Search results for "Bedding"
showing 10 items of 199 documents
The differential Galois group of the rational function field
2020
We determine the absolute differential Galois group of the field $\mathbb{C}(x)$ of rational functions: It is the free proalgebraic group on a set of cardinality $|\mathbb{C}|$. This solves a longstanding open problem posed by B.H. Matzat. For the proof we develop a new characterization of free proalgebraic groups in terms of split embedding problems, and we use patching techniques in order to solve a very general class of differential embedding problems. Our result about $\mathbb{C}(x)$ also applies to rational function fields over more general fields of coefficients.
Hitchhiker's guide to the fractional Sobolev spaces
2012
AbstractThis paper deals with the fractional Sobolev spaces Ws,p. We analyze the relations among some of their possible definitions and their role in the trace theory. We prove continuous and compact embeddings, investigating the problem of the extension domains and other regularity results.Most of the results we present here are probably well known to the experts, but we believe that our proofs are original and we do not make use of any interpolation techniques nor pass through the theory of Besov spaces. We also present some counterexamples in non-Lipschitz domains.
Abstract and concrete tangent modules on Lipschitz differentiability spaces
2020
We construct an isometric embedding from Gigli's abstract tangent module into the concrete tangent module of a space admitting a (weak) Lipschitz differentiable structure, and give two equivalent conditions which characterize when the embedding is an isomorphism. Together with arguments from a recent article by Bate--Kangasniemi--Orponen, this equivalence is used to show that the ${\rm Lip}-{\rm lip}$ -type condition ${\rm lip} f\le C|Df|$ implies the existence of a Lipschitz differentiable structure, and moreover self-improves to ${\rm lip} f =|Df|$. We also provide a direct proof of a result by Gigli and the second author that, for a space with a strongly rectifiable decomposition, Gigli'…
The Fatou coordinate for parabolic Dulac germs
2017
We study the class of parabolic Dulac germs of hyperbolic polycycles. For such germs we give a constructive proof of the existence of a unique Fatou coordinate, admitting an asymptotic expansion in the power-iterated log scale.
Unifying vectors and matrices of different dimensions through nonlinear embeddings
2020
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous parameter $\kappa \in \mathbb{R}$ is being varied, thus allowing the unification of vectors, matrices and tensors in single mathematical structures. This technique is applied to construct warped models in the passage from supergravity in 10 or 11-dimensional spacetimes to 4-dimensional ones. We also show how nonlinear embeddings can be used to connect cellular automata (CAs) to coupled map lattices (CMLs) and to nonlinear partial differential equations, derivi…
The Poisson embedding approach to the Calderón problem
2020
We introduce a new approach to the anisotropic Calder\'on problem, based on a map called Poisson embedding that identifies the points of a Riemannian manifold with distributions on its boundary. We give a new uniqueness result for a large class of Calder\'on type inverse problems for quasilinear equations in the real analytic case. The approach also leads to a new proof of the result by Lassas and Uhlmann (2001) solving the Calder\'on problem on real analytic Riemannian manifolds. The proof uses the Poisson embedding to determine the harmonic functions in the manifold up to a harmonic morphism. The method also involves various Runge approximation results for linear elliptic equations.
Renewable energy for sustainable rural development: synergies and mismatches
2020
Abstract Energy transition is increasingly regarded as a promising opportunity for the economic development of rural areas. This possibility is associated with the siting and (co-)ownership of decentralized (small-scale) renewable energy facilities. The underlying productive link, however, has been taken for granted, rather than conceptually and practically cultivated. Thus, while renewable energy-based rural development has been stated as a desired by-product of energy transitions, its potential has remained largely unfulfilled. This review aims to illuminate the ambiguous interplay between renewable energy and rural development in the context of the current trajectories of the energy tran…
Contribution à l’apprentissage de représentation de données à base de graphes avec application à la catégorisation d’images
2020
Graph-based Manifold Learning algorithms are regarded as a powerful technique for feature extraction and dimensionality reduction in Pattern Recogniton, Computer Vision and Machine Learning fields. These algorithms utilize sample information contained in the item-item similarity and weighted matrix to reveal the intrinstic geometric structure of manifold. It exhibits the low dimensional structure in the high dimensional data. This motivates me to develop Graph-based Manifold Learning techniques on Pattern Recognition, specially, application to image categorization. The experimental datasets of thesis correspond to several categories of public image datasets such as face datasets, indoor and…
Seismogenic rotational slumps and translational glides in pelagic deep-water carbonates. Upper Tithonian-Berriasian of Southern Tethyan margin (W Sic…
2017
Abstract Soft-sediment deformation structures (SSDSs), which reflect sediment mobilization processes, are helpful to identify punctual events of paleoenvironmental stresses. In the upper Tithonian-Berriasian calpionellid pelagic limestone of the Lattimusa Fm. outcropping in the Barracu section (W Sicily), paleoenvironmental restoration reveals the occurrence of a deep-water flat basin, characterised by undeformed planar bedding, laterally passing to a gentle slope where the deformed horizons alternate with undeformed beds. Here, two types of gravity slides have been differentiated on the basis of different kinds of SSDSs, brittle deformation, involved lithofacies, geometry and morphology. T…
Embedding Evolution in Epidemic-Style Forwarding
2007
International audience; In this work, we introduce a framework to let forwarding schemes evolve in order to adapt to changing and a priori unknown environments. The framework is inspired by genetic algorithms: at each node a genotype describes the forwarding scheme used, a selection process fosters the diffusion of the fittest genotypes in the system and new genotypes are created by combining existing ones or applying random changes. A case study implementation is presented and its performance evaluated via numerical simulations.