Search results for "General Mathematics"
showing 10 items of 3795 documents
Characterization of ellipsoids through an overdetermined boundary value problem of Monge–Ampère type
2014
Abstract The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow.
Analysis of a slow–fast system near a cusp singularity
2016
This paper studies a slow fast system whose principal characteristic is that the slow manifold is given by the critical set of the cusp catastrophe. Our analysis consists of two main parts: first, we recall a formal normal form suitable for systems as the one studied here; afterwards, taking advantage of this normal form, we investigate the transition near the cusp singularity by means of the blow up technique. Our contribution relies heavily in the usage of normal form theory, allowing us to refine previous results. (C) 2015 Elsevier Inc. All rights reserved.
Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3
1987
AbstractA cusp type germ of vector fields is a C∞ germ at 0∈ℝ2, whose 2-jet is C∞ conjugate toWe define a submanifold of codimension 5 in the space of germs consisting of germs of cusp type whose 4-jet is C0 equivalent toOur main result can be stated as follows: any local 3-parameter family in (0, 0) ∈ ℝ2 × ℝ3 cutting transversally in (0, 0) is fibre-C0 equivalent to
Blending pieces of Dupin cyclides for 3D modeling and reconstruction : study in the space of spheres
2013
The thesis deals with the blending of canal surfaces in geometric modeling using pieces of Dupin Cyclides. We try to solve a problem of reconstructing real parts manufactured and controlled by the CEA of Valduc. Using the space of spheres in which we can manipulate both points, spheres and canal surfaces, we simplify some problems. This space is represented by a 4-dimensional quadric in a 5-dimensional space, equipped with the Lorentz form, it is the Lorentz space. In the space of spheres, problems of blending canal surfaces by pieces of Dupin cyclides are simplified in linear problems. We give algorithms to make such blends using the space of spheres and after we come back to 3 dimensions …
El coneixement i l'ús de les aplicacions educatives dels estudiants universitaris d'Espanya i la República Txeca
2020
Technological evolution has led to many changes at both professional and academic levels. The inclusion of Information and Communication Technologies (ICT) has caused dizzying changes in the different contexts of life (educational, professional, social). More and more applications are being downloaded by users to their mobile devices, both for entertainment and training. For this reason, this study is based on the need to assess the knowledge and attitude of university students towards downloading existing educational applications. In this way, the use and frequency of these tools in the teaching-learning process of the students will be analyzed. In order to carry out this study, the quanti…
Adaptive control of a seven mode truncation of the Kolmogorov flow with drag
2009
Abstract We study a seven dimensional nonlinear dynamical system obtained by a truncation of the Navier–Stokes equations for a two dimensional incompressible fluid with the addition of a linear term modelling the drag friction. We show the bifurcation sequence leading from laminar steady states to chaotic solutions with increasing Reynolds number. Finally, we design an adaptive control which drives the state of the system to the equilibrium point representing the stationary solution.
Limits of Sobolev homeomorphisms
2017
Let X; Y subset of R-2 be topologically equivalent bounded Lipschitz domains. We prove that weak and strong limits of homeomorphisms h: X (onto)-> Y in the Sobolev space W-1,W-p (X, R-2), p >= 2; are the same. As an application, we establish the existence of 2D-traction free minimal deformations for fairly general energy integrals. Peer reviewed
Dagger closure and solid closure in graded dimension two
2013
We introduce a graded version of dagger closure and prove that it coincides with solid closure for homogeneous ideals in two-dimensional N \mathbb {N} -graded domains of finite type over a field.
Machine learning at the interface of structural health monitoring and non-destructive evaluation
2020
While both non-destructive evaluation (NDE) and structural health monitoring (SHM) share the objective of damage detection and identification in structures, they are distinct in many respects. This paper will discuss the differences and commonalities and consider ultrasonic/guided-wave inspection as a technology at the interface of the two methodologies. It will discuss how data-based/machine learning analysis provides a powerful approach to ultrasonic NDE/SHM in terms of the available algorithms, and more generally, how different techniques can accommodate the very substantial quantities of data that are provided by modern monitoring campaigns. Several machine learning methods will be illu…
Etude numérique d'équations aux dérivées partielles non linéaires et dispersives
2011
Numerical analysis becomes a powerful resource in the study of partial differential equations (PDEs), allowing to illustrate existing theorems and find conjectures. By using sophisticated methods, questions which seem inaccessible before, like rapid oscillations or blow-up of solutions can be addressed in an approached way. Rapid oscillations in solutions are observed in dispersive PDEs without dissipation where solutions of the corresponding PDEs without dispersion present shocks. To solve numerically these oscillations, the use of efficient methods without using artificial numerical dissipation is necessary, in particular in the study of PDEs in some dimensions, done in this work. As stud…