Families of periodic orbits for the spatial isosceles 3-body problem

We study the families of periodic orbits of the spatial isosceles 3-body problem (for small enough values of the mass lying on the symmetry axis) coming via the analytic continuation method from periodic orbits of the circular Sitnikov problem. Using the first integral of the angular momentum, we reduce the dimension of the phase space of the problem by two units. Since periodic orbits of the reduced isosceles problem generate invariant two-dimensional tori of the nonreduced problem, the analytic continuation of periodic orbits of the (reduced) circular Sitnikov problem at this level becomes the continuation of invariant two-dimensional tori from the circular Sitnikov problem to the nonreduced isosceles problem, each one filled with periodic or quasi-periodic orbits. These tori are not KAM tori but just isotropic, since we are dealing with a three-degrees-of-freedom system. The continuation of periodic orbits is done in two different ways, the first going directly from the reduced circular Sitnikov problem to the reduced isosceles problem, and the second one using two steps: first we continue the periodic orbits from the reduced circular Sitnikov problem to the reduced elliptic Sitnikov problem, and then we continue those periodic orbits of the reduced elliptic Sitnikov problem to the reduced isosceles problem. The continuation in one or two steps produces different results. This work is merely analytic and uses the variational equations in order to apply Poincar´e’s continuation method.

Infinitely many periodic orbits for the rhomboidal five-body problem

We prove the existence of infinitely many symmetric periodic orbits for a regularized rhomboidal five-body problem with four small masses placed at the vertices of a rhombus centered in the fifth mass. The main tool for proving the existence of such periodic orbits is the analytic continuation method of Poincaré together with the symmetries of the problem. © 2006 American Institute of Physics.

Double-Antiprism Central Configurations of the 3n-Body Problem

Abstract In this paper we study numerically a new type of central configurations of the 3n-body problem with equal masses which consist of three n-gons contained in three planes z = 0 and z = ±β = 0. The n-gon on z = 0 is scaled by a factor α and it is rotated by an angle of π/n with respect to the ones on z = ±β. In this kind of configurations, the masses on the planes z = 0 and z = β are at the vertices of an antiprism with bases of different size. The same occurs with the masses on z = 0 and z = −β. We call this kind of central configurations double-antiprism central configurations. We will show the existence of central configurations of this type.

On the existence of bi-pyramidal central configurations of the n + 2-body problem with an n-gon base

Abstract. In this paper we prove the existence of central con gurations of the n + 2{body problem where n equal masses are located at the vertices of a regular n{gon and the remaining 2 masses, which are not necessarily equal, are located on the straight line orthogonal to the plane containing the n{gon passing through its center. Here this kind of central con gurations is called bi{pyramidal central con gurations. In particular, we prove that if the masses mn+1 and mn+2 and their positions satisfy convenient relations, then the con guration is central. We give explicitly those relations.

Equilibrium points and central configurations for the Lennard-Jones 2-and 3-body problems

Abstract. In this paper we study the relative equilibria and their stability for a system of three point particles moving under the action of a Lennard{Jones potential. A central con guration is a special position of the particles where the position and acceleration vectors of each particle are proportional, and the constant of proportionality is the same for all particles. Since the Lennard{Jones potential depends only on the mutual distances among the particles, it is invariant under rotations. In a rotating frame the orbits coming from central con gurations become equilibrium points, the relative equilibria. Due to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum of inertia I. In this work we characterize the relative equilibria, we nd the bifurcation values of I for which the number of relative equilibria is changing, we also analyze the stability of the relative equilibria.

Remote collaborative multi-user informal learning experiences: design and evaluation

This paper presents a customizable system used to develop a collaborative multi-user problem solving game. It addresses the increasing demand for appealing informal learning experiences in museum-like settings. The system facilitates remote collaboration by allowing groups of learners tocommunicate through a videoconferencing system and by allowing them to simultaneously interact through a shared multi-touch interactive surface. A user study with 20 user groups indicates that the game facilitates collaboration between local and remote groups of learners. The videoconference and multitouch surface acted as communication channels, attracted students’ interest, facilitated engagement, and promoted inter- and intra-group collaboration—favoring intra-group collaboration. Our findings suggest that augmentingvideoconferencing systems with a shared multitouch space offers newpossibilities and scenarios for remote collaborative environments and collaborative learning.

