Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations

A numerical method based on integral equations is proposed and investigated for the Cauchy problem for the Laplace equation in 3-dimensional smooth bounded doubly connected domains. To numerically reconstruct a harmonic function from knowledge of the function and its normal derivative on the outer of two closed boundary surfaces, the harmonic function is represented as a single-layer potential. Matching this representation against the given data, a system of boundary integral equations is obtained to be solved for two unknown densities. This system is rewritten over the unit sphere under the assumption that each of the two boundary surfaces can be mapped smoothly and one-to-one to the unit sphere. For the discretization of this system, Weinert’s method (PhD, Göttingen, 1990) is employed, which generates a Galerkin type procedure for the numerical solution, and the densities in the system of integral equations are expressed in terms of spherical harmonics. Tikhonov regularization is incorporated, and numerical results are included showing the efficiency of the proposed procedure.

Learning to live with Parkinson’s disease in the family unit:an interpretative phenomenological analysis of well-being

We investigated family members’ lived experience of Parkinson’s disease (PD) aiming to investigate opportunities for well-being. A lifeworld-led approach to healthcare was adopted. Interpretative phenomenological analysis was used to explore in-depth interviews with people living with PD and their partners. The analysis generated four themes: It’s more than just an illness revealed the existential challenge of diagnosis; Like a bird with a broken wing emphasizing the need to adapt to increasing immobility through embodied agency; Being together with PD exploring the kinship within couples and belonging experienced through support groups; and Carpe diem! illuminated the significance of time and fractured future orientation created by diagnosis. Findings were interpreted using an existential-phenomenological theory of well-being. We highlighted how partners shared the impact of PD in their own ontological challenges. Further research with different types of families and in different situations is required to identify services required to facilitate the process of learning to live with PD. Care and support for the family unit needs to provide emotional support to manage threats to identity and agency alongside problem-solving for bodily changes. Adopting a lifeworld-led healthcare approach would increase opportunities for well-being within the PD illness journey.

Commitment language as a predictor of alcohol and marijuana use outcomes among adolescents in school -based group treatment

Despite widespread recognition of the problem of adolescent alcohol and other drug (AOD) abuse, research on its most common treatment modality, group work, is lacking. This research gap is alarming given that outcomes range from positive to potentially iatrogenic. This study sought to identify change mechanisms and/or treatment factors that are observable within group treatment sessions and that may predict AOD use outcomes. This NIH (F31 DA 020233-01A1) study evaluated 108, 10-19 year olds and the 19 school-based treatment groups to which they were previously assigned (R01 AA10246; PI: Wagner). Associations between motivational interviewing (MI) based change talk variables, group leader MI skills, and alcohol and marijuana use outcomes up to 12-months following treatment were evaluated. Treatment session audio recordings and transcripts (1R21AA015679-01; PI: Macgowan) were coded using a new discourse analysis coding scheme for measuring group member change talk (Amrhein, 2003). Therapist MI skills were similarly measured using the Motivational Interviewing Treatment Integrity instrument. Group member responses to commitment predicted group marijuana use at the 1-month follow up. Also, group leader empathy was significantly associated with group commitment for marijuana use at the middle and ending stages of treatment. Both of the above process measures were applied in a group setting for the first time. Building upon MI and social learning theory principles, group commitment and group member responses to commitment are new observable, in-session, process constructs that may predict positive and negative adolescent group treatment outcomes. These constructs, as well as the discourse analysis method and instruments used to measure them, raise many possibilities for future group work process research and practice.

Production planning, pricing and market coordination for news vendor problem with price dependent demand

Thesis (Ph.D.)--University of Washington, 2016-08

Riemann-Hilbert problems for poly-Hardy space on the unit ball

In this paper, we focus on a Riemann–Hilbert boundary value problem (BVP) with a constant coefficients for the poly-Hardy space on the real unit ball in higher dimensions. We first discuss the boundary behaviour of functions in the poly-Hardy class. Then we construct the Schwarz kernel and the higher order Schwarz operator to study Riemann–Hilbert BVPs over the unit ball for the poly- Hardy class. Finally, we obtain explicit integral expressions for their solutions. As a special case, monogenic signals as elements in the Hardy space over the unit sphere will be reconstructed in the case of boundary data given in terms of functions having values in a Clifford subalgebra. Such monogenic signals represent the generalization of analytic signals as elements of the Hardy space over the unit circle of the complex plane.

