We demonstrate that we can carry over the strategy of Finite Element Exterior Calculus (FEEC) to Summation-by-Parts (SBP) Finite Difference (FD) methods to achieve divergence- and curl-free discretizations. This is not obvious at first sight, as for SBP-FD no basis functions are known, but only values and derivatives at points. The key is a remarkable analytic relationship that enables us to construct compatible operators using integral and nodal degrees of free- dom. Pre-existing SBP-FD matrix operators can then be used to obtain nodal values from the integral degrees of freedom to derive a scheme with the desired properties.
Background Teacher education aims to support preservice teachers in becoming competent lesson planners. However, it remains unclear how opportunities to learn (OTL) in university-based teacher education are related to their pedagogical content knowledge (PCK) and lesson-planning skills as facets of professional competence. Aims We examined two forms of OTL—content-related OTL in university coursework and in-school OTL during teaching practice—and related them to preservice teachers’ PCK and lesson-planning skills. Research questions focused on differences in lesson-planning skills across teacher education stages (RQ1), links between teaching-practice OTL and lesson-planning skills (RQ2), and the mediating role of PCK between coursework-related OTL and lesson-planning skills (RQ3). Sample We designed a cohort-sequential study with annual assessments throughout a five-year initial teacher education program. The sample comprised 441 preservice secondary school teachers of German in Germany, of whom 85 provided repeated measurements. Methods PCK and lesson-planning skills were assessed via standardized tests. The lesson-planning assessment used text-vignette items that captured decision-making in three planning situations. OTL were measured using self-report inventories. Results Lesson-planning skills were higher at later stages of teacher education (RQ1). More planning-related teaching-practice activities were associated with higher lesson-planning skills (RQ2). Evidence for PCK as a mediator of the relation between content-related coursework OTL and lesson-planning skills was mixed (RQ3). Conclusions University-based teacher education appears to support the development of preservice teachers’ lesson-planning skills. Lesson-planning skills were associated with both content-related coursework OTL and in-school teaching-practice OTL. PCK and lesson-planning skills were strongly correlated but theoretically and empirically distinct. Findings on mediation are tentative due to measurement limitations.
Value change is often attributed to generational replacement. Modernization theory has popularized the idea that as younger generations expand in the population, their postmaterial emancipative values come to dominate, while more conservative values fade away with older generations. Yet this cohort-centered view discounts that contemporaneous period effects can shift the values of all cohorts simultaneously. Using data on postmaterial emancipative values from the Integrated Values Survey (1981–2022), covering 122,205 respondents in 13 countries, we conduct a bounding age–period–cohort analysis. The analysis leverages modernization theory's own assumption that age effects on emancipative values are not positive. Under this constraint, period effects are positive in seven countries and exceed cohort effects in four throughout the admissible age-effect range. In the remaining nine countries, cohort effects exceed period effects under zero or sufficiently weak negative age effects. Assuming more negative age effects mechanically strengthens period effects while weakening cohort effects. These results challenge cohort replacement as a sufficient general account of long-term value modernization, showing that the relative importance of period and cohort effects depends on the country and assumptions about aging.
Technologies that restore or substitute human functions increasingly shape how consumers with disabilities access and navigate service systems. Yet marketing and service research has largely focused on human enhancement or interpersonal encounters, overlooking technologies as active enablers of well-being. Integrating insights from Transformative Service Research, disability research, and Human Enhancement Technology research, this paper advances a prosthetic perspective that conceptualizes technologies as service-enabling systems supporting self-directed action in physical and virtual servicescapes. Distinguishing physical, hybrid, and virtual prosthetic service realities reveals how these configure transformative mechanisms (i.e., empowerment, participation, and inclusion). A focus on more virtual prosthetic service realities further demonstrates how these mechanisms extend in scale and scope and can enable spillover from virtual to physical well-being. The paper concludes with a research agenda that invites scholars to examine how prosthetic service realities may mitigate structurally disabling servicescapes and promote individual, collective, and societal well-being.
The increasing integration of intermittent renewable energy sources poses challenges in balancing electricity generation and consumption. The vehicle-to-grid (V2G) concept, which utilizes pools of electric vehicles (EVs) as both energy sources and storage units, offers a potential solution. By charging and discharging batteries as required by the grid, V2G can help maintain grid stability by matching electricity production and consumption in real time. These services are contracted in balancing markets. This study explores the economic feasibility of EVs participating in balancing markets by incorporating real energy data, driving patterns, and current technical parameters. The findings suggest that providing balancing services with EVs can be economically viable under the existing regulatory framework, though it was not under the previous one. Profitability increases with the amount of time a vehicle is parked at home and eligible for balancing, generating annual profits of up to 881 €. Users can further increase their profits by giving up some flexibility of their driving schedules if market conditions demand it. A broad range of sensitivity tests suggests that profitability is severely affected by battery degradation costs and adequate distribution network infrastructure. The study identifies key market design elements critical to the successful implementation of V2G systems.
