An analogue of the Magnus problem for associative algebras

We prove an analogue of Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by $n+k$ generators and $k$ relations and has an $n$-element system of generators, then this algebra is a free algebra of rank $n$.

The Cuban school as a context for a proper development of the environmental perception

Environmental Psychology in Cuba is a new discipline that promotes a historical and cultural vision of mankind. Perception is one of the distinct processes that creates environmental consciousness. Depending on the perception of the environment, individuals interact with it, and vice versa. It means that a good perception of the significant elements of the environment also contributes to the formation of an environmental consciousness, in which perception is one of the main processes. In this transformation the school is one of the most important places for creating knowledge, skills, habits, and good attitudes towards the environment. As a result, the evaluation of the environmental perception development in students allows detecting weaknesses in the environmental education and proposing solutions based on specific problems. This study is based on different researches where the subjects were Cuban students from different educational levels and provides a first approach to the dynamic of the environmental perception development in these individuals. Recent researches have used some dimensions of the environment concept as development indicators: material, relational, intrapersonal, behavioural, cognitive, natural or ecological, and cultural. Generally speaking, different investigations show that school is the right context for environmental education.

The unit ball of the complex P(3H)

Let H be a two-dimensional complex Hilbert space and P(3H) the space of 3-homogeneous polynomials on H. We give a characterization of the extreme points of its unit ball, P(3H), from which we deduce that the unit sphere of P(3H) is the disjoint union of the sets of its extreme and smooth points. We also show that an extreme point of P(3H) remains extreme as considered as an element of L(3H). Finally we make a few remarks about the geometry of the unit ball of the predual of P(3H) and give a characterization of its smooth points.

The SDLP and the Europeanization of the Northern Ireland Problem

This article explores the various ways in which the Social Democratic and Labour Party (SDLP) has used Europe – as a source of financial aid, political support, ideas and inspiration – in its attempts to resolve the Northern Ireland conflict. In this, the piece considers the SDLP, not as a subject, but rather as an advocate of the Europeanization of the Northern Ireland problem. In particular, it looks at the role of John Hume, a founding member and later leader of the SDLP, who inculcated a strongly pro-European outlook within the party. In doing so, the article considers the success of Hume and the SDLP in their efforts to bring a European influence to bear on Northern Ireland, especially in relation to the peace process and the 1998 Agreement. However, it also looks at both the limitations of this influence, and the problems involved with the SDLP's pro-European approach, particularly since Hume's departure as party leader in 2001. In conclusion, the article suggests that the party may have been ‘over-Europeanized’, with its long-term focus on European issues and ideas now becoming electorally disadvantageous. In this way, the Europeanization of the Northern Ireland problem, and by extension the SDLP, has proven costly to the party.

On the Uncoded BER Performance Bound of the IEEE 802.16d Channel

In this letter, the performance bound of the IEEE 802.16d channel is examined analytically in order to gain an insight into its theoretical potential. Different design strategies, such as orthogonal frequency division multiplexing (OFDM) and single-carrier frequency-domain equalization (SC-FDE), time-domain decision feedback equalization (DFE), and sphere decoder (SD) techniques are discussed and compared to the theoretical bound.

The Fourteenth Session of the UN Commission on Sustainable Development: The Energy Session

A review of the Fourteenth Session of the UN Commission on Sustainable Development, focusing on international energy issues.

Deliberative Equality and the Transgovernmental Politics of the Global Financial Architecture

Revisiting the concept of transgovernmentalism, originally developed by Robert Keohane and Joseph Nye, can shed considerable light on the nature of interstate cooperation in contemporary global financial governance. Transgovernmentalism highlights how certain technocratic policy communities, composed of finance ministries, central banks, and regulators, dominate the global financial architecture. It also provides insights into the political and social basis of these actors' interactions and deliberations. Most importantly, renovating the concept of transgovernmentalism brings the participatory deficits in the current global financial architecture into sharp focus and points us in the direction of a workable reform agenda that would expand inclusion and participation. This article advocates basing future reform on efforts to achieve a closer realization of the principle of “deliberative equality.” Unfortunately, “transgovernmentalism” is incompatible with deliberative equality, meaning that it is precisely the transgovernmental characteristics of the current global financial architecture that have to be challenged and overturned if we are to arrive at anything approximating deliberative equality.

'Like waking up in a Franz Kafka novel': Service users' experiences of the child protection system when domestic violence and acrimonious separations are involved

The challenges that arise in respect of child abuse reports made in the context of domestic violence and/or acrimonious separation have been the subject of recent academic discussion. This paper adds a service user perspective to the debate and reports on the findings from a study conducted in the Republic of Ireland. In addition to the previously established evidence about such cases, it demonstrates the level of powerlessness and frustration experienced by families who found it difficult to have their needs heard or met. It also illustrates the very detrimental emotional impact on children and parents who frequently encountered indifference as well as insensitive and gendered responses from child protection staff. The findings indicate that mainstream statutory child protection services do not have the capacity to deal with these complex cases, and advocates the adoption of alternative approaches. Importantly, the study demonstrates the necessity to pay attention to the views of service users in developing an appropriate response.

The ‘Public Interest’ Agency of International Organizations? The case of the OECD Principles of Corporate Governance

This article seeks to outline and explore some of the conditions necessary for International Organizations (IOs) to perform in a public interest fashion through a case study of the Principles of corporate governance formulated by the OECD. Rather than the more commonly documented pathological and dysfunctional behavioural forms of IOs, the case of the Principles, both in their formulation by the OECD, and in their assessment by the World Bank through the ROSC process, represent an episode of IO agency protecting and promoting a wider public interest. In exercising their agency, IO staff, have made the Principles more agreeable to a wider range of interested parties, giving them a general interest orientation, in accordance with a proceduralist definition of public interest. This case should therefore encourage IPE scholars to consider carefully and systematically the sets of circumstances and conditions, which might be required for IO agency to take more socially useful forms. In the final section, three indicators are identified which might be evaluated in future research into the positive public interest agency of IOs across a range of cases.