Search results for "Operator"

Traced tensor norms and multiple summing multilinear operators

2016

[EN] Using a general tensor norm approach, our aim is to show that some distinguished classes of summing operators can be characterized by means of an 'order reduction' procedure for multiple summing multilinear operators, which becomes the keystone of our arguments and can be considered our main result. We work in a tensor product framework involving traced tensor norms and the representation theorem for maximal operator ideals. Several applications are given not only to multi-ideals, but also to linear operator ideals. In particular, we get applications to multiple p-summing bilinear operators, (p, q)-factorable linear operators, tau(p)-summing linear operators and absolutely p-summing li…

Closed injective ideals of multilinear operators, related measures and interpolation

2020

[EN] We introduce and discuss several ways of extending the inner measure arisen from the closed injective hull of an ideal of linear operators to the multilinear case. In particular, we consider new measures that allow to characterize the operators that belong to a closed injective ideal of multilinear operators as those having measure equal to zero. Some interpolation formulas for these measures, and consequently interpolation results involving ideals of multilinear operators, are established. Examples and applications related to summing multilinear operators are also shown.

Electric scalar potential estimations for non-invasive brain activity detection through multinode Shepard method

2022

Electric scalar potential estimation is a key step for non-invasive investigations of brain activity with high time resolutions. The neural sources can be reconstructed by solving a typical inverse problem based on a forward problem formulated as a set of boundary value problems coupled by interface conditions. In this paper, we propose a Shepard multinode method to numerically estimate electric scalar potentials via collocation. The method is based on a special kind of inverse distance weighting partition of unity method to increase polynomial precision, approximation order, and accuracy of the classical Shepard approximation. The barycentric form, through the use of cardinal basis functio…

Quasi *-Algebras and Multiplication of Distributions

1997

AbstractA self-adjoint operatorAinL2(Ω,μ) defines in a natural way a space of test functions SA(Ω) and a corresponding space of distributions S′A(Ω). These are considered as quasi *-algebras and the problem of multiplying distributions is studied in terms of multiplication operators defined on a rigged Hilbert space.

On coefficients of vector-valued Bloch functions

2004

A Grid Enabled Parallel Hybrid Genetic Algorithm for SPN

2004

This paper presents a combination of a parallel Genetic Algorithm (GA) and a local search methodology for the Steiner Problem in Networks (SPN). Several previous papers have proposed the adoption of GAs and others metaheuristics to solve the SPN demonstrating the validity of their approaches. This work differs from them for two main reasons: the dimension and the features of the networks adopted in the experiments and the aim from which it has been originated. The reason that aimed this work was namely to assess deterministic and computationally inexpensive algorithms which can be used in practical engineering applications, such as the multicast transmission in the Internet. The large dimen…

Simulation of electronic states in a nanowire field-effect transistor

2015

De acuerdo con la ley empírica de Moore, el número de transistores en un circuito integrado se ve duplicado aproximadamente cada dos años. Una vez traspasada la frontera hacia la escala nanométrica, estos dispositivos comienzan a padecer efectos adversos al funcionamiento deseable de un transistor, como la pérdida de integridad eléctrica, efectos debidos a la corta longitud del canal o la falta de reproducibilidad. Las nanoestructuras cristalinas semiconductoras conocidas como nanohilos están emergiendo como candidatos prometedores para formar una nueva base alternativa de los transistores de efecto campo y continuar la miniaturización tecnológica en la escala nanométrica. Esto es debido al…

Model-Based Transfer Entropy Analysis of Brain-Body Interactions with Penalized regression techniques

2020

The human body can be seen as a functional network depicting the dynamical interactions between different organ systems. This exchange of information is often evaluated with information-theoretic approaches which comprise the use of vector autoregressive (VAR) and state space (SS) models, normally identified with the Ordinary Least Squares (OLS). However, the number of time series to be included in the model is strictly related to the length of data recorded thus limiting the use of the classical approach. In this work, a new method based on penalized regressions, the so-called LASSO, was compared with OLS on physiological time-series extracted from 18 subjects during different stress condi…

Local and nonlocal weighted pLaplacian evolution equations with Neumann boundary conditions

2011

In this paper we study existence and uniqueness of solutions to the local diffusion equation with Neumann boundary conditions and a bounded nonhomogeneous diffusion coefficient g ≥ 0, {ut = div (g|∇u|p-2∇u) in ]0; T[×Ωg|∇u|p-2u·n = 0 on ]0; T[×∂Ω; for 1 ≤ p < ∞. We show that a nonlocal counterpart of this diffusion problem is ut(t; x)= ∫ω J(x-y)g(x+y/2)|u(t; y)-u(t; x)| p-2 (u(t; y)-u(t; x)) dy in ]0; T[× Ω,where the diffusion coefficient has been reinterpreted by means of the values of g at the point x+y/2 in the integral operator. The fact that g ≥ 0 is allowed to vanish in a set of positive measure involves subtle difficulties, specially in the case p = 1.

Sharp estimates for eigenfunctions of a Neumann problem

2009

In this paper we provide some bounds for the eigenfunctions of the Laplacian with homogeneous Neumann boundary conditions in a bounded domain Ω of R^n. To this aim we use the so-called symmetrization techniques and the obtained estimates are asymptotically sharp, at least in the bidimensional case, when the isoperimetric constant relative to Ω goes to 0.