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.     

The effects of provocation, intentions, and consequences on children's moral judgments.

Dutch boys 8 and 12 years old read brief stories about a harm doer whose intentions were either good or bad and whose actions resulted in either minor or serious injury to a victim. The harm doer had previously been either strongly provoked or not provoked by the victim. The older boys differentiated their evaluations of the harm doer's naughtiness on the basis of provocation and intentions, while the younger boys failed to differentiate their evaluations of the provoked harm doer on the basis of intentions. Both age groups strongly differentiated their judgments of the victim's naughtiness on the basis of his role as provoker, except when the victim was seriously injured by a bad-intentioned aggressor.     

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.     

X-ray photoemission and the electronic structure of solids

The principles of X-ray photoelectron spectroscopy are outlined. The application of this technique to the study of the electronic structure of metals, alloys and compounds is illustrated using data in Ag, β-brass, ReO₃ and VO₂. In the latter a major change in the density of states is observed on passing through the metal-insulator transition.