A simple algebraic method is presented to determine the necessary condition for the existence of a Hamiltonian circuit in a directed graph of n vertices. A search procedure is then introduced to identify any or all of the existing Hamiltonian circuits. The procedure is based upon finding a set of edges which will then be candidates for being parts of circuits of length n at any vertex of the graph.
ABSTRACT. This paper presents a method of the determination of the steady state response for a class of nonlinear systems. The response of a nonlinear system to a given input is first obtained in the form of a series solution in the multidimensional frequency domain. Conditions are then determined for which this series solution will converge. The conversion from multidimensions to a single dimension is then made by the method of association of variables, and thus an equivalent linear model of the nonlinear system is obtained. The steady state response is then found by any technique employed with linear system.
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