Search results for "Geometry"
showing 10 items of 4487 documents
The case of equality in the dichotomy of Mohammadi-Oh
2017
If $n \geq 3$ and $\Gamma$ is a convex-cocompact Zariski-dense discrete subgroup of $\mathbf{SO}^o(1,n+1)$ such that $\delta_\Gamma=n-m$ where $m$ is an integer, $1 \leq m \leq n-1$, we show that for any $m$-dimensional subgroup $U$ in the horospheric group $N$, the Burger-Roblin measure associated to $\Gamma$ on the quotient of the frame bundle is $U$-recurrent.
A Survey of Some Arithmetic Applications of Ergodic Theory in Negative Curvature
2017
This paper is a survey of some arithmetic applications of techniques in the geometry and ergodic theory of negatively curved Riemannian manifolds, focusing on the joint works of the authors. We describe Diophantine approximation results of real numbers by quadratic irrational ones, and we discuss various results on the equidistribution in \(\mathbb{R}\), \(\mathbb{C}\) and in the Heisenberg groups of arithmetically defined points. We explain how these results are consequences of equidistribution and counting properties of common perpendiculars between locally convex subsets in negatively curved orbifolds, proven using dynamical and ergodic properties of their geodesic flows. This exposition…
Surface canal, squelette et espace des sphères
2016
A canal surface is the envelope of a one-parameter familly of oriented spheres. With the knowledge of center an radius functions associated to it, it is easy to compute a parametrisation of the surface. In this article, we study the inverse operation, which is the search for the spheres in the canal surface. By selecting a point on the boundary and using the sphere space, we estimate the maximal sphere tangent with this point and a second point on the boundary. Furthermore, we estimate a second sphere, which allows to build the characteiristic circle of the canal surface. So this article consists in a new approach of the skeletonization of an object. Indeed, a skeleton is a shape representa…
A formula for the Euler characteristic of $\overline{{\cal M}}_{2,n}$
2001
In this paper we compute the generating function for the Euler characteristic of the Deligne-Mumford compactification of the moduli space of smooth n-pointed genus 2 curves. The proof relies on quite elementary methods, such as the enumeration of the graphs involved in a suitable stratification of \(\overline{{\cal M}}_{2,n}\).
Euler Characteristics of Moduli Spaces of Curves
2005
Let ${mathcal M}_g^n$ be the moduli space of n-pointed Riemann surfaces of genus g. Denote by ${\bar {\mathcal M}}_g^n$ the Deligne-Mumford compactification of ${mathcal M}_g^n$. In the present paper, we calculate the orbifold and the ordinary Euler characteristic of ${\bar {\mathcal M}}_g^n$ for any g and n such that n>2-2g.
Along-arc, inter-arc and arc-to-arc variations in volcanic gas CO 2 /S T ratios reveal dual source of carbon in arc volcanism
2017
Abstract Some 300–600 Tg of volatiles are globally vented each year by arc volcanism. Such arc gas emissions have contributed to past and present-day evolution of the Earth atmosphere and climate by recycling mineral-bound volatiles subducted along active slabs. Carbon dioxide (CO 2 ) and total sulphur (S T ) are, after water, the major components of volcanic arc gases. Understanding their relative abundances (e.g., the CO 2 /S T ratio) in arc volcanic gases is important to constrain origin and recycling efficiency of these volatiles along the subduction factory, and to better constrain the global arc volcanic CO 2 flux. Here, we review currently available information on global variations o…
Stability of Embankments Resting on Foundation Soils with A Weak Layer
2021
The presence of weak layers in geotechnical systems, including soil or rock masses, both natural and man-made, is more frequent than is normally believed. Weak layers can affect both failure mechanisms, in drained and in undrained conditions, as well as in static and seismic conditions, and the safety factor. In the present study, conducted numerically using the finite-element method (FEM) Plaxis 2D code, the influence of a horizontal thin weak layer on stress and strain distribution, on failure mechanisms and on the overall stability of an embankment was evaluated. The results obtained prove that when the weak layer is located at a significant depth from the foundation plane, the failure m…
Espace de Minkowski-Lorentz et des sphères : un état de l'art
2016
International audience; Dans cet article, nous faisons une présentation de l'espace de Minkowski-Lorentz généralisant, à Ê 5 l'espace utilisé dans la théorie de la relativité. Cet espace de dimension 5 contient un paraboloïde de dimension 3 et isométrique à l'espace affine euclidien usuel E 3 , l'ensembles des sphères et plans orientés de E 3 regroupés sur une pseudo-sphère unité de dimension 4. Une premier avantage de cet espace est l'écriture intuitive d'une sphère qui est caractérisée par un point, un vecteur normal en ce point et une courbure. Un deuxième avantage est la manipulation de surfaces canal qui sont représentées par des courbes. Un troisième avantage concernant la simplificat…
Toward the Development of Load Transfer Efficiency Evaluation of Rigid Pavements by a Rolling Wheel Deflectometer
2020
The jointed rigid pavement is currently evaluated by the Falling weight deflectometer which is rather slow for the testing of the jointed pavements. Continuous nondestructive evaluation of rigid pavements with a rolling wheel deflectometer can be used to measure the load transfer and is investigated. Load transfer is an important indicator of the rigid pavement&rsquo
A Curvature Based Method for Blind Mesh Visual Quality Assessment Using a General Regression Neural Network
2016
International audience; No-reference quality assessment is a challenging issue due to the non-existence of any information related to the reference and the unknown distortion type. The main goal is to design a computational method to objectively predict the human perceived quality of a distorted mesh and deal with the practical situation when the reference is not available. In this work, we design a no reference method that relies on the general regression neural network (GRNN). Our network is trained using the mean curvature which is an important perceptual feature representing the visual aspect of a 3D mesh. Relatively to the human subjective scores, the trained network successfully asses…