New classes of spatial central configurations for the n+3-body problem

In this paper, we show the existence of new families of spatial central configurations for the n + 3-body problem, n >= 3. We study spatial central configurations where n bodies are at the vertices of a regular n-gon T and the other three bodies are symmetrically located on the straight line that is perpendicular to the plane that contains T and passes through the center of T. The results have simple and analytic proofs. (c) 2010 Elsevier Ltd. All rights reserved.

Stacked central configurations for the spatial six-body problem

In this paper we show the existence of three new families of stacked spatial central configurations for the six-body problem with the following properties: four bodies are at the vertices of a regular tetrahedron and the other two bodies are on a line connecting one vertex of the tetrahedron with the center of the opposite face. (c) 2009 Elsevier B.V. All rights reserved.

Dynamic portrait of the planetary 2/1 mean-motion resonance - I. Systems with a more massive outer planet

We analyse the global structure of the phase space of the planar planetary 2/1 mean-motion resonance in cases where the outer planet is more massive than its inner companion. Inside the resonant domain, we show the existence of two families of periodic orbits, one associated to the librational motion of resonant angle (sigma-family) and the other related to the circulatory motion of the difference in longitudes of pericentre (Delta pi-family). The well-known apsidal corotation resonances (ACR) appear as intersections between both families. A complex web of secondary resonances is also detected for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system. The construction of dynamical maps for various values of the total angular momentum shows the evolution of the families of stable motion with the eccentricities, identifying possible configurations suitable for exoplanetary systems. For low-moderate eccentricities, several different stable modes exist outside the ACR. For larger eccentricities, however, all stable solutions are associated to oscillations around the stationary solutions. Finally, we present a possible link between these stable families and the process of resonance capture, identifying the most probable routes from the secular region to the resonant domain, and discussing how the final resonant configuration may be affected by the extension of the chaotic layer around the resonance region.

Dynamic portrait of the planetary 2/1 mean-motion resonance - II. Systems with a more massive inner planet

This paper presents the second part in our study of the global structure of the planar phase space of the planetary three-body problem, when both planets lie in the vicinity of a 2/1 mean-motion resonance. While Paper I was devoted to cases where the outer planet is the more massive body, the present work is devoted to the cases where the more massive body is the inner planet. As before, outside the well-known Apsidal Corotation Resonances (ACR), the phase space shows a complex picture marked by the presence of several distinct regimes of resonant and non-resonant motion, crossed by families of periodic orbits and separated by chaotic zones. When the chosen values of the integrals of motion lead to symmetric ACR, the global dynamics are generally similar to the structure presented in Paper I. However, for asymmetric ACR the resonant phase space is strikingly different and shows a galore of distinct dynamical states. This structure is shown with the help of dynamical maps constructed on two different representative planes, one centred on the unstable symmetric ACR and the other on the stable asymmetric equilibrium solution. Although the study described in the work may be applied to any mass ratio, we present a detailed analysis for mass values similar to the Jupiter-Saturn case. Results give a global view of the different dynamical states available to resonant planets with these characteristics. Some of these dynamical paths could have marked the evolution of the giant planets of our Solar system, assuming they suffered a temporary capture in the 2/1 resonance during the latest stages of the formation of our Solar system.

Modelling the secular evolution of migrating planet pairs

The subject of this paper is the secular behaviour of a pair of planets evolving under dissipative forces. In particular, we investigate the case when dissipative forces affect the planetary semimajor axes and the planets move inwards/outwards the central star, in a process known as planet migration. To perform this investigation, we introduce fundamental concepts of conservative and dissipative dynamics of the three-body problem. Based on these concepts, we develop a qualitative model of the secular evolution of the migrating planetary pair. Our approach is based on the analysis of the energy and the orbital angular momentum exchange between the two-planet system and an external medium; thus no specific kind of dissipative forces is invoked. We show that, under the assumption that dissipation is weak and slow, the evolutionary routes of the migrating planets are traced by the Mode I and Mode II stationary solutions of the conservative secular problem. The ultimate convergence and the evolution of the system along one of these secular modes of motion are determined uniquely by the condition that the dissipation rate is sufficiently smaller than the proper secular frequency of the system. We show that it is possible to reassemble the starting configurations and the migration history of the systems on the basis of their final states and consequently to constrain the parameters of the physical processes involved.

On S-matrix factorization of the Landau-Lifshitz model

We consider the three-particle scattering S-matrix for the Landau-Lifshitz model by directly computing the set of the Feynman diagrams up to the second order. We show, following the analogous computations for the non-linear Schrdinger model [1, 2], that the three-particle S-matrix is factorizable in the first non-trivial order.

