Semi-classical spectrum of the Homogeneous sine-Gordon theories

The semi-classical spectrum of the Homogeneous sine-Gordon theories associated with an arbitrary compact simple Lie group G is obtained and shown to be entirely given by solitons. These theories describe quantum integrable massive perturbations of Gepner's G-parafermions whose classical equations-of-motion are non-abelian affine Toda equations. One-soliton solutions are constructed by embeddings of the SU(2) complex sine-Gordon soliton in the regular SU(2) subgroups of G. The resulting spectrum exhibits both stable and unstable particles, which is a peculiar feature shared with the spectrum of monopoles and dyons in N=2 and N=4 supersymmetric gauge theories.Comment: 28 pages, plain TeX, no figure

Vertex Operator Superalgebras and Odd Trace Functions

We begin by reviewing Zhu's theorem on modular invariance of trace functions associated to a vertex operator algebra, as well as a generalisation by the author to vertex operator superalgebras. This generalisation involves objects that we call `odd trace functions'. We examine the case of the N=1 superconformal algebra. In particular we compute an odd trace function in two different ways, and thereby obtain a new representation theoretic interpretation of a well known classical identity due to Jacobi concerning the Dedekind eta function.Comment: 13 pages, 0 figures. To appear in Conference Proceedings `Advances in Lie Superalgebras

On classical finite and affine W-algebras

This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.Comment: 12 page

Extensions of the matrix Gelfand-Dickey hierarchy from generalized Drinfeld-Sokolov reduction

The $p\times p$ matrix version of the $r$-KdV hierarchy has been recently treated as the reduced system arising in a Drinfeld-Sokolov type Hamiltonian symmetry reduction applied to a Poisson submanifold in the dual of the Lie algebra $\widehat{gl}_{pr}\otimes {\Complex}[\lambda, \lambda^{-1}]$. Here a series of extensions of this matrix Gelfand-Dickey system is derived by means of a generalized Drinfeld-Sokolov reduction defined for the Lie algebra $\widehat{gl}_{pr+s}\otimes {\Complex}[\lambda,\lambda^{-1}]$ using the natural embedding $gl_{pr}\subset gl_{pr+s}$ for $s$ any positive integer. The hierarchies obtained admit a description in terms of a $p\times p$ matrix pseudo-differential operator comprising an $r$-KdV type positive part and a non-trivial negative part. This system has been investigated previously in the $p=1$ case as a constrained KP system. In this paper the previous results are considerably extended and a systematic study is presented on the basis of the Drinfeld-Sokolov approach that has the advantage that it leads to local Poisson brackets and makes clear the conformal ($\cal W$-algebra) structures related to the KdV type hierarchies. Discrete reductions and modified versions of the extended $r$-KdV hierarchies are also discussed.Comment: 60 pages, plain TE

On Z-graded loop Lie algebras, loop groups, and Toda equations

Toda equations associated with twisted loop groups are considered. Such equations are specified by Z-gradations of the corresponding twisted loop Lie algebras. The classification of Toda equations related to twisted loop Lie algebras with integrable Z-gradations is discussed.Comment: 24 pages, talk given at the Workshop "Classical and Quantum Integrable Systems" (Dubna, January, 2007

Reciclado de escorias de fondo de central térmica para su uso como áridos en la elaboración de componentes prefabricados de hormigón

The need to eliminate waste generates costs. When considering the preservation of the environment, the minimization of the consumption of natural resources and energy savings criteria, the need and advisability of studying the feasibility of waste re-use seems clear. However, waste re-use depends on whether they are economically competitive. Therefore, the aim of this study is to evaluate the possible use of slag from a steam power station as aggregate in the manufacture of concrete. This study included the determination of the physical, chemical and thermal properties of the material, comparing the results to those required by the Spanish structural concrete code (EHE) in determining their acceptance or rejection as a concrete component. The ultimate aim of the research was to determine the highest slag content that could be added to concrete without modifying its strength or durability, with a view to obtaining savings in the manufacture of precast structures.La necesidad de eliminar residuos genera gastos. Considerando criterios de conservación ambiental, minimización del consumo de recursos naturales y ahorro de energía parece claro la necesidad y conveniencia de estudiar la viabilidad del uso de residuos. Sin embargo la utilización de residuos depende de que sean competitivos económicamente. Por tanto el propósito de esta investigación es evaluar el posible uso de las escorias de fondo de una central térmica como áridos para la fabricación de hormigón. En este estudio se incluye la determinación de características físicas, químicas y térmicas y se han comparado los resultados a los requeridos por la EHE para determinar su aceptación o rechazo como componente de un hormigón. El objetivo final de la investigación responde a la utilización de hormigón con el máximo contenido en escorias sin modificar las condiciones de resistencia y durabilidad, consiguiendo un ahorro económico en la fabricación de estructuras prefabricadas

