On parabolic final value problems and well-posedness

We prove that a large class of parabolic final value problems is well posed.This results via explicit Hilbert spaces that characterise the data yielding existence, uniqueness and stability of solutions. This data space is the graph normed domain of an unbounded operator, which represents a new compatibility condition pertinent for final value problems. The framework is evolution equations for Lax--Milgram operators in vector distribution spaces. The final value heat equation on a smooth open set is also covered, and for non-zero Dirichlet data a non-trivial extension of the compatibility condition is obtained by addition of an improper Bochner integral.Comment: 6 pages. Accepted version; a short announcement of results from our full paper on final value problems. Appeared in Comptes Rendu Mathematique

Final value problems for parabolic differential equations and their well-posedness

This article concerns the basic understanding of parabolic final value problems, and a large class of such problems is proved to be well posed. The clarification is obtained via explicit Hilbert spaces that characterise the possible data, giving existence, uniqueness and stability of the corresponding solutions. The data space is given as the graph normed domain of an unbounded operator occurring naturally in the theory. It induces a new compatibility condition, which relies on the fact, shown here, that analytic semigroups always are invertible in the class of closed operators. The general set-up is evolution equations for Lax--Milgram operators in spaces of vector distributions. As a main example, the final value problem of the heat equation on a smooth open set is treated, and non-zero Dirichlet data are shown to require a non-trivial extension of the compatibility condition by addition of an improper Bochner integral.Comment: 39 pages. Revised version, with minor improvements. Essentially identical to the accepted version, which appeared in Axioms on 9 May 201

Re-purposing MOOCs for academic credit: a student and tutor perspective

The presentation briefly outlines practices in respect of the Accreditation of Prior Learning and their use in awarding credit for students who complete an automated assessment from a Massive Online Learning Course (MOOC). The presentation tells the story of how this was achieved for the first time from the perspective of the tutor and student. Some preliminary research findings indicate that this is probably unique in the UK

Multispecies justice in the wetlands

This essay discusses the rise of "justice" as a central concept around which environmental thought and debates have been organized over the last thirty years, and briefly places the notions of environmental justice and multispecies justice into the more general context of theories of justice since John Rawls. It uses the case of the Ballona Wetlands Ecological Reserve in Los Angeles, whose future is hotly contested between different environmentalist groups, as a case study to illustrate the complex trade-offs that environmental decision-making currently confronts, and to suggest in what ways the invocation of multispecies justice changes the participants in the community of justice and the way in which their claims on humans' moral consideration should be weighed.Este ensayo analiza el ascenso de la “justicia” como concepto central sobre el que se han organizado el pensamiento y los debates medioambientales en los últimos treinta años, y localiza brevemente las nociones de justicia medioambiental y de justicia multiespecie dentro del contexto más general de las teorías de justicia desde John Rawls. Utiliza el caso de la Reserva Ecológica de los Humedales Ballona en Los Ángeles, cuyo futuro está muy disputado por diferentes grupos medioambientalistas, como caso práctico para ilustrar la compleja compensación a la que se enfrenta actualmente la toma de decisiones medioambiental, y sugerir de qué forma la invocación de la justicia multiespecie cambia los participantes en la comunidad de justicia y la forma en que deberían sopesarse sus demandas sobre la consideración moral de los humanos

A Descriptive Exploratory Study of the Experience of Gay Partners of HIV-Positive Men

HIV disease/AIDS has been the focus of much research since its introduction in 1981 and continues to have profound implications for those living with the disease and for those who are in close social relationships with them. One group that has received minimal attention in the HIV/AIDS literature is gay partners of HIV infected men. The aim of this study was to explore and describe the experiences of gay men living with a life partner who has HIV disease/AIDS who were not primary caregivers. A qualitative study using an interpretive descriptive approach was employed to study the experiences of ten gay men whose partner had HIV disease/AIDS. The study was conducted in a large urban area in one of the western states within the USA, using a purposeful convenience sample. An unstructured interview process was utilized, the interviews transcribed verbatim, analyzed, and themes and patterns developed into a professional narrative conveying the most important findings focusing on clinical implications for nursing practice. Significant findings that emerged from analysis of the study data included: (a) issues of disclosure of HIV serostatus both within and outside of the relationship; (b) influences on daily life including the impact on day-to-day routines and plans, effective coping, perceptions of the future of the relationship, and ways in which the relationship had been enhanced; and (e) perceptions of the healthcare system including care by physicians and care by nurses. Implications for nursing practice included: (a) acknowledgement by the nurse of the role and importance of the participant in the lives of their HIV-positive partner is crucial in establishing rapport and developing a family-centered approach to care; (b) the need to combat the notions of homophobia and heterosexism by introducing the needs of this vulnerable population in early nursing curricula; (e) the ongoing need for education regarding HIV transmission; (d) assisting the study participants in identifying and implementing effective coping interventions by providing emotional support and by including them in their partner\u27s care; (e) assisting the participant in identifying and developing skills and behaviors that will better allow them to normalize their lives; and (f) recognition that these participants may need increased community resources to assist in coping as well as integrating into the community as a whole. The results of the study suggest that even though societal views on gay relationships are changing, issues regarding secondary stigma, disclosure, health, and support and education from the healthcare community continue to impact gay men and their partners

An empirical study of algorithms for point feature label placement

A major factor affecting the clarity of graphical displays that include text labels is the degree to which labels obscure display features (including other labels) as a result of spatial overlap. Point-feature label placement (PFLP) is the problem of placing text labels adjacent to point features on a map or diagram so as to maximize legibility. This problem occurs frequently in the production of many types of informational graphics, though it arises most often in automated cartography. In this paper we present a comprehensive treatment of the PFLP problem, viewed as a type of combinatorial optimization problem. Complexity analysis reveals that the basic PFLP problem and most interesting variants of it are NP-hard. These negative results help inform a survey of previously reported algorithms for PFLP; not surprisingly, all such algorithms either have exponential time complexity or are incomplete. To solve the PFLP problem in practice, then, we must rely on good heuristic methods. We propose two new methods, one based on a discrete form of gradient descent, the other on simulated annealing, and report on a series of empirical tests comparing these and the other known algorithms for the problem. Based on this study, the first to be conducted, we identify the best approaches as a function of available computation time.Engineering and Applied Science