Search results for "Infinitesimal"
showing 10 items of 67 documents
Universal infinitesimal Hilbertianity of sub-Riemannian manifolds
2019
We prove that sub-Riemannian manifolds are infinitesimally Hilbertian (i.e., the associated Sobolev space is Hilbert) when equipped with an arbitrary Radon measure. The result follows from an embedding of metric derivations into the space of square-integrable sections of the horizontal bundle, which we obtain on all weighted sub-Finsler manifolds. As an intermediate tool, of independent interest, we show that any sub-Finsler distance can be monotonically approximated from below by Finsler ones. All the results are obtained in the general setting of possibly rank-varying structures.
On the advantages of combining differential algorithms and log-polar vision for detection of self-motion from a mobile robot
2001
Abstract This paper describes the design and implementation on programmable hardware (FPGAs) of an algorithm for the detection of self-mobile objects as seen from a mobile robot. In this context, ‘self-mobile’ refers to those objects that change in the image plane due to their own movement, and not to the movement of the camera on board of the mobile robot. The method consists on adapting the original algorithm from Chen and Nandhakumar [A simple scheme for motion boundary detection, in: Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, 1994] by using foveal images obtained with a special camera whose optical axis points towards the direction of advance. It i…
Infinitesimal deformations of double covers of smooth algebraic varieties
2003
The goal of this paper is to give a method to compute the space of infinitesimal deformations of a double cover of a smooth algebraic variety. The space of all infinitesimal deformations has a representation as a direct sum of two subspaces. One is isomorphic to the space of simultaneous deformations of the branch locus and the base of the double covering. The second summand is the subspace of deformations of the double covering which induce trivial deformations of the branch divisor. The main result of the paper is a description of the effect of imposing singularities in the branch locus. As a special case we study deformations of Calabi--Yau threefolds which are non--singular models of do…
On Riemann’s Ideas on Space and Schwinger’s Treatment of Low-Energy Pion-Nucleon Physics
2020
We begin with a demonstration of how great an influence Riemann’s habilitation essay had on the development of field theory. His ideas about the origin of physical space and the importance of a metric field were clearly outlined as early as 1854, and praised highly by the old C.F. Gauss, who died 1 year later. There is but one formula in Riemann’s article. This formula and its relevance will be explained at the beginning of the present chapter. The basic principle which is omnipresent in Riemann’s entire work is to understand the physical behavior of nature from its smallness. Hence partial differential equations stand at the beginning of any field theory. In our case, it is not the metric …
Experimental evidence for fractional time evolution in glass forming materials
2002
The infinitesimal generator of time evolution in the standard equation for exponential (Debye) relaxation is replaced with the infinitesimal generator of composite fractional translations. Composite fractional translations are defined as a combination of translation and the fractional time evolution introduced in [Physica A, 221 (1995) 89]. The fractional differential equation for composite fractional relaxation is solved. The resulting dynamical susceptibility is used to fit broad band dielectric spectroscopy data of glycerol. The composite fractional susceptibility function can exhibit an asymmetric relaxation peak and an excess wing at high frequencies in the imaginary part. Nevertheless…
New Results on Identifiability of Nonlinear Systems
2004
Abstract In this paper, we recall definition of identifiability of nonlinear systems. We prove equivalence between identifiability and smooth identifiability. This new result justifies our definition of identifiability. In a previous paper (Busvelle and Gauthier, 2003), we have established that • If the number of observations is three or more, then, systems are generically identifiable. • If the number of observations is 1 or 2, then the situation is reversed. Identifiability is not at all generic. Also, we have completely classified infinitesimally identifiable systems in the second case, and in particular, we gave normal forms for identifiable systems. Here, we will give similar results i…
La corrispondenza epistolare Niccolò De Martino - Girolamo Settimo. Con un saggio sull’inedito Trattato delle Unghiette Cilindriche di Settimo
2008
Infinitesimal Hilbertianity of Weighted Riemannian Manifolds
2018
AbstractThe main result of this paper is the following: anyweightedRiemannian manifold$(M,g,\unicode[STIX]{x1D707})$,i.e., a Riemannian manifold$(M,g)$endowed with a generic non-negative Radon measure$\unicode[STIX]{x1D707}$, isinfinitesimally Hilbertian, which means that its associated Sobolev space$W^{1,2}(M,g,\unicode[STIX]{x1D707})$is a Hilbert space.We actually prove a stronger result: the abstract tangent module (à la Gigli) associated with any weighted reversible Finsler manifold$(M,F,\unicode[STIX]{x1D707})$can be isometrically embedded into the space of all measurable sections of the tangent bundle of$M$that are$2$-integrable with respect to$\unicode[STIX]{x1D707}$.By following the…
A sequence of positive solutions for sixth-order ordinary nonlinear differential problems
2021
Infinitely many solutions for a nonlinear sixth-order differential equation are obtained. The variational methods are adopted and an oscillating behaviour on the nonlinear term is required, avoiding any symmetry assumption.
Calculation of the elastic–plastic strain energy density under cyclic and random loading
2001
Abstract The paper presents a method of identification and calculation of the components of strain energy density under cyclic and random loading causing elastic–plastic strain in the material. The method consists in integration of the history of the strain instantaneous power.