Spectral and variational characterizations of solutions to semilinear eigenvalue problems

Die vorliegende Arbeit befaßt sich mit einer Klasse von nichtlinearen Eigenwertproblemen mit Variationsstrukturin einem reellen Hilbertraum. Die betrachteteEigenwertgleichung ergibt sich demnach als Euler-Lagrange-Gleichung eines stetig differenzierbarenFunktionals, zusätzlich sei der nichtlineare Anteil desProblems als ungerade und definit vorausgesetzt.Die wichtigsten Ergebnisse in diesem abstrakten Rahmen sindKriterien für die Existenz spektral charakterisierterLösungen, d.h. von Lösungen, deren Eigenwert gerade miteinem vorgegeben variationellen Eigenwert eines zugehörigen linearen Problems übereinstimmt. Die Herleitung dieserKriterien basiert auf einer Untersuchung kontinuierlicher Familien selbstadjungierterEigenwertprobleme und erfordert Verallgemeinerungenspektraltheoretischer Konzepte.Neben reinen Existenzsätzen werden auch Beziehungen zwischenspektralen Charakterisierungen und denLjusternik-Schnirelman-Niveaus des Funktionals erörtert.Wir betrachten Anwendungen auf semilineareDifferentialgleichungen (sowieIntegro-Differentialgleichungen) zweiter Ordnung. Diesliefert neue Informationen über die zugehörigenLösungsmengen im Hinblick auf Knoteneigenschaften. Diehergeleiteten Methoden eignen sich besonders für eindimensionale und radialsymmetrische Probleme, während einTeil der Resultate auch ohne Symmetrieforderungen gültigist.

Spectral estimates and preconditioning for saddle point systems arising from optimization problems

In this thesis, we consider the problem of solving large and sparse linear systems of saddle point type stemming from optimization problems. The focus of the thesis is on iterative methods, and new preconditioning srategies are proposed, along with novel spectral estimtates for the matrices involved.

Direct and Inverse Spectral Problems for (2N + 1)-Diagonal, Complex, Symmetric, Non-Hermitian Matrices

2000 Mathematics Subject Classification: 42C05.

The Direct and Inverse Spectral Problems for some Banded Matrices

2000 Mathematics Subject Classification: 15A29.

The knowledge gap: A perspective on trade, industry, technology and policy from pre-war Australian music technology manufacturing (1903-30)

Australia struggles to achieve economic competitiveness, prevent expansion of the trade deficit and develop value-added production despite applications of policy strategies from protectionism to trade liberalisation. This article argues that these problems were emerging at the turn of the century, and that an investigation of music technology manufacturing in the first two decades of this century reveals fundamental problems in the conduct of relevant policy analysis. Analysis has focused on the trade or technology gap which is only symptomatic of an underlying knowledge gap. The article calls for a knowledge policy approach which can allow protection without the negative effects of isolation from global markets and without having to resort to unworkable utopian free-trade dogma. A shift of focus from a 'goods traded' view to a knowledge transaction (or diffusion) perspective is advocated.

Spectral linewidth narrowing by a narrow bandwidth squeezed vacuum in a cavity

The fluorescence spectrum of a strongly driven two-level atom located inside an optical cavity damped by a narrow-bandwidth squeezed vacuum is studied. We use a dressed atom model approach, first applied to squeezed vacuum problems by Yeoman and Barnett, to derive the master equation of the system and discuss the role of the cavity and the squeezed vacuum in the narrowing of the spectral lines and the population trapping effect. We find that in the presence of a single-mode cavity the effect of squeezing on the fluorescence spectrum is more evident in the linewidths of the Rabi sidebands rather than in the linewidth of the central component. Even in the absence of squeezing, the cavity can reduce the linewidth of the central component almost to zero, whereas the Rabi sidebands can be narrowed only to some finite value. In the presence of a two-mode cavity and a two-mode squeezed vacuum the signature of squeezing is evident in the linewidths of all spectral lines. We also establish that the narrowing of the spectral lines is very sensitive to the detuning of the driving field from the atomic resonance. Moreover, we find that the population trapping effect, predicted for the broadband squeezed vacuum case, may appear in a narrow-bandwidth case only if the input squeezed modes are perfectly matched to the cavity modes and if there is non-zero squeezing at the Rabi sidebands.

Time evolution in the unimolecular master equation at low temperatures: full spectral solution with scalable iterative methods and high precision

A new method is presented to determine an accurate eigendecomposition of difficult low temperature unimolecular master equation problems. Based on a generalisation of the Nesbet method, the new method is capable of achieving complete spectral resolution of the master equation matrix with relative accuracy in the eigenvectors. The method is applied to a test case of the decomposition of ethane at 300 K from a microcanonical initial population with energy transfer modelled by both Ergodic Collision Theory and the exponential-down model. The fact that quadruple precision (16-byte) arithmetic is required irrespective of the eigensolution method used is demonstrated. (C) 2001 Elsevier Science B.V. All rights reserved.

A monolithic smoothing-gap algorithm for contact-impact based on the signed distance function

A new algorithm has been developed for smoothing the surfaces in finite element formulations of contact-impact. A key feature of this method is that the smoothing is done implicitly by constructing smooth signed distance functions for the bodies. These functions are then employed for the computation of the gap and other variables needed for implementation of contact-impact. The smoothed signed distance functions are constructed by a moving least-squares approximation with a polynomial basis. Results show that when nodes are placed on a surface, the surface can be reproduced with an error of about one per cent or less with either a quadratic or a linear basis. With a quadratic basis, the method exactly reproduces a circle or a sphere even for coarse meshes. Results are presented for contact problems involving the contact of circular bodies. Copyright (C) 2002 John Wiley Sons, Ltd.

