Infinite electrical networks and transistor modeling

The theory and applications of infinite electrical networks are investigated. Methods were devised for computing the currents and voltages in uniform and non-uniform, grounded and ungrounded semi-infinite electrical grids. These results were applied to the numerical simulation of bipolar transistors and to the computational techniques arising in geophysical exploration. A complete and rigorous theory for infinite lumped transmission lines was at last achieved by closing a long-standing lacuna, and this was extended to ladder networks whose parameters are operators on a Hilbert space. A parametric representation for a general class of linear time-varying systems was devised. A new matroid for a certain class of infinite graphs was discovered.