Search results for "Geometric"
showing 10 items of 652 documents
Real quadrics in C n , complex manifolds and convex polytopes
2006
In this paper, we investigate the topology of a class of non-Kähler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics Cn which are invariant with respect to the natural action of the real torus (S1)n onto Cn. The quotient space is a simple convex polytope. The problem reduces thus to the study of the topology of certain real algebraic sets and can be handled using combinatorial results on convex polytopes. We prove that the homology groups of these compact complex manifolds can have arbitrary amount of torsion so that their topology is extremely rich. We also resolve an associated wall-cros…
Tailoring a pair of pants
2021
Abstract We show how to deform the map Log : ( C ⁎ ) n → R n such that the image of the complex pair of pants P ∘ ⊂ ( C ⁎ ) n is the tropical hyperplane by showing an (ambient) isotopy between P ∘ ⊂ ( C ⁎ ) n and a natural polyhedral subcomplex of the product of the two skeleta S × Σ ⊂ A × C of the amoeba A and the coamoeba C of P ∘ . This lays the groundwork for having the discriminant to be of codimension 2 in topological Strominger-Yau-Zaslow torus fibrations.
Mappings of Finite Distortion : Compactness of the Branch Set
2017
We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire, continuous, open and discrete mapping of finite distortion which is piecewise smooth, has a branch set homeomorphic to an (n - 2)-dimensional torus and distortion arbitrarily close to the asymptotic bound. Peer reviewed
Geometric inequivalence of metric and Palatini formulations of General Relativity
2020
Projective invariance is a symmetry of the Palatini version of General Relativity which is not present in the metric formulation. The fact that the Riemann tensor changes nontrivially under projective transformations implies that, unlike in the usual metric approach, in the Palatini formulation this tensor is subject to a gauge freedom, which allows some ambiguities even in its scalar contractions. In this sense, we show that for the Schwarzschild solution there exists a projective gauge in which the (affine) Kretschmann scalar, K≡R R , can be set to vanish everywhere. This puts forward that the divergence of curvature scalars may, in some cases, be avoided by a gauge transformation of the …
Irregular motion recovery in fluorescein angiograms
1997
Abstract Fluorescein angiography is a common procedure in ophthalmic practice, mainly to evaluate vascular retinopathies and choroidopathies from sequences of ocular fundus images. In order to compare the images, a reliable overlying is essential. This paper proposes some methods for the recovery of irregular motion in fluorescein angiograms (FA). The overlying is done by a three step procedure: detection of relevant points, matching points from different images and estimation of the assumed linear geometric transformation. A stochastic model (closely related to the general linear model) allows to fuse the second and third steps. Two different estimators of the geometric transformation are …
Design of the CGAL 3D Spherical Kernel and application to arrangements of circles on a sphere
2009
AbstractThis paper presents a cgal kernel for algorithms manipulating 3D spheres, circles, and circular arcs. The paper makes three contributions. First, the mathematics underlying two non-trivial predicates are presented. Second, the design of the kernel concept is developed, and the connexion between the mathematics and this design is established. In particular, we show how two different frameworks can be combined: one for the general setting, and one dedicated to the case where all the objects handled lie on a reference sphere. Finally, an assessment about the efficacy of the 3D Spherical Kernel is made through the calculation of the exact arrangement of circles on a sphere. On average w…
Recovery of time-dependent coefficients from boundary data for hyperbolic equations
2019
We study uniqueness of the recovery of a time-dependent magnetic vector-valued potential and an electric scalar-valued potential on a Riemannian manifold from the knowledge of the Dirichlet to Neumann map of a hyperbolic equation. The Cauchy data is observed on time-like parts of the space-time boundary and uniqueness is proved up to the natural gauge for the problem. The proof is based on Gaussian beams and inversion of the light ray transform on Lorentzian manifolds under the assumptions that the Lorentzian manifold is a product of a Riemannian manifold with a time interval and that the geodesic ray transform is invertible on the Riemannian manifold.
GAPP Compiler for Hardware Accelerated Geometric Algebra Computing
2016
Because of the high numeric complexity of Geometric Algebra, its use in engineering applications relies heavily on tools for ecient implementations. In this article, we introduce a new quality of Geometric Algebra Computing solutions based on a new compiler for Geometric Algebra Parallelism Programs (GAPP). These programs are already optimized in a sense that only the really needed computations are left. The GAPP compiler is able to generate two output formats leading to advanced hardware accelerated Geometric Algebra Computing. On one hand, there is the direct generation of HSAIL code, in order to more eciently support the solutions of the broad range of heterogeneous computing architectur…
HETEROGENEITY IN RISK PREFERENCES LEADS TO STOCHASTIC VOLATILITY
2018
This paper studies the price processes of a claim on terminal endowment and of a claim on firm book value when the underlying variables follow a bivariate geometric Brownian motion. If the state-price process is multiplicatively separable into time and endowment functions, our main result shows that firm (endowment) price volatility is stochastic (state-dependent) if, and only if, the endowment function is not a power function. In a pure exchange economy populated by two agents with constant relative risk aversion (CRRA) preferences we confirm the separability, and we show furthermore that firm (endowment) price volatility is stochastic (state-dependent) if, and only if, both agents are he…
Solving stochastic differential equations on Homeo(S1)
2004
Abstract The Brownian motion with respect to the metric H 3/2 on Diff( S 1 ) has been constructed. It is realized on the group of homeomorphisms Homeo( S 1 ). In this work, we shall resolve the stochastic differential equations on Homeo( S 1 ) for a given drift Z .