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

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

Temporal Lau effect: Noncoherent regeneration of periodic pulse trains

We present an optical method for implementing the temporal Talbot effect with a spectrally incoherent optical source and a linear dispersive medium, at the first-order dispersion regime. We state the condition for achieving this effect, here denoted as the temporal Lau effect

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

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

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

Renormalization group flow with unstable particles

The renormalization group flow of an integrable two dimensional quantum field theory which contains unstable particles is investigated. The analysis is carried out for the Virasoro central charge and the conformal dimensions as a function of the renormalization group flow parameter. This allows to identify the corresponding conformal field theories together with their operator content when the unstable particles vanish from the particle spectrum. The specific model considered is the $SU(3)_{2}$-homogeneous Sine-Gordon model.Comment: 5 pages Latex, 3 figure

Impact of Neuroprotection on Incidence of Alzheimer's Disease

Converging evidence suggests that high levels of education and intellectual activity increase the cognitive reserve and reduce the risk of dementia. However, little is known about the impact that different neuroprotective strategies may have on the incidence of Alzheimer's disease. Using a simple mathematical regression model, it is shown here that age-specific counts of basic cognitive units (surrogate of neurons or synapses) in the normal population can be estimated from Alzheimer's incidence rates. Hence, the model can be used to test the effect of neuroprotection on Alzheimer's incidence. It was found that the number of basic cognitive units decreases with age, but levels off in older people. There were no gender differences after correcting for survival. The model shows that even modest neuroprotective effects on basic cognitive units can lead to dramatic reductions in the number of Alzheimer's cases. Most remarkably, a 5% increase in the cognitive reserve would prevent one third of Alzheimer's cases. These results suggest that public health policies aimed at increasing the cognitive reserve in the general population (e.g., implementing higher levels of education) are likely the most effective strategy for preventing Alzheimer's disease