A note on permutation regularity

The existence of a small partition of a combinatorial structure into random-like subparts, a so-called regular partition, has proven to be very useful in the study of extremal problems, and has deep algorithmic consequences. The main result in this direction is the Szemeredi Regularity Lemma in graph theory. In this note, we are concerned with regularity in permutations: we show that every permutation of a sufficiently large set has a regular partition into a small number of intervals. This refines the partition given by Cooper (2006) [10], which required an additional non-interval exceptional class. We also introduce a distance between permutations that plays an important role in the study of convergence of a permutation sequence. (C) 2011 Elsevier B.V. All rights reserved.

THE IMPLICATIONS OF A PSYCHOEDUCATION GROUP ON THE EVERYDAY LIVES OF INDIVIDUALS WITH BIPOLAR AFFECTIVE DISORDER

There is growing evidence that the course of Bipolar Affective Disorder (BAD) can be altered by psychotherapeutic approaches, such as Psychoeducation. Therefore, this study was performed with the objective of identifying the implications of a Psychoeducation group on the everyday lives of individuals with BAD. To do this, the authors chose to perform a qualitative case study. Participants included twelve individuals with BAD who had attended at least six meetings of the Psychoeducation Group held at the Sao Jose do Rio Preto Faculty of Medicine (FAMERP). Semi-structured interviews were performed, which were recorded and then transcribed and subjected to Thematic Analysis. The present study showed that the referred group experience promoted the individuals' knowledge acquisition; their awareness regarding the disease and adherence to treatment; their making positive changes in life; the possibility of helping other patients to benefit from the knowledge learned in the group; and their awareness regarding other realities and coping strategies, obtained by exchanging experiences with other participants.

The Everyday Life in Public Health Research: a theoretical and methodological framework

The aim of this paper is to present some reflections on possibilities to investigate everyday life by examining ways of life, so as to broaden perspectives to the field of research in public health, in light of the fact that the study of daily ways of life involves the analysis of trajectories that contextualize routines, interactions and meanings of life. This allows the social researcher in the health field to have, based on a theoretical framework, a flexible methodology that offers mobility in the choice of the technique that best favors the understanding of the issue to be investigated. We have here, as a conceptual reference, the idea of everyday life investigated from interactive processes and contexts, as opposed to a categorial objectification between subject and object. In this context, from the theoretical reflection, we take, as the research's empirical reference, the waiting room of the outpatient clinic of the Osteoarticular Metabolism Department of a Health Care Unit in the city of Fortaleza/, Northeastern Brazil, in order to foster an interpretive understanding of the daily routine that involves the life and health situations of women with osteoporosis.

Regularity at infinity of real mappings and a Morse-Sard theorem

We prove a new Morse-Sard-type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for C-2 mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the p-regularity and its bridge toward the rho-regularity which implies topological triviality at infinity.

Food-Retail Development and the Myth of Everyday Low Prices: The Case of Brazil

This article analyses the changes in Brazilian food retailing by investigating the co-existence of, and the pricing variation across, large supermarket chains and small independent supermarkets. It uses cointegration tests to show that, despite the widespread belief that small supermarkets are inefficient and charge higher prices, they in fact charge lower prices. Accordingly, in contrast to the prevailing literature on food-retail development, competition in food retail is complex and cannot be described as a simple Darwinian process of market concentration. The article explores the survival of small retail and its consequences for the current discussion on modern food retail in developing countries.