Identification of emerging hazards in mussels by the Galician Emerging Food Safety Risks Network (RISEGAL). A first approach

Emerging risk identification is a priority for the European Food Safety Authority (EFSA). The goal of the Galician Emerging Food Safety Risks Network (RISEGAL) is the identification of emerging risks in foods produced and commercialized in Galicia (northwest Spain) in order to propose prevention plans and mitigation strategies. In this work, RISEGAL applied a systematic approach for the identification of emerging food safety risks potentially affecting bivalve shellfish. First, a comprehensive review of scientific databases was carried out to identify hazards most quoted as emerging in bivalves in the period 2016–2018. Then, identified hazards were semiquantitatively assessed by a panel of food safety experts, who scored them accordingly with the five evaluation criteria proposed by EFSA: novelty, soundness, imminence, scale, and severity. Scores determined that perfluorinated compounds, antimicrobial resistance, Vibrio parahaemolyticus, hepatitis E virus (HEV), and antimicrobial residues are the emerging hazards that are considered most imminent and severe and that could cause safety problems of the highest scale in the bivalve value chain by the majority of the experts consulted (75%). Finally, in a preliminary way, an exploratory study carried out in the Galician Rías highlighted the presence of HEV in mussels cultivated in class B production areas.info:eu-repo/semantics/publishedVersio

Regular Conjugacy Classes in the Weyl Group and Integrable Hierarchies

Generalized KdV hierarchies associated by Drinfeld-Sokolov reduction to grade one regular semisimple elements from non-equivalent Heisenberg subalgebras of a loop algebra \G\otimes{\bf C}[\lambda,\lambda^{-1}] are studied. The graded Heisenberg subalgebras containing such elements are labelled by the regular conjugacy classes in the Weyl group {\bf W}(\G) of the simple Lie algebra \G. A representative w\in {\bf W}(\G) of a regular conjugacy class can be lifted to an inner automorphism of \G given by $\hat w=\exp\left(2i\pi {\rm ad I_0}/m\right)$, where $I_0$ is the defining vector of an $sl_2$ subalgebra of \G.The grading is then defined by the operator $d_{m,I_0}=m\lambda {d\over d\lambda} + {\rm ad} I_0$ and any grade one regular element $\Lambda$ from the Heisenberg subalgebra associated to $[w]$ takes the form $\Lambda = (C_+ +\lambda C_-)$, where $[I_0, C_-]=-(m-1) C_-$ and $C_+$ is included in an $sl_2$ subalgebra containing $I_0$. The largest eigenvalue of ${\rm ad}I_0$ is $(m-1)$ except for some cases in $F_4$, $E_{6,7,8}$. We explain how these Lie algebraic results follow from known results and apply them to construct integrable systems.If the largest ${\rm ad} I_0$ eigenvalue is $(m-1)$, then using any grade one regular element from the Heisenberg subalgebra associated to $[w]$ we can construct a KdV system possessing the standard \W-algebra defined by $I_0$ as its second Poisson bracket algebra. For \G a classical Lie algebra, we derive pseudo-differential Lax operators for those non-principal KdV systems that can be obtained as discrete reductions of KdV systems related to $gl_n$. Non-abelian Toda systems are also considered.Comment: 44 pages, ENSLAPP-L-493/94, substantial revision, SWAT-95-77. (use OLATEX (preferred) or LATEX