14 research outputs found

    Semi-classical spectrum of the Homogeneous sine-Gordon theories

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    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

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    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

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    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

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

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    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

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    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 w^=exp(2iπadI0/m)\hat w=\exp\left(2i\pi {\rm ad I_0}/m\right), where I0I_0 is the defining vector of an sl2sl_2 subalgebra of \G.The grading is then defined by the operator dm,I0=mλddλ+adI0d_{m,I_0}=m\lambda {d\over d\lambda} + {\rm ad} I_0 and any grade one regular element Λ\Lambda from the Heisenberg subalgebra associated to [w][w] takes the form Λ=(C++λC)\Lambda = (C_+ +\lambda C_-), where [I0,C]=(m1)C[I_0, C_-]=-(m-1) C_- and C+C_+ is included in an sl2sl_2 subalgebra containing I0I_0. The largest eigenvalue of adI0{\rm ad}I_0 is (m1)(m-1) except for some cases in F4F_4, E6,7,8E_{6,7,8}. We explain how these Lie algebraic results follow from known results and apply them to construct integrable systems.If the largest adI0{\rm ad} I_0 eigenvalue is (m1)(m-1), then using any grade one regular element from the Heisenberg subalgebra associated to [w][w] we can construct a KdV system possessing the standard \W-algebra defined by I0I_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 glngl_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

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    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)2SU(3)_{2}-homogeneous Sine-Gordon model.Comment: 5 pages Latex, 3 figure

    Impact of Neuroprotection on Incidence of Alzheimer's Disease

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    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
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