A comparison of duality and energy a posteriori estimates for $\mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ in parabolic problems

We use the elliptic reconstruction technique in combination with a duality approach to prove a posteriori error estimates for fully discrete backward Euler scheme for linear parabolic equations. As an application, we combine our result with the residual based estimators from the a posteriori estimation for elliptic problems to derive space-error indicators and thus a fully practical version of the estimators bounding the error in the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ norm. These estimators, which are of optimal order, extend those introduced by Eriksson and Johnson in 1991 by taking into account the error induced by the mesh changes and allowing for a more flexible use of the elliptic estimators. For comparison with previous results we derive also an energy-based a posteriori estimate for the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$-error which simplifies a previous one given by Lakkis and Makridakis in 2006. We then compare both estimators (duality vs. energy) in practical situations and draw conclusions.

Psychological contracts and independent sales contractors: an examination of the predictors of contractor-level outcomes

Over the past decade, the independent sales contractor (ISC) has emerged as both an important distribution channel and a management challenge. This study makes two contributions to this evolving field. First, it explores the interrelations of the psychological contract with sales performance, voluntary turnover and organisational advocacy of ISCs, which have hitherto been largely unexplored. Second, it examines differences between high- and low-performing sales contractors on these linkages, due to findings in the literature that a small number of sales contractors often achieve a majority of sales. Based on survey data as well as 7 years of contractor-level data related to sales performance and voluntary turnover (n = 189), results indicate that psychological contract fulfilment and perceived dependency are important determinants of subsequent sales performance, voluntary turnover and organisational advocacy, with significant differences reported between high- and low-performing ISCs. A notable finding pertinent for sales managers responsible for managing ISCs is that high-performing sales contractors are motivated by psychological contract fulfilment and a low perception of dependency, while low-performing sales contractors are more likely to act as advocates for the firm due to perceived dependency, but may concurrently engage in organisational advocacy as a means to leave the firm.

Standing on the shoulders of giants: an examination of the interdisciplinary foundation of relationship marketing

In the 20th century, the scholarly study of human relationships both grew dramatically and simultaneously fragmented into various disciplines and subdisciplines. Although diversity of thought is generally considered helpful for the evolution of scientific fields, the value accrued from interdisciplinary discourse depends on the ability of scholars to integrate multiple perspectives and synthesize foundational works in a systematic manner. The goal of this study is to synthesize foundational theories from social and behavioral sciences that have contributed to an understanding of relationship marketing. In seeking to provide a holistic understanding of the field, we incorporate contributions from the disciplines of marketing, management, psychology, and sociology. In building on our analysis, we synthesize our findings into a conceptual model that examines the systematic dimensions of relationship marketing. The article concludes by identifying key themes for contributors to the Journal of Relationship Marketing to consider going forward.

Using proxies to calculate the carbon impact of investment into electricity network assets

Replacement and upgrading of assets in the electricity network requires financial investment for the distribution and transmission utilities. The replacement and upgrading of network assets also represents an emissions impact due to the carbon embodied in the materials used to manufacture network assets. This paper uses investment and asset data for the GB system for 2015-2023 to assess the suitability of using a proxy with peak demand data and network investment data to calculate the carbon impacts of network investments. The proxies are calculated on a regional basis and applied to calculate the embodied carbon associated with current network assets by DNO region. The proxies are also applied to peak demand data across the 2015-2023 period to estimate the expected levels of embodied carbon that will be associated with network investment during this period. The suitability of these proxies in different contexts are then discussed, along with initial scenario analysis to calculate the impact of avoiding or deferring network investments through distributed generation projects. The proxies were found to be effective in estimating the total embodied carbon of electricity system investment in order to compare investment strategies in different regions of the GB network.

