An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.

Numerical solution of parabolic Cauchy problems in planar corner domains

An iterative method for the parabolic Cauchy problem in planar domains having a finite number of corners is implemented based on boundary integral equations. At each iteration, mixed well-posed problems are solved for the same parabolic operator. The presence of corner points renders singularities of the solutions to these mixed problems, and this is handled with the use of weight functions together with, in the numerical implementation, mesh grading near the corners. The mixed problems are reformulated in terms of boundary integrals obtained via discretization of the time-derivative to obtain an elliptic system of partial differential equations. To numerically solve these integral equations a Nyström method with super-algebraic convergence order is employed. Numerical results are presented showing the feasibility of the proposed approach. © 2014 IMACS.

Stability, causality, and quasinormal modes of cosmic strings and cylinders

In this work we consider the evolution of a massive scalar field in cylindrically symmetric space-times. Quasinormal modes have been calculated for static and rotating cosmic cylinders. We found unstable modes in some cases. Rotating as well as static cosmic strings, i.e., without regular interior solutions, do not display quasinormal oscillation modes. We conclude that rotating cosmic cylinder space-times that present closed timelike curves are unstable against scalar perturbations.

On the loss of regularity for a class of weakly hyperbolic operators

In this paper we determine bounds for the optimal loss of regularity in the Sobolev scale for a class of weakly hyperbolic operators. (C) 2009 Elsevier Inc. All rights reserved.

The influence of oscillations on global existence for a class of semi-linear wave equations

The goal of this paper is to study the global existence of small data solutions to the Cauchy problem for the nonlinear wave equation u(tt) - a(t)(2) Delta u = u(t)(2) - a(t)(2)vertical bar del u vertical bar(2). In particular we are interested in statements for the 1D case. We will explain how the interplay between the increasing and oscillating behavior of the coefficient will influence global existence of small data solutions. Copyright c 2011 John Wiley & Sons, Ltd.

Análisis de la adecuación de libros de texto de E. Primaria a la enseñanza a estudiantes de altas capacidades matemáticas

Un problema al que se enfrentan los profesores de matemáticas de Enseñanza Primaria es la necesidad de hacer adaptaciones en sus programaciones para ofrecer una educación adecuada a sus alumnos de altas capacidades matemáticas. Las editoriales de libros de texto de matemáticas de estos niveles educativos ofrecen diversas soluciones que, usualmente, consisten en incluir, en el libro del alumno, algunos problemas más difíciles y, en la documentación del profesor, una propuesta de problemas de ampliación. Una cuestión que se plantea al analizar un libro de texto de matemáticas es valorar cómo de útil puede ser el material proporcionado por la editorial (libro de texto y materiales complementarios) para un profesor que necesita una programación específica para sus alumnos de altas capacidades matemáticas. En este artículo proponemos diversas variables con las que valorar el grado de adecuación a estudiantes de altas capacidades matemáticas de los documentos proporcionados a los profesores por las editoriales. Después ponemos en práctica esta propuesta analizando el tema dedicado a los cuadriláteros en 4º curso de Enseñanza Primaria de una editorial de amplia difusión en España. Las conclusiones globales son que los materiales del profesor analizados prestan poca atención a los estudiantes de altas capacidades matemáticas y que la metodología de análisis que hemos empleado permite identificar direcciones para plantear actividades interesantes para estos estudiantes.

A gestão dos resíduos hospitalares e o papel da autoridade de saúde : caso do concelho da Amad

