Head-Media Interaction in Magnetic Recording

The head‐tape interaction in magnetic recording is modelled by a coupled system of a second‐order differential equation for the pressure and a fourth‐order differential equation for the tape deflection. There is also the constraint that the spacing between the head and tape remains positive. In this paper, we study the stationary one‐dimensional case: We establish the existence of a smooth solution and a boundary layer phenomenon observed both numerically and experimently. The two‐dimensional case is briefly discussed. Accepted April 24, 1996     

über die Streuung relativistischer Elektronen im Coulombfeld

An approximative method for summing the partial wave series for the scattering amplitude of the relativistic scattering of electrons by an atomic nucleus is investigated in the simplest case of a point charge nucleus for electron energies not less 10 MeV. In the course of the computationΒ=1 is assumed (Β=v/c,v andc denote the velocity of the electron and of light, respectively). The Sommerfeld-Watson-transformation is the starting point. The method consists in setting up an asymptotic expansion in 1/sin² (θ/2) (θ is the scattering angle) of the amount coming from the Regge-poles. Two further amounts, the dependence of which on the scattering angle especially for easy nuclei is little, are computed numerically without simplification, which should be possible. The method is developed from a special way of summing the partial wave series for the non-relativistic Rutherford scattering, which may be done analytically.Mott's scattering formula is verified and finally the applicability of the method is examined for summing the relativistic partial wave series with the exact S-Matrix. The results are as exact as the expension of the cross section to order (Z/137)⁵ (Z is the nuclear charge). The method should in principle be applicable for an extended nucleus, but in this case there remain still several problems.     

A Preliminary Test in Discriminant Analysis

One of the aims of discriminant analysis is the allocation of unknown entities to populations that are knowna priori. Considerkpopulations. LetXdenote the vector of observations on an experimental unit, whose origin is uncertain. For the general parametric case, a test is proposed to verify the hypothesis thatXis coming from a new population. The case of normal population with equal variance is fully derived.     

Vanishing periods of cusp forms over modular symbols

partially supported by NSF grant #DMS-8919696