Search results for "Dean"
showing 10 items of 278 documents
On bounds for total absolute curvature of surfaces in hyperbolic 3-space
2003
Abstract We construct examples of surfaces in hyperbolic space which do not satisfy the Chern–Lashof inequality (which holds for immersed surfaces in Euclidean space). To cite this article: R. Langevin, G. Solanes, C. R. Acad. Sci. Paris, Ser. I 336 (2003).
Isolated roundings and flattenings of submanifolds in Euclidean spaces
2005
We introduce the concepts of rounding and flattening of a smooth map $g$ of an $m$-dimensional manifold $M$ to the euclidean space $\R^n$ with $m<n$, as those points in $M$ such that the image $g(M)$ has contact of type $\Sigma^{m,\dots,m}$ with a hypersphere or a hyperplane of $\R^n$, respectively. This includes several known special points such as vertices or flattenings of a curve in $\R^n$, umbilics of a surface in $\R^3$, or inflections of a surface in $\R^4$.
Principal configurations and umbilicity of submanifolds in $\mathbb R^N$
2004
We consider the principal configurations associated to smooth vector fields $\nu$ normal to a manifold $M$ immersed into a euclidean space and give conditions on the number of principal directions shared by a set of $k$ normal vector fields in order to guaranty the umbilicity of $M$ with respect to some normal field $\nu$. Provided that the umbilic curvature is constant, this will imply that $M$ is hyperspherical. We deduce some results concerning binormal fields and asymptotic directions for manifolds of codimension 2. Moreover, in the case of a surface $M$ in $\mathbb R^N$, we conclude that if $N>4$, it is always possible to find some normal field with respect to which $M$ is umbilic and …
Constant angle surfaces in 4-dimensional Minkowski space
2019
Abstract We first define a complex angle between two oriented spacelike planes in 4-dimensional Minkowski space, and then study the constant angle surfaces in that space, i.e. the oriented spacelike surfaces whose tangent planes form a constant complex angle with respect to a fixed spacelike plane. This notion is the natural Lorentzian analogue of the notion of constant angle surfaces in 4-dimensional Euclidean space. We prove that these surfaces have vanishing Gauss and normal curvatures, obtain representation formulas for the constant angle surfaces with regular Gauss maps and construct constant angle surfaces using PDE’s methods. We then describe their invariants of second order and show…
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…
Villamalea. 1900-1939. Estudio sobre una comunidad rural de La Mancha. Del caciquismo a la aparición de las organizaciones de clase.
1980
El objeto de la Tesis Doctoral es el estudio de una comunidad rural en La Mancha, Villamalea (Albacete) durante el período 1900-1939. El interés por el estudio de Villamalea tiene su base en el fuerte desarrollo político y sindical, como consecuencia de la conciencia política y social, que alcanza su mayor expresión en la década de los años 60 y 70 del siglo XX. El alto nivel de conflictividad con el régimen del general Franco, el arraigo y la extensión de la conciencia de clase de los vecinos, la forma original con que se enfrentaron los problemas económicos y la crisis de la agricultura, las alternativas planteadas a la situación existente y otros hechos acaecidos en la década de los años…
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.