Emission spectrum of electron excited solid nitrogen

We report a new emission band in solid nitrogen between 1490 Å and 2320 Å, due to the de-excitation of the a′¹Σ^?_u molecular level and on the temperature dependence of some structures, in particular the ²D → ⁴S atomic nitrogen transition and the Vegard Kaplan bands.     

Excitonic luminescence spectrum of electron excited solid xenon

The luminescence spectrum of electron excited solid Xenon shows a broad structure around 1750 Å attributed to molecular excitons (excimers) and sharp excitonic lines around 1500 Å.     

Temperature variation of the radiative recombination spectrum of the solid rare gases

We present detailed spectra of the electron excited solid rare gases in the exciton region. The variation of the temperature gives a red-shift of the structures when the temperature increases. This evolution for Xe, Kr and Ar can be related to the variation of the lattice parameter.     

Qualitative properties of modified equations

Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations.     

How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.