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.

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.

Do protein–protein interaction databases identify moonlighting proteins?

One of the most striking results of the human (and mammalian) genomes is the low number of protein-coding genes. To-date, the main molecular mechanism to increase the number of different protein isoforms and functions is alternative splicing. However, a less-known way to increase the number of protein functions is the existence of multifunctional, multitask, or ‘‘moonlighting’’, proteins. By and large, moonlighting proteins are experimentally disclosed by serendipity. Proteomics is becoming one of the very active areas of biomedical research, which permits researchers to identify previously unseen connections among proteins and pathways. In principle, protein–protein interaction (PPI) databases should contain information on moonlighting proteins and could provide suggestions to further analysis in order to prove the multifunctionality. As far as we know, nobody has verified whether PPI databases actually disclose moonlighting proteins. In the present work we check whether well-established moonlighting proteins present in PPI databases connect with their known partners and, therefore, a careful inspection of these databases could help to suggest their different functions. The results of our research suggest that PPI databases could be a valuable tool to suggest multifunctionality.

Contribució a l'estudi de la presència de Balmes en l'obra de Verdaguer

A partir d’una recerca exhaustiva dins l’obra de Verdaguer, l’article ressegueix la presència de Balmes en la producció de l’escriptor de Folgueroles. Tot i no ésser irrellevant, es constata que el reflex de l’obra balmesiana en la verdagueriana és menor del que, en principi, caldria suposar en un membre tan destacat de la Renaixença vigatana, un moviment que va sentir pel pensador de Vic una pregona admiració. De fet, només dos poemes de l’extensa producció de Verdaguer són dedicats a Balmes, per bé que un altre, molt ideològic, en mostra una influència evident.

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 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 periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

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.

La puesta en práctica de la interseccionalidad política: el caso de las políticas LGTB en Cataluña

En el marco de la discusión académica está emergiendo con fuerza la necesidad de abordar la interacción entre distintas desigualdades en el diseño e implementación de políticas públicas, siendo el enfoque interseccional una propuesta teórica muy interesante. Se detecta, sin embargo, que hacen falta más análisis empíricos que permitan dar cuenta de los avances y obstáculos con que se encuentran las políticas públicas para implementar la interseccionalidad entre diversas desigualdades. En este artículo analizamos las recientes políticas de igualdad LGTB, centrándonos en el caso catalán, para ver cómo adoptan la relación entre desigualdades, y detectar cuáles son los factores clave que interfieren en la implementación de un modelo interseccional.

Carnatic music: Svara, Gamaka, Motif and Raga identity

Over the last century in Karnatik music, the method ofunderstanding raga has been to break it down into its variouscomponents, svara, scale, gamaka, and phrases. In this paper, an attempt is made to define the abstract concept of raga in its entirety within the aesthetics of Karnatik music considering the various components and their symbiotic relationship. This paper also attempts to prove that theidentity of a raga exists as a whole. Section 2 explains theconcept of a fundamental musical note or svara. Section 3 illustrates the concept of gamaka or inflections. Section 4 delves into the concept of raga in detail and then flows into Section 5 which enunciates the identity of a raga in terms of svara, gamaka, and phraseology. The paper concludes in Section 6, and Section 7 gives the references.

Hormonal control of spermatogenesis in men: therapeutic aspects in hypogonadotropic hypogonadism.

During the first two trimesters of intrauterine life, fetal sex steroid production is driven by maternal human chorionic gonadotropin (hCG). The HPG axis is activated around the third trimester and remains active for the first 6-months of neonatal life. This so-called mini-puberty is a developmental window that has profound effects on future potential for fertility. In early puberty, GnRH secretion is reactivated first at night and then night and day. Pulsatile GnRH stimulates both LH and FSH, which induce maturation of the seminiferous tubules and Leydig cells. Congenital hypogonadotropic hypogonadism (CHH) results from GnRH deficiency. Men with CHH lack the mini-pubertal and pubertal periods of Sertoli Cell proliferation and thus present with prepubertal testes (<4mL) and low inhibin serum levels --reflecting diminished SC numbers. To induce full maturation of the testes, GnRH-deficient patients can be treated with either pulsatile GnRH, hCG or combined gonadotropin therapy (FSH+hCG). Fertility outcomes with each of these regimens are highly variable. Recently, a randomized, open label treatment study (n=13) addressed the question of whether a sequential treatment with FSH alone prior to LH and FSH (via GnRH pump) could enhance fertility outcomes. All men receiving the sequential treatment developed sperm in the ejaculate, whereas 2/6 men in the other group remained azoospermic. A large, multicenter clinical trial is needed to definitively prove the optimal treatment approach for severe CHH.

Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.