Search results for "Vector"

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.

Response Power Spectrum of Multi-Degree-of-Freedom Nonlinear Systems by a Galerkin Technique

2003

This paper deals with the estimation of spectral properties of randomly excited multi-degree-of-freedom (MDOF) nonlinear vibrating systems. Each component of the vector of the stationary system response is expanded into a trigonometric Fourier series over an adequately long interval T. The unknown Fourier coefficients of individual samples of the response process are treated by harmonic balance, which leads to a set of nonlinear equations that are solved by Newton’s method. For polynomial nonlinearities of cubic order, exact solutions are developed to compute the Fourier coefficients of the nonlinear terms, including those involved in the Jacobian matrix associated with the implementation o…

Efficient computation of stable bifurcating branches of nonlinear eigenvalue problems

1983

Ober Ein Rayleigh-Ritz-Verfahren zur Bestimmung Kritischer Werte

1980

This paper is concerned with the existence of critical points for a functional f defined on the level set of a second functional g. Existence of nontrivial solutions for the nonlinear eigenvalue-problem f′(u) = λg′(u) and convergence for a nonlinear analogue to the Rayleigh-Ritz-Method is proven. The results are applied to a nonlinear ordinary eigenvalue problem where it is shown that the lowest point in the continuous spectrum of the associated linearized operator is a bifurcation point of infinite multiplicity.

The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS

2002

In this paper I propose a method for solving in closed form a general class of four-dimension non-linear modified Hamiltonian dynamic systems. This method may be used to study several intertemporal optimization problems with a predetermined structure, involving unbounded technological constraints as well as multiple controls and state variables. The method is developed here by solving the first order conditions corresponding to the socially optimal solution to the Lucas (1988) two-sector model of endogenous growth.

Eigenvalue Accumulation for Singular Sturm–Liouville Problems Nonlinear in the Spectral Parameter

1999

Abstract For certain singular Sturm–Liouville equations whose coefficients depend continuously on the spectral parameter λ in an interval Λ it is shown that accumulation/nonaccumulation of eigenvalues at an endpoint ν of Λ is essentially determined by oscillatory properties of the equation at the boundary λ = ν . As applications new results are obtained for the radial Dirac operator and the Klein–Gordon equation. Three other physical applications are also considered.

NONVANISHING ELEMENTS FOR BRAUER CHARACTERS

2015

Let $G$ be a finite group and $p$ a prime. We say that a $p$-regular element $g$ of $G$ is $p$-nonvanishing if no irreducible $p$-Brauer character of $G$ takes the value $0$ on $g$. The main result of this paper shows that if $G$ is solvable and $g\in G$ is a $p$-regular element which is $p$-nonvanishing, then $g$ lies in a normal subgroup of $G$ whose $p$-length and $p^{\prime }$-length are both at most 2 (with possible exceptions for $p\leq 7$), the bound being best possible. This result is obtained through the analysis of one particular orbit condition in linear actions of solvable groups on finite vector spaces, and it generalizes (for $p>7$) some results in Dolfi and Pacifici [‘Zero…

Combining Inter-Subject Modeling with a Subject-Based Data Transformation to Improve Affect Recognition from EEG Signals

2019

Existing correlations between features extracted from Electroencephalography (EEG) signals and emotional aspects have motivated the development of a diversity of EEG-based affect detection methods. Both intra-subject and inter-subject approaches have been used in this context. Intra-subject approaches generally suffer from the small sample problem, and require the collection of exhaustive data for each new user before the detection system is usable. On the contrary, inter-subject models do not account for the personality and physiological influence of how the individual is feeling and expressing emotions. In this paper, we analyze both modeling approaches, using three public repositories. T…

How do normalization schemes affect net spillovers? A replication of the Diebold and Yilmaz (2012) study

2019

Abstract This paper replicates the Diebold and Yilmaz (2012) study on the connectedness of the commodity market and three other financial markets: the stock market, the bond market, and the FX market, based on the Generalized Forecast Error Variance Decomposition, GEFVD. We show that the net spillover indices (of directional connectedness), used to assess the net contribution of one market to overall risk in the system, are sensitive to the normalization scheme applied to the GEFVD. We show that, considering data generating processes characterized by different degrees of persistence and covariance, a scalar-based normalization of the Generalized Forecast Error Variance Decomposition is pref…

Spin-flip M1 giant resonance as a challenge for Skyrme forces

2010

Despite a great success of the Skyrme mean-field approach in exploration of nuclear dynamics, it seems to fail in description of the spin-flip M1 giant resonance. The results for different Skyrme parameterizations are contradictory and poorly agree with experiment. In particular, there is no parameterization which simultaneously describes the one-peak gross structure of M1 strength in doubly magic nuclei and two-peak structure in heavy deformed nuclei. The reason of this mismatch could lie in an unsatisfactory treatment of spin correlations and spin-orbit interaction. We discuss the present status of the problem and possible ways of its solution. In particular, we inspect i) the interplay o…