We present here a direct elementary construction of continuous utility functions on perfectly separable totally preordered sets that does not make use of the well-known Debreu’s open gap lemma. This new construction leans on the concept of a separating countable decreasing scale. Starting from a perfectly separable totally ordered structure, we give an explicit construction of a separating countable decreasing scale, from which we show how to get a continuous utility map.

In this paper weak utilities are obtained for acyclic binary relations satisfying a condition weaker than semicontinuity on second countable topological spaces. In fact, in any subset of such a space we obtain a weak utility that characterizes the maximal elements as maxima of the function. The addition of separability of the relation yields the existence of semicontinuous representations. This property of the utility provides a result of existence of maximal elements for a class of spaces that include compact spaces. (...) However, we offer a negative result that continuity may not be reached under such hypotheses. (shrink)

In a previous paper we have shown that in quantum chromodynamics the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole. These results were obtained after angular averaging, but in the current paper we go beyond this approximation and perform an exact calculation of the angular integrals. The powers of the infrared behaviour of the propagators are changed substantially. We find the very intriguing result that the gluon propagator vanishes in the (...) infrared exactly like p2, whilst the ghost propagator is exactly as singular as 1/p4. We also find that the value of the infrared fixed point of the QCD coupling is much decreased from the y-max estimate: it is now equal to 4π/3. Following a recent study by von Smekal et al.[1], we analyzed in Ref.[2] the coupled Dyson- Schwinger equations for the gluon and ghost form factors F and G. The approximations were two-fold: firstly the vertices were taken bare, and secondly angular averaging was introduced (the so-called y-max approximation). Deferring to later work an improvement of the vertices. (shrink)

Company–community agreements are widely considered to be a practical mechanism for recognising the rights, needs and priorities of peoples impacted by mining, for managing impacts and ensuring that mining-derived benefits are shared. The use and application of company–community agreements is increasing globally. Notwithstanding the utility of these agreements, the gender dimensions of agreement processes in mining have rarely been studied. Prior research on women and mining demonstrates that women are often more adversely impacted by mining than men, and face greater (...) challenges in accessing development opportunities that mining can bring. Nonetheless, there is currently little guidance for companies, government or communities in bringing a gender perspective to the fore in mining and agreement processes. It is undisputed in human development literature that investment in women and sensitivity to gender delivers long-term health, education and local development outcomes. In mining and development, a number of key factors remain unexplored. These include: women’s participation in agreement processes, the gendered distribution of agreement benefits, and the extent to which impacts and benefits influence women’s development and economic inclusion. This paper presents the results of the first phase of an applied research project undertaken by the Centre for Social Responsibility in Mining at The University of Queensland and funded by the Minerals Council of Australia and the Department of Foreign Affairs and Trade. The project sought to connect with experienced practitioners who had been directly involved in mining and agreement processes to document and analyse grounded perspectives on gender dynamics and agreements, and connect those experiences with the broader literature. Findings from this study have implications for the role of mining companies and governments in promoting gender equality and empowerment as part of their commitments to sustainable development. They also have implications for community groups and their representatives in terms of how they might engage in agreement processes to maximise women’s participation and influence. In many social contexts, a key challenge will be navigating the territory of cultural norms and gender equality, particularly in cultures where women’s influence in the public sphere is not strong. The authors argue that without consideration of a gender perspective, including gender’s intersection with other factors such as class, race, poverty level, ethnic group and age, mining agreements will not be inclusive, may exacerbate gender inequalities, and fail to contribute to long-term sustainable development. (shrink)

High-hope and low-hope research participants (males and females), as preselected on the basis of a dispositional self-report scale, choose freely between brief audiotaped messages that varied in depressive content. In the first experiment, the messages were of either positive or negative content. Highhope as compared to low-hope persons preferred listening to the positive tapes (no differences related to Gender), and this Hope main effect remained after the shared variance related to depression and positive and negative affectivity were removed. In a (...) modified replication, the contents of the tapes were comprised of successful or unsuccessful goal-attainment statements related to hopeful thinking. High-hope as compared to low-hope persons again preferred to listen to the successful goal pursuit messages (no differences related to Gender), and this Hope main effect on listening choices remained after the shared variances related to depression, positive and negative affectivity, and self-esteem were removed. Implications are discussed. (shrink)

(1983). Robert Hooke's Trinity College ‘Musick Scripts’, his music theory and the role of music in his cosmology. Annals of Science: Vol. 40, No. 6, pp. 559-595.

