A novel and general approach to scaling diffraction intensities is presented. The method minimizes the disagreement among multiple measurements of symmetry-related re¯ections using a stable re®nement procedure. The scale factors are described by a¯exible exponential function that allows different scaling corrections to be chosen and combined according to the needs of the experiment. The scaling model presented here includes: scale and temperature factor per batch of data; temperature factor as a continuous function of the radiation dose; absorption in the crystal; uneven exposure within a single diffraction image; and corrections for phenomena that depend on the diffraction peak position on the detector. This scaling model can be extended to include additional corrections for various instrumental and data-collection problems.

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A generalization of the Pistone-Sempi argument, demonstrating the utility of non-commutative Orlicz spaces, is presented. The question of lifting positive maps defined on von Neumann algebra to maps on corresponding noncommutative Orlicz spaces is discussed. In particular, we describe those Jordan * -morphisms on semifinite von Neumann algebras which in a canonical way induce quantum composition operators on noncommutative Orlicz spaces. Consequently, it is proved that the framework of noncommutative Orlicz spaces is well suited for an analysis of a large class of interesting noncommutative dynamical systems.

Rotationally resolved fluorescence excitation spectra of three vibronic bands in the S1←S0 transitions of 1- and 2-methylnaphthalene (1 and 2MN) have been obtained. Each band exhibits perturbations that are produced by an interaction between the restricted torsional motion of the attached methyl group and the overall rotational motion of the entire molecule. A complete analysis of these effects yields values of the torsional barrier heights, the rotational constants, and the torsion–rotation perturbation coefficients of all vibronic levels that participate in the transitions. These values depend significantly on the position of the methyl group attachment, on the electronic state of the naphthalene chromophore, and on its vibrational state, as well. For example, V3 (the threefold torsional barrier) decreases from 809 cm−1 in 00 1MN to 128 cm−1 in 00 2MN. D (the largest first-order torsion–rotation perturbation term) increases from 0.03 MHz in 00 1MN to 406 MHz in 00 2MN, a change of more than 4 orders of magnitude. The V3 values of 00 and 8̄1 1MN are 563 and ≤ 373 cm−1, respectively. A full discussion of these dynamically relevant effects and their dependence upon both electronic and geometric factors is given.