Non-uniqueness in conformal formulations of the Einstein constraints

Standard methods in non-linear analysis are used to show that there exists a parabolic branching of solutions of the Lichnerowicz-York equation with an unscaled source. We also apply these methods to the extended conformal thin sandwich formulation and show that if the linearised system develops a kernel solution for sufficiently large initial data then we obtain parabolic solution curves for the conformal factor, lapse and shift identical to those found numerically by Pfeiffer and York. The implications of these results for constrained evolutions are discussed.Comment: Arguments clarified and typos corrected. Matches published versio

Study of multi black hole and ring singularity apparent horizons

We study critical black hole separations for the formation of a common apparent horizon in systems of $N$ - black holes in a time symmetric configuration. We study in detail the aligned equal mass cases for $N=2,3,4,5$, and relate them to the unequal mass binary black hole case. We then study the apparent horizon of the time symmetric initial geometry of a ring singularity of different radii. The apparent horizon is used as indicative of the location of the event horizon in an effort to predict a critical ring radius that would generate an event horizon of toroidal topology. We found that a good estimate for this ring critical radius is $20/(3\pi) M$. We briefly discuss the connection of this two cases through a discrete black hole 'necklace' configuration.Comment: 31 pages, 21 figure

Publisher Correction: Hydro-climatic changes of wetlandscapes across the world (Scientific Reports, (2021), 11, 1, (2754), 10.1038/s41598-021-81137-3)

In the original version of this Article, V. H. Rivera-Monroy was incorrectly affiliated with ‘Alexander von Humboldt Biological Resources Research Institute, Calle 28 A No. 15-09, Bogotá, DC, 70803, Colombia’. The correct affiliation is listed below. Department of Oceanography and Coastal Sciences, College of the Coast and Environment, Louisiana State University, Baton Rouge, LA 70803, USA As a result, Affiliations 22–27 were incorrectly listed as Affiliations 21–26 respectively. The original Article has been corrected

Hydro-climatic changes of wetlandscapes across the world

Assessments of ecosystem service and function losses of wetlandscapes (i.e., wetlands and their hydrological catchments) suffer from knowledge gaps regarding impacts of ongoing hydro-climatic change. This study investigates hydro-climatic changes during 1976–2015 in 25 wetlandscapes distributed across the world’s tropical, arid, temperate and cold climate zones. Results show that the wetlandscapes were subject to precipitation (P) and temperature (T) changes consistent with mean changes over the world’s land area. However, arid and cold wetlandscapes experienced higher T increases than their respective climate zone. Also, average P decreased in arid and cold wetlandscapes, contrarily to P of arid and cold climate zones, suggesting that these wetlandscapes are located in regions of elevated climate pressures. For most wetlandscapes with available runoff (R) data, the decreases were larger in R than in P, which was attributed to aggravation of climate change impacts by enhanced evapotranspiration losses, e.g. caused by land-use changes

Sublittoral soft bottom communities and diversity of Mejillones Bay in northern Chile (Humboldt Current upwelling system)

The macrozoobenthos of Mejillones Bay (23°S; Humboldt Current) was quantitatively investigated over a 7-year period from austral summer 1995/1996 to winter 2002. About 78 van Veen grab samples taken at six stations (5, 10, 20 m depth) provided the basis for the analysis of the distribution of 60 species and 28 families of benthic invertebrates, as well as of their abundance and biomass. Mean abundance (2,119 individuals m-2) was in the same order compared to a previous investigation; mean biomass (966 g formalin wet mass m-2), however, exceeded prior estimations mainly due to the dominance of the bivalve Aulacomya ater. About 43% of the taxa inhabited the complete depth range. Mean taxonomic Shannon diversity (H', Log e) was 1.54 ± 0.58 with a maximum at 20 m (1.95 ± 0.33); evenness increased with depth. The fauna was numerically dominated by carnivorous gastropods, polychaetes and crustaceans (48%). About 15% of the species were suspensivorous, 13% sedimentivorous, 11% detritivorous, 7% omnivorous and 6% herbivorous. Cluster analyses showed a significant difference between the shallow and the deeper stations. Gammarid amphipods and the polychaete family Nephtyidae characterized the 5-mzone, the molluscs Aulacomya ater, Mitrella unifasciata and gammarids the intermediate zone, while the gastropod Nassarius gayi and the polychaete family Nereidae were most prominent at the deeper stations. The communities of the three depth zones did not appear to be limited by hypoxia during non-El Niño conditions. Therefore, no typical change in community structure occurred during El Niño 1997–1998, in contrast to what was observed for deeper faunal assemblages and hypoxic bays elsewhere in the coastal Humboldt Current system

Taxing the Informal Economy: The Current State of Knowledge and Agendas for Future Research

This paper reviews the literature on taxation of the informal economy, taking stock of key debates and drawing attention to recent innovations. Conventionally, the debate on whether to tax has frequently focused on the limited revenue potential, high cost of collection, and potentially adverse impact on small firms. Recent arguments have increasingly emphasised the more indirect benefits of informal taxation in relation to economic growth, broader tax compliance, and governance. More research is needed, we argue, into the relevant costs and benefits for all, including quasi-voluntary compliance, political and administrative incentives for reform, and citizen-state bargaining over taxation