This paper and its predecessor () are about the question: 'Are the events in the entire universe encoded in and predictable from any of its parts?' To approach a positive answer in classical physics, the following result is proved and commented on: in Newton's theory of gravitation, the entire trajectory of a particle can be predicted given any segment of it, regardless of how the other particles are moving-provided that there is only a finite number of particles and that their (...) speeds remain bounded. (It is this condition, together with a set of parameters characterising the motion of the other particles, which enables us to estimate the effect of the other particles on the trajectory of the given particle.) The extension of this result to other theories, in particular to special relativity, is discussed. (shrink)

Psychiatry is rapidly changing. The authors review the history of psychiatry in the United States, its gradual integration into medicine and society, and the dialectic between its “biologic” and “mentalist” outlooks. After describing the current state of the profession and its knowledge base, they discuss the likely future of the field: psychiatry's projected mode of practice and economics; its future as a science for understanding human behavior; its expected boundaries with other treatment disciplines; its anticipated relationship with academia and with (...) the community at large; and internal issues for the profession. Unprecedented internal and external pressures on the field are likely to require important reconceptualizations of psychiatry both by its members and by the rest of the American public. (shrink)

The Oxford Handbook of Positive Psychology, Second Edition is the seminal reference in the burgeoning field of positive psychology, which, in recent years, has transcended academia to capture the imagination of the general public. The handbook provides a roadmap for the psychology needed by the majority of the population--those who don't need treatment, but want to achieve the lives to which they aspire. The 65 chapters summarize all of the relevant literature in the field, and each of the international slate (...) of contributors is essentially defining a lifetime of research. The content's breadth and depth provide an unparalleled cross-disciplinary look at positive psychology from diverse fields and all branches of psychology, including social, clinical, personality, counseling, school, and developmental psychology. Topics include not only happiness--which has been perhaps misrepresented in the popular media as the entirety of the field--but also hope, strengths, positive emotions, life longings, creativity, emotional creativity, courage, and more, plus guidelines for applying what has worked for people across time and cultures. (shrink)

The "justice of markets" is intricately connected to the treatment of the poor and the disadvantaged in market economies. The increased interest of multinational corporations in low-income market segments affords, on one hand, the opportunity for a more inclusive capitalism, and on the other, the threat of greater exploitation of poor and disadvantaged consumers. This article traces the contributions of Catholic Social Teaching and its basic principles toward providing insight into what constitutes "justice" in such "marketing to the impoverished" situations.

A subspace V of an infinite dimensional fully effective vector space V ∞ is called decidable if V is r.e. and there exists an r.e. W such that $V \oplus W = V_\infty$ . These subspaces of V ∞ are natural analogues of recursive subsets of ω. The set of r.e. subspaces forms a lattice L(V ∞ ) and the set of decidable subspaces forms a lower semilattice S(V ∞ ). We analyse S(V ∞ ) and its relationship with L(V (...) ∞ ). We show: Proposition. Let U, V, W ∈ L(V ∞ ) where U is infinite dimensional and $U \oplus V = W$ . Then there exists a decidable subspace D such that U |oplus D = W. Corollary. Any r.e. subspace can be expressed as the direct sum of two decidable subspaces. These results allow us to show: Proposition. The first order theory of the lower semilattice of decidable subspaces, Th(S(V ∞ )), is undecidable. This contrasts sharply with the result for recursive sets. Finally we examine various generalizations of our results. In particular we analyse S * (V ∞ ), that is, S(V ∞ ) modulo finite dimensional subspaces. We show S * (V ∞ ) is not a lattice. (shrink)

The Oxford Handbook of Positive Psychology is the seminal reference in the field of positive psychology, which in recent years has transcended academia to capture the imagination of the general public. The handbook provides a roadmap for the psychology needed by the majority of the population -- those who don't need treatment but want to achieve the lives to which they aspire. These 65 chapters summarize all of the relevant literature in the field. The content's breadth and depth provide an (...) unparalleled cross-disciplinary look at positive psychology from diverse fields and all branches of psychology, including social, clinical, personality, counseling, school, and developmental psychology. Topics include not only happiness but also hope, strengths, positive emotions, life longings, creativity, emotional creativity, courage, and more, plus guidelines for applying what has worked for people across time and cultures. (shrink)