The Fourier theorem

It has been tacitly understood that Fourier's representation theorem applies only to a very restricted class of functions. On the contrary, by adopting an appropriate algebraic viewpoint, it is explained in this article how the theorem can be readily extended to include all (non-pathological) functions.     

Perceptual training of height and brightness seriation in kindergarten children.

A study of seriation was conducted from the perspective of Gibson's theory of perceptual development. Kindergarten children who evidenced little seriation of height or brightness were assigned to either 1 of 3 perceptual training conditions or to a fourth, control condition. Training consisted of nonreinforced same-different judgments to wooden dowels varying in height, or in brightness, or simultaneously in height and brightness. The theoretical rationale for this training was that it would facilitate perception of the stimulus dimension(s) on which the dowels differed. It was found that perceptual training did facilitate seriation, particularly if both the height and brightness dimensions varied simultaneously in training.     

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.