RESUMO O Problema. A natureza, diversidade e perigosidade dos resíduos hospitalares (RH) exige procedimentos específicos na sua gestão. A sua produção depende do número de unidades de prestação de cuidados de saúde (upcs), tipo de cuidados prestados, número de doentes observados, práticas dos profissionais e dos órgãos de gestão das upcs, inovação tecnológica, entre outros. A gestão integrada de RH tem evoluído qualitativamente nos últimos anos. Existe uma carência de informação sobre os quantitativos de RH produzidos nas upcs e na prestação de cuidados domiciliários, em Portugal. Por outro lado, os Serviços de Saúde Pública, abrangendo o poder de Autoridade de Saúde, intervêm na gestão do risco para a saúde e o ambiente associado à produção de RH, necessitando de indicadores para a sua monitorização. O quadro legal de um país nesta matéria estabelece a estratégia de gestão destes resíduos, a qual é condicionada pela classificação e definição de RH por si adoptadas. Objectivos e Metodologias. O presente estudo pretende: quantificar a produção de RH resultantes da prestação de cuidados de saúde, em seres humanos e animais nas upcs, do sistema público e privado, desenvolvendo um estudo longitudinal, onde se quantifica esta produção nos Hospitais, Centros de Saúde, Clínicas Médicas e Dentárias, Lares para Idosos, Postos Médicos de Empresas, Centros de Hemodiálise e Clínicas Veterinárias do Concelho da Amadora, e se compara esta produção em dois anos consecutivos; analisar as consequências do exercício do poder de Autoridade de Saúde na gestão integrada de RH pelas upcs; quantificar a produção média de RH, por acto prestado, nos cuidados domiciliários e, com um estudo analítico transversal, relacionar essa produção média com as características dos doentes e dos tratamentos efectuados; proceder à análise comparativa das definições e classificações de RH em países da União Europeia, através de um estudo de revisão da legislação nesta matéria em quatro países, incluindo Portugal. Resultados e Conclusões. Obtém-se a produção média de RH, por Grupos I+II, III e IV: nos Hospitais, por cama.dia, considerando a taxa de ocupação; por consulta, nos Centros de Saúde, Clínicas Médicas e Dentárias e Postos Médicos de Empresas; por cama.ano, nos Lares para Idosos, considerando a sua taxa de ocupação; e por ano, nas Clínicas de Hemodiálise e Veterinárias. Verifica-se que a actuação da Autoridade de Saúde, produz nas upcs uma diferença estatisticamente significativa no aumento das contratualizações destas com os operadores de tratamento de RH. Quantifica-se o peso médio de resíduos dos Grupos III e IV produzido por acto prestado nos tratamentos domiciliários e relaciona-se esta variável dependente com as características dos doentes e dos tratamentos efectuados. Comparam-se os distintos critérios utilizados na elaboração das definições e classificações destes resíduos inscritas na legislação da Alemanha, Reino Unido, Espanha e Portugal. Recomendações. Apresentam-se linhas de investigação futura e propõe-se uma reflexão sobre eventuais alterações de aspectos específicos no quadro legal português e nos planos de gestão integrada de RH, em Portugal. ABSTRACT The problem: The nature, diversity and hazardousness of hospital wastes (HW) requires specific procedures in its management. Its production depends on the number and patterns of healthcare services, number of patients, professional and administration practices and technologic innovations, among others. Integrated management of HW has been developping, in the scope of quality, for the past few years. There is a lack of information about the amount of HW produced in healthcare units and in the domiciliary visits, in Portugal. On the other hand, the Public Health Services, embracing the Health Authority’s power, play a very important role in managing the risk of HW production to public and environmental health. They need to use some indicators in its monitorization. In a country, rules and regulations define hospital waste management policies, which are confined by the addopted classification and definition of HW. Goals and Methods: This research study aims to quantify the production of HW as a result of healthcare services in human beings and animals, public service and private one. Through a longitudinal study, this production is quantified in Hospitals, Health Centers, Medical and Dental Clinics, Residential Centers for old people, Companies Medical Centers and Veterinary and Haemodyalisis Clinics in Amadora’s Council, comparing this production in two consecutive years. This study also focus the consequences of the Health Authority’s role in the healthcare services integrated management of HW. The middle production of HW in the