The sigma-isotypic decomposition and the sigma-index of reversible-equivariant systems

This work is concerned with dynamical systems in presence of symmetries and reversing symmetries. We describe a construction process of subspaces that are invariant by linear Gamma-reversible-equivariant mappings, where Gamma is the compact Lie group of all the symmetries and reversing symmetries of such systems. These subspaces are the sigma-isotypic components, first introduced by Lamb and Roberts in (1999) [10] and that correspond to the isotypic components for purely equivariant systems. In addition, by representation theory methods derived from the topological structure of the group Gamma, two algebraic formulae are established for the computation of the sigma-index of a closed subgroup of Gamma. The results obtained here are to be applied to general reversible-equivariant systems, but are of particular interest for the more subtle of the two possible cases, namely the non-self-dual case. Some examples are presented. (C) 2011 Elsevier BM. All rights reserved.

The perception of sleep quality in kidney transplant patients during the first year of transplantation

OBJECTIVE: Poor sleep quality is one of the factors that adversely affects patient quality of life after kidney transplantation, and sleep disorders represent a significant cardiovascular risk factor. The objective of this study was to investigate the prevalence of changes in sleep quality and their outcomes in kidney transplant recipients and analyze the variables affecting sleep quality in the first years after renal transplantation. METHODS: Kidney transplant recipients were evaluated at two time points after a successful transplantation: between three and six months (Phase 1) and between 12 and 15 months (Phase 2). The following tools were used for assessment: the Pittsburgh Sleep Quality Index; the quality of life questionnaire Short-Form-36; the Hospital Anxiety and Depression scale; the Karnofsky scale; and assessments of social and demographic data. The prevalence of poor sleep was 36.7% in Phase 1 and 38.3% in Phase 2 of the study. RESULTS: There were no significant differences between patients with and without changes in sleep quality between the two phases. We found no changes in sleep patterns throughout the study. Both the physical and mental health scores worsened from Phase 1 to Phase 2. CONCLUSION: Sleep quality in kidney transplant recipients did not change during the first year after a successful renal transplantation.

Axioms for the coincidence index of maps between manifolds of the same dimension

We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in Z circle plus Z(2). We also show in each setting that the group of values for the index (either Z or Z circle plus Z(2)) is determined by the axioms. Finally, for the general case of coincidence theory for arbitrary pairs of maps between two manifolds we provide a set of axioms which characterize the local Reidemeister trace which is an element of an abelian group which depends on the pair of functions. These results extend known results for coincidences between orientable differentiable manifolds. (C) 2012 Elsevier B.V. All rights reserved.

The nitrogen sufficiency index underlying estimates of nitrogen fertilization requirements of common bean

Chlorophyll determination with a portable chlorophyll meter can indicate the period of highest N demand of plants and whether sidedressing is required or not. In this sense, defining the optimal timing of N application to common bean is fundamental to increase N use efficiency, increase yields and reduce the cost of fertilization. The objectives of this study were to evaluate the efficiency of N sufficiency index (NSI) calculated based on the relative chlorophyll index (RCI) in leaves, measured with a portable chlorophyll meter, as an indicator of time of N sidedressing fertilization and to verify which NSI (90 and 95 %) value is the most appropriate to indicate the moment of N fertilization of common bean cultivar Perola. The experiment was carried out in the rainy and dry growing seasons of the agricultural year 2009/10 on a dystroferric Red Nitosol, in Botucatu, São Paulo State, Brazil. The experiment was arranged in a randomized complete block design with five treatments, consisting of N managements (M1: 200 kg ha-1 N (40 kg at sowing + 80 kg 15 days after emergence (DAE) + 80 kg 30 DAE); M2: 100 kg ha-1 N (20 kg at sowing + 40 kg 15 DAE + 40 kg 30 DAE); M3: 20 kg ha-1 N at sowing + 30 kg ha-1 when chlorophyll meter readings indicated NSI < 95 %; M4: 20 kg ha-1 N at sowing + 30 kg ha-1 N when chlorophyll meter readings indicated NSI < 90 % and, M5: control (without N application)) and four replications. The variables RCI, aboveground dry matter, total leaf N concentration, production components, grain yield, relative yield, and N use efficiency were evaluated. The RCI correlated with leaf N concentrations. By monitoring the RCI with the chlorophyll meter, the period of N sidedressing of common bean could be defined, improving N use efficiency and avoiding unnecessary N supply to common bean. The NSI 90 % of the reference area was more efficient to define the moment of N sidedressing of common bean, to increase N use efficiency.