Rank one discrete valuations of power series fields

In this paper we study the rank one discrete valuations of the field $k((X_1,..., X_n))$ whose center in k\lcor\X\rcor is the maximal ideal. In sections 2 to 6 we give a construction of a system of parametric equations describing such valuations. This amounts to finding a parameter and a field of coefficients. We devote section 2 to finding an element of value 1, that is, a parameter. The field of coefficients is the residue field of the valuation, and it is given in section 5. The constructions given in these sections are not effective in the general case, because we need either to use the Zorn's lemma or to know explicitly a section $\sigma$ of the natural homomorphism R_v\to\d between the ring and the residue field of the valuation $v$. However, as a consequence of this construction, in section 7, we prove that k((\X)) can be embedded into a field L((\Y)), where $L$ is an algebraic extension of $k$ and the {\em ``extended valuation'' is as close as possible to the usual order function}

Memory effect in triglycine sulfate induced by a transverse electric field: specific heat measurement

The influence of a transverse electric field in the specific heat of triglycine sulphate (TGS) has been studied. The specific heat of TGS has been measured heating the sample from ferroelectric to paraelectric phase after prolonged transverse electric field (i.e. perpendicular to the ferroelectric axis). It is shown that the specific heat of TGS can remember the temperature $T_s$ at which the transverse field was previously applied.Comment: ReVTeX4 Twocolumn 4 pages, 4 figure

Key polynomials for simple extensions of valued fields

Let $\iota:K\hookrightarrow L\cong K(x)$ be a simple transcendental extension of valued fields, where $K$ is equipped with a valuation $\nu$ of rank 1. That is, we assume given a rank 1 valuation $\nu$ of $K$ and its extension $\nu'$ to $L$. Let $(R_\nu,M_\nu,k_\nu)$ denote the valuation ring of $\nu$. The purpose of this paper is to present a refined version of MacLane's theory of key polynomials, similar to those considered by M. Vaqui\'e, and reminiscent of related objects studied by Abhyankar and Moh (approximate roots) and T.C. Kuo. Namely, we associate to $\iota$ a countable well ordered set $$\mathbf{Q}=\{Q_i\}_{i\in\Lambda}\subset K[x];$$ the $Q_i$ are called {\bf key polynomials}. Key polynomials $Q_i$ which have no immediate predecessor are called {\bf limit key polynomials}. Let $\beta_i=\nu'(Q_i)$. We give an explicit description of the limit key polynomials (which may be viewed as a generalization of the Artin--Schreier polynomials). We also give an upper bound on the order type of the set of key polynomials. Namely, we show that if $\operatorname{char}\ k_\nu=0$ then the set of key polynomials has order type at most $\omega$, while in the case $\operatorname{char}\ k_\nu=p>0$ this order type is bounded above by $\omega\times\omega$, where $\omega$ stands for the first infinite ordinal.Comment: arXiv admin note: substantial text overlap with arXiv:math/060519

Pushing the limits of concertedness. A waltz of wandering carbocations.

Among the array of complex terpene-forming carbocation cyclization/rearrangement reactions, the so-called "triple shift" reactions are among the most unexpected. Such reactions involve the asynchronous combination of three 1,n-shifts into a concerted process, e.g., a 1,2-alkyl shift followed by a 1,3-hydride shift followed by a second 1,2-alkyl shift. This type of reaction so far has been proposed to occur during the biosynthesis of diterpenes and the sidechains of sterols. Here we describe efforts to push the limits of concertedness in this type of carbocation reaction by designing, and characterizing with quantum chemical computations, systems that could couple additional 1,n-shift events to a triple shift leading, in principle to quadruple, pentuple, etc. shifts. While our designs did not lead to clear-cut examples of quadruple, etc. shifts, they did lead to reactions with surprisingly flat energy surfaces where more than five chemical events connect reactants and plausible products. Ab initio molecular dynamics simulations demonstrate that the formal minima on these surfaces interchange on short timescales, both with each other and with additional unexpected structures, allowing us a glimpse into a very complex manifold that allows ready access to great structural diversity

El hastial sur de la catedral de León: patología existente derivada de la utilización de azufre en el retacado de grapas y tochos en las obras de restauración realizadas en el siglo XIX

During the restorations carried out in the nineteenth century in the cathedral of Leon, the architect-restorers Juan de Madrazo and Demetrio de los Rios proposed in their projects the use of liquid sulphur to caulk iron or bronze staples, or billets that linked edge elements and solids from the masonry. This solution, not previously used, has produced important construction pathology in the south gable today: cracks in a large number of blocks and partial detachment of them. Some of these detachments have been falling to the court of the temple with the risk to cause harm to people and things. It is worth to point out that this unpublished work has a great importance because, according to the content of the projects of both architects, this practice spread to more parts of the monument, so this localized pathology is expected to manifest itself in other areas with the consequent risk.Durante las restauraciones efectuadas en el siglo xix en la catedral de León, los arquitectos restauradores Juan de Madrazo y Demetrio de los Ríos propusieron en sus proyectos el empleo de azufre líquido para retacar los tochos y engrapados de hierro o bronce que enlazaban los elementos de remate y los sólidos de las fábricas. Esta solución, no utilizada con anterioridad, ha dado lugar a la aparición hoy en día de una importante patología en el hastial sur: la fractura de un gran número de sillares y el desprendimiento parcial de éstos, cayendo al atrio del templo con el consecuente peligro. Este trabajo es una contribución inédita que reviste gran importancia porque, según el contenido de los proyectos de ambos arquitectos, esta práctica se extendió a más partes del monumento, por lo que esta patología localizada es previsible que se manifieste en otras zonas del mismo con el consecuente riesgo

Good practice in mental health care for socially marginalised groups in Europe: a qualitative study of expert views in 14 countries

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited