None

A review of recent developments in the quantum differential calculus. The quantum group GL[sub q](n) is treated by considering it as a particular quantum space. Functions on SL[sub q] (n) are defined as a subclass of functions on GL[sub q](n). The case of SO[sub q](n) is also briefly considered. These notes cover part of a lecture given at the XIX International Conference on Group Theoretic Methods in Physics, Salamanca, Spain 1992.

A review of recent developments in the quantum differential calculus. The quantum group GL{sub q}(n) is treated by considering it as a particular quantum space. Functions on SL{sub q} (n) are defined as a subclass of functions on GL{sub q}(n). The case of SO{sub q}(n) is also briefly considered. These notes cover part of a lecture given at the XIX International Conference on Group Theoretic Methods in Physics, Salamanca, Spain 1992.

The goal of this program is the construction of an x-ray laser in the kilovolt regime. Recent experimental results indicate that a new technique for the generation of strong amplification of x-ray wavelengths is feasible. It involves the combination of (1) a new ultrahigh brightness subpicosecond laser technology and (2) a recently discovered unique mode of strong-field interaction, particularly applicable to molecules. A concept of molecular x-ray design emerges from the considerations which matches the mode of excitation to the structure of the molecular system. The molecular approach enables the combination of very highly electronically excited conditions with an environment characteristic of dense cold matter, a general situation exceptionally conducive to x-ray amplification. Both high efficiency and wavelength tunability are intrinsic features of this method. Recent results discussed in this report are revealing important characteristics of the molecular strong-field coupling pertinent to this goal. A continued program of research is proposed to evaluate this method for the production of x-ray amplification in the kilovolt region.

The goal of this program is the construction of an x-ray laser in the kilovolt regime. Recent experimental results indicate that a new technique for the generation of strong amplification of x-ray wavelengths is feasible. It involves the combination of (1) a new ultrahigh brightness subpicosecond laser technology and (2) a recently discovered unique mode of strong-field interaction, particularly applicable to molecules. A concept of molecular x-ray design emerges from the considerations which matches the mode of excitation to the structure of the molecular system. The molecular approach enables the combination of very highly electronically excited conditions with an environment characteristic of dense cold matter, a general situation exceptionally conducive to x-ray amplification. Both high efficiency and wavelength tunability are intrinsic features of this method. Recent results discussed in this report are revealing important characteristics of the molecular strong-field coupling pertinent to this goal. A continued program of research is proposed to evaluate this method for the production of x-ray amplification in the kilovolt region.

We suggest a phenomenological model describing the sum rules for the real and virtual polarized photon absorption on the nucleon. The contribution of the isobar delta-(1232) electroproduction, essential at small Q{sup 2}, has been subtracted quantitatively. The model predictions are compared with the results of the EMC polarized structure function measurements on the photon.