Search results for " math"

Relationship between volume and energy of vector fields

2001

Abstract A unified study of energy and volume functionals is presented here by determining the critical points of a functional that extends simultaneously energy and volume and that is defined on the product of the manifold of smooth maps C∞(M,N) times the manifold M of riemannian metrics on M. The restriction of this functional to different submanifolds of the space of vector fields X (M)× M is also considered, and used to study several functionals generalizing volume and energy or total bending of vector fields

R. Ghezzi - Volume measures in non equiregular sub-Riemannian manifolds

2017

In this talk we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it to a smooth volume. First we give the Lebesgue decomposition of the Hausdorff volume. Then we focus on the regular part, show that it is not commensurable with a smooth volume and give conditions under which it is a Radon measure. Finally we give a complete characterization of the singular part. This is a joint work with F. Jean (ENSTA).

The mechanically based non-local elasticity: an overview of main results and future challenges

2013

The mechanically based non-local elasticity has been used, recently, in wider and wider engineering applications involving small-size devices and/or materials with marked microstructures. The key feature of the model involves the presence of non-local effects as additional body forces acting on material masses and depending on their relative displacements. An overview of the main results of the theory is reported in this paper.

Wyzwalanie dziecięcej aktywności matematycznej w trakcie rozwiązywania zadań

2018

Aktywność ucznia ma ogromne znaczenie w kształtowaniu i rozwijaniu abstrakcyjnych pojęć matematycznych. Jednak aktywność ta nie powinna ograniczać się jedynie do aktywności zewnętrznej, często jedynie pozornej, ale przede wszystkim powinna być to aktywność umysłowa ucznia. Zachowania i postawy specyficzne dla aktywności matematycznej można bowiem rozwijać u ucznia jedynie w toku jego aktywności poznawczej (intelektualnej). W opracowaniu podjęto próbę ukazania możliwości stymulowania i rozwijania oraz przejawy aktywności matematycznej uczniów w wieku wczesnoszkolnym w trakcie rozwiązywania zadań.

Deformation Quantization in White Noise Analysis

2007

We define and present an example of a deformation quantization product on a Hida space of test functions endowed with a Wick product.

Modelling and analysing oriented fibrous structures

2014

Abstract. A mathematical model for fibrous structures using a direction dependent scaling law is presented. The orientation of fibrous nets (e.g. paper) is analysed with a method based on the curvelet transform. The curvelet-based orientation analysis has been tested successfully on real data from paper samples: the major directions of fibrefibre orientation can apparently be recovered. Similar results are achieved in tests on data simulated by the new model, allowing a comparison with ground truth. peerReviewed

Measuring Working Memory for the diagnosis of mathematics learning disabilities: The PML test battery.

2012

Composition and corrosion phases of Etruscan Bronzes from Villanovan Age

2008

A neutron diffraction (ND) and neutron tomography (NT) study of laminated ancient bronzes was performed at the ISIS (Rutherford Appleton Laboratory, UK) neutron source and at the BENSC reactor (Hahn-Meitner Institut, Germany). The samples are part of an 8th century BC Etruscan collection discovered in the necropolises of Osteria-Poggio Mengarelli and Cavalupo in the Vulci area (Viterbo, Italy). The study allowed us to derive-in a totally non-destructive manner-information related to the main composition of the objects, possible presence of alterations and their nature, crusts and inclusions, as well as structure of the bulk. The presence of some components is linked to a variety of question…

Compression and load balancing for efficient sparse matrix-vector product on multicore processors and graphics processing units

2021

We contribute to the optimization of the sparse matrix-vector product by introducing a variant of the coordinate sparse matrix format that balances the workload distribution and compresses both the indexing arrays and the numerical information. Our approach is multi-platform, in the sense that the realizations for (general-purpose) multicore processors as well as graphics accelerators (GPUs) are built upon common principles, but differ in the implementation details, which are adapted to avoid thread divergence in the GPU case or maximize compression element-wise (i.e., for each matrix entry) for multicore architectures. Our evaluation on the two last generations of NVIDIA GPUs as well as In…

First and second order rational solutions to the Johnson equation and rogue waves

2018

Rational solutions to the Johnson equation are constructed as a quotient of two polynomials in x, y and t depending on several real parameters. We obtain an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2N (N + 1) in x, and t, 4N (N + 1) in y, depending on 2N − 2 real parameters for each positive integer N. We construct explicit expressions of the solutions in the cases N = 1 and N = 2 which are given in the following. We study the evolution of the solutions by constructing the patterns of their modulus in the (x, y) plane, and this for different values of parameters.