753 research outputs found
Generalized Lenard Chains, Separation of Variables and Superintegrability
We show that the notion of generalized Lenard chains naturally allows
formulation of the theory of multi-separable and superintegrable systems in the
context of bi-Hamiltonian geometry. We prove that the existence of generalized
Lenard chains generated by a Hamiltonian function defined on a four-dimensional
\omega N manifold guarantees the separation of variables. As an application, we
construct such chains for the H\'enon-Heiles systems and for the classical
Smorodinsky-Winternitz systems. New bi-Hamiltonian structures for the Kepler
potential are found.Comment: 14 pages Revte
Multi-Hamiltonian structures for r-matrix systems
For the rational, elliptic and trigonometric r-matrices, we exhibit the links
between three "levels" of Poisson spaces: (a) Some finite-dimensional spaces of
matrix-valued holomorphic functions on the complex line; (b) Spaces of spectral
curves and sheaves supported on them; (c) Symmetric products of a surface. We
have, at each level, a linear space of compatible Poisson structures, and the
maps relating the levels are Poisson. This leads in a natural way to Nijenhuis
coordinates for these spaces. At level (b), there are Hamiltonian systems on
these spaces which are integrable for each Poisson structure in the family, and
which are such that the Lagrangian leaves are the intersections of the
symplective leaves over the Poisson structures in the family. Specific examples
include many of the well-known integrable systems.Comment: 26 pages, Plain Te
Noncoding RNAs in Duchenne and Becker muscular dystrophies: role in pathogenesis and future prognostic and therapeutic perspectives
Noncoding RNAs (ncRNAs), such as miRNAs and long noncoding RNAs, are key regulators of gene expression at the post-transcriptional level and represent promising therapeutic targets and biomarkers for several human diseases, including Duchenne and Becker muscular dystrophies (DMD/BMD). A role for ncRNAs in the pathogenesis of muscular dystrophies has been suggested, even if it is still incompletely understood. Here, we discuss current progress leading towards the clinical utility of ncRNAs for DMD/BMD. Long and short noncoding RNAs are differentially expressed in DMD/BMD and have a mechanism of action via targeting mRNAs. A subset of muscle-enriched miRNAs, the so-called myomiRs (miR-1, miR-133, and miR-206), are increased in the serum of patients with DMD and in dystrophin-defective animal models. Interestingly, myomiRs might be used as biomarkers, given that their levels can be corrected after dystrophin restoration in dystrophic mice. Remarkably, further evidence demonstrates that ncRNAs also play a role in dystrophin expression; thus, their modulations might represent a potential therapeutic strategy with the aim of upregulating the dystrophin protein in combination with other oligonucleotides/gene therapy approaches
A Novel Hierarchy of Integrable Lattices
In the framework of the reduction technique for Poisson-Nijenhuis structures,
we derive a new hierarchy of integrable lattice, whose continuum limit is the
AKNS hierarchy. In contrast with other differential-difference versions of the
AKNS system, our hierarchy is endowed with a canonical Poisson structure and,
moreover, it admits a vector generalisation. We also solve the associated
spectral problem and explicity contruct action-angle variables through the
r-matrix approach.Comment: Latex fil
Engineering Silicon Nanocrystals: Theoretical study of the effect of Codoping with Boron and Phosphorus
We show that the optical and electronic properties of nanocrystalline silicon
can be efficiently tuned using impurity doping. In particular, we give
evidence, by means of ab-initio calculations, that by properly controlling the
doping with either one or two atomic species, a significant modification of
both the absorption and the emission of light can be achieved. We have
considered impurities, either boron or phosphorous (doping) or both (codoping),
located at different substitutional sites of silicon nanocrystals with size
ranging from 1.1 nm to 1.8 nm in diameter. We have found that the codoped
nanocrystals have the lowest impurity formation energies when the two
impurities occupy nearest neighbor sites near the surface. In addition, such
systems present band-edge states localized on the impurities giving rise to a
red-shift of the absorption thresholds with respect to that of undoped
nanocrystals. Our detailed theoretical analysis shows that the creation of an
electron-hole pair due to light absorption determines a geometry distortion
that in turn results in a Stokes shift between adsorption and emission spectra.
In order to give a deeper insight in this effect, in one case we have
calculated the absorption and emission spectra going beyond the single-particle
approach showing the important role played by many-body effects. The entire set
of results we have collected in this work give a strong indication that with
the doping it is possible to tune the optical properties of silicon
nanocrystals.Comment: 14 pages 19 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
Marked pseudoepitheliomatous hyperplasia secondary to a red-pigmented tattoo. a case report
Tattooing is gaining increasing popularity in developed countries in recent years. Adverse cutaneous reactions of many different types against coumponds in tattoo inks are being reported more and more often in medical literature,especially against red-pigmented tattoo. Delayed immune-mediated reactions can manifest in several ways and different histological patterns have been described This article is protected by copyright. All rights reserved
Ophthalmoplegia due to Miller Fisher syndrome in a patient with myasthenia gravis
Here, we describe a 79-year-old man, admitted to our unit for worsening diplopia and fatigue, started a few weeks after an episode of bronchitis and flu vaccination. Past medical history includes myasthenia gravis (MG), well-controlled by Pyridostigmine, Azathioprine, and Prednisone. During the first days, the patient developed progressive ocular movement abnormalities up to complete external ophthalmoplegia, severe limb and gait ataxia, and mild dysarthria. Deep tendon reflexes were absent in lower limbs. Since not all the symptoms were explainable with the previous diagnosis of myasthenia gravis, other etiologies were investigated. Brain MRI and cerebrospinal fluid analysis were normal. Electromyography showed a pattern of predominantly sensory multiple radiculoneuritis. Suspecting Miller Fisher syndrome (MFS), the patient was treated with plasmapheresis with subsequent clinical improvement. Antibodies against GQ1b turned out to be positive. MFS is an immune-mediated neuropathy presenting with ophthalmoplegia, ataxia, and areflexia. Even if only a few cases of MFS overlapping with MG have been described so far, the coexistence of two different autoimmune disorders can occur. It is always important to evaluate possible differential diagnosis even in case of known compatible diseases, especially when some clinical features seem atypical
Dispersionless integrable equations as coisotropic deformations. Extensions and reductions
Interpretation of dispersionless integrable hierarchies as equations of
coisotropic deformations for certain algebras and other algebraic structures
like Jordan triple systInterpretation of dispersionless integrable hierarchies
as equations of coisotropic deformations for certain algebras and other
algebraic structures like Jordan triple systems is discussed. Several
generalizations are considered. Stationary reductions of the dispersionless
integrable equations are shown to be connected with the dynamical systems on
the plane completely integrable on a fixed energy level. ems is discussed.
Several generalizations are considered. Stationary reductions of the
dispersionless integrable equations are shown to be connected with the
dynamical systems on the plane completely integrable on a fixed energy level.Comment: 21 pages, misprints correcte
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
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