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

Influence of body composition on bone mass in postmenopausal osteoporotic women

We aimed at evaluating the relationship of lean and fat mass to bone mass in osteoporotic postmenopausal women. We invited 65 women who were being treated at the Sao Paulo Hospital osteoporosis outpatients` clinic to participate. Body composition and bone mineral density (BMD) measurements were performed using Dual-energy X-ray absorptiometry methodology (DXA). The mean age and weight were 69.7 +/- 6.4 years and 56.3 +/- 7.6 kg, respectively. Accordingly to the body mass index (BMI), 52.8% were of normal weight and 47.1% of the patients were overweight. Overweight women had significantly higher bone mass. Similarly, skeletal muscle index (SMI) showed a positive effect on BMD measurements and women with sarcopenia had significantly lower BMD measurements in total femur and femoral neck. In multiple regression analysis only lean mass and age, after adjustments to fat mass and BMI, were able to predict total body bone mineral content (BMC) (R(2) = 28%). Also lean mass adjusted to age and BMI were able to predict femoral neck BMD (R(2) = 14%). On the other hand, none of the components of the body composition (lean mass or fat mass) contributed significantly to explaining total femur BMD and neither body composition measurements were associated with spine BMD. These findings suggest that lean mass has a relevant role in BMC and BMD measurements. In addition, lower BMI and lean mass loss (sarcopenia) is associated to lower BMC and BMD of femoral neck and total femur and possible higher risk of osteoporotic fracture. (C) 2010 Elsevier Ireland Ltd. All rights reserved.

Trends in Morbid Obesity and in Bariatric Surgeries Covered by the Brazilian Public Health System

Obesity is an increasingly serious public health problem on a global level. Morbid obesity, defined as a body mass index greater than 40 kg/m(2), is associated with increased mortality and a high burden of obesity-related morbidities. To study the prevalence of morbid obesity in Brazil, three national anthropometric surveys were reanalyzed. Data about bariatric surgeries were obtained from the Ministry of Health Hospital Information System, which is available online. A 255% rise in the prevalence of morbid obesity was observed, starting at 0.18% in 1975-1976 and growing to 0.33% in 1989 and 0.64% in 2002-2003. There was a higher rate in the South in the first two surveys, but the prevalence in the Southeast rose steadily, reaching 0.77% in 2002-2003 and overtaking the South. Since 1999, the Brazilian Unified Health System has covered surgical treatment for morbid obesity. From 2000 to 2006, there was a sixfold increase in the number of surgeries, which topped the 2,500 mark in 2006. The geographic distribution of these surgeries is heavily concentrated in the Southeast, the most developed region of Brazil, where there is also the highest prevalence of morbid obesity. This was followed by the Southern region. The figures for the rise in morbid obesity in Brazil are startling, especially the increase among men. This is a situation that calls for further study, alongside measures to encourage the adoption of healthy lifestyles. Preventive measures aimed at slowing down or reversing the obesity epidemic are urgently required.

Dietary omega-3 fatty acid and omega-3: omega-6 fatty acid ratio predict improvement in glucose disturbances in Japanese Brazilians

Objective: We investigated whether lifestyle-induced changes in dietary fat quality are related to Improvements on glucose metabolism disturbances in Japanese Brazilians at high risk of type 2 diabetes Methods: One hundred forty-eight first- and second-generation subjects with impaired glucose tolerance or impaired fasting glycemia who attended a lifestyle intervention program for 12 mo were studied in the city of Bauru. State of Sao Paulo, Brazil Dietary fatty acid intakes at baseline and after 12 mo were estimated using three 24-h recalls. The effect of dietary fat intake on glucose metabolism was investigated by multiple logistic regression models Results: At baseline, mean standard deviation age and body mass index were 60 II y and 25 5 4.2 kg/m2, respectively After 12 mo. 92 subjects had normal plasma glucose levels and 56 remained in prediabetic conditions. Using logistic regression models adjusted for age, gender, generation, basal intake of explanatory nutrient, energy intake, physical activity, and waist circumference, the odds ratios (95% confidence intervals) for reversion to normoglycemia were 3 14 (1 22-8 10) in the second wrote of total w-3 fatty acid, 4 26 (1.34-13 57) in the second tunic of eicosapentaenoic acid, and 280 (1 10-7.10) in the second tertile of linolenic acid. Similarly. subjects in the highest wrote of w-3.w-6 fatty acid ratio showed a higher chance of improving glucose disturbances (2 51, 1.01-6.37) Conclusions: Our findings support the evidence of an independent protective effect of omega-3 fatty acid and of a higher omega-3:omega-6 fatty acid ratio on the glucose metabolism of high-risk individuals (C) 2010 Elsevier Inc All rights reserved.