Maintenance of A/P body regions in planarians by TCEN49, a putative cystine-knot neurotrophin.

In freshwater planarians, the protein TCEN49 has been linked to the regional specification of the central body region, which includes the pharynx.

Pluralité des corps. 1. Les corps de La medicine [Multifaceted body. I. The bodies of medicine].

Le corps humain est l'objet privilégié d'action de la médecine, mais aussi réalité vécue, image, symbole, représentation et l'objet d'interprétation et de théorisation. Tous ces éléments constitutifs du corps influencent la façon dont la médecine le traite. Dans cette série de trois articles, nous abordons le corps sous différentes perspectives : médicale (1), phénoménologique (2), psychosomatique et socio-anthropologique (3). Ce premier article traite des représentations du corps en médecine, dont nous décrivons quatre types distincts, qui renvoient à autant de démarches scientifiques spécifiques et de formes de légitimité clinique : le corps-objet de l'anatomie, le corps-machine de la physiologie, le corps cybernétique de la biologie et le corps statistique de l'épidémiologie. The human body is the object upon which medicine is acting, but also lived reality, image, symbol, representation and the object of elaboration and theory. All these elements which constitute the body influence the way medicine is treating it. In this series of three articles, we address the human body from various perspectives: medical (1), phenomenological (2), psychosomatic and socio-anthropological (3). This first article discusses four distinct types of representation of the body within medicine, each related to a specific epistemology and shaping a distinct kind of clinical legitimacy: the body-object of anatomy, the body-machine of physiology, the cybernetic body of biology, the statistical body of epidemiology.

Body fat levels in children and adolescents: effects on the prevalence of obesity

BACKGROUND AND AIMS: There is little information regarding the effect of different definitions of obesity on nutritional epidemiology. The aim was thus to assess: (a) the values of percentage of body fat (%BF) by gender and age; (b) the prevalence of obesity according to different %BF cut-offs; and (c) the sensitivity and specificity of BMI according to different %BF cut-offs used to define obesity. METHODS: Cross-sectional study on 2494 boys and 2519 girls aged 10­18 years from the Lisbon area. %BF was measured using a hand-held device. In a sub sample of 211 boys and 724 girls %BF was assessed using skin folds. RESULTS: %BF levels were higher in girls and decreased with age in both genders. Prevalence of obesity varied considerably according to the %BF cut-off used: in boys, it ranged from 4.7% (age-specific 95th percentile) to 26.5% (fixed 25% cut-off), whereas by BMI it was 5.3%. In girls, prevalence of obesity ranged from 0.4% (age-specific BMI-derived %BF values) to 25.4% (fixed 30% cut-off), whereas by BMI it was 4.7%. The specificity of BMI criteria was over 95% irrespective of the %BF cut-off used; conversely, most sensitivities were below 40%. Sensitivities over 50% were obtained for the age-specific BMI-derived %BF values in boys and the age-specific 95th %BF percentile in both genders. Using %BF derived from the skin fold measurements leads to similar results. CONCLUSIONS: Prevalence of obesity varies considerably according to the %BF cut-off used. BMI cut-offs have a low sensitivity but a high specificity. Age- and gender-specific cut-offs for %BF should be used to define pediatric obesity.

Body lipid deposition in Nile tilapia fed on rations containing tannin

The aim of this work was to evaluate the effect of tannin sources and levels in rations, on the productive performance and body lipid deposition of Nile tilapias (Oreochromis niloticus) during the finishing phase. Three hundred and forty-two fishes were distributed in 18 tanks. Rations were prepared using corn, sorghum varieties, with low and high tannin content, and tannic acid at 0.08, 0.34, and 0.60%. Weight gain, apparent feed conversion and protein efficiency rate were not influenced by the treatments. The highest body lipid deposition was observed for the tannic acid treatment (14.39%), while the diet containing sorghum with high tannin content yielded leaner body (12.01%) than that of sorghum with low tannin content (13.31%). Diets containing sorghum provided lower levels of visceral fat. Rations with tannin contents did not harm the productive performance of Nile tilapia.