Strategy for succession in family owned small businesses as a wicked problem to be tamed

Contemporary strategic-planning processes don’t help family businesses cope with some of the big problems they face. Owner managers admit that they are confronted with issues, such as those associated with succession and inter-generational transfer that cannot be resolved merely by gathering additional data, defining issues more clearly, or breaking them down into small problems. Preparing for succession is often put off or ignored, many planning techniques don’t generate fresh ideas and implementing solutions is often fraught with political peril. This paper presents a framework to explore the idea of wicked problems, its relevance to succession planning in family businesses and its implications for practice and policy. A wicked problem has many and varied elements, and is complex as well as challenging. These problems are different to hard but ordinary problems, which people can solve in a finite time period by applying standard techniques. In this paper the authors argue that the wicked problem of family business succession requires a different approach to strategy, founded on social planning processes to engage multiple stakeholders and reconcile family/business interests to foster a joint commitment to possible ways of resolution. This requires academics and practitioners to re-frame traditional business strategic planning processes to achieve more sustainable family business futures.

Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert's method [24] is employed, which generates a Galerkin-type procedure for the numerical solution via rewriting the boundary integrals over the unit sphere and expanding the densities in terms of spherical harmonics. Numerical results are included as well.

Traditional Toys and Student Motivation and Commitment in Technological Education

Problem Statement: This research aims to understand the contribution of traditional toys as catalysts for motivation and student commitment in the development of Technological Education projects and activities. Research Questions: To what extent do work units related to traditional toys promote student motivation and commitment in the subject of Technological Education. Purpose of Study: Technological Education requires students to gain knowledge and know-how such that motivation and commitment are crucial for the development of classroom projects and activities. It is in this context that traditional toys are assumed to be catalysts for motivation and student interest. Research Methods: In terms of methodology, an exploratory research of a qualitative nature was carried out, based on semi-structured interviews to teachers and students within a 2nd cycle of Basic Education environment, encompassing five state schools in the Viseu municipality, Portugal. Nine teachers and forty-five technological education pupils, aged between 10 and 12, attending the 5th and 6th years of schooling participated. Findings: Content analysis of the answers revealed that the implementation of work units involving the construction of traditional toys are conducive to student motivation and commitment. Starting off with an initial idea, pupils are enabled to experience all the stages of toy building, from conception to completion, contributing to greater student satisfaction in the teaching-learning process. Conclusions: The traditional toys constitute an added value in the subject of Technological Education, promoting student motivation and commitment in the development of projects and activities. Students acquire knowledge and skills, which will enable them to analyze and thus resolve specific situations and prepare them for an increasingly technological world.

Ordonnancement des opérations dans une unité d’extrusion

Les travaux de ce mémoire traitent du problème d’ordonnancement et d’optimisation de la production dans un environnement de plusieurs machines en présence de contraintes sur les ressources matérielles dans une usine d’extrusion plastique. La minimisation de la somme pondérée des retards est le critère économique autour duquel s’articule cette étude car il représente un critère très important pour le respect des délais. Dans ce mémoire, nous proposons une approche exacte via une formulation mathématique capable des donner des solutions optimales et une approche heuristique qui repose sur deux méthodes de construction de solution sérielle et parallèle et un ensemble de méthodes de recherche dans le voisinage (recuit-simulé, recherche avec tabous, GRASP et algorithme génétique) avec cinq variantes de voisinages. Pour être en totale conformité avec la réalité de l’industrie du plastique, nous avons pris en considération certaines caractéristiques très fréquentes telles que les temps de changement d’outils sur les machines lorsqu’un ordre de fabrication succède à un autre sur une machine donnée. La disponibilité des extrudeuses et des matrices d’extrusion représente le goulot d’étranglement dans ce problème d’ordonnancement. Des séries d’expérimentations basées sur des problèmes tests ont été effectuées pour évaluer la qualité de la solution obtenue avec les différents algorithmes proposés. L’analyse des résultats a démontré que les méthodes de construction de solution ne sont pas suffisantes pour assurer de bons résultats et que les méthodes de recherche dans le voisinage donnent des solutions de très bonne qualité. Le choix du voisinage est important pour raffiner la qualité de la solution obtenue. Mots-clés : ordonnancement, optimisation, extrusion, formulation mathématique, heuristique, recuit-simulé, recherche avec tabous, GRASP, algorithme génétique

Clustering of Territorial Areas: A Multicriteria Districting problem

The success of regional development policies depends on the homogeneity of the territorial units. This paper aims to propose a framework for obtaining homogenous territorial clusters based on a Pareto frontier considering multiple criteria related to territories’ endogenous resources, economic profile and socio-cultural features. This framework is developed in two phases. First, the criteria correlated with development at the territorial unit level are determined through statistical and econometric methods. Then, a multi-criteria approach is developed to allocate each territorial unit (parishes) to a territorial agglomerate, according to the Pareto frontier established.

Smoothing a Discrete Hazard Function for the Number of Patients Colonized with Methicillin-Resistance Staphylococcus Aureus in an Intensive Care Unit

A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.