Remarks on the classification of a pair of commuting semilinear operators

Gelfand and Ponomarev [I.M. Gelfand, V.A. Ponomarev, Remarks on the classification of a pair of commuting linear transformations in a finite dimensional vector space, Funct. Anal. Appl. 3 (1969) 325-326] proved that the problem of classifying pairs of commuting linear operators contains the problem of classifying k-tuples of linear operators for any k. We prove an analogous statement for semilinear operators. (C) 2011 Elsevier Inc. All rights reserved.

Assessment of leisure-time physical activity for the prediction of inflammatory status and cardiometabolic profile

Objectives: Associations of leisure-time physical activity (LTPA), commuting and total physical activity with inflammatory markers, insulin resistance and metabolic profile in individuals at high cardiometabolic risk were investigated. Design: This was a cross-sectional study. Methods: A total of 193 prediabetic adults were compared according to physical activity levels measured by the international physical activity questionnaire; p for trend and logistic regression was employed. Results: The most active subset showed lower BMI and abdominal circumference, reaching significance only for LTPA (p for trend = 0.02). Lipid profile improved with increased physical activity levels. Interleukin-6 decreased with increased total physical activity and LTPA (p for trend = 0.02 and 0.03, respectively), while adiponectin increased in more active subsets for LTPA (p for trend = 0.03). Elevation in adjusted OR for hypercholesterolemia was significant for lower LTPA durations (p for trend = 0.04). High apolipoprotein B/apolipoprotein A ratio was inversely associated with LTPA, commuting and total physical activity. Increase in adjusted OR for insulin resistance was found from the highest to the lowest category of LTPA (p for trend = 0.04) but significance disappeared after adjustments for BMI and energy intake. No association of increased C-reactive protein with physical activity domains was observed. Conclusions: In general, the associations of LTPA, but not commuting or total physical activity, with markers of cardiometabolic risk reinforces the importance of initiatives to increase this domain in programs for the prevention of lifestyle-related diseases. (C) 2012 Sports Medicine Australia. Published by Elsevier Ltd. All rights reserved.

Evaluation of the prevalence and nutritional and social determinants of overweight in a population of schoolchildren: a cross-sectional analysis of 5,037 children

Objective: To evaluate the prevalence and nutritional and social determinants of overweight in a population of schoolchildren in Southern Brazil. Methods: Cross-sectional descriptive study of 5,037 children of both genders, between 6 and 10.9 years of age, from public and private schools of Maringa, Parana, Brazil. Evaluation of factors associated with excess weight (overweight and obesity) included gender, age, school type, socioeconomic level, education of the head of the family, eating habits, and means of commuting to school. After univariate analysis (Fisher's exact test), we adjusted a logistic regression model and used Wald's test for decision-making (p < 0.05). Results: The mean age was 8.7 +/- 1.3 years, with 52.8% females; 79.1% of the students attended public school and 54.6% had families of socioeconomic class A or B. Regarding nutritional status, 24% of children were overweight (7% obesity, 17% overweight). Being male, attending a private school, and having a head of the family with over four years of education were significantly associated with excess weight. In relation to food, inadequate intake of,carbohydrates was associated with a 48% greater chance of overweight/obesity (p < 0.001; OR: 1.48; 95% CI: 1.25-1.76), Conclusion: The prevalence of overweight found in this study is approximate to that reported in national studies. Its association with gender and inadequate food intake indicates that these factors should be considered in initiatives aimed at preventive measures in childhood.

ON THE CONSISTENCY OF TWISTED GENERALIZED WEYL ALGEBRAS

A twisted generalized Weyl algebra A of degree n depends on a. base algebra R, n commuting automorphisms sigma(i) of R, n central elements t(i) of R and on some additional scalar parameters. In a paper by Mazorchuk and Turowska, it is claimed that certain consistency conditions for sigma(i) and t(i) are sufficient for the algebra to be nontrivial. However, in this paper we give all example which shows that this is false. We also correct the statement by finding a new set of consistency conditions and prove that the old and new conditions together are necessary and sufficient for the base algebra R to map injectively into A. In particular they are sufficient for the algebra A to be nontrivial. We speculate that these consistency relations may play a role in other areas of mathematics, analogous to the role played by the Yang-Baxter equation in the theory of integrable systems.

Vortices in the extended Skyrme-Faddeev model

We construct analytical and numerical vortex solutions for an extended Skyrme-Faddeev model in a (3 + 1) dimensional Minkowski space-time. The extension is obtained by adding to the Lagrangian a quartic term, which is the square of the kinetic term, and a potential which breaks the SO(3) symmetry down to SO(2). The construction makes use of an ansatz, invariant under the joint action of the internal SO(2) and three commuting U(1) subgroups of the Poincare group, and which reduces the equations of motion to an ordinary differential equation for a profile function depending on the distance to the x(3) axis. The vortices have finite energy per unit length, and have waves propagating along them with the speed of light. The analytical vortices are obtained for a special choice of potentials, and the numerical ones are constructed using the successive over relaxation method for more general potentials. The spectrum of solutions is analyzed in detail, especially its dependence upon special combinations of coupling constants.

Genetic and environmental influences on blood pressure and physical activity: a study of nuclear families from Muzambinho, Brazil

Blood pressure (BP) and physical activity (PA) levels are inversely associated. Since genetic factors account for the observed variation in each of these traits, it is possible that part of their association may be related to common genetic and/or environmental influences. Thus, this study was designed to estimate the genetic and environmental correlations of BP and PA phenotypes in nuclear families from Muzambinho, Brazil. Families including 236 offspring (6 to 24 years) and their 82 fathers and 122 mothers (24 to 65 years) were evaluated. BP was measured, and total PA (TPA) was assessed by an interview (commuting, occupational, leisure time, and school time PA). Quantitative genetic modeling was used to estimate maximal heritability (h²), and genetic and environmental correlations. Heritability was significant for all phenotypes (systolic BP: h² = 0.37 ± 0.10, P < 0.05; diastolic BP: h² = 0.39 ± 0.09, P < 0.05; TPA: h² = 0.24 ± 0.09, P < 0.05). Significant genetic (r g) and environmental (r e) correlations were detected between systolic and diastolic BP (r g = 0.67 ± 0.12 and r e = 0.48 ± 0.08, P < 0.05). Genetic correlations between BP and TPA were not significant, while a tendency to an environmental cross-trait correlation was found between diastolic BP and TPA (r e = -0.18 ± 0.09, P = 0.057). In conclusion, BP and PA are under genetic influences. Systolic and diastolic BP share common genes and environmental influences. Diastolic BP and TPA are probably under similar environmental influences.