Search results for "Mathematics::Symplectic Geometry"
showing 10 items of 184 documents
Current status of the torus palatinus and torus mandibularis
2007
While there is a hereditary component to tori, this does not explain all cases. Tori tend to appear more frequently during middle age of life; the torus palatinus is more commonly observed in females, but this is not the case with the torus mandibularis. Certain ethnic groups are more prone to one torus or the other. The torus is mainly removed due to prostodontic reasons, as it may also be used as biomaterial, not only in periodontology, but also in implantology. The aim of this study was a review of the literature from the past twenty years. Sin financiación 1.071 JCR (2010) Q3, 52/77 Dentistry, oral surgery & medicine UEM
Strong enhancement of the Breit-Wigner-Fano Raman line in carbon nanotube bundles caused by plasmon band formation
2002
We investigate the origin of the Breit-Wigner-Fano line in the Raman spectra of individual single-walled carbon nanotubes and their bundles. Using confocal Raman microscopy and atomic-force microscopy we found that the Breit-Wigner-Fano line intensity increases strongly with the bundle thickness. We confirmed this result by Raman investigations of partially decomposed bundles, which were additionally investigated by transmission electron microscopy. Our random-phase approximation based theory, which identifies the Breit-Wigner-Fano line as an excited band of plasmon-phonon modes, is fully consistent with the experimental results.
Strange attractor for the renormalization flow for invariant tori of Hamiltonian systems with two generic frequencies
1999
We analyze the stability of invariant tori for Hamiltonian systems with two degrees of freedom by constructing a transformation that combines Kolmogorov-Arnold-Moser theory and renormalization-group techniques. This transformation is based on the continued fraction expansion of the frequency of the torus. We apply this transformation numerically for arbitrary frequencies that contain bounded entries in the continued fraction expansion. We give a global picture of renormalization flow for the stability of invariant tori, and we show that the properties of critical (and near critical) tori can be obtained by analyzing renormalization dynamics around a single hyperbolic strange attractor. We c…
Enumerative aspects of the Gross-Siebert program
2014
We present enumerative aspects of the Gross-Siebert program in this introductory survey. After sketching the program's main themes and goals, we review the basic definitions and results of logarithmic and tropical geometry. We give examples and a proof for counting algebraic curves via tropical curves. To illustrate an application of tropical geometry and the Gross-Siebert program to mirror symmetry, we discuss the mirror symmetry of the projective plane.
Symmetric locally free resolutions and rationality problems
2022
We show that the birationality class of a quadric surface bundle over $\mathbb{P}^2$ is determined by its associated cokernel sheaves. As an application, we discuss stable-rationality of very general quadric bundles over $\mathbb{P}^2$ with discriminant curves of fixed degree. In particular, we construct explicit models of these bundles for some discriminant data. Among others, we obtain various birational models of a nodal Gushel-Mukai fourfold, as well as of a cubic fourfold containing a plane. Finally, we prove stable irrationality of several types of quadric surface bundles.
Toric G-solid Fano threefolds
2020
We study toric G-solid Fano threefolds that have at most terminal singularities, where G is an algebraic subgroup of the normalizer of a maximal torus in their automorphism groups.
Semianalyticity of isoperimetric profiles
2009
It is shown that, in dimensions $<8$, isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic.
Diffeomorphism classes of Calabi-Yau varieties
2016
In this article we investigate diffeomorphism classes of Calabi-Yau threefolds. In particular, we focus on those embedded in toric Fano manifolds. Along the way, we give various examples and conclude with a curious remark regarding mirror symmetry.
Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed
2015
We prove that the bihamiltonian cohomology of a semisimple pencil of Poisson brackets of hydrodynamic type vanishes for almost all degrees. This implies the existence of a full dispersive deformation of a semisimple bihamiltonian structure of hydrodynamic type starting from any infinitesimal deformation.
Supermanifolds, symplectic geometry and curvature
2015
We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.