K-r/K-c but not d(N)/d(S) correlates positively with body mass in birds, raising implications for inferring lineage-specific selection

Background: The ratio of the rates of non-synonymous and synonymous substitution (d(N)/d(S)) is commonly used to estimate selection in coding sequences. It is often suggested that, all else being equal, d(N)/d(S) should be lower in populations with large effective size (Ne) due to increased efficacy of purifying selection. As N-e is difficult to measure directly, life history traits such as body mass, which is typically negatively associated with population size, have commonly been used as proxies in empirical tests of this hypothesis. However, evidence of whether the expected positive correlation between body mass and d(N)/d(S) is consistently observed is conflicting. Results: Employing whole genome sequence data from 48 avian species, we assess the relationship between rates of molecular evolution and life history in birds. We find a negative correlation between dN/dS and body mass, contrary to nearly neutral expectation. This raises the question whether the correlation might be a method artefact. We therefore in turn consider non-stationary base composition, divergence time and saturation as possible explanations, but find no clear patterns. However, in striking contrast to d(N)/d(S), the ratio of radical to conservative amino acid substitutions (K-r/K-c) correlates positively with body mass. Conclusions: Our results in principle accord with the notion that non-synonymous substitutions causing radical amino acid changes are more efficiently removed by selection in large populations, consistent with nearly neutral theory. These findings have implications for the use of d(N)/d(S) and suggest that caution is warranted when drawing conclusions about lineage-specific modes of protein evolution using this metric.

Body condition score to predict the postpartum fertility of crossbred beef cows

The relationship between changes in body condition score (BCS) during the postpartum and fertility in beef cows suckling calves under extensive conditions were investigated. Cows were subjected to four BCS evaluations over the postpartum period, starting around one month after calving. In the second evaluation cows were treated with medroxy-progesterone acetate impregnated pessaries and received an injection of estradiol benzoate. At the third evaluation, pessaries were removed and calves were separated from the cows for 96 hours, during which time estrous was observed twice a day, and animals artificially inseminated 12 hours after detection. When calves returned to their dams, bulls were introduced until a 60-day mating period was reached. The distribution of BCS differed among calving groups and evaluations. Results indicated that only cows comprising a BCS 3 (1 to 5 scale) around the first month postpartum can be used in an artificial insemination program with possibilities of becoming pregnant. There was no statistical difference between the calving groups in pregnancy rate. The evolution of the BCS of the cows during postpartum can be used to adjust the start of the breeding season to coincide with the time of the year where herd pregnancy rates will be highest.

Evidence of energy sparing in Gambian women during pregnancy: a longitudinal study using whole-body calorimetry.

Components of daily energy expenditure were measured serially by whole-body calorimetry in Gambian women before pregnancy and at 6, 12, 18, 24, 30, and 36 wk gestation. Weight gain was (mean +/- SD) 6.8 +/- 2.8 kg, fat deposition was 2.0 +/- 2.5 kg and lean tissue deposition was 5.0 +/- 2.5 kg. Basal metabolic rate (BMR) was depressed during the first 18 wk of gestation, causing total cumulative maintenance costs by week 36 to be 8.4 MJ. Individual responses to pregnancy correlated with changes in body mass (36 wk: delta BMR vs delta weight; r = 0.60, P < 0.01 delta BMR vs delta LBM; r = 0.62, P < 0.01). There was no significant increase in the cost of treadmill exercise (0% slope: F = 0.71, P = 0.64; 5% slope: F = 1.97, P = 0.10), 24-h energy expenditure (F = 0.72, P = 0.64), activity or diet-induced thermogenesis (F = 1.02, P = 0.43), during pregnancy in spite of body weight gain. Total metabolic costs over 36 wk were 144 MJ (fetus 43 MJ, fat deposition 92 MJ, cumulative maintenance costs 8.4 MJ). These were far lower than reported for well-nourished Western populations.