The use of micro-XRD for the study of glaze color decorations

The compounds responsible for the colours and decorations in glass and glazed ceramics include: colouring agents (transition metal ions), pigments (micro-and nano-precipitates of compounds that either do not dissolve or recrystallize in the glassy matrix) and opacifiers (microcrystalline compounds with high light scattering capability). Their composition, structure and range of stability are highly dependent not only on the composition but also on the procedures followed to obtain them. Chemical composition of the colorants and crystallites may be obtained by means of SEM-EDX and WDX. Synchrotron Radiation micro-X-ray Diffraction has a small beam size adequate (10 to 50 microns footprint size) to obtain the structural information of crystalline compounds and high brilliance, optimal for determining the crystallites even when present in low amounts. In addition, in glass decorations the crystallites often appear forming thin layers (from 10 to 100 micrometers thick) and they show a depth dependent composition and crystal structure. Their nature and distribution across the glass/glazes decorations gives direct information on the technology of production and stability and may be related to the color and appearance. A selection of glass and glaze coloring agents and decorations are studied by means of SR-micro- XRD and SEM-EDX including: manganese brown, antimony yellow, red copper lusters and cobalt blue. The selection includes Medieval (Islamic, and Hispano Moresque) and renaissance tin glazed ceramics from the 10th to the 17th century AD.

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.

Food Indicators and Their Relationship with 10 to 12 Year-olds' Subjective Well-Being

This study aimed to test subjective indicators designed to analyze the role food plays in children’s lives, explore children’s personal well-being, and evaluate the relationship between these two phenomena. It was conducted on 371 children aged 10 to 12 by means of a selfadministered questionnaire. Results showed a marked interest in food on the part of children, who consider taste and health the most important indicators when it comes to eating. They demonstrated a high level of personal well-being, measured using Cummins & Lau’s adapted version of the Personal Well- Being Index–School Children (PWI-SC) (2005), overall life satisfaction (OLS) and satisfaction with various life domains (friends, family, sports, food and body). Regression models were conducted to explain satisfaction with food, taking as independent variables the interest children have in food, the importance they give to different reasons for eating, scores from the PWI-SC, OLS and satisfaction with various life domains. In the final model, it was found that OLS, health indicators, satisfaction with health from the PWI-SC and satisfaction with your body contribute to explaining satisfaction with food. The results obtained suggest that satisfaction with food is a relevant indicator in the exploration of children’s subjective well-being, calling into question the widespread belief that these aspects are of exclusive interest to adults. They also seem to reinforce the importance of including food indicators in any study aimed at exploring the well-being of the 10 to 12 year-old population.

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.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

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.