Erhaltungssätze für die Wirkung in elektromagnetischen und gravischen Strahlungsfeldern

Two generally covariant integral conservation laws concerning electromagnetic null fields and vacuum gravitational fields of type II with vanishing Riemanneigenvalue respectively are proved. The conserved quantities both have the dimensions of action. The electromagnetic law shows that with respect to the propagation of energy a null field may be represented by a stream of photons. The gravitational conservation theorem is in many respects similar to the electromagnetic one; it admits to calculate the change of intensity along a gravitational ray.     

Strategies for the representation of a tone in background noise in the temporal aspects of the discharge patterns of auditory-nerve fibers

The responses of populations of auditory-nerve fibers to both a 1.0-kHz tone, and 1.0-kHz tone in broadband noise, have been measured. Period histograms were generated from fiber spike trains and discrete Fourier transforms (DFTs) with a resolution of 125 Hz were computed from each histogram. Sample mean and sample variance statistics were generated for period histograms of response and for temporal response measures derived from discrete Fourier transforms. It is demonstrated how the statistical properties of auditory-nerve fiber response determine the strategy for the estimation and discrimination of particular stimulus components. When the tone is presented alone, the entire population of auditory-nerve fibers provides statistically reliable estimates of the 1.0-kHz tone. Upon addition of the broadband noise stimulus only those units with characteristic frequencies which are close in frequency to the 1.0-kHz stimulus provide spectral estimates which have high signal-to-noise ratios (mean-squared-to-variance ratios). Estimates of the 1.0-kHz-tone stimulus derived from auditory-nerve fibers with characteristic frequencies which are far from the 1.0-kHz stimulus are statistically unreliable. Based on the responses of the population of auditory-nerve fibers, the strategy for estimating the 1.0-kHz-tone stimulus is to derive estimates of the 1.0-kHz stimulus from the subpopulation of neurons with characteristic frequencies close to the 1.0-kHz stimulus. It is concluded that neurons which are tuned close to 1.0-kHz provide the central nervous system (CNS) with the most salient information about the 1.0-kHz stimulus in the presence of the broadband background.     

Perfect matchings in hexagonal systems

A simple algorithm is developed which allows to decide whether or not a given hexagonal system has a perfect matching (and to find such a matching). This decision is also of chemical relevance since a hexagonal system is the skeleton of a benzenoid hydrocarbon molecule if and only if it has a perfect matching. Dedicated to Paul Erdős on his seventieth birthday     

The lamb shift in helium from a self-consistent field theory of electrodynamics

In this paper we present the results of an investigation of the finite self-consistent field theory of electrodynamics applied earlier to the calculation of the Lamb shift in hydrogen (Sachs & Schwebel, 1961; Sachs, 1972), now applied to the problem of the Lamb shift in the low-lying states of Helium. We construct the covariant nonlinear field equations of this theory for Helium, from the Lagrangian formalism. In the linear approximation, the Hamiltonian associated with this field theory for the two-electron atom is set up. It is equivalent to the Breit Hamiltonian plus two extra terms. This generalization is a direct consequence of the two-component spinor formalism of the factorization of the Maxwell theory of electromagnetism that is contained in this theory of electrodynamics (Sachs, 1971). Thus, the energy spectrum predicted for the Helium atom is the spectrum predicted by the Breit Hamiltonian, shifted by amounts in the different energy states according to the effects of the extra terms in the Hamiltonian. The latter can be associated with the corrections to the Helium spectrum that are conventionally attributed to the Lamb shift. The level shifts for the 1¹ S and 2³ S states are calculated using the Foldy-Wouthuysen transformation, with the generalization of Charplvy for the two-electron atom. The results are found to be in close agreement with the experimental values for the energy shifts not predicted by the Dirac theory, and with the theoretical values predicted by quantum electrodynamics.