Data are compiled and evaluated for collision processes of excitation, dissociation, ionization, attachment, and recombination of hydrogen molecules and molecular ions (H 2+ , H 3+) by electron impact as well as for properties of their collision products.

Abstract. In an earlier paper, the first author showed that certain normalized formal solutions of homogeneous linear partial di¤erential equations with constant coe‰cients are multisummable, with a multisummability type that can be determined from a Newton polygon associated with the PDE. In this article, some of the results obtained there are extended in several directions: First of all, arbitrary formal solutions of inhomogeous PDE are considered, and it is shown that, in some sense, they can be computed completely explicitly. Secondly, the Gevrey order of these formal solutions is determined. Finally, formal power series are discussed that, in general, do not satisfy a PDE with constant coe‰cients, but instead may be considered as solutions of singularly perturbed ODE, or integro-di¤erential equations of a certain form.

This paper concerns perturbations of smooth vector fields on T n (constant if n 3) with zeroth-order C ∞ and Gevrey G σ , σ 1, pseudodifferential operators. Simultaneous resonance is introduced and simultaneous resonant normal forms are exhibited (via conjugation with an elliptic pseudodifferential operator) under optimal simultaneous Diophantine conditions outside the resonances. In the C ∞ category the results are complete, while in the Gevrey category the effect of the loss of the Gevrey regularity of the conjugating operators due to Diophantine conditions is encountered. The normal forms are used to study global hypoellipticity in C ∞ and Gevrey G σ . Finally, the exceptional sets associated with the simultaneous Diophantine conditions are studied. A generalized Hausdorff dimension is used to give precise estimates of the 'size' of different exceptional sets, including some inhomogeneous examples.

No abstract