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.     

Theory for incompressible fluid turbulence

The functional integral representation for the space-time Hopf characteristic functional associated with boundary-free incompressible fluid turbulence is evaluated accurately to order R^-2, where R is the dimensionless Reynolds number in the theory. This work extends the results obtained previously for C-dominant turbulence to the regime of experimentally accessible large Reynolds numbers. We obtain a characteristic functional of non-Gaussian form as an asymptotically exact solution to the theory for large values of R. Two-point and three-point velocity correlation tensors of physical interest are derived from the characteristic functional.     

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.