domiciliary treatments is also quantified and, with a transversal analytic study, its association with patients and treatments’ characteristics is enhanced. Finally, the definitions and classifications in the European Union Countries are compared through a study that revises this matter’s legislation in four countries, including Portugal. Results and Conclusions: We get the middle production of Groups I+II, III and IV: HW: in Hospitals, by bed.day, bearing the occupation rate; by consultation, in Health Centers, Medical and Dental Clinics and Companies Medical Centers; by bed.year in Residential Centers for old people, considering their occupation rate; by year, in Veterinary and Haemodyalisis Clinics. We verify that the Health Authority’s role produces a significative statistical difference in the rise of the contracts between healthcare services and HW operators. We quantify the Groups III and IV’s wastes middle weight, produced by each medical treatment in domiciliary visits and relate this dependent variable with patients and treatments’ characteristics. We compare the different criteria used in the making of definitions and classifications of these wastes registered in German, United Kingdom, Spain and Portugal’s laws. Recommendations: Lines of further investigation are explaned. We also tender a reflexion about potential changes in rules, in regulations and in the integrated plans for managing hospital wastes in Portugal. RÉSUMÉ Le Problème. La gestion des déchets d'activités hospitalières (DAH) et de soins de santé (DSS) exige des procédures spécifiques en raison de leur nature, diversité et dangerosité. Leur production dépend, parmi d’autres, du nombre d’unités de soins de santé (USS), du type de soins administrés, du nombre de malades observés, des pratiques des professionnels et des organes de gestion des USS, de l’innovation technologique. La gestion intégrée des DAH et des DSS subit une évolution qualitative dans les dernières années. Il existe un déficit d’information sur les quantitatifs de DAH et de DSS provenant des USS et de la prestation de soins domiciliaires, au Portugal. D’autre part les Services de Santé Publique, y compris le pouvoir de l’Autorité de Santé, qui interviennent dans la gestion du risque pour la santé et pour l’environnement associé à la production de DAH et de DSS, ont besoin d’indicateurs pour leur surveillance. Dans cette matière le cadre légal établit la stratégie de gestion de ces déchets, laquelle est conditionnée par la classification et par la définition des DAH et des DSS adoptées par le pays. Objectifs et Méthodologie. Cet étude prétend: quantifier la production de DAH et de DSS provenant de la prestation de soins de santé, en êtres humains et animaux dans les USS du système public et privé. À travers un étude longitudinal, on quantifie cette production dans les Hôpitaux, Centres de Santé, Cliniques Médicales et Dentaires, Maisons de Repos pour personnes âgées, Cabinets Médicaux d’ Entreprises, Centres d’Hémodialyse et Cliniques Vétérinaires du municipe d’ Amadora, en comparant cette production en deux ans consécutifs; analyser les conséquences de l’exercice du pouvoir de l’Autorité de Santé dans la gestion intégrée des DAH et des DSS par les USS; quantifier la production moyenne de DAH et de DSS dans la prestation de soins domiciliaires et, avec un étude analytique transversal, rapporter cette production moyenne avec les caractéristiques des malades et des soins administrés; procéder à l’ analyse comparative des définitions et classifications des DAH et des DSS dans des pays de l’Union Européenne, à travers un étude de révision de la législation relative à cette matière dans quatre pays, Portugal y compris. Résultats et Conclusions. On obtient la production moyenne de DAH et des DSS, par Classes I+II, III et IV: dans les hôpitaux, par lit.jour, en considérant le taux d’occupation; par consultation, dans les Centres de Santé, Cliniques Médicales et Dentaires et Cabinets Médicaux d’ Entreprises par lit.an dans les Maisons de Repos pour personnes âgées en considérant le taux d’occupation; et par an, dans les Cliniques d’Hémodialyse et Vétérinaires. On constate que l’actuation de l’Autorité de Santé produit dans les USS une différence statistiquement significative dans l’accroissement de leurs contractualisations avec les opérateurs de traitement de DAH et de DSS. On quantifie le poids moyen des déchets des Classes III et IV produit par acte de prestation de soins à domicile et on rapporte cette variable dépendante avec les caractéristiques des malades et des soins administrés. On compare les différents critères utilisés dans l’élaboration des définitions et des classifications de ces déchets inscrites dans la légis

