Exceptional Θ-Correspondences I

Let G be either a split SO(2n+2), or a split adjoint group of type En, (n=6,7,8), over a p-adic field. In this article we study correspondences arising by restricting the minimal representation of G to various dual pairs in G.     

An application of radon inversion to diffraction tomography

Basic equations of linear computer tomography are considered; a connection of the mathermatical formulation of problems of computer tomography with problems of integral geometry is indicated; the properties of the Radon transform for even- and odd-dimensional spaces are analyzed, and applications of Radon inversion to problems of diffraction tomography are presented. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 264–277. Translated by V. N. Troyan.     

Inclusive two-jet production at HERA: direct and resolved cross sections in next-to-leading order QCD

We have calculated inclusive two-jet cross sections in next-to-leading order QCD for low Q ² ep collisions superimposing direct and resolved contributions. Infrared and collinear singularities in the virtual and real contributions are cancelled with the phase space slicing method. Various inclusive two-jet distributions have been computed. The results are compared with recent data from the ZEUS collaboration at HERA.     

Laser systems specialized for laser spectroscopy at storage rings

Laser spectroscopy at storage rings often suffers from a limited resolution due to Doppler-broadened resonances. Broadening is caused by the velocity spread of the ions stored in the beam. In the following, the present status of our work on laser systems specialized on the specific needs of laser spectroscopy at storage rings is reported. Two pulsed laser systems were developed. One is a dye laser whose spectral bandwidth can be switched by inserting different Littrow-prisms into the resonator. An increase in bandwidth up to a factor of 45 was achieved. This laser was used for fast qualitative scans and high resolution measurements. The other laser system is a Nd : YAG laser pumped optical parametric oscillator. It is a tunable laser system covering the spectral range from 410 to 4000 nm. Furthermore, a continuous wave laser with a frequency shifted feedback cavity is described. It shows broadband emission with an adjustable bandwidth of up to 4.5 GHz. This laser can be advantageous for laser cooling of ion beams. This revised version was published online in August 2006 with corrections to the Cover Date.     

Concerning the multiplicators of Fourier series in the trigonometric system

In this paper we prove theorems on multiplicators of Fourier series inL _p, where the conditions depend on a parameterp. An example illustrating the importance of these conditions is constructed. Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 235–247, February, 1998.     

Role of stationary photon statistics in a high-Q cavity mode while it is exciting the active laser medium

It has been shown by Yu. M. Golubev, M. I. Kolobov, and I. V. Sokolov, Zh. éksp. Teor. Fiz. 111, 1579 (1997) [JETP 84, 864 (1997)], that when an optical cavity is excited by external radiation from a sub-Poisson laser the cavity mode may be in either a sub-Poisson or a Poisson stationary state. This is not important for a resonant medium which is excited into the upper laser level while interacting with this mode inside the cavity. The degree of regularity of the excitation will be identical to that of the initial light flux incident on the cavity, and this ultimately ensures the same sub-Poisson lasing as for strictly regular pumping of the resonant medium. Zh. éksp. Teor. Fiz. 113, 1223–1234 (April 1998)