A theorem of ordered duality

We associate, to any ordered configuration of n points or ordered arrangement of n lines in the plane, a periodic sequence of permutations of [1, n] in a way which reflects the order and convexity properties of the configuration or arrangement, and prove that a sequence of permutations of [1, n] is associated to some configuration of points if and only if it is associated to some arrangement of lines. We show that this theorem generalizes the standard duality principle for the projective plane, and we use it to derive duals of several well-known theorems about arrangements, including a version of Helly's theorem for convex polygons.     

Lie algebras of unbounded derivations

In this paper some new results on analytic domination of operators and on integrability of Lie algebras of operators are proved and then our methods are applied to the study of Lie algebras of unbounded derivations in $\text{C}{}^1$ algebras.     

Statistical properties of mutual intensity with finite measurement time

The accuracy with which the amplitude and phase of an interference fringe can be measured in quasi-thermal light is limited by the finite integration time used. The statistical errors expected in such a measurement are derived analytically, and their dependence on measurement time, the coherence time of the light, and the complex coherence factor are explored. An example illustrating the utility of the results is presented. Work supported by the Office of Naval Research