Exploring methods to evaluate the carbon impact of network investment deferral

Replacement, expansion and upgrading of assets in the electricity network represents financial investment for the distribution utilities. Network Investment Deferral (NID) is a well discussed benefit of wider adoption of Distributed Generation (DG). There have been many attempts to quantify and evaluate the financial benefit for the distribution utilities. While the carbon benefits of NID are commonly mentioned, there is little attempt to quantify these impacts. This paper explores the quantitative methods previously used to evaluate financial benefits in order to discuss the carbon impacts. These carbon impacts are important for companies owning DG equipment for internal reporting and emissions reductions ambitions. Currently, a GB wide approach is taken as a means for discussing more regional and local methods to be used in future work. By investigating these principles, the paper offers a novel approach to quantifying carbon emissions from various DG technologies.

Conversion in late antiquity: Christianity, Islam, and beyond

The papers in this volume were presented at a Mellon-Sawyer Seminar held at the University of Oxford in 2009-2010, which sought to investigate side by side the two important movements of conversion that frame late antiquity: to Christianity at its start, and to Islam at the other end. Challenging the opposition between the two stereotypes of Islamic conversion as an intrinsically violent process, and Christian conversion as a fundamentally spiritual one, the papers seek to isolate the behaviours and circumstances that made conversion both such a common and such a contested phenomenon. The spread of Buddhism in Asia in broadly the same period serves as an external comparator that was not caught in the net of the Abrahamic religions. The volume is organised around several themes, reflecting the concerns of the initial project with the articulation between norm and practice, the role of authorities and institutions, and the social and individual fluidity on the ground. Debates, discussions, and the expression of norms and principles about conversion conversion are not rare in societies experiencing religious change, and the first section of the book examines some of the main issues brought up by surviving sources. This is followed by three sections examining different aspects of how those principles were - or were not - put into practice: how conversion was handled by the state, how it was continuously redefined by individual ambivalence and cultural fluidity, and how it was enshrined through different forms of institutionalization. Finally, a topographical coda examines the effects of religious change on the iconic holy city of Jerusalem.

Written Cypriot Greek in online chat: Usage and attitudes

This paper investigates the attitudes of Greek-Cypriot internet users towards written Cypriot Greek (CG) in online chat. CG does not have a standard official orthography and it is only used in informal oral communication. With the emergence of computer-mediated communication (CMC), a novel Romanized form of CG is used instead of Standard Greek (SG) in online environments (Themistocleous 2005). To investigate language attitudes, an online questionnaire was distributed electronically to Greek-Cypriot internet users. The results show that the majority of the informants have positive attitudes towards written CG, a practice that goes against the results of previous attitudinal surveys. In this paper, I demonstrate how the internet can influence and change the attitudes of Greek-Cypriots towards their regional variety. It is argued that the unconventional and norm-free character of CMC allows internet users to use their non-standard variety in a domain where the standard would be expected to be used.

Responsibility effects in decision making under risk

We systematically explore decision situations in which a decision maker bears responsibility for somebody else's outcomes as well as for her own in situations of payoff equality. In the gain domain we confirm the intuition that being responsible for somebody else's payoffs increases risk aversion. This is however not attributable to a 'cautious shift' as often thought. Indeed, looking at risk attitudes in the loss domain, we find an increase in risk seeking under responsibility. This raises issues about the nature of various decision biases under risk, and to what extent changed behavior under responsibility may depend on a social norm of caution in situations of responsibility versus naive corrections from perceived biases. To further explore this issue, we designed a second experiment to explore risk-taking behavior for gain prospects offering very small or very large probabilities of winning. For large probabilities, we find increased risk aversion, thus confirming our earlier finding. For small probabilities however, we find an increase of risk seeking under conditions of responsibility. The latter finding thus discredits hypotheses of a social rule dictating caution under responsibility, and can be explained through flexible self-correction models predicting an accentuation of the fourfold pattern of risk attitudes predicted by prospect theory. An additional accountability mechanism does not change risk behavior, except for mixed prospects, in which it reduces loss aversion. This indicates that loss aversion is of a fundamentally different nature than probability weighting or utility curvature. Implications for debiasing are discussed.

Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics

We give an a priori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (SIAM J Math Anal 46(5):3518–3539, 2014). The estimate we derive is optimal in the L∞(0,T;dG) norm for the strain and the L2(0,T;dG) norm for the velocity, where dG is an appropriate mesh dependent H1-like space.

On the structure of infinity-harmonic maps

Let H ∈ C 2(ℝ N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = ‖H(Du)‖ L ∞(Ω) defined on maps u: Ω ⊆ ℝ n → ℝ N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ℝ N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.

Consulting young children about barriers and supports to learning

From consideration of children's rights in general and equal opportunities for disabled children in particular, it is important to consult children about barriers and supports to learning and participation. Finding appropriate and feasible ways, however, to incorporate this into educational programmes for younger children can present challenges. Here we report on what happened when teachers from reception classes in England for children aged 4–5 years implemented activities designed to access pupils' views about what helps or hinders at school. Teachers evaluated the feasibility and usefulness of the activities and, together with a small sample of children's responses, this showed that young children could indeed identify aspects of school life they like or dislike, laying the foundations for identifying barriers and supports to learning. Teachers' responses highlighted the importance of careful choice of activity to meet the needs of young children, particularly those with communication difficulties and/or low self-confidence, with staff in some cases adapting and merging activities to suit pupils' needs. Sensitive issues emerged concerning the introduction of consultation activities early in children's school careers. The implications of a compliant rather than collaborative approach by teachers are discussed in the context of children's right to have their views heard, and their developing understanding of difference.

Reasonable adjustments for disabled pupils: what support do parents want for their child?

Schools in England (as elsewhere in Europe) have a duty to promote equality for disabled people and make reasonable adjustments for disabled children. There is, however, a degree of uncertainty about how well-placed parents are addressed to use the legislation to ensure their child’s needs. This paper presents data drawn from a national questionnaire designed for schools to use to identify their disabled pupils and examines, in detail, parental responses to a question on the kinds of support their child finds helpful in offsetting any difficulties they experience. It illustrates the complex and varied nature of the ‘reasonable adjustments’ that are required and an overriding sense that need to be underpinned by the values of a responsive child-centred approach, one that recognises that parents’ knowledge and understanding of their child are important. Schools need to have in place the two-way communication process that supports them in ‘knowing’ about the visible and invisible challenges that pupils with difficulties and disabilities face in participating in school life.

Supporting schools in identifying and safeguarding the needs of disabled children: the challenges for data collection

Conceptualisations of disability that emphasise the contextual and cultural nature of disability and the embodiment of these within a national system of data collection present a number of challenges especially where this process is devolved to schools. The requirement for measures based on contextual and subjective experiences gives rise to particular difficulties in achieving parity in the way data is analysed and reported. This paper presents an account of the testing of a tool intended for use by schools as they collect data from parents to identify children who meet the criteria of disability established in Disability Discrimination Acts (DDAs). Data were validated through interviews with parents and teachers and observations of children and highlighted the pivotal role of the criterion of impact. The findings are set in the context of schools meeting their legal duties to identify disabled children and their support needs in a way that captures the complexity of disabled children’s school lives and provides useful and useable data.

The use and usefulness of a parent questionnaire to help schools identify disability

The Equality Act 2010 will be implemented in full in 2011, and schools in the UK will have to provide special aids or services for children with disabilities where this provision is considered reasonable. This paper reports on staff perspectives on the use and usefulness of a parental questionnaire on disability from a sample of 49 schools (mainstream and special) located in 12 local authorities. Most schools found the process of administering the parent questionnaire undemanding; just under half of the sample indicated that they would take some action as a result of the data collected from the parental questionnaire (e.g., to inform plans for targeting or monitoring support for children, and to contact parents and follow-up issues they had mentioned); and about one-third of schools recorded unanticipated findings from the parental questionnaire, that is, the identification of children whose disabilities were not previously known to the school. Implications for schools are discussed.