The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge

We prove in this thesis that the Schwarzschild family of black holes are linearly stable as solutions to the Einstein vacuum equations as expressed in a generalised wave gauge: all sufficiently regular solutions to the system of equations that result from linearising the Einstein vacuum equations, as expressed in a generalised wave gauge, about a fixed Schwarzschild solution remain uniformly bounded on the Schwarzschild exterior region and in fact decay to a member of the linearised Kerr family. The dispersion is at an inverse polynomial rate and therefore in principle sufficient for future nonlinear applications. The result thus fits into the wider goal of establishing the full nonlinear stability of the exterior Kerr family as solutions to the Einstein vacuum equations by employing a generalised wave gauge.Open Acces

The Linear Stability of the Schwarzschild Solution to Gravitational Perturbations in the Generalised Wave Gauge

Funder: FP7 Ideas: European Research Council; doi: http://dx.doi.org/10.13039/100011199; Grant(s): 337488Abstract: We prove in this paper that the Schwarzschild family of black holes are linearly stable as a family of solutions to the system of equations that result from expressing the Einstein vacuum equations in a generalised wave gauge. In particular we improve on our recent work (Johnson in The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge, arXiv: 1803.04012, 2018) by modifying the generalised wave gauge employed therein so as to establish asymptotic flatness of the associated linearised system. The result thus complements the seminal work (Dafermos et al. in The linear stability of the Schwarzschild solution to gravitational perturbations, arXiv:1601.06467, 2016) of Dafermos–Holzegel–Rodnianski in a similar vein as to how the work (Lindblad and Rodnianski. in Ann Math 171:1401–1477, 2010) of Lindblad–Rodnianski complemented that of Christodoulou–Klainerman (Christodoulou and Klainerman in The global nonlinear stability of the Minkowski space. Princeton Mathematical Series, vol 41. Princeton University Press, Princeton, 1993) in establishing the nonlinear stability of the Minkowski space

A MULTIVARIATE ANALYSIS OF FACTORS INFLUENCING FARM MACHINERY PURCHASE DECISIONS

This paper presents a model of the farm management process. The model suggests that certain socioeconomic characteristics of farm managers will influence their decision-making process. Several characteristics are hypothesized an tested using multivariate techniques (multivariate analysis of variance, range tests, and multiple comparisons). The analysis indicates that the soil zone, value of machinery inventory, operator's age, and operator's education influence the importance placed on each of 20 factors. On the basis of the analysis it was concluded that such a model of the farm management process can contribute to an understanding of farm management decisions. In addition, it was concluded that farm managers, farm machinery dealers, and extension agents had significantly different perceptions of the importance of these factors to farm managers. This latter conclusion suggests that more research related to the actual process of decision making is warranted.Farm Management,

A nucleotide resolution map of Top2-linked DNA breaks in the yeast and human genome

DNA topoisomerases are required to resolve DNA topological stress. Despite this essential role, abortive topoisomerase activity generates aberrant protein-linked DNA breaks, jeopardising genome stability. Here, to understand the genomic distribution and mechanisms underpinning topoisomerase-induced DNA breaks, we map Top2 DNA cleavage with strand-specific nucleotide resolution across the S. cerevisiae and human genomes—and use the meiotic Spo11 protein to validate the broad applicability of this method to explore the role of diverse topoisomerase family members. Our data characterises Mre11-dependent repair in yeast and defines two strikingly different fractions of Top2 activity in humans: tightly localised CTCF-proximal, and broadly distributed transcription-proximal, the latter correlated with gene length and expression. Moreover, single nucleotide accuracy reveals the influence primary DNA sequence has upon Top2 cleavage—distinguishing sites likely to form canonical DNA double-strand breaks (DSBs) from those predisposed to form strand-biased DNA single-strand breaks (SSBs) induced by etoposide (VP16) in vivo

Freshwater and airborne textile fibre populations are dominated by ‘natural’, not microplastic, fibres

The potential role of natural textile fibres as environmental pollutants has been speculated upon by some environmental scientists, however, there is a general consensus that their biodegradability reduces their environmental threat. Whilst the risks that they pose remain poorly understood, their environmental prevalence has been noted in several recent microplastic pollution manuscripts. Here we highlight the extent to which natural textile fibres dominate fibre populations of upstream reaches of the River Trent, UK, as well as the atmospheric deposition within its catchment, over a twelve month microplastic sampling campaign. Across 223 samples, natural textile fibres represented 93.8% of the textile fibre population quantified. Moreover, though microplastic particles including synthetic fibres are known to be pervasive environmental pollutants, extruded textile fibres were absent from 82.8% of samples. Natural textile fibres were absent from just 9.7% of samples

Denominational Support for Clergy Mental Health

To date, minimal research has addressed the actual services provided to maintain the mental health of leadership in the church. Three major Protestant denominations were consulted within this study, including a total of 434 pastors across the United States. Among these three denominations, a range of services are now being offered to support clergy, with services such as time off, prayer support groups, and clergy retreats among the most valued, adequately provided, and utilized. Still, clergy do not see the provision of services as fully adequate, and report a number of obstacles to utilizing services. Generally, the most highly rated obstacle was financial limitations, followed by difficulty getting time off and concerns about confidentiality. Recommendations offered by clergy respondents are provided

Bypass and embolization for a vertebral artery aneurysm in a patient with Marfan syndrome

Extracranial vertebral artery aneurysms represent an uncommon presentation of collagen vascular disease. We performed staged proximal embolization of large left vertebral artery aneurysm after distal common carotid-to-vertebral bypass at C2 in a young adult patient with Marfan syndrome and a hypoplastic contralateral vertebral artery. Dilation of the autogenous saphenous vein graft occurred at 1 year with proximal graft stenosis requiring operative revision. Subsequent dilation of the basilar artery led to symptoms of pontine compression at 18 months that have resolved at 31 months of follow-up