Boundaries of Disk-like Self-affine Tiles

Let $T:= T(A, {\mathcal D})$ be a disk-like self-affine tile generated by an integral expanding matrix $A$ and a consecutive collinear digit set ${\mathcal D}$, and let $f(x)=x^{2}+px+q$ be the characteristic polynomial of $A$. In the paper, we identify the boundary $\partial T$ with a sofic system by constructing a neighbor graph and derive equivalent conditions for the pair $(A,{\mathcal D})$ to be a number system. Moreover, by using the graph-directed construction and a device of pseudo-norm $\omega$, we find the generalized Hausdorff dimension $\dim_H^{\omega} (\partial T)=2\log \rho(M)/\log |q|$ where $\rho(M)$ is the spectral radius of certain contact matrix $M$. Especially, when $A$ is a similarity, we obtain the standard Hausdorff dimension $\dim_H (\partial T)=2\log \rho/\log |q|$ where $\rho$ is the largest positive zero of the cubic polynomial $x^{3}-(|p|-1)x^{2}-(|q|-|p|)x-|q|$, which is simpler than the known result.Comment: 26 pages, 11 figure

Quantum Measurement Theory in Gravitational-Wave Detectors

The fast progress in improving the sensitivity of the gravitational-wave (GW) detectors, we all have witnessed in the recent years, has propelled the scientific community to the point, when quantum behaviour of such immense measurement devices as kilometer-long interferometers starts to matter. The time, when their sensitivity will be mainly limited by the quantum noise of light is round the corner, and finding the ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned interferometric detectors of gravitational radiation of the first and second generation. Special attention is paid to the concept of Standard Quantum Limit and the methods of its surmounting.Comment: 147 pages, 46 figures, 1 table. Published in Living Reviews in Relativit

Spinal involvement in mucopolysaccharidosis IVA (Morquio-Brailsford or Morquio A syndrome): presentation, diagnosis and management.

Mucopolysaccharidosis IVA (MPS IVA), also known as Morquio-Brailsford or Morquio A syndrome, is a lysosomal storage disorder caused by a deficiency of the enzyme N-acetyl-galactosamine-6-sulphate sulphatase (GALNS). MPS IVA is multisystemic but manifests primarily as a progressive skeletal dysplasia. Spinal involvement is a major cause of morbidity and mortality in MPS IVA. Early diagnosis and timely treatment of problems involving the spine are critical in preventing or arresting neurological deterioration and loss of function. This review details the spinal manifestations of MPS IVA and describes the tools used to diagnose and monitor spinal involvement. The relative utility of radiography, computed tomography (CT) and magnetic resonance imaging (MRI) for the evaluation of cervical spine instability, stenosis, and cord compression is discussed. Surgical interventions, anaesthetic considerations, and the use of neurophysiological monitoring during procedures performed under general anaesthesia are reviewed. Recommendations for regular radiological imaging and neurologic assessments are presented, and the need for a more standardized approach for evaluating and managing spinal involvement in MPS IVA is addressed

Heavy metals in the irrigation water, soils and vegetables in the Philippi horticultural area in the Western Cape Province of South Africa

The aims of this study were to investigate the extent of heavy metal contamination in the Philippi horticultural area in the Western Cape Province, South Africa. Concentrations of Cd, Cr, Cu, Mn, Ni, Pb and Zn were determined in the irrigation water, soils and vegetables in both winter and summer cropping seasons with an ICP-AES and tested against certified standards. Differences were found in heavy metal concentrations between the winter and summer cropping seasons in the irrigation water, soils and vegetables. Certain heavy metals exceeded the maximum permissible concentrations in the irrigation water, soils and vegetables produced in South Africa. These toxic concentrations were predominantly found in the summer cropping season for the soils and in the crops produced in winter. It is thus suggested that further studies are carried out in the Philippi horticultural area to determine the sources of the heavy metals to try and mitigate the inputs thereof and therefore reduce the amount of heavy metals entering the human food chain.ISI & Scopu

Development of the infant foot as a load bearing structure : study protocol for a longitudinal evaluation (the Small Steps study)

