Foraminiferal associations of the Mid-Tertiary Edegem Sands at Terhagen, Belgium

A factor-analytic approach (varimax rotated factors) was used in studying the benthonic foraminiferal associations of the Mid-Tertiary Edegem Sands at Terhagen (near Antwerpen) Belgium. The fauna can be described by two groups. The lower and upper part of the stratigraphic section are characterized by one group and the middle transitional part by a second group. The results can be correlated with the number of the planktonic forms and with the fossil richness of the sediment.     

Topological properties of disjoint channel networks within enclosed regions

Enclosure of some portion of one or more natural stream-drainage basins by superposition of a rectangle on a map of drainage network results in fragmentation of the natural basins into a set of disjoint channel networks. Each of these may have some channel links and forks of the natural network plus truncated links intersected by the enclosure boundary. The topological properties of the network elements in the enclosure are used to set up a model of random network patterns, in which the number of disjoint channel networks is expressed as a function of the number of links and forks in the enclosures. This function is shown to be a multiplicative constant times the square root of the number of links or forks. Empirical data on square and rectangular enclosures of several sizes from the Inez (Kentucky)Quadrangle map showed that the predicted multiplicative constants do not agree with observation, but that the square-root relation seems to hold at least to a first approximation. The models thus can be used as a norm against which deviations of real-world enclosures from network pattern randomness can be studied.     

Energy spectrum of HeII in a strong magnetic field and bound-bound transition probabilities

The ground state energy of the Heii (singly ionized helium) atom is determined in magnetic fields up to 10¹² G. The 13 lowest excited states and bound-bound transition probabilities are calculated in magnetic fields from 10⁷ to 10⁹ G.     

Trajectoires rectilignes du problème des 3 corps,lorsque la constante des forces vives est nulle

This problem is reducible to the integration of the EulerChazy's differential equation. We give a new simplified version of the equation, and we interpret in the corresponding diagram the study of two extreme degenerate cases.

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Presenté à la Conference du Mécanique Céleste, Oberwolfach, Germany, août 27–septembre 2, 1972.