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The paper discusses the relationships between electrical quantities, such as voltages, currents, and frequency, and geometrical ones, namely curvature and torsion. The proposed approach is based on the Frenet frame utilized in differential geometry and provides a general framework for the definition of the time derivative of electrical quantities in stationary as well as transient conditions. As a byproduct, the proposed approach unifies and generalizes the time- and phasor-domain frameworks. Other noteworthy results are a new interpretation of the link between frequency and the time derivatives of voltage and current; and a definition of the rate of change of frequency that includes the novel concept of “torsional frequency.” Several numerical examples based on balanced, unbalanced, harmonically-distorted and transient voltages illustrate the findings of the paper. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to analyze how mixes of COVID-19 policy responses are shaping the context in which companies will compete in the following years, defining how the crisis might impact firms' ability to keep their commitments to sustainable practices. Design/methodology/approach: European country-performance data for the years 2019 and 2020 were grouped into indicators of macro sustainability, then cross-analyzed against the policies adopted during the period (also grouped based on their impacts on sustainability pillars), using correlations, factor analysis and clustering. Findings: The influence of traditional sustainability determinants was reframed according to the novel context shaped by the policy responses to the pandemic crisis. The social and digitalization aspects gained the most relevance and appeared interconnected, with digitalization of employment attaining overall more traction. Moreover, changes in the leadership within sustainability domains were observed for each identified country-cluster, due to newly implemented emergency policies. In fact, environmental innovation, digitalization and social support policies appeared to be the main variables to be impacted by the intensity of the policy efforts. Practical implications: Businesses monitoring the developments of sustainability policies closely, will observe novel trends in technological applications. Social implications: Policymakers and researchers may gauge the efficacy of policies against the COVID-19 crisis in the domain of sustainable development and resilience. Originality/value: This paper provides a cross-analysis of quantitative macroeconomic and quantified policy responses to the 2020 pandemic crisis, linking each indicator to the pillars of sustainability that were relevant for companies between the crucial pandemic outbreak years 2019 and 2020. [ABSTRACT FROM AUTHOR]

Article 7 of the European Water Framework Directive (WFD) promotes a prevention-led approach to European Drinking Water Directive (DWD) compliance for those parameters that derive from anthropogenic influences on raw water quality. However, the efficacy of pollution prevention interventions is currently uncertain and likely to be variable, which makes absolute compliance with the drinking water standard a significant challenge. Member State governments, the WFD competent authority, the DWD competent authority, water suppliers and agriculture are all affected by and have a different perspective on the nature of this challenge. This paper presents a discussion of these perspectives applicable to stakeholders in all European Member States; the analysis is supported with examples from England and Wales. Improved understanding of the challenges faced by each group is needed if these groups are to achieve the shared goals of WFD Article 7 compliance and DWD compliance without a disproportionately negative impact on agricultural productivity. In addition, the European Commission needs to be aware of and address a potential incompatibility between WFD Article 7 and the DWD. With this in mind, targeted recommendations for action are presented for each stakeholder group. [ABSTRACT FROM AUTHOR]