1,153 research outputs found
A chiral aperiodic monotile
The recently discovered "hat" aperiodic monotile mixes unreflected and
reflected tiles in every tiling it admits, leaving open the question of whether
a single shape can tile aperiodically using translations and rotations alone.
We show that a close relative of the hat -- the equilateral member of the
continuum to which it belongs -- is a weakly chiral aperiodic monotile: it
admits only non-periodic tilings if we forbid reflections by fiat. Furthermore,
by modifying this polygon's edges we obtain a family of shapes called Spectres
that are strictly chiral aperiodic monotiles: they admit only chiral
non-periodic tilings based on a hierarchical substitution system.Comment: 23 pages, 12 figure
An aperiodic monotile
A longstanding open problem asks for an aperiodic monotile, also known as an
"einstein": a shape that admits tilings of the plane, but never periodic
tilings. We answer this problem for topological disk tiles by exhibiting a
continuum of combinatorially equivalent aperiodic polygons. We first show that
a representative example, the "hat" polykite, can form clusters called
"metatiles", for which substitution rules can be defined. Because the metatiles
admit tilings of the plane, so too does the hat. We then prove that generic
members of our continuum of polygons are aperiodic, through a new kind of
geometric incommensurability argument. Separately, we give a combinatorial,
computer-assisted proof that the hat must form hierarchical -- and hence
aperiodic -- tilings.Comment: 89 pages, 57 figures; Minor corrections, renamed "fylfot" to
"triskelion", added the name "turtle", added references, new H7/H8 rules (Fig
2.11), talk about reflection
Experiences of women who have lost young children to AIDS in KwaZulu-Natal, South Africa: a qualitative study
Background AIDS continues to be the leading cause of death in South Africa. Little is known about the experiences of mothers who have lost a young child to AIDS. The purpose of this qualitative study was to explore the attitudes and experiences of women who had lost a young child to HIV/AIDS in KwaZulu-Natal Province, South Africa.
Methods In-depth interviews were conducted with 10 women who had lost a child to AIDS. The average age of the deceased children was six years. Interviews were also conducted with 12 key informants to obtain their perspectives on working with women who had lost a child to AIDS. A thematic analysis of the transcripts was performed.
Results In addition to the pain of losing a child, the women in this study had to endure multiple stresses within a harsh and sometimes hostile environment. Confronted with pervasive stigma and extreme poverty, they had few people they could rely on during their child\u27s sickness and death. They were forced to keep their emotions to themselves since they were not likely to obtain much support from family members or people in the community. Throughout the period of caring for a sick child and watching the child die, they were essentially alone. The demands of caring for their child and subsequent grief, together with daily subsistence worries, took its toll. Key informants struggled to address the needs of these women due to several factors, including scarce resources, lack of training around bereavement issues, reluctance by people in the community to seek help with emotional issues, and poverty.
Conclusions The present study offers one of the first perspectives on the experiences of mothers who have lost a young child to AIDS. Interventions that are tailored to the local context and address bereavement issues, as well as other issues that affect the daily lives of these mothers, are urgently needed. Further studies are needed to identify factors that promote resilience among these women
Price's Law on Nonstationary Spacetimes
In this article we study the pointwise decay properties of solutions to the
wave equation on a class of nonstationary asymptotically flat backgrounds in
three space dimensions. Under the assumption that uniform energy bounds and a
weak form of local energy decay hold forward in time we establish a
local uniform decay rate (Price's law \cite{MR0376103}) for linear waves. As a
corollary, we also prove Price's law for certain small perturbations of the
Kerr metric.
This result was previously established by the second author in \cite{Tat} on
stationary backgrounds. The present work was motivated by the problem of
nonlinear stability of the Kerr/Schwarzschild solutions for the vacuum Einstein
equations, which seems to require a more robust approach to proving linear
decay estimates.Comment: 32 pages, no figures, typos correcte
The inter-personal work of dental conscious sedation: a qualitative analysis
Aims
Whilst there is a considerable body of literature examining the pharmacology of conscious sedation, the social tasks required to successfully provide conscious sedation have not been reported. This paper discusses data regarding the interpersonal work integral to effective conscious sedation provision, from a larger qualitative study exploring how patients and clinicians engage with secondary care conscious sedation provided within the UK.
Method
Semi-structured interviews were conducted with 13 conscious sedation providers and nine patients within UK-based secondary care sedation settings. Digital audio-recordings were transcribed verbatim and subsequently analysed using a constant comparative method within NVivo Data Analysis Software.
Results
Four main themes of interpersonal work were reported by participants: displaying care, containing emotions, demonstrating competence and maximizing the effect.
Conclusion
This study shows that performing conscious sedation requires more than technical delivery, and involves the projection of attributes in a literal “performance.” The importance of managing outward emotional appearance reflects previous dental research. The need to manage outward appearance, and the emotional impact this has, is of relevance to all clinicians
Global well-posedness of the 3-D full water wave problem
We consider the problem of global in time existence and uniqueness of
solutions of the 3-D infinite depth full water wave problem. We show that the
nature of the nonlinearity of the water wave equation is essentially of cubic
and higher orders. For any initial interface that is sufficiently small in its
steepness and velocity, we show that there exists a unique smooth solution of
the full water wave problem for all time, and the solution decays at the rate
.Comment: 60 page
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