We study the asymptotic behavior of the time delay (defined as the trace of the Eisenbud–Wigner time delay operator) for scattering by potential and by magnetic field with two compact supports as the separation of supports goes to infinity. The emphasis is placed on analyzing how different the asymptotic formulae are in potential and magnetic scattering.… (More)
We study the semiclassical asymptotic behavior of the spectral shift function and of its derivative in magnetic scattering by two solenoidal fields in two dimensions under the assumption that the total magnetic flux vanishes. The system has a trajectory oscillating between the centers of two solenoidal fields. The emphasis is placed on analysing how the… (More)
For the last one and a half decades it has been known that the exponential product formula holds also in norm in nontrivial cases. In this note, we review the results on its convergence in norm as well as pointwise of the integral kernels in the case for Schrödinger operators, with error bounds. Optimality of the error bounds is elaborated.
This paper describes the scalar processor of the VPP500. The 64-bit long instruction word (LIW) architecture allows the issue of up to three operations every clock cycle. Notable features of the architecture are the PC-relative conditional branch operations, asynchronous operations to allow out-of-order execution, and interruption facility which can handle… (More)