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This paper gives the Volterra functional analysis of nonlinear time-varying systems with deterministic and stochastic inputs. Representative classes of systems are studied, and illustrative examples are shown. A comparison of the Volterra Functional Method with the Transform Ensemble Method is given in the Appendix.

Recent investigations have revealed that copper deficiency results in abnormal elastin formation ( O'Dell et al. , 1961 ; Coulson and Carnes, 1963 ; Shields et al. , 1962 ; Starcher et al. , 1964 ). The abnormality is characterized by both a decrease in elastin synthesis and an increase in the lysine content of the elastin that is synthesized. Partridge et al. (1964) reported that the cross linkage groups of elastin are synthesized from lysine residues and proposed that the epsilon amino group of lysine was oxidized to an aldehyde prior to condensation to the cross-linkage groups, desmosine and isodesmosine. Such a reaction would be catalyzed by an amine oxidase. The fact that those amine oxidases which have been isolated contain copper ( Yamada and Yasunobu, 1962 ; Hill and Mann, 1962 ; Buffoni and Blaschko, 1964 ) led to the speculation that the role of copper in elastin formation is a reflection of its role in amine oxidase activity. The investigations presented in this report were undertaken to examine this hypothesis.

The induction of tryptophan pyrrolase in chick liver by hydrocortisone was studied in copper- and magnesium-deficient chicks. Magnesium deficiency did not influence the induction of the enzyme, whereas copper deficiency significantly decreased it. These results suggest that tryptophan pyrrolase of chick liver, like that in Pseudomonas, is a copper-containing enzyme.