Sums and products of ultracomplete topological spaces

AbstractIn 1987 V.I. Ponomarev and V.V. Tkachuk characterized strongly complete topological spaces as those spaces which have countable character in their Stone–Čech compactification. On the other hand, in 1998 S. Romaguera introduced the notion of cofinally Čech complete spaces and he showed that a metrizable space admits a cofinally complete metric (otherwise, called ultracomplete metric), a term introduced independently by N.R. Howes in 1971 and A. Császár in 1975, if and only if it is cofinally Čech complete. In a recent paper the authors showed that these two notions are equivalent and in this way answered a question raised by Ponomarev and Tkachuk [Vestnik MGU 5 (1987) 16–19] about giving an internal characterization for strongly complete topological spaces (termed ultracomplete by the authors). In this paper, sums and products of ultracomplete spaces are studied

On the lattice structure of probability spaces in quantum mechanics

Let C be the set of all possible quantum states. We study the convex subsets of C with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models' approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics.Comment: arXiv admin note: substantial text overlap with arXiv:1008.416

Social difference, cultural arbitrary and identity : an analysis of a new national curriculum document in a non-secular environment

This article focuses on the idea of the Curriculum as a 'selection from the cultures of society' and as a site of contestation for legitimacy and identity affirmation. The purpose is to shed some light on the nature of curricular reform being advocated in a specific context - Malta. Throughout the past four years, there has been a revamping of the National Minimum Curriculum (NMC) document in Malta, established in 1988. The 'old' National Minimum Curriculum was subject to criticism focusing on a variety of issues (echoing criticisms levelled at similar National Curricula elsewhere), including issues concerning difference and identity. The first part of the article deals briefly with the issues concerning difference raised in this criticism, focusing on the issues of class, race/ethnicity, gender and disability. The second part focuses on the long and gradual build up towards the development of the new National Curriculum document. The process centres around two documents, the preliminary Tomorrow's Schoolsdocument and the draft NMC document. The issues of equity and the affirmation of social difference, as well as the move towards de-streaming, are discussed. It is argued that this process of reform benefited from the criticism of the earlier NMC document. The process of reform involved an attempt at widespread participation by various stakeholders - parents, teachers, students, unions, women's organisations, disabled person's organisations etc. The final section focuses on the final new NMC document. In this section, the authors explore the compromises, which have been made in reaction to the draft document, indicating the interests at play. Whose cultural arbitrary is reflected in the final document? The article concludes with a discussion centring around lessons to be drawn from a process of curricular reform, involving issues related to identity and difference, carried out in a country characterised by a non-secular environment.peer-reviewe

Essential oil composition of different parts of Tetraclinis articulata

The work evaluates the yield and the composition of the essential oil extracted from leafy and woody branches, cones, and seeds of a cultivated stand of Tetraclinis articulata (Vahl) Masters (Cupressaceae) growing in Malta. The main components were α-pinene, limonene, camphor, bornyl acetate, borneol and germacrene D. Our results show a number of differences in composition to a Moroccan study of the essential oil derived from homologous parts

Understanding political participation in media discourse: A social representations approach

Various forms of political participation are found in democratic societies, and these are diversifying at a steady pace. Scholarly literature presents us with an array of typologies of participation, some of which were conceived theoretically, and others derived from empirical research. This paper studies how political participation surfaces in media discourse in Italy and Greece. Specifically, it seeks to understand the social representations of political participation in both countries between 2000 and 2015, and to see which typologies of political participation are reflected in such representations. A media analysis was carried out on a sizeable corpus of newspaper articles in both countries. Data were analysed using a combination of correspondence and cluster analysis. The results indicate higher internal differentiation and gradualness characterising the social representations of political participation in the Italian corpus. In Greece, there was the presence of more radical ideological alternatives to electoral participation. Moreover, results indicate temporal stability in the themes pertaining to political participation over the years. The main contribution of this paper lies in showing that content pertaining to various typologies of political participation (e.g., relating to influence, in/formality and protest) features in the social representations of political participation in newspaper media. Findings are discussed in view of the temporal distribution of representational content, and by comparing countryspecific typologies (for Italy and Greece) with those present in the literature. © 2020 The Authors