Measurement of Wiener kernels

1984 ◽  
Vol 16 (1) ◽  
pp. 11-12
Author(s):  
Yoshifusa Ito
Keyword(s):  
Differential Operator ◽  
Mathematical Models ◽  
White Noise ◽  
Linear Systems ◽  
Main Part ◽  
The Other ◽  
Linear Functionals ◽  
Wiener Kernels ◽  
Non Linear ◽  
Non Linear Systems

Since the late 1960s Wiener's theory on the non-linear functionals of white noise has been widely applied to the construction of mathematical models of non-linear systems, especially in the field of biology. For such applications the main part is the measurement of Wiener's kernels, for which two methods have been proposed: one by Wiener himself and the other by Lee and Schetzen. The aim of this paper is to show that there is another method based on Hida's differential operator.

Oscillatory models of vibro-impact type for essentially non-linear systems

2008 ◽  
Vol 222 (10) ◽  
pp. 2007-2043 ◽  
Author(s):  
L I Manevitch ◽  
O V Gendelman
Keyword(s):  
Mathematical Models ◽  
Linear Systems ◽  
Smooth Functions ◽  
Oscillatory Systems ◽  
Inelastic Impact ◽  
Non Linear ◽  
Recent Developments ◽  
Non Linear Systems ◽  
Methods Of Treatment ◽  
Impact Models

This paper reviews recent developments related to oscillatory systems, their impact on and relationship to the cases of smooth, essentially anharmonic (non-linearizable) potentials, and vice versa. Special methods of treatment that allow the response regimes in dynamic vibro-impact systems to be computed have been discussed. Mathematical models that approximate purely elastic as well as inelastic impact, with the help of smooth functions, are presented and illustrated by specific examples. The use of ideas based on non-smooth time transforms to treat essentially non-linear systems with smooth potentials has also been discussed. Special attention has been paid to uncommon applications of vibro-impact models.

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