Vermerke über das Wesen der Parakristalle und ihre Beteiligung an Zerebrosiden und Phosphatiden als plasmatischen Bestandteilen

Ohne Zusammenfassung Der Freiburger Wissenschaftlichen Gesellschaft sei für gütige Unterstützung obiger Untersuchung bestens gedankt.     

Net polarization of a molecular beam by strong electrostatic or radiative fields

We present a simple analytic approximation for evaluating the ensemble-averaged orientation or alignment of a beam of molecules subjected to a strong static or radiative field. This approximation is based on the eigenproperties which polar or polarizable molecules exhibit in the strong-field, harmonic-librator limit, and on the Boltzmann statistics of the free rotor states which adiabatically correlate with the harmonic librator states. For either the permanent or induced dipole case, the resultant formula involves just two dimensionless parameters which characterize the strength of the molecule-field interaction and the rotational temperature. The net polarization of a molecular beam thus obtained is shown to be in an excellent agreement with the exact values computed numerically from first principles. The validity range of the approximation includes the large-interaction, high temperature regions of the parameter space where first-principle calculations are onerous.     

Methods for computing lower bounds to eigenvalues of self-adjoint operators

Summary. New approaches for computing tight lower bounds to the eigenvalues of a class of semibounded self-adjoint operators are presented that require comparatively little a priori spectral information and permit the effective use of (among others) finite-element trial functions. A variant of the method of intermediate problems making use of operator decompositions having the form is reviewed and then developed into a new framework based on recent inertia results in the Weinstein-Aronszajn theory. This framework provides greater flexibility in analysis and permits the formulation of a final computational task involving sparse, well-structured matrices. Although our derivation is based on an intermediate problem formulation, our results may be specialized to obtain either the Temple-Lehmann method or Weinberger's matrix method. Received December 12, 1992 / Revised version received October 5, 1994