How do business schools create reflective, affective, and transformative environments to develop leaders, business, and society? This paper answers this question by developing a conceptual and pedagogical framework that places practical wisdom at the center of management education. Grounded in virtue ethics, the framework treats experiential learning as a pedagogical condition and decision making under uncertainty as the practical process through which judgment is exercised. It integrates three acts associated with practical wisdom—awareness, judgment, and command—with three pedagogical conditions—reflection, dialogue, and affect—and three moments of decision making—challenge definition, criteria formation, and decision. The paper then introduces the live case as a pedagogical approach that extends traditional case teaching by engaging students and stakeholders alike, with real, evolving challenges and immediate feedback. Two illustrations from business school practice show how live cases can broaden problem perception, expose learners to competing interpretations, and connect deliberation with provisional action. The paper contributes by integrating practical wisdom, experiential learning, and decision making within a holistic model of management education, extending research on case-based learning and educational value co-creation, and offering a pedagogically actionable design for judgment formation under uncertainty.
Let Ps(n) denote the n-th s-gonal number. Consider the Diophantine equation Ps(n)=tm for integers n,s,t and m>2. All solutions to this equation are known for m>2 and s∈{3,5,6,8,10,20}. Here we extend these results to the cases s=2k+4 (where k=4,6 or 5≤k≤97 is a prime number) and s=k+4 (where k=9,15 or 3≤k≤97 is a prime number). The proofs of our results use the modular and hypergeometric methods, linear forms in logarithms and extensive calculations. We were unable to completely solve the above Diophantine equations, but we expect (based on GRH and the weak effective abc conjecture) that there will be no additional solutions beyond those explicitly shown in Theorem 1, Theorem 2, Theorem 3.
Carbon nanotube wires are promising candidates for next-generation beam instrumentation because of their ultralow mass, radiation tolerance, and potential for stable mechanical and structural behaviour under extreme operating conditions. However, their performance is strongly influenced by catalyst contamination, graphitic disorder, and residual microstrain inherited from fabrication and bundle architecture. Understanding how these factors vary across different CNT wire architectures is essential for developing reliable low-density conductors for future accelerator systems. This study presents a comparative structural and mechanical investigation of carbon nanotube wires spanning distinct nanotube types, fabrication routes, and diameters from 10 mu m to 50 mu m, examined before and after nitric-acid purification and twist fixation. Raman spectroscopy, scanning electron microscopy, energy-dispersive X-ray analysis, tensile testing, and in situ synchrotron X-ray diffraction were combined to quantify graphitic order, lattice spacing, and spatial heterogeneity. Strong architecture-dependent behaviour was observed. The 10 mu m wire exhibited compressed basal-plane spacing and large spatial variability, whereas the 50 mu m multi-walled-dominant wire remained close to relaxed turbostratic spacing. Purification reduced impurity content, improved graphitic coherence, and enhanced tensile stiffness, including an increase from 30.8 GPa to 68.4 GPa in the 10 mu m wire, while preserving the underlying hierarchy of residual strain across suppliers. The results demonstrate that purification improves structural uniformity and mechanical consistency, but that the dominant lattice strain state is primarily governed by nanotube architecture and bundle topology rather than chemical treatment.
We examine how both conventional monetary policy tools and central bank communication impact firms’ green transition in the United States and the euro area. Monetary tightening is associated with increased climate risk exposure for firms in both regions, more strongly in Europe and among high-exposure firms, and shifts the composition of corporate innovation by reducing green patenting more than non-green patenting. Positive central bank information shocks, announcement surprises that signal a stronger economic outlook, reduce climate risk exposure for European firms only. Targeted ECB climate-related forward guidance raises brown firms’ climate risk exposure, suggesting that firms front-load emissions-intensive production ahead of a signal of future climate-policy tightening. The tightening evidence is consistent with a cost-of-capital channel in which higher discount rates disproportionately penalize long-horizon green investment. Overall, our results suggest mixed effects of policy tools on the green transition.
The signal generation capabilities of a novel data augmentation framework are examined in aerospace structures. First, the framework learns class-conditional temporal and spectral characteristics of the measured structural responses. It uses conditional generative adversarial network training and Monte Carlo dropout uncertainty quantification as a Bayesian approximation. This step enables stochastic signal synthesis and uncertainty quantification. Second, the generated responses are rigorously compared against experimental measurements across time, frequency, uncertainty, variability, and feature domains to assess physical realism, statistical consistency, and distributional fidelity. Finally, the synthetic data are evaluated to determine whether they should be incorporated into a supervised damage classification workflow. The framework is validated on the full-scale benchmark dataset from a BAE Systems Hawk T1A aircraft tested at the University of Sheffield’s Structural Dynamics Laboratory for Verification and Validation. The test involves acceleration, fibre Bragg grating strain, and nonlinear dynamic response measurements. The results demonstrate that the model accurately captures dominant structural dynamics, it guides on signal use for classification improvement based on uncertainty characteristics, and it provides meaningful uncertainty estimates linked to signal complexity and excitation characteristics. Importantly, the framework offers a realistic generative modelling plan as a robust digital twin component for data-driven structural health monitoring, supporting resilient decision-making for condition assessment in safety-critical aerospace systems.