Web-assisted tobacco intervention in Portuguese : intentions to make behavioural changes and behavioural changes

ABSTRACT - The problem of how to support “intentions to make behavioural changes” (IBC) and “behaviour changes” (BC) in smoking cessation when there is a scarcity of resources is a pressing issue in public health terms. The present research focuses on the use of information and communications technologies and their role in smoking cessation. It is developed in Portugal after the ratification of WHO Framework Convention on Tobacco Control (on 8 November 2005). The prevalence of smokers over fifteen years of age within the population stood at 20.9% (30.9% for men and 11.8% for women). While the strategy of helping people to quit smoking has been emphasised at National Health Service (NHS) level, the uptake of cessation assistance has exceeded the capacity of the service. This induced the search of new theoretical and practical venues to offer alternative options to people willing to stop smoking. Among these, the National Health Plan (NHP) of Portugal (2004-2010), identifies the use of information technologies in smoking cessation. eHealth and the importance of health literacy as a means of empowering people to make behavioural changes is recurrently considered an option worth investigating. The overall objective of this research is to understand, in the Portuguese context, the use of the Internet to help people to stop smoking. Research questions consider factors that may contribute to “intentions to make behavioural changes” (IBC) and “behavioural changes” (BC) while using a Web-Assisted Tobacco Intervention Probe (WATIP). Also consideration is given to the trade-off on the use of the Web as a tool for smoking cessation: can it reach a vast number of people for a small cost (efficiency) demonstrating to work in the domain of smoking cessation (efficacy)”? In addition to the introduction, there is a second chapter in which the use of tobacco is discussed as a public health menace. The health gains achieved by stopping smoking and the means of quitting are also examined, as is the use of the Internet in smoking cessation. Then, several research issues are introduced. These include background theory and the theoretical framework for the Sense of Coherence. The research model is also discussed. A presentation of the methods, materials and of the Web-Assisted Tobacco Intervention Probe (WATIP) follows. In chapter four the results of the use of the Web-Assisted Tobacco Intervention Probe (WATIP) are presented. This study is divided into two sections. The first describes results related to quality control in relation to the Web-Assisted Tobacco Intervention Probe (WATIP) and gives an overview of its users. Of these, 3,150 answered initial eligibility questions. In the end, 1,463 met all eligibility requirements, completed intake, decided on a day to quit smoking (Dday) and declared their “intentions to make behavioural changes” (IBC) while a second targeted group of 650 did not decide on a Dday. With two quit attempts made before joining the platform, most of the participants had experienced past failures while wanting to stop. The smoking rate averaged 21 cigarettes per day. With a mean age of 35, of the participants 55% were males. Among several other considerations, gender and the Sense of Coherence (SOC) influenced the success of participants in their IBC and endeavour to set quit dates. The results of comparing males and females showed that, for current smokers, establishing a Dday was related to gender differences, not favouring males (OR=0.76, p<0.005). Belonging to higher Socio-economic strata (SES) was associated with the intention to consider IBC (when compared to lower SES condition) (OR=1.57, p<0.001) and higher number of school years (OR=0.70, p<0.005) favoured the decision to smoking cessation. Those who demonstrated higher confidence in their likelihood of success in stopping in the shortest time had a higher rate of setting a Dday (OR=0.51, p<0.001). There were differences between groups in IBC reflecting the high and low levels of the SOC score (OR=1.43, p=0.006), as those who considered setting a Dday had higher levels of SOC. After adjusting for all variables, stages of readiness to change and SOC were kept in the model. This is the first Arm of this research where the focus is a discussion of the system’s implications for the participants’ “intentions to make behavioural changes” (IBC). Moreover, a second section of this study (second Arm) offers input collected from 77 in-depth interviews with the Web-Assisted Tobacco Intervention Probe (WATIP) users. Here, “Behaviour Change” (BC) and the usability of the platform are explored a year after IBC was declared. A percentage of 32.9% of self-reported, 12-month quitters in continuous abstinence from smoking from Dday to the 12-month follow- up point of the use of the Web-Assisted Tobacco Intervention Probe (WATIP) has been assessed. Comparing the Sense of Coherence (SOC) scores of participants by their respective means, according to the two groups, there was a significant difference in these scores of non smokers (BC) (M=144,66, SD=22,52) and Sense of Coherence (SOC) of smokers (noBC) (M=131,51, SD=21,43) p=0.014. This WATIP strategy and its contents benefit from the strengthening of the smoker’s sense of coherence (SOC), so that the person’s progress towards a life without tobacco may be experienced as comprehensible, manageable and meaningful. In this sample the sense of coherence (SOC) effect is moderate although it is associated with the day to quit smoking (Dday). Some of the limitations of this research have to do with self-selection bias, sample size (power) and self-reporting (no biochemical validation). The enrolment of participants was therefore not representative of the smoking population. It is not possible to verify the Web-Assisted Tobacco Intervention Probe (WATIP) evaluation of external validity; consequently, the results obtained cannot be applied generalized. No participation bias is provided. Another limitation of this study is the associated limitations of interviews. Interviewees’ perception that fabricating answers could benefit them more than telling the simple truth in response to questions is a risk that is not evaluated (with no external validation like measuring participants’ carbon monoxide levels). What emerges in this analysis is the relevance of the process that leads to the establishment of the quit day (Dday) to stop using tobacco. In addition, technological issues, when tailoring is the focus, are key elements for scrutiny. The high number of dropouts of users of the web platform mandates future research that should concentrate on the matters of the user-centred design of portals. The focus on gains in health through patient-centred care needs more research, so that technology usability be considered within the context of best practices in smoking cessation.

Caracterização dos incidentes na administração de medicamentos num serviço de Medicina Interna

