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.

Symmetric periodic orbits near heteroclinic loops at infinity for a class of polynomial vector fields

For polynomial vector fields in R3, in general, it is very difficult to detect the existence of an open set of periodic orbits in their phase portraits. Here, we characterize a class of polynomial vector fields of arbitrary even degree having an open set of periodic orbits. The main two tools for proving this result are, first, the existence in the phase portrait of a symmetry with respect to a plane and, second, the existence of two symmetric heteroclinic loops.

Dextramers: new generation of fluorescent MHC class I/peptide multimers for visualization of antigen-specific CD8+ T cells.

Direct identification as well as isolation of antigen-specific T cells became possible since the development of "tetramers" based on avidin-fluorochrome conjugates associated with mono-biotinylated class I MHC-peptide monomeric complexes. In principle, a series of distinct class I MHC-peptide tetramers, each labelled with a different fluorochrome, would allow to simultaneously enumerate as many unique antigen-specific CD8(+) T cells. Practically, however, only phycoerythrin and allophycocyanin conjugated tetramers have been generally available, imposing serious constraints for multiple labeling. To overcome this limitation, we have developed dextramers which are multimers based on a dextran backbone bearing multiple fluorescein and streptavidin moieties. Here we demonstrate the functionality and optimization of these new probes on human CD8(+) T cell clones with four independent antigen specificities. Their applications to the analysis of relatively low frequency antigen-specific T cells in peripheral blood, as well as their use in fluorescence microscopy, are demonstrated. The data show that dextramers produce a stronger signal than their fluoresceinated tetramer counterparts. Thus, these could become the reagents of choice as the antigen-specific T cell labeling transitions from basic research to clinical application.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

The role of Cysteine 6.47 in class A GPCRs

Abstract Background: The CWxP motif of transmembrane helix 6 (x: any residue) is highly conserved in class A GPCRs. Within this motif, W6.48 is a big star in the theory of the global “toggle switch” because of its key role in the activation mechanism of GPCRs upon ligand binding. With all footlights focused on W6.48, the reason why the preceding residue, C6.47, is largely conserved is still unknown. The present study is aimed to fill up this lack of knowledge by characterizing the role of C6.47 of the CWxP motif. Results: A complete analysis of available crystal structures has been made alongside with molecular dynamics simulations of model peptides to explore a possible structural role for C6.47. Conclusions: We conclude that C6.47 does not modulate the conformation of the TM6 proline kink and propose that C6.47 participates in the rearrangement of the TM6 and TM7 interface accompanying activation.

The evolution of the thyroid hormone distributor protein transthyretin in the order insectivora, class mammalia.

Thyroid hormones are involved in the regulation of growth and metabolism in all vertebrates. Transthyretin is one of the extracellular proteins with high affinity for thyroid hormones which determine the partitioning of these hormones between extracellular compartments and intracellular lipids. During vertebrate evolution, both the tissue pattern of expression and the structure of the gene for transthyretin underwent characteristic changes. The purpose of this study was to characterize the position of Insectivora in the evolution of transthyretin in eutherians, a subclass of Mammalia. Transthyretin was identified by thyroxine binding and Western analysis in the blood of adult shrews, hedgehogs, and moles. Transthyretin is synthesized in the liver and secreted into the bloodstream, similar to the situation for other adult eutherians, birds, and diprotodont marsupials, but different from that for adult fish, amphibians, reptiles, monotremes, and Australian polyprotodont marsupials. For the characterization of the structure of the gene and the processing of mRNA for transthyretin, cDNA libraries were prepared from RNA from hedgehog and shrew livers, and full-length cDNA clones were isolated and sequenced. Sections of genomic DNA in the regions coding for the splice sites between exons 1 and 2 were synthesized by polymerase chain reaction and sequenced. The location of splicing was deduced from comparison of genomic with cDNA nucleotide sequences. Changes in the nucleotide sequence of the transthyretin gene during evolution are most pronounced in the region coding for the N-terminal region of the protein. Both the derived overall amino sequences and the N-terminal regions of the transthyretins in Insectivora were found to be very similar to those in other eutherians but differed from those found in marsupials, birds, reptiles, amphibians, and fish. Also, the pattern of transthyretin precursor mRNA splicing in Insectivora was more similar to that in other eutherians than to that in marsupials, reptiles, and birds. Thus, in contrast to the marsupials, with a different pattern of transthyretin gene expression in the evolutionarily "older" polyprotodonts compared with the evolutionarily "younger" diprotodonts, no separate lineages of transthyretin evolution could be identified in eutherians. We conclude that transthyretin gene expression in the liver of adult eutherians probably appeared before the branching of the lineages leading to modern eutherian species.