The origins of modern viscoelasticity theories (and, more generally, of “hereditary ” systems theories) are usually traced back to the work of Ludwig Boltzmann and Vito Volterra. This indication poses a first task to the historian: going beyond a generic reference in order to analyze Boltzmann's and Volterra's contributions and to place them within the scientific context of their times. However, as one faces this study many problems arise, so forcing to extend the analysis to a much more complex framework than a mere description. Historiography on “hereditary ” theories is extremely poor, being limited to some papers written by Volterra. In his first writings on these topics, 1 Volterra appropriately mentioned other contributions preceding his own work which was considered by him, at least in part, as a development

LUNSFORD II, PHILIP J. The Frequency Domain Behavioral Modeling and Simulation of Nonlinear Analog Circuits and Systems. (Under the direction of Michael B. Steer.) A new technique for the frequency-domain behavioral modeling and simulation of nonautonomous nonlinear analog subsystems is presented. This technique extracts values of the Volterra nonlinear transfer functions and stores these values in binary files. Using these files, the modeled substem can be simulated for an arbitrary periodic input expressed as a finite sum of sines and cosines. Furthermore, the extraction can be based on any circuit simulator that is capable of steady state simulation. Thus a large system can be divided into smaller subsystems, each of which is characterized by circuit level simulations or lab measurements. The total system can then be simulated using the subsystem characterization stored as tables in binary files.

In this thesis, the mapping capability of the Gabor polynomial is reviewed and the nonlinear mapping capability of Multi-layer perceptron(MLP) is discussed in terms of the number of parameters used to represent them. It is shown that the pattern storage capability of multi-variate polynomial is much higher than the commonly used lower bound on multilayer perceptron pattern storage. It is also shown that multi-layer perceptron networks having second and third degree polynomial activations can be constructed which implement Gabor polynomials and therefore have the same high pattern storage capability. The polynomial networks are mapped to a conventional sigmoidal MLP resulting in highly efficient network. It is shown clearly that albeit techniques like output weight optimization and con...