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.

Central configurations of nested rotated regular tetrahedra

In this paper we prove that there are only two different classes of central configura- tions with convenient masses located at the vertices of two nested regular tetrahedra: either when one of the tetrahedra is a homothecy of the other one, or when one of the tetrahedra is a homothecy followed by a rotation of Euler angles = = 0 and = of the other one. We also analyze the central configurations with convenient masses located at the vertices of three nested regular tetrahedra when one them is a homothecy of the other one, and the third one is a homothecy followed by a rotation of Euler angles = = 0 and = of the other two. In all these cases we have assumed that the masses on each tetrahedron are equal but masses on different tetrahedra could be different.

Central configurations of nested regular polyhedra for the spatial 2n–body problem

We consider 2n masses located at the vertices of two nested regular polyhedra with the same number of vertices. Assuming that the masses in each polyhedron are equal, we prove that for each ratio of the masses of the inner and the outer polyhedron there exists a unique ratio of the length of the edges of the inner and the outer polyhedron such that the configuration is central.

Central configurations of three nested regular polyhedra for the spatial 3n–body problem

Three regular polyhedra are called nested if they have the same number of vertices n, the same center and the positions of the vertices of the inner polyhedron ri, the ones of the medium polyhedron Ri and the ones of the outer polyhedron Ri satisfy the relation Ri = ri and Ri = Rri for some scale factors R > > 1 and for all i = 1, . . . , n. We consider 3n masses located at the vertices of three nested regular polyhedra. We assume that the masses of the inner polyhedron are equal to m1, the masses of the medium one are equal to m2, and the masses of the outer one are equal to m3. We prove that if the ratios of the masses m2/m1 and m3/m1 and the scale factors and R satisfy two convenient relations, then this configuration is central for the 3n–body problem. Moreover there is some numerical evidence that, first, fixed two values of the ratios m2/m1 and m3/m1, the 3n–body problem has a unique central configuration of this type; and second that the number of nested regular polyhedra with the same number of vertices forming a central configuration for convenient masses and sizes is arbitrary.

Symmetric planar central configurations of five bodies: Euler plus two

We study planar central configurations of the five-body problem where three of the bodies are collinear, forming an Euler central configuration of the three-body problem, and the two other bodies together with the collinear configuration are in the same plane. The problem considered here assumes certain symmetries. From the three bodies in the collinear configuration, the two bodies at the extremities have equal masses and the third one is at the middle point between the two. The fourth and fifth bodies are placed in a symmetric way: either with respect to the line containing the three bodies, or with respect to the middle body in the collinear configuration, or with respect to the perpendicular bisector of the segment containing the three bodies. The possible stacked five-body central configurations satisfying these types of symmetries are: a rhombus with four masses at the vertices and a fifth mass in the center, and a trapezoid with four masses at the vertices and a fifth mass at the midpoint of one of the parallel sides.

The number of planar central configurations for the 4-body problem is finite when 3 mass positions are fixed

In the n{body problem a central con guration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for n = 3 and for n > 4 that if n ? 1 masses are located at xed points in the plane, then there are only a nite number of ways to position the remaining nth mass in such a way that they de ne a central con guration. Lindstrom leaves open the case n = 4. In this paper we prove the case n = 4 using as variables the mutual distances between the particles.

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.

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.

Nested central volcanism related to rift development and giant landsliding in oceanic islands

Centro Superior de Investigaciones Científicas, Museo Nacional de Ciencias Naturales, Estación Volcanológica de Canarias

Configurações centrais planares do tipo pipa

Neste artigo estudamos configurações centrais planares do tipo pipa para o problema de quatro corpos. Mostramos a existência de tais configurações para as pipas côncavas, quando uma das massas está no interior do triângulo formado pelas outras três massas, e para as pipas convexas, quando uma das massas está no exterior do triângulo formado pelas outras três massas.

Human Herpesvirus Infections Of The Central Nervous System: Laboratory Diagnosis Based On Dna Detection By Nested Pcr In Plasma And Cerebrospinal Fluid Samples.

Infections of the central nervous systems (CNS) present a diagnostic problem for which an accurate laboratory diagnosis is essential. Invasive practices, such as cerebral biopsy, have been replaced by obtaining a polymerase chain reaction (PCR) diagnosis using cerebral spinal fluid (CSF) as a reference method. Tests on DNA extracted from plasma are noninvasive, thus avoiding all of the collateral effects and patient risks associated with CSF collection. This study aimed to determine whether plasma can replace CSF in nested PCR analysis for the detection of CNS human herpesvirus (HHV) diseases by analysing the proportion of patients whose CSF nested PCR results were positive for CNS HHV who also had the same organism identified by plasma nested PCR. In this study, CSF DNA was used as the gold standard, and nested PCR was performed on both types of samples. Fifty-two patients with symptoms of nervous system infection were submitted to CSF and blood collection. For the eight HHV, one positive DNA result-in plasma and/or CSF nested PCR-was considered an active HHV infection, whereas the occurrence of two or more HHVs in the same sample was considered a coinfection. HHV infections were positively detected in 27/52 (51.9%) of the CSF and in 32/52 (61.5%) of the plasma, difference not significant, thus nested PCR can be performed on plasma instead of CSF. In conclusion, this findings suggest that plasma as a useful material for the diagnosis of cases where there is any difficulty to perform a CSF puncture.

How central and connected am I in my family? Bridging and bonding social capital in family configurations of young adults with psychiatric disorders

AIMS: This article explores the structures of relational resources that individuals with psychiatric disorders get from their family configurations using the concept of social capital. METHODS: The research is based on a sample of 54 individuals with psychiatric disorders and behavioural problems, and a comparison sample of 54 individuals without a clinical record matched to the clinical respondents for age and sex. Standard measures of social capital from social network methods are applied on family configurations of individuals from both samples. Differences are tested by variance analysis. RESULTS: Structures of family resources available to individuals with psychiatric disorders are distinct. Individuals with psychiatric disorders perceive themselves as less central in their family configurations and less connected to their family members. Their significant family members are perceived as less connected with each other. As a whole, their family configurations are smaller and do not include spouses or partners. Therefore bridging and bonding social capitals are not readily available for them. CONCLUSION: As family configurations of individuals with psychiatric disorders provide fewer relational resources than other families, they are not able to deal with social integration of individuals with psychiatric disorders on their own.

First isolation and molecular characterization of Ehrlichia canis in Costa Rica, Central America

The present study investigated Ehrlichia species in blood samples from dogs suspected of clinical ehrlichiosis, using molecular and isolation techniques in cell culture. From a total of 310 canine blood samples analyzed by 16S rRNA nested PCR, 148 (47.7%) were positive for Ehrlichia canis. DNA from Ehrlichia chaffeensis or Ehrlichia ewingii was not detected in any sample using species-specific primers in separated reactions. Leukocytes from five PCR-positive dogs were inoculated into DH82 cells; successful isolation of E. canis was obtained in four samples. Partial sequence of the dsb gene of eight canine blood samples (including the five samples for in vitro isolation) was obtained by PCR and their analyses through BLAST showed 100% of identity with the corresponding sequence of E. canis in GenBank. This study represents the first molecular diagnosis, isolation, and molecular characterization of E. canis in dogs from Costa Rica. (C) 2010 Elsevier Ltd. All rights reserved.