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.     

Circular Plate on Multipoint Supports

Formulae are derived for the deflection surface of a symmetrically loaded circular plate having several points supports which are situated at equal distances apart on a single concentric circle. There is no restriction on the diameter of the support circle, which may be as large as the diameter of the plate itself. The results of this paper compare favorably with published experimental results. Numerical deflection coefficients for a uniformly loaded plate are provided, and these could be utilized for optimizing the positions and the number of concentrated supports.