Effects of calcium supplementation on body weight reduction in overweight calcium stone formers

A randomized, placebo-controlled trial was conducted in overweight calcium stone-forming (CSF) patients, to evaluate the effect of calcium supplementation associated with a calorie-restricted diet on body weight (BW) and fat reduction and its potential changes upon serum and urinary parameters. Fifteen patients were placed on a hypocaloric diet for 3 months, supplemented with either calcium carbonate (CaCO(3), n = 8) or placebo (n = 7), 500 mg bid. Blood and 24-h urine samples were collected and body composition was assessed at baseline and after the intervention. At the end of the study, final BW was significantly lower vs baseline in both CaCO(3) (74 +/- A 14 vs. 80 +/- A 14 kg, P = 0.01) and placebo groups (80 +/- A 10 vs. 87 +/- A 9 kg, P = 0.02) but the mean percentage of loss of body weight and body fat did not differ between CaCO(3) and placebo (7.0 +/- A 2.0 vs. 8.0 +/- A 3.0%, P = 0.40 and 13.0 +/- A 7.0 vs. 13.0 +/- A 10.0%; P = 0.81, respectively). After CaCO(3) or placebo, no significant differences versus baseline were observed for urinary parameters in both CaCO(3) and placebo, except for a higher mean urinary citrate in placebo group. These data suggest that increasing calcium intake by calcium carbonate supplementation did not contribute to a further reduction of BW and fat in overweight CSF patients submitted to a hypocaloric diet nor altered urinary lithogenic parameters.

Body mass index values for newborns according to gestational age

Objective: The combination of twho anthropometric parameters has been more appropriate to assess body composition and proportions in children, with special attention to the Body Mass Index (BMI), as it relates weight and length. However the BMI values for the neonatal period have not been determined yet. This study shows the BMI for newborns at different gestational ages represented in a normal smoothed percentile curve. Methods: Retrospective study including 2,406 appropriate for gestational age newborns following the Alexander et al curve (1996) from 29 to 42 weeks of gestational age. Weight and lenght were measured following standard procedures. For the construction aof a normal smoothed percentile curve, the 3(rd) 5(th), 10(th), 25(th), 5(th), 75(th), 90(th) and 95(th) percentiles were determined and a statistical procedure based on the mathematical model ""sinosuoidal fit"" was applied to establish a curve that estimates biological growth parameters. Results: The Body Mass Index values for gestational age in all percentiles shows a steady increase up to 38 weeks, levels off up to the 40(th) week, followed by a slight decrease to the 42(nd) week in both genders. Conclusion: The results show a direct correlation between gestational age and Body Mass Index for both genders in the nine percentiles, and can provide a useful reference to assess intra-uterine proportional growth.

Self-reported Body Changes and Associated Factors in Persons Living with HIV

The study aimed at verifying the associated factors of self-perceived body changes in adults living with HIV in highly-active antiretroviral therapy (HAART) in the city of Sao Paulo, Brazil. This cross-sectional study was conducted among people living with HIV on HAART for at least three months. A standardized questionnaire was used for assessing self-perceived body changes. Associated factors relating to self-reported body changes in people living with HIV (PLHIV) were assessed with Student`s t-test and chi-square test. In total, 507 patients were evaluated. The mean time since diagnosis was 6.6 years [standard deviation (SD)+/-4.1], and the mean duration of HAART was 5.1 years (SD+/-3.3). Self-perceived body changes were reported by 79.5% of the participants and were associated with viral load and duration of HAART. Fibre intake was lower among males who gained in abdominal fat (p=0.035). HAART-related body changes were reported by the large majority of the population and were associated with demographic and clinical variables.

Dynamics in dumbbell domains II. The limiting problem

In this work we continue the analysis of the asymptotic dynamics of reaction-diffusion problems in a dumbbell domain started in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2) (2006) 551-597]. Here we study the limiting problem, that is, an evolution problem in a ""domain"" which consists of an open, bounded and smooth set Omega subset of R(N) with a curve R(0) attached to it. The evolution in both parts of the domain is governed by a parabolic equation. In Omega the evolution is independent of the evolution in R(0) whereas in R(0) the evolution depends on the evolution in Omega through the continuity condition of the solution at the junction points. We analyze in detail the linear elliptic and parabolic problem, the generation of linear and nonlinear semigroups, the existence and structure of attractors. (C) 2009 Elsevier Inc. All rights reserved.

The constrained compartmentalized knapsack problem: mathematical models and solution methods

The constrained compartmentalized knapsack problem can be seen as an extension of the constrained knapsack problem. However, the items are grouped into different classes so that the overall knapsack has to be divided into compartments, and each compartment is loaded with items from the same class. Moreover, building a compartment incurs a fixed cost and a fixed loss of the capacity in the original knapsack, and the compartments are lower and upper bounded. The objective is to maximize the total value of the items loaded in the overall knapsack minus the cost of the compartments. This problem has been formulated as an integer non-linear program, and in this paper, we reformulate the non-linear model as an integer linear master problem with a large number of variables. Some heuristics based on the solution of the restricted master problem are investigated. A new and more compact integer linear model is also presented, which can be solved by a branch-and-bound commercial solver that found most of the optimal solutions for the constrained compartmentalized knapsack problem. On the other hand, heuristics provide good solutions with low computational effort. (C) 2011 Elsevier BM. All rights reserved.