Quantum number theoretic transforms on multipartite finite systems.

A quantum system composed of p-1 subsystems, each of which is described with a p-dimensional Hilbert space (where p is a prime number), is considered. A quantum number theoretic transform on this system, which has properties similar to those of a Fourier transform, is studied. A representation of the Heisenberg-Weyl group in this context is also discussed.

Narcolepsy and psychopathology: is there an association?

BACKGROUND: It is widely believed that patients with narcolepsy show high rates of associated psychiatric disturbance, especially schizophrenia and depression. However, surveys have produced conflicting findings and have not addressed the potential confounding effects of stimulant drug treatment. METHOD: Forty-five patients with narcolepsy attending a sleep disorder clinic and 50 matched normal controls underwent structured psychiatric interview. Using a 'lifetime' approach, psychiatric symptoms and diagnoses were established for both groups. RESULTS: Four of the narcolepsy patients but none of the controls had experienced psychotic symptoms. All four patients were taking amphetamines, and the symptoms resolved when the dose was lowered or treatment was changed to modafinil. The lifetime frequency of various depressive syndromes did not differ significantly between the groups. CONCLUSIONS: Contrary to previous claims this study found little to suggest that narcolepsy is associated with schizophrenia. Nor, despite its serious social and occupational consequences, does narcolepsy appear to be associated with an increased frequency of diagnosable depressive disorders.

Wave propagation in one-dimensional optical quasiperiodic systems.

One-dimensional quasiperiodic optical systems are studied, using a Schrödinger-like equation with a potential V(x)=2lambda(1) cos x+2lambda(2) cos alphax as an approximation to the wave equation in the slowly-varying wave approximation. It is shown that small changes in the parameter alpha produce major changes in the band structure of the system. For certain values of alpha, the band structure consists of many "thin bands" and allows the possibility of dense multiplexing. The propagation of "noisy optical waves" that contain many frequencies with a thermal distribution is also studied with a thermodynamic model. Quantities like the thermodynamically averaged group velocity and the thermodynamically averaged inverse effective mass are introduced in order to quantify the complex relation between the frequency and wave vector in these systems.

Fractional Fourier transform for quasi-periodic Bloch functions.

The fractional Fourier transform (FRFT) for quasi-periodic Bloch functions is studied. An isomorphism between square-integrable functions on the real line and quasi-periodic Bloch functions is used to extend existing work on the fractional Fourier transform for the former functions to the latter. The properties of the FRFT for quasi-periodic Bloch functions are discussed, and various numerical examples are presented.

Time-frequency analysis and filtering of kinematic signals with impacts using the Wigner function: accurate estimation of the second derivative.

Biomechanical signals are represented in the time-frequency domain using the Wigner distribution function. Filtering of this representation for the case of a non-stationary displacement signal with impact is studied. Smoothed displacement data are then double differentiated and compared with references accelerometer data. It is shown that this technique is able to remove noise from these signals in a better way than conventional filtering techniques currently used in biomechanics.