We generalize the method of computing functional determinants with a single excluded zero eigenvalue developed by McKane and Tarlie to differential operators with multiple zero eigenvalues. We derive general formulas for such functional determinants of $r\times r$ matrix second order differential operators O with $0 < n \leqslant 2r$ linearly independent zero modes. We separately discuss the cases of the homogeneous Dirichlet boundary conditions, when the number of zero modes cannot exceed r, and the case of twisted boundary conditions, including the periodic and anti-periodic ones, when the number of zero modes is bounded above by 2r. In all cases the determinants with excluded zero eigenvalues can be expressed only in terms of the n zero modes and other $r-n$ or $2r-n$ (depending on the boundary conditions) solutions of the homogeneous equation $O h=0$ , in the spirit of Gel'fand–Yaglom approach. In instanton calculations, the contribution of the zero modes is taken into account by introducing the so-called collective coordinates. We show that there is a remarkable cancellation of a factor (involving scalar products of zero modes) between the Jacobian of the transformation to the collective coordinates and the functional fluctuation determinant with excluded zero eigenvalues. This cancellation drastically simplifies instanton calculations when one uses our formulas.
DOCUMENT
Immersive journalism (IJ) is often assumed to be inherently emotion-inducing. Through using inclusive technology, interaction possibilities and immersive narratives, the audience should ideally experience what feels like to be in a certain situation. However, for the most part we do not know to which extent and in what form IJ influences the experience of emotions. We wanted to investigate, whether, and if so, which characteristics of IJ are related to the experience of emotions, and which role the personality trait empathy tendency plays in this respect. This is important, as the evaluation of IJ often relies on the emotion-inducing assumption thereof. Four different experiments comparing one immersive journalistic characteristic (level of inclusion, interaction possibilities, immersive narratives) to the respective non-immersive counterpart were conducted. Results indicate that while the level of inclusion and interaction possibility increase the intensity of the experience, the immersive narrative influences the valence dimension of emotions. Additionally, empathy tendency is found to be a relevant moderator for these effects. Conclusions are threefold. First, the narrative form of IJ is key; second, the analysis of IJ needs to go beyond the level of inclusion; third, including emotions when assessing IJ is fundamental to understand its impact.
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The transition from diesel-driven urban freight transport towards more electric urban freight transport turns out to be challenging in practice. A major concern for transport operators is how to find a reliable charging strategy for a larger electric vehicle fleet that provides flexibility based on different daily mission profiles within that fleet, while also minimizing costs. This contribution assesses the trade-off between a large battery pack and opportunity charging with regard to costs and operational constraints. Based on a case study with 39 electric freight vehicles that have been used by a parcel delivery company and a courier company in daily operations for over a year, various scenarios have been analyzed by means of a TCO analysis. Although a large battery allows for more flexibility in planning, opportunity charging can provide a feasible alternative, especially in the case of varying mission profiles. Additional personnel costs during opportunity charging can be avoided as much as possible by a well-integrated charging strategy, which can be realized by a reservation system that minimizes the risk of occupied charging stations and a dense network of charging stations.
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