On the complexity of computing determinants

We present new baby steps/giant steps algorithms of asymptotically fast running time for dense matrix problems. Our algorithms compute the determinant, characteristic polynomial, Frobenius normal form and Smith normal form of a dense n × n matrix A with integer entries in and bit operations; here denotes the largest entry in absolute value and the exponent adjustment by +o(1) captures additional factors for positive real constants C₁, C₂, C₃. The bit complexity results from using the classical cubic matrix multiplication algorithm. Our algorithms are randomized, and we can certify that the output is the determinant of A in a Las Vegas fashion. The second category of problems deals with the setting where the matrix A has elements from an abstract commutative ring, that is, when no divisions in the domain of entries are possible. We present algorithms that deterministically compute the determinant, characteristic polynomial and adjoint of A with n^3.2+o(1) and O(n^2.697263) ring additions, subtractions and multiplications.To B. David Saunders on the occasion of his 60th birthday     

Robustness study of the pseudo open-loop controller for multiconjugate adaptive optics

Robustness of the recently proposed "pseudo open-loop control" algorithm against various system errors has been investigated for the representative example of the Gemini-South 8-m telescope multiconjugate adaptive-optics system. The existing model to represent the adaptive-optics system with pseudo open-loop control has been modified to account for misalignments, noise and calibration errors in deformable mirrors, and wave-front sensors. Comparison with the conventional least-squares control model has been done. We show with the aid of both transfer-function pole-placement analysis and Monte Carlo simulations that POLC remains remarkably stable and robust against very large levels of system errors and outperforms in this respect least-squares control. Approximate stability margins as well as performance metrics such as Strehl ratios and rms wave-front residuals averaged over a 1-arc min field of view have been computed for different types and levels of system errors to quantify the expected performance degradation.     

Chirped holographic grating used as the dispersive element in an optical spectrometer

We have developed a new design of optical spectrometer based on the use of a chirped holographic grating inscribed on a flat substrate. This type of grating has a surface modulation with a spatially varying period. The ability of the chirped grating to focus a beam is exploited to reduce significantly the physical dimensions of the instrument. Wavelength selection is achieved by a pure translation of the chirped grating. The properties of the chirped grating spectrometer have been characterized with different lasers and arc lamps and compared with those of two commercial spectrometers. A performance parameter has been defined, enabling the various instruments to be compared.     

Infrared detection of chlorinated hydrocarbons in water at ppb levels of concentrations

Infrared sensor, based on attenuated total reflection phenomenon, for the detection of chlorinated hydrocarbons (CHCs) represents a big advantage compared to chromatographic and mass spectroscopic techniques since it is a one step detector. Pre-concentration and separation take place in the polymer film with simultaneous identification of pollutants by the infrared beam. The analysis is rapid, sample does not require any initial preparation, and can be easily performed in the field. The main default of the latest version of the sensor was a low sensibility (above 1 ppm) compared to the threshold levels of the contaminants. In the present work, it is documented that the response dynamics of the optical sensor and its sensitivity depend strongly on the diffusion of pollutants through a boundary layer formed between polymer film and the monitored solution and in the polymer film. The reduction of thickness of the boundary layer through a controlled high flow rate, and the optimization of thickness (volume) of polymer films result in a tremendous improvement of the response dynamics. It is demonstrated that the sensor can detect simultaneously six CHCs: monochlorobenzene, 1,2-dichlorobenzene, 1,2,4-trichlorobenzene, chloroform, trichloroethylene, and perchloroethylene in their mixture with a sensitivity as low as a few ppb. This level of detection opens up numerous applications for the optical sensor.     

La solution solide Ca2MnO4−xFx. Etude radiocristallographique et dilatometrique

The Ca₂MnO_4?xF_x solid solution (0 ? × ? 0.30) has tetragonal symmetry in its whole homogeneity range and belongs to the K₂NiF₄ type. The fluorine ions seem to be preferentially in the (001) planes, at the common corners of the octahedra. The thermal variation of c parameter shows a minimum : an crystal chemical explanation is proposed for this unusual effect.     

Phases ε obtenues par decomposition des spinelles non-stoechiometriques dans les systemes Ga2O3-MgO,Al2O3-NiO,Al2O3-AlN et Al2O3-Li2O

In the systems Al₂O₃-AlN, Al₂O₃-NiO, Al₂O₃-Li₂O and Ga₂O₃-MgO, non-stoechiometric spinels, when decomposed at high temperatures, form an intermediate metastable phase ε. This phase has a one-dimensional periodic antiphase-domain structure. The antiphase boundaries are parallel to the (310) plane and the displacement vector is $\text{1}\text{4}$ [110] when referred to the spinel structure. Across each antiphase boundary, some octahedral and tetrahedral sites share faces instead of corners. In the case of ε_AlN, cationic vacancies occupy these sites; in the other cases, this is likely to go along with a segregation of the more charged ions.