A lower bound to the spectral threshold in curved tubes

We consider the Laplacian in curved tubes of arbitrary cross-section rotating together with the Frenet frame along curves in Euclidean spaces of arbitrary dimension, subject to Dirichlet boundary conditions on the cylindrical surface and Neumann conditions at the ends of the tube. We prove that the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Dirichlet Laplacian in a torus determined by the geometry of the tube.Comment: LaTeX, 13 pages; to appear in R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sc

Spectroscopy of drums and quantum billiards: perturbative and non-perturbative results

We develop powerful numerical and analytical techniques for the solution of the Helmholtz equation on general domains. We prove two theorems: the first theorem provides an exact formula for the ground state of an arbirtrary membrane, while the second theorem generalizes this result to any excited state of the membrane. We also develop a systematic perturbative scheme which can be used to study the small deformations of a membrane of circular or square shapes. We discuss several applications, obtaining numerical and analytical results.Comment: 29 pages, 12 figures, 7 tabl

Development and fabrication of radiation resistant high efficiency solar cells Final periodic report, 24 Aug. 1966 - 24 Feb. 1967

Diffusion process for lithium doping of solar cells, and electrical characteristics and radiation resistance of solar cell

Validation of the inverted adsorption structure for free-base tetraphenyl porphyrin on Cu(111)

Utilising normal incidence X-ray standing waves we rigourously scrutinise the “inverted model” as the adsorption structure of free-base tetraphenyl porphyrin on Cu(111). We demonstrate that the iminic N atoms are anchored at near-bridge adsorption sites on the surface displaced laterally by 1.1 ± 0.2 Å in excellent agreement with previously published calculations

Shell-model calculations for the three-nucleon system

We use Faddeev's decomposition to solve the shell-model problem for three nucleons. The dependence on harmonic-oscillator excitations allowed in the model space, up to $32 \hbar\Omega$ in the present calculations, and on the harmonic-oscillator frequency is studied. Effective interactions derived from Nijmegen II and Reid93 potentials are used in the calculations. The binding energies obtained are close to those calculated by other methods. The structure of the Faddeev equations is discussed and a simple formula for matrix elements of the permutation operators in a harmonic-oscillator basis is given. The Pauli principle is properly treated in the calculations.Comment: 11 pages. REVTEX. 6 PostScript figure

Study of state-of-the-art static inverter design Final report, 6 Jan. - 6 Jun. 1966

Multiple purpose inverter design based on phase demodulated inverter circuit selected from state-of-the-art assessment of ten inverter circuit

Spectacular recovery in the Ord River catchment

Regeneration work on severely damaged country in what is now known as the Ord River Regeneration Reserve (ORRR) commenced in 1960. The ORRR is in the East Kimberley area of Western Australia with an associated small area in the Northern Territory. The work included strip contour cultivation and seeding (which proceeded at various levels of intensity during the 1960s, 1970s and 1980s), fencing and destocking of cattle by mustering over many years, and the eradication of donkeys

An inventory and condition survey of rangelands in the Carnarvon Basin, Western Australia

The inventory and condition survey of rangelands in the Carnarvon Basin, undertaken by the Department of Agriculture and Food, Western Australia (DAFWA) between 1980 and 1982, describes and maps the natural resources of the region’s pastoral leasehold land. This survey report provides a baseline record of the existence and condition of the natural area’s resources, to assist with the planning and implementation of land management practices. The report identified and described the condition of soils, landforms, vegetation, habitat, ecosystems, and declared plants and animals. It also assessed the impact of pastoralism and made land management recommendations. The area surveyed covers about 74 500km² in the Carnarvon Basin and Shark Bay regions, and includes the catchments of the Lyndon and Minilya rivers and the lower reaches of the Gascoyne and Wooramel Rivers. The vegetation of the Carnarvon Basin area is mainly dominated by perennial shrubs. A small number of botanical families contain a large proportion of the dominant perennials in the area. Of these Acacia, Eremophila and Cassia are pre-eminent in the taller shrub communities, Atriplex and Maireana in the low chenopod shrublands, Eucalyptus in the low woodlands and Triodia and Plectrachne in the hummock grasslands

The Balian-Br\'ezin Method in Relativistic Quantum Mechanics

The method suggested by Balian and Br\'ezin for treating angular momentum reduction in the Faddeev equations is shown to be applicable to the relativistic three-body problem.Comment: 14 pages in LaTe

Componential coding in the condition monitoring of electrical machines Part 2: application to a conventional machine and a novel machine

This paper (Part 2) presents the practical application of componential coding, the principles of which were described in the accompanying Part 1 paper. Four major issues are addressed, including optimization of the neural network, assessment of the anomaly detection results, development of diagnostic approaches (based on the reconstruction error) and also benchmarking of componential coding with other techniques (including waveform measures, Fourier-based signal reconstruction and principal component analysis). This is achieved by applying componential coding to the data monitored from both a conventional induction motor and from a novel transverse flux motor. The results reveal that machine condition monitoring using componential coding is not only capable of detecting and then diagnosing anomalies but it also outperforms other conventional techniques in that it is able to separate very small and localized anomalies