Laser method for finding axis of rotation

Illumination of rotating surface with laser beam and examination of interference patterns resulting from diffused reflections determines position of axis and direction of motion. Interference patterns are viewed through a lens or recorded on film as circular streaking patterns

Optimal reconstruction systems for erasures and for the q-potential

We introduce the $q$-potential as an extension of the Benedetto-Fickus frame potential, defined on general reconstruction systems and we show that protocols are the minimizers of this potential under certain restrictions. We extend recent results of B.G. Bodmann on the structure of optimal protocols with respect to 1 and 2 lost packets where the worst (normalized) reconstruction error is computed with respect to a compatible unitarily invariant norm. We finally describe necessary and sufficient (spectral) conditions, that we call $q$-fundamental inequalities, for the existence of protocols with prescribed properties by relating this problem to Klyachko's and Fulton's theory on sums of hermitian operators

Measurement of temperature and density fluctuations in turbulence using an ultraviolet laser

Noninvasive measurement of density and temperature fluctuations in turbulent air flow was examined. The approach used fluorescence of oxygen molecules which are selectively excited by a tunable vacuum ultraviolet laser beam. The strength of the fluorescence signal and its dependence on laser wavelength vary with the density and temperature of the air in the laser beam. Because fluorescence can be detected at 90 degrees from the beam propagation direction, spatial resolution in three dimensions, rather than path-integrated measurements can be achieved. With spatial resolutions of the order of a millimeter and at supersonic air velocities it is necessary to perform each measurement in a time of the order of a microsecond; this is possible by by using laser pulses of ten nanosecond duration. In this method atmospheric O2 is excited by the emission of a tunable ArF excimer laser, and the fluorescence, which spans the 210 to 420 range, is detected by an ultraviolet phototube

Study of vibration measurement by laser methods

Laser techniques for detecting and measuring vibrations of spacecraft model on shake tabl

The Massive Wolf-Rayet Binary SMC WR7

We present a study of optical spectra of the Wolf--Rayet star AzV 336a (= SMC WR7) in the Small Magellanic Cloud. Our study is based on data obtained at several Observatories between 1988 and 2001. We find SMC WR7 to be a double lined WN+O6 spectroscopic binary with an orbital period of 19.56 days. The radial velocities of the He absorption lines of the O6 component and the strong He{\sc ii} emission at $\lambda$4686\AA of the WN component describe antiphased orbital motions. However, they show a small phase shift of $\sim$ 1 day. We discuss possible explanations for this phase shift. The amplitude of the radial velocity variations of He {\sc ii} emission is twice that of the absorption lines. The binary components have fairly high minimum masses, $\sim$ 18 \modot and 34 \modot for the WN and O6 components, respectively.Comment: Accepted by MNRA

The Physical Properties of the Red Supergiant WOH G64: The Largest Star Known?

WOH G64 is an unusual red supergiant (RSG) in the Large Magellanic Cloud (LMC), with a number of properties that set it apart from the rest of the LMC RSG population, including a thick circumstellar dust torus, an unusually late spectral type, maser activity, and nebular emission lines. Its reported physical properties are also extreme, including the largest radius for any star known and an effective temperature that is much cooler than other RSGs in the LMC, both of which are at variance with stellar evolutionary theory. We fit moderate-resolution optical spectrophotometry of WOH G64 with the MARCS stellar atmosphere models, determining an effective temperature of 3400 +/- 25 K. We obtain a similar result from the star's broadband V - K colors. With this effective temperature, and taking into account the flux contribution from the aysmmetric circumstellar dust envelope, we calculate log(L/L_sun) = 5.45 +/- 0.05 for WOH G64, quite similar to the luminosity reported by Ohnaka and collaborators based on their radiative transfer modeling of the star's dust torus. We determine a radius of R/R_sun = 1540, bringing the size of WOH G64 and its position on the H-R diagram into agreement with the largest known Galactic RSGs, although it is still extreme for the LMC. In addition, we use the Ca II triplet absorption feature to determine a radial velocity of 294 +/- 2 km/s for the star; this is the same radial velocity as the rotating gas in the LMC's disk, which confirms its membership in the LMC and precludes it from being an unusual Galactic halo giant. Finally, we describe the star's unusual nebula emission spectrum; the gas is nitrogen-rich and shock-heated, and displays a radial velocity that is significantly more positive than the star itself by 50 km/s.Comment: 25 pages, 5 figures; accepted for publication in The Astronomical Journa

Multiplicative Lidskii's inequalities and optimal perturbations of frames

In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame \cF for \hil\cong\C^d we compute those dual frames \cG of \cF that are optimal perturbations of the canonical dual frame for \cF under certain restrictions on the norms of the elements of \cG. On the other hand, for a fixed finite frame \cF=\{f_j\}_{j\in\In} for \hil we compute those invertible operators $V$ such that $V^*V$ is a perturbation of the identity and such that the frame V\cdot \cF=\{V\,f_j\}_{j\in\In} - which is equivalent to \cF - is optimal among such perturbations of \cF. In both cases, optimality is measured with respect to submajorization of the eigenvalues of the frame operators. Hence, our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error. The key tool for these results is a multiplicative analogue of Lidskii's inequality in terms of log-majorization and a characterization of the case of equality.Comment: 22 page