Positive solutions of fourth order problems with clamped beam boundary conditions

n this paper we make an exhaustive study of the fourth order linear operator u((4)) + M u coupled with the clamped beam conditions u(0) = u(1) = u'(0) = u'(1) = 0. We obtain the exact values on the real parameter M for which this operator satisfies an anti-maximum principle. Such a property is equivalent to the fact that the related Green's function is nonnegative in [0, 1] x [0, 1]. When M < 0 we obtain the best estimate by means of the spectral theory and for M > 0 we attain the optimal value by studying the oscillation properties of the solutions of the homogeneous equation u((4)) + M u = 0. By using the method of lower and upper solutions we deduce the existence of solutions for nonlinear problems coupled with this boundary conditions. (C) 2011 Elsevier Ltd. All rights reserved.

SiC pinpin photonic for linking the visible spectrum to the telecom gap

Expanding far beyond traditional applications at telecommunications wavelengths, the SiC photonic devices has recently proven its merits for working with visible range optical signals. Reconfigurable wavelength selectors are essential sub-systems for implementing reconfigurable WDM networks and optical signal processing. Visible range to telecom band spectral translation in SiC/Si can be accomplished using wavelength selector under appropriated optical bias, acting as reconfigurable active filters. In this paper we present a monolithically integrated wavelength selector based on a multilayer SiC/Si integrated optical filters that requires optical switches to select wavelengths. The selector filter is realized by using double pin/pin a-SiC:H photodetector with front and back biased optical gating elements. Red, green, blue and violet communication channels are transmitted together, each one with a specific bit sequence. The combined optical signal is analyzed by reading out the generated photocurrent, under different background wavelengths applied either from the front or the back side. The backgrounds acts as channel selectors that selects one or more channels by splitting portions of the input multi-channel optical signals across the front and back photodiodes. The transfer characteristics effects due to changes in steady state light, irradiation side and frequency are presented. The relationship between the optical inputs and the digital output levels is established. (C) 2014 Elsevier B.V. All rights reserved.

Zerebrale Probleme in der pädiatrischen Intensivmedizin [Cerebral problems in pediatric intensive care]

This paper presents a review of different methods enabling the monitoring of cerebral function in neonatal and paediatric intensive care. EEG, evoked potentials, conventional radiological studies, computerized tomography, ultrasound, intracranial pressure measurements, nuclear magnetic resonance, Doppler ultrasound, radioisotope studies, angiography, infra-red spectral analysis and last, but not least, clinical examination produce information regarding the neurological state of the patient which must be critically analysed in order to ensure optimal management of the case. Unfortunately, and in spite of impressive progress in non-invasive monitoring of the cerebral function, we are still forced to make important medical and ethical decisions without precise information about the neurological state of our patients.

A Study of Alcohol Problems and Marriage from a Treatment Perspective

This thesis is concerned with alcohol problems and marital relationships. It is particularly interested in these dynamics from a treatment perspective. The study addresses theory, research and clinical practice in the field of alcohol problems. It specifically considers these areas as they relate to enhancing understanding of the dynamics between alcohol problems and marriage. The study examines three theoretical paradigms, the disease concept of addiction, behavioural/cognitive behavioural and systems based approaches to understanding alcohol addiction. This provides a multiple theory base from which research in the field and the clinical data collected in the current research is analysed and interpreted. The study reviews research findings that have contributed to the recognition of marital treatment interventions as significant in the alcohol field. It highlights the discrepancies between such research findings and developments in actual clinical practice. In doing so, the study illustrates the gap between theory, research and clinical practice. The need for a more effective framework of information exchange across these areas of activity is identified and a model for better exchange is presented and discussed. This model highlights the importance of including clients' experiences to influence policy, practice, theory and research. In the research, specific attention is focused on the experiences of couples in alcohol treatment. Clinical data is collected from a series of alcohol treatment couples group therapy sessions. The research analysis of the clinical data identifies and extracts concerns as expressed by couples in treatment. Interpretation of these identified concerns or themes is conducted by employing the theoretical constructs of the three selected theoretical paradigms in conjunction with group work theory. On the basis of the findings in this thesis a model for a maritally sensitive assessment framework is developed. The model identifies a number of factors that should be considered in order to enhance appreciation of the interaction between alcohol problems and marital dynamics. This has particular significance for treatment interventions.This resource was contributed by The National Documentation Centre on Drug Use.

Cleaning up neighbourhoods - Environmental Problems and Service Provision in Deprived areas

There has been growing concern that the quality of public services can be affected by the nature and scale of problems in deprived neighbourhoods and that poor services can contribute to a widening gap۪ between deprived and non-deprived neighbourhoods. There is also an increased emphasis within national policy on the quality of neighbourhood environments the so-called liveability۪ agenda. This report explores the challenges of delivering street scene۪ environmental services such as street sweeping and refuse collection in deprived and less deprived areas and examines the gap in environmental amenity between these different neighbourhoods. It also contributes to our understanding of the interplay between poor services and neighbourhood decline. The research involved a telephone survey of chief officers in local authority environmental service departments across the UK and detailed case studies of policy and practice in environmental service provision in four local authorities with significant levels of deprivation. Each case study involved work in three neighbourhoods within the authority two deprived and one less deprived as well as focus groups with residents and frontline environmental operatives, interviews with senior council staff and observation on the ground