The DT-Polynomial Approach to Discrete Time-Varying Network Flow Problems

This paper introduces a polynomial operator called the DT-polynomial as a novel approach to network flow problems. The class of networks dealt with is time-varying in the sense that the capacity, cost, and travel-time of each edge may vary in discrete time. The Dt-polynomial is a polynomial in two operators, D (delay) and T (time), which is used for describing the time-varying transmission characteristics. The paper starts with the mathematics involving the DT-polynomials. A new shortest arrival route algorithm is presented, and its computational complexity is found to be favorable in comparison with others such as Dijkstra's method and the potential method derived from Ford-Fulkerson's technique. Furthermore, a dynamic flow problem is formulated and analyzed in terms of DT-polynomials, and a latest-departure earliest-arrival schedule is given. Finally, a modified DT-polynomial is applied to digital filter networks.     

An efficient computation of thick microstrip properties on anisotropic substrates

The reproducibility of microwave integrated circuits can be improved by employing substrates which are anisotropic. A method is presented which facilitates the computation of the characteristics of distributed integrated microwave circuits of finite conductor thickness on anisotropic and inhomogeneous substrates. The method is variational and it relies on a quasi-static approach which assumes that the charge distribution on each side of the conductor can be represented by a spatially dependent set of exponential functions.     

Adjacency matrix concepts for the analysis of the interconnection of networks

A mathematical theory is developed for an imagined device termed a “junctor”. A junctor could be used to interconnect two n-terminal networks giving rise to another n-terminal network. Actually a junctor is itself a simple network with three banks of n-terminals internally connected in some fashion by perfectly conducting wires. Adjacency matrices are formulated to analyze various junctors and their current flows. The main problem treated concerns conditions which would ensure that the junctor operation is associative.     

Stability analysis of nonlinear control systems with characteristics equations having complex coefficients

In this paper, the stability equation method is applied to the analysis of nonlinear systems with characteristics equations having complex coefficients. Three types of systems are studied: those with unstable open-loop poles, unstable characteristics roots or an equal number of open-loop poles and zeros.