Search results for "vector"

Equivariant algebraic vector bundles over cones with smooth one dimensional quotient

1998

Vector Bundles and Torsion Free Sheaves on Degenerations of Elliptic Curves

2006

In this paper we give a survey about the classification of vector bundles and torsion free sheaves on degenerations of elliptic curves. Coherent sheaves on singular curves of arithmetic genus one can be studied using the technique of matrix problems or via Fourier-Mukai transforms, both methods are discussed here. Moreover, we include new proofs of some classical results about vector bundles on elliptic curves.

Fuzzy algebras as a framework for fuzzy topology

2011

The paper introduces a variety-based version of the notion of the (L,M)-fuzzy topological space of Kubiak and Sostak and embeds the respective category into a suitable modification of the category of topological systems of Vickers. The new concepts provide a common framework for different approaches to fuzzy topology and topological systems existing in the literature, paving the way for studying the problem of interweaving algebra and topology in mathematics, which was raised by Denniston, Melton and Rodabaugh in their recent research on variable-basis topological systems over the category of locales.

Vectors and Vector Fields

2012

The purpose of this book is to explain in a rigorous way Stokes’s theorem and to facilitate the student’s use of this theorem in applications. Neither of these aims can be achieved without first agreeing on the notation and necessary background concepts of vector calculus, and therein lies the motivation for our introductory chapter.

Gibbs measures in a markovian context and dimension

2001

A Teaching proposal for the study of eigenvectors and eigenvalues

2017

[EN] In this work, we present a teaching proposal which emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. These concepts are introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was motivated after observing students¿ difficulties when treating eigenvectors and eigenvalues from a geometric point of view. It was designed following a particular sequence of activities with the schema: exploration, introduction of concepts, structuring of knowledge and application, and considering the three worlds of mathematical thinking provided by Tall: embodied, symbolic and formal.

Electromechanical Numerical Analysis of an Air-Core Pulsed Alternator via Equivalent Network Formulation

2017

In this paper, the numerical analysis on an air-core pulsed alternator is presented. Since compulsators are characterized by very fast electromechanical transients, their accurate analysis requires strong coupling between the equations governing the electrical and the mechanical behaviors. The device is investigated by using a dedicated numerical code capable to take into account eddy currents, compensating windings, as well as the excitation/control circuits. Furthermore, the code is capable of modeling centrifugal forces and vibrations acting on the shaft due to electric and mechanical unbalances or to misalignments of the shaft from its centered position. This makes the code a very power…

Motion sensors for activity recognition in an ambient-intelligence scenario

2013

In recent years, Ambient Intelligence (AmI) has attracted a number of researchers due to the widespread diffusion of unobtrusive sensing devices. The availability of such a great amount of acquired data has driven the interest of the scientific community in producing novel methods for combining raw measurements in order to understand what is happening in the monitored scenario. Moreover, due the primary role of the end user, an additional requirement of any AmI system is to maintain a high level of pervasiveness. In this paper we propose a method for recognizing human activities by means of a time of flight (ToF) depth and RGB camera device, namely Microsoft Kinect. The proposed approach is…

Machine Learning-Based Classification of Vector Vortex Beams.

2020

Structured light is attracting significant attention for its diverse applications in both classical and quantum optics. The so-called vector vortex beams display peculiar properties in both contexts due to the non-trivial correlations between optical polarization and orbital angular momentum. Here we demonstrate a new, flexible experimental approach to the classification of vortex vector beams. We first describe a platform for generating arbitrary complex vector vortex beams inspired to photonic quantum walks. We then exploit recent machine learning methods -- namely convolutional neural networks and principal component analysis -- to recognize and classify specific polarization patterns. O…

Extraordinary tuning of a nanocavity by a near-field probe

2011

Abstract We report here an experimental observation of an extraordinary near-field interaction between a local probe and a small-volume solid-state nanocavity. We directly compare the normally observed near-field interaction regime driven by the perturbation theory and then report the extraordinary interaction regime. Subsequently, we show that the cavity can take up to 2 min to recover from this interaction after removing the probe and that leads to an extraordinary blue-shift of the cavity resonance wavelength (∼15 nm) which depends on the probe motion above the cavity and not the position. The reasons for this effect are not fully understood yet but we try to give some explanations.