and XRF spectra improves SOC prediction relative to vis-NIR alone, and whether the resulting performance is fit for purpose for monitoring SOC variability at farm scale. A national spectral library of 12,829 Brazilian soil samples with laboratory spectral readings was used to build global Cubist models, and eight local libraries (952 samples) were used to build local partial least squares (PLS) models. Two sensing scenarios were compared: vis-NIR alone and vis-NIR + XRF data fusion. Performance was evaluated using conventional accuracy metrics and a fitness-for-purpose framework based on analytical tolerances and percentile error profiles. The results support the added value of XRF as complementary information to vis-NIR for SOC prediction under both modelling strategies, with the largest relative improvement observed under the global-Cubist strategy (RMSE of 1.11 g kg–1 for vis-NIR+XRF, versus 1.52 g kg–1 for vis-NIR alone) and the best absolute performance achieved under the local-PLS strategy (RMSE of 0.97 g kg–1 with vis-NIR+XRF, versus 1.15 g kg–1 with vis-NIR alone). Using an application-specific analytical tolerance framework, sensor-based monitoring was fit-for-purpose mainly under medium and high within-farm SOC variability, but not under low variability. These results support sensor-based SOC inference as a practical tool for farm-scale monitoring.
Competent authorities are increasingly expected to report publicly on the effectiveness of project-level Environmental Impact Assessment (EIA) as part of broader accountability obligations. In many jurisdictions, this expectation is reflected in accountability reports that summarise activities, performance information, indicators, and targets. Yet no previous study has systematically examined such reports as a primary object of analysis. In this paper, we examine what indicators compiled from competent authorities' accountability reports across 23 jurisdictions reveal about project-level EIA effectiveness in practice, and distil a practice-based selection of indicators together with broader recommendations for accountability reporting. Drawing on a set of guiding questions across four effectiveness dimensions (procedural, substantive, transactive, and legitimacy), we identify relevant topics already addressed in current reporting, particularly around quality control, compliance and enforcement, public participation opportunities, and access to justice. We also highlight important effectiveness-related topics that remain largely absent from the analysed sample, notably EIA-induced changes to project design and mitigation, the realisation of expected outcomes over time, resource adequacy for delivering proportionate EIA, and stakeholder perceptions of outcomes. Because reported information shapes stakeholders' ability to evaluate EIA, we recommend further research on the measurement and communication of project-level EIA effectiveness as an integral part of accountability. Developing context-sensitive indicators grounded in what each competent authority is realistically mandated and resourced to deliver can provide renewed grounds for the long-running and foundational debate on EIA effectiveness.
In recent years, energy transition has boosted the expansion of new electrical generation sources, most of which are inverter-based, significantly altering the behavior of voltage and current signals. Thus, fault diagnosis methods should be validated and adapted to operate in this new scenario. This paper evaluates the performance of five classic fault detection methods and, addressing their identified limitations, proposes a fault detection algorithm based on ATs combined with a rule-based internal and external fault discriminator for medium-voltage collector networks in onshore wind farms. The method is robust, eliminating the need for prior parameterization in the primary detection stage. The proposed methodology was validated on an actual system located in Northeast Brazil, modeled in PSCAD/EMTDC and through hardware-in-the-loop tests using the RTDS interfaced with a Texas Instruments F28379D development board. The performance was tested under diverse operating conditions, including variations in fault resistance, different circuit topologies, and event types, while also considering wind turbine shutdowns and fluctuations in wind penetration levels. The results are highly promising and compatible with modern protection requirements, demonstrating an average primary pickup of under 1.36 ms, confirmed within 18 ms, and an accuracy rate exceeding 99.8%, even in the presence of noisy signal conditions.
