Search results for "eigenvalues"
showing 10 items of 315 documents
Tunnel effect and symmetries for Kramers–Fokker–Planck type operators
2011
AbstractWe study operators of Kramers–Fokker–Planck type in the semiclassical limit, assuming that the exponent of the associated Maxwellian is a Morse function with a finite number n0 of local minima. Under suitable additional assumptions, we show that the first n0 eigenvalues are real and exponentially small, and establish the complete semiclassical asymptotics for these eigenvalues.
The ∞-Eigenvalue Problem
1999
. The Euler‐Lagrange equation of the nonlinear Rayleigh quotient \( \left(\int_{\Omega}|\nabla u|^{p}\,dx\right) \bigg/ \left(\int_{\Omega}|u|^{p}\,dx\right)\) is \( -\div\left( |\nabla u|^{p-2}\nabla u \right)= \Lambda_{p}^{p} |u |^{p-2}u,\) where \(\Lambda_{p}^{p}\) is the minimum value of the quotient. The limit as \(p\to\infty\) of these equations is found to be \(\max \left\{ \Lambda_{\infty}-\frac{|\nabla u(x)|}{u(x)},\ \ \Delta_{\infty}u(x)\right\}=0,\) where the constant \(\Lambda_{\infty}=\lim_{p\to\infty}\Lambda_{p}\) is the reciprocal of the maximum of the distance to the boundary of the domain Ω.
Lower bounds for eigenvalues of a quadratic form relative to a positive quadratic form
1968
Abstract : A method is presented for the calculation of lower bounds to eigenvalues of operators that arise from variational problems for one quadratic form relative to a positive definite quadratic form. Eigenvalue problems of this kind occur, for example, in the theory of buckling of continuous linear elastic systems. The technique used is a modification of one introduced earlier, (1) sections II and IVB, for the determination of lower bounds to eigenvalues of semi-bounded self-adjoint operators. Other methods for the latter problem can be carried over without essential changes. The particular difficulty in the case we consider is that some operators which enter the calculation for the lo…
The eigen-structure of the Jacobian in multi-class Lighthill-Whitham-Richards traffic flow models
2007
Characteristic-based High Resolution Shock Capturing schemes for hyperbolic systems of conservation laws require, in their basic design structure, knowledge on the complete eigen-decomposition of the Jacobian matrix of the system. For the Multi-Class Lighthill-Witham-Richards (MCLWR) Traffic flow model considered in [4], there is no explicit formula for the eigenvalues of the Jacobian matrix, which can only be determined numerically. However, once they are determined, the eigen-vectors are easily computed and straightforward formulas can be obtained by exploiting the specific structure of the Jacobian matrix in these models. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Clustering ball possession duration according to players’ role in football small-sided games
2022
This study aimed to explore which offensive variables best discriminate the ball possession duration according to players specific role (defenders, midfielders, attackers) during a Gk+3vs3+Gk football small-sided games. Fifteen under-15 players (age 13.2±1.0 years, playing experience 4.2±1.0 years) were grouped according to their positions (team of defenders, n = 5; team of midfielders, n = 7; team of attackers, n = 3). On each testing day (n = 3), each team performed one bout of 5-min against each team in a random order, accounting for a total of nine bouts in the following scenarios: i) defenders vs midfielders; ii) defenders vs attackers; iii) midfielders vs attackers. Based on video, a …
Digital simulation of multivariate earthquake ground motions
2000
In this paper a new generation procedure of multivariate earthquake ground motion is presented. The technique takes full advantage of the decomposition of the power spectral density matrix by means of its eigenvectors. The application of the method to multivariate ground accelerations shows some very interesting physical properties which allows one to obtain significant reduction of the computational effort in the generation of sample functions relative to multivariate earthquake ground motion processes. Copyright © 2000 John Wiley & Sons, Ltd.
Multivariate stochastic wave generation
1996
Abstract In this paper, for the case of the fluid particle velocity, a procedure that substantially reduces the computational effort to generate a multivariate stochastic process is proposed. It is shown that, for a fully coherent wave field, it is possible to decompose the Power Spectral Density (PSD) matrix into the eigenvectors of the matrix itself. This leads to generate each field's process as independent, and the time generation increases linearly with the processes' number in the field. A numerical example to evaluate the statistical properties, in terms of correlation and cross-correlation functions, of the processes is also presented.
Evolution of worldwide stock markets, correlation structure and correlation based graphs
2011
We investigate the daily correlation present among market indices of stock exchanges located all over the world in the time period Jan 1996 - Jul 2009. We discover that the correlation among market indices presents both a fast and a slow dynamics. The slow dynamics reflects the development and consolidation of globalization. The fast dynamics is associated with critical events that originate in a specific country or region of the world and rapidly affect the global system. We provide evidence that the short term timescale of correlation among market indices is less than 3 trading months (about 60 trading days). The average values of the non diagonal elements of the correlation matrix, corre…
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.
Attracteurs de Lorenz de variété instable de dimension arbitraire
1997
Abstract We construct the first examples of flows with robust multidimensional Lorenz-like attractors: the singularity contained in the attractor may have any number of expanding eigenvalues, and the attractor remains transitive in a whole neighbourhood of the initial flow. These attractors support a Sinai-Ruelle-Bowen SRB-measure and, contrary to the usual (low-dimensional) Lorenz models, they have infinite modulus of structural stability.