Formal degree and existence of stable arithmetic lattices of cuspidal representations ofp-adic reductive groups

Research at MSRI supported in part by NSF Grant DMS-812079-05     

Certain problems of the approximation of functions in two variables by Fourier-Hermite sums in the space L 2(Γ², e -x ² -y ²)

Summary We give an exact estimate of the deviation of the "triangular" partial sums of the double Fourier-Hermite series of functions of the class L^r₂(D) in the space L₂(Γ2, e^-x2-y2).     

Resonance Raman scattering by excitonic polaritons in CuGaS2

Resonance Raman scattering by exciton polaritons in crystals of CuGaS₂ under excitation with the 4880 and 4765 Å lines of an Ar⁺ laser at 9 K is studied. Lines of one-and two-phonon scattering of excitonic polaritons are found and studied. It is shown that the 1LO and 2LO phonons are arranged in accordance with their energies as the Stokes shifts move farther away from the excitation energy.     

Similarity and the structure of unital matrix quadratic trinomials with pairwise different characteristic roots

The normal form of certain polynomial matrices is found.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 63–68, 1989.     

Envelope expansion methods for speech enhancement

The last decade has seen increasing interest in techniques for the enhancement of digital speech signals. Significant gains have been made in terms of signal-to-noise ratio (SNR) and quality, but few techniques have produced improvements in intelligibility. A method for speech enhancement based on nonlinear expansion of the spectral envelope is presented. The expansion is consistent with both the long-term spectrum of the speech and with the probability that speech is present in a given sample. Objective SNR measures are used to compare this algorithm with the well-known spectral subtraction method, with an alternative expansion scheme, and with limiting SNRs resulting from perfect recovery of the amplitude spectrum. For the purpose of intelligibility assessments, a simplified version of the algorithm has been implemented on a Texas Instruments TMS320-C25 system. Listening trials with this real-time system, conducted using a modified rhyme test, have produced small, but consistent, improvements in articulation scores.     

Neutron interferometry in gravitational field with torsion

We consider the possibility of finding experimental evidence of the fifth force with the measurement of a phase shift of neutron beams via an interferometric apparatus and also a possible rotation of the polarization plane of polarized neutron beams when torsion is introduced in a gravitational field.