Neural network approach to determine nonsmooth one-dimensional profiles in inverse scattering theory

2007 ◽  
Vol 49 (12) ◽  
pp. 3158-3162 ◽  
Author(s):  
Fatih Yaman ◽  
Serkan Simçsek
Keyword(s):  
Neural Network ◽  
Inverse Scattering ◽  
Scattering Theory ◽  
Network Approach ◽  
Neural Network Approach ◽  
One Dimensional ◽  
Inverse Scattering Theory

scholarly journals ESTIMATION OF THE LYAPUNOV SPECTRUM FROM ONE-DIMENSIONAL OBSERVATIONS USING NEURAL NETWORKS

2014 ◽  
pp. 30-34
Author(s):  
Vladimir Golovko
Keyword(s):  
Neural Network ◽  
Dynamical System ◽  
Neural Networks ◽  
Time Series ◽  
Lyapunov Spectrum ◽  
Network Approach ◽  
Neural Network Approach ◽  
One Dimensional ◽  
The Neural Network ◽  
Attractor Dynamics

This paper discusses the neural network approach for computing of Lyapunov spectrum using one dimensional time series from unknown dynamical system. Such an approach is based on the reconstruction of attractor dynamics and applying of multilayer perceptron (MLP) for forecasting the next state of dynamical system from the previous one. It allows for evaluating the Lyapunov spectrum of unknown dynamical system accurately and efficiently only by using one observation. The results of experiments are discussed.

scholarly journals PERTURBATIONS AND STABILITY OF BLACK ELLIPSOIDS

2003 ◽  
Vol 12 (03) ◽  
pp. 461-478 ◽  
Author(s):  
SERGIU I. VACARU
Keyword(s):  
Black Hole ◽  
Inverse Scattering ◽  
Scattering Theory ◽  
Einstein Equations ◽  
Schwarzschild Solution ◽  
Small Eccentricity ◽  
One Dimensional ◽  
Vacuum Einstein Equations ◽  
The One ◽  
Inverse Scattering Theory

We study the perturbations of two classes of static black ellipsoid solutions of four-dimensional vacuum Einstein equations. Such solutions are described by generic off-diagonal metrics which are generated by anholonomic transforms of diagonal metrics. The analysis is performed in the approximation of small eccentricity deformations of the Schwarzschild solution. We conclude that such anisotropic black hole objects may be stable with respect to the perturbations parametrized by the Schrodinger equations in the framework of the one-dimensional inverse scattering theory.

Inverse scattering theory: Inverse scattering series method for one dimensional non-compact support potential

2014 ◽  
Vol 55 (12) ◽  
pp. 123512 ◽  
Author(s):  
Jie Yao ◽  
Anne-Cécile Lesage ◽  
Bernhard G. Bodmann ◽  
Fazle Hussain ◽  
Donald J. Kouri
Keyword(s):  
Inverse Scattering ◽  
Compact Support ◽  
Scattering Theory ◽  
Series Method ◽  
One Dimensional ◽  
Inverse Scattering Series ◽  
Inverse Scattering Theory
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