Search results for "Euclidean"

Subdivisions of Ring Dupin Cyclides Using Bézier Curves with Mass Points

2021

Dupin cyclides are algebraic surfaces introduced for the first time in 1822 by the French mathematician Pierre-Charles Dupin. A Dupin cyclide can be defined as the envelope of a one-parameter family of oriented spheres, in two different ways. R. Martin is the first author who thought to use these surfaces in CAD/CAM and geometric modeling. The Minkowski-Lorentz space is a generalization of the space-time used in Einstein’s theory, equipped of the non-degenerate indefinite quadratic form $$Q_{M} ( \vec{u} ) = x^{2} + y^{2} + z^{2} - c^{2} t^{2}$$ where (x, y, z) are the spacial components of the vector $$ \vec{u}$$ and t is the time component of $$ \vec{u}$$ and c is the constant of the spee…

Smooth surjections and surjective restrictions

2017

Given a surjective mapping $f : E \to F$ between Banach spaces, we investigate the existence of a subspace $G$ of $E$, with the same density character as $F$, such that the restriction of $f$ to $G$ remains surjective. We obtain a positive answer whenever $f$ is continuous and uniformly open. In the smooth case, we deduce a positive answer when $f$ is a $C^1$-smooth surjection whose set of critical values is countable. Finally we show that, when $f$ takes values in the Euclidean space $\mathbb R^n$, in order to obtain this result it is not sufficient to assume that the set of critical values of $f$ has zero-measure.

Trace and density results on regular trees

2019

We give characterizations for the existence of traces for first order Sobolev spaces defined on regular trees.

Intelligent Sampling for Vegetation Nitrogen Mapping Based on Hybrid Machine Learning Algorithms

2021

Upcoming satellite imaging spectroscopy missions will deliver spatiotemporal explicit data streams to be exploited for mapping vegetation properties, such as nitrogen (N) content. Within retrieval workflows for real-time mapping over agricultural regions, such crop-specific information products need to be derived precisely and rapidly. To allow fast processing, intelligent sampling schemes for training databases should be incorporated to establish efficient machine learning (ML) models. In this study, we implemented active learning (AL) heuristics using kernel ridge regression (KRR) to minimize and optimize a training database for variational heteroscedastic Gaussian processes regression (V…

Rescaling principle for isolated essential singularities of quasiregular mappings

2012

We establish a rescaling theorem for isolated essential singularities of quasiregular mappings. As a consequence we show that the class of closed manifolds receiving a quasiregular mapping from a punctured unit ball with an essential singularity at the origin is exactly the class of closed quasiregularly elliptic manifolds, that is, closed manifolds receiving a non-constant quasiregular mapping from a Euclidean space.

Conformal Metrics on the Unit Ball in Euclidean Space

1998

Non-Abelian Ball-Chiu vertex for arbitrary Euclidean momenta

2017

We determine the non-Abelian version of the four longitudinal form factors of the quark-gluon vertex, using exact expressions derived from the Slavnov-Taylor identity that this vertex satisfies. In addition to the quark and ghost propagators, a key ingredient of the present approach is the quark-ghost scattering kernel, which is computed within the one-loop dressed approximation. The vertex form factors obtained from this procedure are evaluated for arbitrary Euclidean momenta, and display features not captured by the well-known Ball-Chiu vertex, deduced from the Abelian (ghost-free) Ward identity. The potential phenomenological impact of these results is evaluated through the study of spec…

Detection of Internet robots using a Bayesian approach

2015

A large part of Web traffic on e-commerce sites is generated not by human users but by Internet robots: search engine crawlers, shopping bots, hacking bots, etc. In practice, not all robots, especially the malicious ones, disclose their identities to a Web server and thus there is a need to develop methods for their detection and identification. This paper proposes the application of a Bayesian approach to robot detection based on characteristics of user sessions. The method is applied to the Web traffic from a real e-commerce site. Results show that the classification model based on the cluster analysis with the Ward's method and the weighted Euclidean metric is very effective in robot det…

Scenery Flow, Conical Densities, and Rectifiability

2015

We present an application of the recently developed ergodic theoretic machinery on scenery flows to a classical geometric measure theoretic problem in Euclidean spaces. We also review the enhancements to the theory required in our work. Our main result is a sharp version of the conical density theorem, which we reduce to a question on rectifiability.

Darboux curves on surfaces I

2017

International audience; In 1872, G. Darboux defined a family of curves on surfaces of $\mathbb{R}^3$ which are preserved by the action of the Mobius group and share many properties with geodesics. Here, we characterize these curves under the view point of Lorentz geometry and prove that they are geodesics in a 3-dimensional sub-variety of a quadric $\Lambda^4$ contained in the 5-dimensional Lorentz space $\mathbb{R}^5_1$ naturally associated to the surface. We construct a new conformal object: the Darboux plane-field $\mathcal{D}$ and give a condition depending on the conformal principal curvatures of the surface which guarantees its integrability. We show that $\mathcal{D}$ is integrable w…