Nodal domains, spectral minimal partitions, and their relation to Aharonov-Bohm operators

This survey is a short version of a chapter written by the first two authors in the book [A. Henrot, editor. Shape optimization and spectral theory. Berlin: De Gruyter, 2017] (where more details and references are given) but we have decided here to put more emphasis on the role of the Aharonov-Bohm operators which appear to be a useful tool coming from physics for understanding a problem motivated either by spectral geometry or dynamics of population. Similar questions appear also in Bose-Einstein theory. Finally some open problems which might be of interest are mentioned.Comment: arXiv admin note: substantial text overlap with arXiv:1506.0724

Can species richness be maintained in logged endemic Acacia Heterophylla forests (Reunion Island, Indian Ocean) ?

It is assumed that forests can serve multiple uses, including wood production and maintenance of high biodiversity level. We tested this hypothesis by studying eradication methods of invasive plants currently implemented in exploited endemic Acacia heterophylla forests located in a tropical highland forest region on the island of Réunion. We also compared species richness in logged (over time) and natural forests. Our results show that all individuals of the widespread alien invasive plant Rubus alceifolius were generated from cuttings. We quantifi ed the high growth capability of this species by comparing with those of Acacia heterophylla along with Rubus apetalus var. apetalus, a close non-invasive congener. The substantial multiplicative and vegetative growth ability of R. alceifolius enabled it to form monospecific patches in only 2.5 years. The species richness of the exploited Acacia heterophylla forest was thus very affected. Although the species richness increased over time after logging, the extent of the resulting richness was not as great as that in natural forests which, moreover, included numerous exotic plants. The authors assess the impact of highly disturbing logging operations and, based on the results of the comparisons, are very pessimistic about the possibility of maintaining species richness in logged forests. Nevertheless, the results indicate that the situation is not beyond hope and an eradication program specifi cally tailored to this kind of forest is proposed if exploitation will stop

Assessing tree effect on total soil carbon in agroforestry parklands systems along a rainfall gradient in Burkina Faso (West Africa)

Trees contribution in improving soil carbon is well established, but few works addressed how this was affected by a climatic gradient. This research investigated effects of Vitellaria paradoxa C. F Gaertn and Parkia biglobosa (Jacq.) Benth on total soil carbon in parklands along a rainfall gradient for recommendations of tree species which better improve soil carbon under specific climatic conditions for parklands adaptation to climate change. Total soil carbon at topsoil and subsoil layers measured using spectrophotometry infrared method, was higher when rainfall increased and were respectively (1.598 ± 0.040; 1.033 ± 0.022; 0.834 ± 0.014; 0.857 ± 0.016%). It was higher at topsoil (0.529 ± 0.015%) and subsoil (0.282 ± 0.019%) under V. paradoxa when rainfall decreased while it was higher under P. biglobosa and V. paradoxa when rainfall increased slightly. Its improvement was higher under V. paradoxa and P. biglobosa when rainfall respectively decreased and increased. A decrease trend of total soil carbon under both tree species from trunk to outside the canopy whatever rainfall levels and soil layers was observed. Tree species choice could play an important role in improving total soil carbon and crop productivity according to rainfall level for parklands adaptation to climate change

L’économie politique de la filière du charbon de bois à Kinshasa et à Lubumbashi

Charcoal use in urban Congo expanded significantly in the early 1990s. While recourse to charcoal (makala) as cooking fuel existed during the early independence period, most urban households had access to electricity for domestic use. Population, pressure, poorly maintained infrastructures and state crisis combined to force people to rely on makala for their daily cooking needs. Trade networks developed to make the link between makala producers and consumers. This can be considered as a popular response to state failure and is the subject of this working paper. Our research followed the trade network that includes charcoal producers, transporters, middlemen, wholesalers and retailers and a host of other peripheral supporting actors who claim to „live miraculously? from the network. The main conclusion of the research is that this informal trade network thrives, despite hassles from state agents, because it provides a vital service to Congo's urban poor.