Orthogonality relations for Chebyshev polynomials,

"C00-1469-0154."

Parallel methods and bounds of evaluating polynomials.

Bibliography: p. 24.

The use of Chebyshev matrix polynomials in the iterative solution of linear equations compared to the method of successive overrelaxtion /

"(This is being submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics, June 1959.)"

Zur theorie des Legendre-Jacobischen symbols (n/m).

Mode of access: Internet.

Cahiers de géométrie élémentaire, pour servir de complément au traité de Legendre,

Mode of access: Internet.

Financing the unemployment insurance program has shifted from a system based on individual employer's responsibility towards a socialized system.

Mode of access: Internet.

On decomposition of sub-linearised polynomials

We give a detailed exposition of the theory of decompositions of linearised polynomials, using a well-known connection with skew-polynomial rings with zero derivative. It is known that there is a one-to-one correspondence between decompositions of linearised polynomials and sub-linearised polynomials. This correspondence leads to a formula for the number of indecomposable sub-linearised polynomials of given degree over a finite field. We also show how to extend existing factorisation algorithms over skew-polynomial rings to decompose sub-linearised polynomials without asymptotic cost.

1220km propagation of 40Gbit/s single channel RZ data over dispersion managed standard (non-dispersion shifted) fibre

Error free propagation of a single polarisation optical time division multiplexed 40 Gbit/s dispersion managed pulsed data stream over dispersion (non-shifted) fibre. This distance is twice the previous record at this data rate.

Perception of concurrent sentences with harmonic or frequency-shifted voiced excitation:performance of human listeners and of computational models based on autocorrelation

Keyword identification in one of two simultaneous sentences is improved when the sentences differ in F0, particularly when they are almost continuously voiced. Sentences of this kind were recorded, monotonised using PSOLA, and re-synthesised to give a range of harmonic ?F0s (0, 1, 3, and 10 semitones). They were additionally re-synthesised by LPC with the LPC residual frequency shifted by 25% of F0, to give excitation with inharmonic but regularly spaced components. Perceptual identification of frequency-shifted sentences showed a similar large improvement with nominal ?F0 as seen for harmonic sentences, although overall performance was about 10% poorer. We compared performance with that of two autocorrelation-based computational models comprising four stages: (i) peripheral frequency selectivity and half-wave rectification; (ii) within-channel periodicity extraction; (iii) identification of the two major peaks in the summary autocorrelation function (SACF); (iv) a template-based approach to speech recognition using dynamic time warping. One model sampled the correlogram at the target-F0 period and performed spectral matching; the other deselected channels dominated by the interferer and performed matching on the short-lag portion of the residual SACF. Both models reproduced the monotonic increase observed in human performance with increasing ?F0 for the harmonic stimuli, but not for the frequency-shifted stimuli. A revised version of the spectral-matching model, which groups patterns of periodicity that lie on a curve in the frequency-delay plane, showed a closer match to the perceptual data for frequency-shifted sentences. The results extend the range of phenomena originally attributed to harmonic processing to grouping by common spectral pattern.

1000 Km transmission of 40 Gbit/s single channel RZ data over dispersion managed standard (non-dispersion shifted) fibre

Error-free transmission of a single polarization optical time division multiplexed 40 Gbit/s dispersion managed pulse data stream over 1009 km has been achieved in dispersion-compensated standard (non-dispersion shifted) fibre. This distance is twice the previous record at this data rate.

1220km propagation of 40Gbit/s single channel RZ data over dispersion managed standard (non-dispersion shifted) fibre

Error free propagation of a single polarisation optical time division multiplexed 40 Gbit/s dispersion managed pulsed data stream over dispersion (non-shifted) fibre. This distance is twice the previous record at this data rate.