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.

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.

El proyecto ‘Ecosportech’ como ejemplo de universidad emprendedora. Una experiencia a base del ‘Problem Based Learning’

El objetivo de este artículo es presentar el proyecto EcoSPORTech, cuya finalidad es la creación de una empresa social con jóvenes para la realización de actividades deportivas/ocio en el medio natural, integrando las nuevas tecnologías. Este proyecto supone una colaboración interdisciplinaria dentro de la Universidad de Vic, entre las facultades de Empresa y Comunicación (FEC), la de Ciencias de la Salud y el Bienestar (FCSB) y la de Educación (FE) e integra un equipo de profesionales procedentes de los ámbitos de la empresa, el marketing, el periodismo, el deporte y la terapia ocupacional. Estos profesores formarán al grupo de jóvenes con los que se creará la empresa y dirigirán la misma. Esta empresa (cooperativa) se integra en el vivero de empresas sociales que se está creando en la Universidad de Vic.

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.

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.

Learning about Bayesian networks for forensic interpretation : An example based on the "the problem of multiple propositions"

Both, Bayesian networks and probabilistic evaluation are gaining more and more widespread use within many professional branches, including forensic science. Notwithstanding, they constitute subtle topics with definitional details that require careful study. While many sophisticated developments of probabilistic approaches to evaluation of forensic findings may readily be found in published literature, there remains a gap with respect to writings that focus on foundational aspects and on how these may be acquired by interested scientists new to these topics. This paper takes this as a starting point to report on the learning about Bayesian networks for likelihood ratio based, probabilistic inference procedures in a class of master students in forensic science. The presentation uses an example that relies on a casework scenario drawn from published literature, involving a questioned signature. A complicating aspect of that case study - proposed to students in a teaching scenario - is due to the need of considering multiple competing propositions, which is an outset that may not readily be approached within a likelihood ratio based framework without drawing attention to some additional technical details. Using generic Bayesian networks fragments from existing literature on the topic, course participants were able to track the probabilistic underpinnings of the proposed scenario correctly both in terms of likelihood ratios and of posterior probabilities. In addition, further study of the example by students allowed them to derive an alternative Bayesian network structure with a computational output that is equivalent to existing probabilistic solutions. This practical experience underlines the potential of Bayesian networks to support and clarify foundational principles of probabilistic procedures for forensic evaluation.

Use of phycoerythrin and allophycocyanin for fluorescence resonance energy transfer analyzed by flow cytometry: advantages and limitations.

BACKGROUND: This study validates the use of phycoerythrin (PE) and allophycocyanin (APC) for fluorescence energy transfer (FRET) analyzed by flow cytometry. METHODS: FRET was detected when a pair of antibody conjugates directed against two noncompetitive epitopes on the same CD8alpha chain was used. FRET was also detected between antibody conjugate pairs specific for the two chains of the heterodimeric alpha (4)beta(1) integrin. Similarly, the association of T-cell receptor (TCR) with a soluble antigen ligand was detected by FRET when anti-TCR antibody and MHC class I/peptide complexes (<<tetramers>>) were used. RESULTS: FRET efficiency was always less than 10%, probably because of steric effects associated with the size and structure of PE and APC. Some suggestions are given to take into account this and other effects (e.g., donor and acceptor concentrations) for a better interpretation of FRET results obtained with this pair of fluorochromes. CONCLUSIONS: We conclude that FRET assays can be carried out easily with commercially available antibodies and flow cytometers to study arrays of multimolecular complexes.

A genomic island present along the bacterial chromosome of the Parachlamydiaceae UWE25, an obligate amoebal endosymbiont, encodes a potentially functional F-like conjugative DNA transfer system.

BACKGROUND: The genome of Protochlamydia amoebophila UWE25, a Parachlamydia-related endosymbiont of free-living amoebae, was recently published, providing the opportunity to search for genomic islands (GIs). RESULTS: On the residual cumulative G+C content curve, a G+C-rich 19-kb region was observed. This sequence is part of a 100-kb chromosome region, containing 100 highly co-oriented ORFs, flanked by two 17-bp direct repeats. Two identical gly-tRNA genes in tandem are present at the proximal end of this genetic element. Several mobility genes encoding transposases and bacteriophage-related proteins are located within this chromosome region. Thus, this region largely fulfills the criteria of GIs. The G+C content analysis shows that several modules compose this GI. Surprisingly, one of them encodes all genes essential for F-like conjugative DNA transfer (traF, traG, traH, traN, traU, traW, and trbC), involved in sex pilus retraction and mating pair stabilization, strongly suggesting that, similarly to the other F-like operons, the parachlamydial tra unit is devoted to DNA transfer. A close relatedness of this tra unit to F-like tra operons involved in conjugative transfer is confirmed by phylogenetic analyses performed on concatenated genes and gene order conservation. These analyses and that of gly-tRNA distribution in 140 GIs suggest a proteobacterial origin of the parachlamydial tra unit. CONCLUSIONS: A GI of the UWE25 chromosome encodes a potentially functional F-like DNA conjugative system. This is the first hint of a putative conjugative system in chlamydiae. Conjugation most probably occurs within free-living amoebae, that may contain hundreds of Parachlamydia bacteria tightly packed in vacuoles. Such a conjugative system might be involved in DNA transfer between internalized bacteria. Since this system is absent from the sequenced genomes of Chlamydiaceae, we hypothesize that it was acquired after the divergence between Parachlamydiaceae and Chlamydiaceae, when the Parachlamydia-related symbiont was an intracellular bacteria. It suggests that this heterologous DNA was acquired from a phylogenetically-distant bacteria sharing an amoebal vacuole. Since Parachlamydiaceae are emerging agents of pneumonia, this GI might be involved in pathogenicity. In future, conjugative systems might be developed as genetic tools for Chlamydiales.

Precast Concrete Panel Thickness for Epoxy-Coated Prestressing Strands, Volume 2, HR-353, 1994

This final report for Phase 1 of the research on epoxy-coated, prestressing strands in precast prestressed concrete (PC) panels has been published in two volumes. Volume 1--Technical Report contains the problem description, literature review, and survey results; descriptions of the test specimens, experimental tests, and analytical models; discussions of the analytical and experimental results; summary, conclusions, and recommendations; list of references; and acknowledgments. Volume 2--Supplemental Report contains additional information in the form of appendix material for Volume 1 on the questionnaires, strand forces, geometry of the specimens, concrete crack patterns that formed in the strand transfer length and strand development length specimens, concrete strains in the strand transfer length specimens, and load-point deflections and strand-slip measurements for the strand development length specimens. Appendix A contains the questionnaires that were sent to the design agencies and precast concrete producers. A summary of the results to the questions on the surveys are given as the number of respondents who provided the same answers and as paraphrased comments from the respondents. Appendix B contains graphs of strand force versus time, strand force versus temperature, and strand force versus strand cutting sequence for the concrete castings. Appendix C contains figures that show the location of each specimen in the prestress bed, the geometrical configurations for the strand transfer length (T-type) specimens and strand development length (D-type) specimens, and the concrete cracks that developed in some of the T-type specimens when they were prestressed. Appendix D contains figures that show the concrete cracks that developed in the D-type specimens during the strand development length tests. For each of these tests, the sequence of the failure for the specimen is specified. Appendix E contains graphs of concrete strain versus distance from the end of the T-type specimens that were instrumented with internal embedment strain gages. Appendix F contains graphs of load versus load-point deflection and load versus strand-slip for the strand development length tests of the D-type specimens.