RESUMO - O problema do erro de medicação tem vindo a adquirir uma importância e um interesse crescentes nos últimos anos. As consequências directas no doente que condicionam frequentemente o prolongamento do internamento, a necessidade de utilização adicional de recursos e a diminuição de satisfação por parte dos doentes, são alguns dos aspectos que importa analisar no sentido de se aumentar a segurança do doente. No circuito do medicamento em meio hospitalar estão envolvidos diversos profissionais, estando o enfermeiro no final da cadeia quando administra a medicação ao doente. Na bibliografia internacional, são referidas incidências elevadas de eventos adversos relacionados com o medicamento. Em Portugal, não existem estudos disponíveis que nos permitam conhecer, nem o tipo de incidentes, nem a dimensão do problema do erro de medicação. Efectuamos um estudo descritivo, prospectivo, exploratório, utilizando a técnica de observação não participante, da administração de medicamentos. Os objectivos são, por um lado, determinar a frequência de incidentes na administração de medicação num Serviço de Medicina Interna e, por outro, caracterizar o tipo de incidentes na administração da medicação e identificar as suas possíveis causas. A população em estudo foi constituída pelos enfermeiros que administraram medicamentos aos doentes internados no Serviço de Medicina Interna seleccionado, durante os meses de junho a agosto de 2012, sendo observadas 1521 administrações. Foi utilizada uma grelha de observação, que incluiu os seguintes elementos: doente certo; medicamento certo; dose certa; hora certa; via certa; técnica de administração correcta (assépsia); tempo de infusão; monitorização correcta. Constatou-se que em 43% das doses administradas apresentavam pelo menos um erro, num total de 764 erros. Não foi observado nenhum erro de doente, de medicamento, de dose extra, de via, de forma farmacêutica, nem a administração de medicamento não prescrito. Detectaram-se 0,19% de erros na preparação, 0,72% de erros de dose, 1,7% erros de omissão, 1,97% de erros de administração, 13,52% de erros de monitorização, 28,73% de erros de v horário. O tempo de infusão da terapêutica parentérica não foi cumprida em 27,69% das oportunidades, tendo sido sempre administrado em tempo inferior ao preconizado. Não encontramos relação entre as interrupções durante a administração de terapêutica e os erros. Pelo contrário constatou-se haver relação entre o número de doses com erro e o turno em que ocorreram, sendo mais frequentes no turno da noite. Constatamos também que aos fins de semana os erros eram mais frequentes e o risco da ocorrência de um erro na administração de medicação aumenta 1,5 vezes quando o número de enfermeiros é insuficiente.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Ekvivalenssin ongelma vertailututkimuksessa

Abstract: The problem of equivalence in comparative research

Spectral Analysis of Symmetric and Anti-Symmetric Pairwise Kernels

This work investigates theoretical properties of symmetric and anti-symmetric kernels. First chapters give an overview of the theory of kernels used in supervised machine learning. Central focus is on the regularized least squares algorithm, which is motivated as a problem of function reconstruction through an abstract inverse problem. Brief review of reproducing kernel Hilbert spaces shows how kernels define an implicit hypothesis space with multiple equivalent characterizations and how this space may be modified by incorporating prior knowledge. Mathematical results of the abstract inverse problem, in particular spectral properties, pseudoinverse and regularization are recollected and then specialized to kernels. Symmetric and anti-symmetric kernels are applied in relation learning problems which incorporate prior knowledge that the relation is symmetric or anti-symmetric, respectively. Theoretical properties of these kernels are proved in a draft this thesis is based on and comprehensively referenced here. These proofs show that these kernels can be guaranteed to learn only symmetric or anti-symmetric relations, and they can learn any relations relative to the original kernel modified to learn only symmetric or anti-symmetric parts. Further results prove spectral properties of these kernels, central result being a simple inequality for the the trace of the estimator, also called the effective dimension. This quantity is used in learning bounds to guarantee smaller variance.

On the convergence of the no response test

The no response test is a new scheme in inverse problems for partial differential equations which was recently proposed in [D. R. Luke and R. Potthast, SIAM J. Appl. Math., 63 (2003), pp. 1292–1312] in the framework of inverse acoustic scattering problems. The main idea of the scheme is to construct special probing waves which are small on some test domain. Then the response for these waves is constructed. If the response is small, the unknown object is assumed to be a subset of the test domain. The response is constructed from one, several, or many particular solutions of the problem under consideration. In this paper, we investigate the convergence of the no response test for the reconstruction information about inclusions D from the Cauchy values of solutions to the Helmholtz equation on an outer surface $\partial\Omega$ with $\overline{D} \subset \Omega$. We show that the one‐wave no response test provides a criterion to test the analytic extensibility of a field. In particular, we investigate the construction of approximations for the set of singular points $N(u)$ of the total fields u from one given pair of Cauchy data. Thus, the no response test solves a particular version of the classical Cauchy problem. Also, if an infinite number of fields is given, we prove that a multifield version of the no response test reconstructs the unknown inclusion D. This is the first convergence analysis which could be achieved for the no response test.

Estudo da equação de Klein-Gordon linear

Pós-graduação em Matemática - IBILCE

Comportamento assintótico e controlabilidade exata para a equação de Klein-Gordon

Pós-graduação em Matemática - IBILCE