Background An improved understanding of the structural and functional development of the paediatric foot is fundamental to a strong theoretical framework for health professionals and scientists. An infant’s transition from sitting, through crawling and cruising, to walking is when the structures and function of the foot must adapt to bearing load. The adaptation of skin and other hard and soft tissue, and foot and gait biomechanics, during this time is poorly understood. This is because data characterising the foot tissue and loading pre-walking onset does not exist. Of the existing kinematic and plantar pressure data, few studies have collected data which reflects the real-life activities of infants with modern equipment. Methods This is a longitudinal study and part of the Great Foundations Initiative, a collaborative project between the University of Brighton and the University of Salford, which is seeking to improve foot health in children. Two cohorts of 50 infants will be recruited at the two sites (University of Brighton, Eastbourne, UK and University of Salford, Salford, UK). Infants will be recruited when they first reach for their feet and attend four laboratory visits at milestones related to foot loading, with experienced independent walking being the final milestone. Data collection will include tissue characteristics (skin thickness, texture, elasticity, pH and tendon thickness and cross-sectional area), plantar pressures and kinematics captured during real world locomotion tasks. Discussion This study will provide a database characterising the development of the infant foot as it becomes a weight bearing structure. The data will allow effective comparison and quantification of changes in structure and function due to maturation and loading by measuring pre and post established walking. Additional variables which impact on the development of the foot (gender, ethnicity and body weight) will also be factored into our analysis. This will help us to advance understanding of the determinants of foot development in early childhood

Assessing anti-rabies baiting – what happens on the ground?

BACKGROUND: Rabies is one of the most hazardous zoonoses in the world. Oral mass vaccination has developed into the most effective management method to control fox rabies. The future need to control the disease in large countries (i.e. Eastern Europe and the Americas) forces cost-benefit discussions. The 'Increase bait density' option refers to the usual management assumption that more baits per km(2 )could compensate for high fox abundance and override the imperfect supply of bait pieces to the individual fox. METHODS: We use a spatial simulation, which combines explicitly fox space use (tessellation polygons) and aeroplane flight lines (straight lines). The number of baits actually falling into each polygon is measured. The manager's strategic options are converted into changes of the resulting bait distribution on the ground. The comparison enables the rating of the options with respect to the management aim (i.e. accessibility of baits). RESULTS: Above 5% (approx. 10%) of all fox groups without any bait (at most 5 baits) relate to the baiting strategy applied in the field (1 km spaced parallel flight lines, 20 baits per km(2 )distributed) under habitat conditions comparable to middle and western Europe (fox group home-range 1 km(2), 2.5 adults; reference strategy). Increasing the bait density on the same flight-line pattern neither reduces the number of under-baited fox group home-ranges, nor improves the management outcome and hence wastes resources. However, reducing the flight line distance provides a more even bait distribution and thus compensates for missed fox groups or extra high fox density. The reference strategy's bait density can be reduced when accounting for the missed fox groups. The management result with the proper strategy is likely the same but with reduced costs. CONCLUSION: There is no overall optimal strategy for the bait distribution in large areas. For major parts of the landscape, the reference strategy will be more competitive. In situations where set backs are attributed to non-homogeneous bait accessibility the distribution scheme has to be refined zone-based (i.e. increase of the flight line length per unit area). However, increase in bait density above the reference strategy appears inappropriate at least for non-urban abundance conditions of the red fox

A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Eteokles in Spain? On Brecht’s Mein Bruder war ein Flieger

One of Bertolt Brecht’s most famous poems, Mein Bruder war ein Flieger, is often invoked as a manifesto for pacifist ideals, but some essential questions (who is the lyric I? what is the literal meaning of the poem?) have hardly received any attention. By evoking the poem’s nature as a Kinderlied, the context of its first publication, and its relationship with Brecht’s play Die Gewehre der Frau Carrar, this article tentatively identifies the source of its final pointe in a famous passage of Aeschylus’ Seven against Thebes, thereby suggesting—on the basis of textual comparisons—an example of far-reaching, ideological Antikerezeption in Brecht’s oeuvre, working all the way down to his Kalendergeschichten and to his Antigone