Lyapunov 1-forms for flows

In this paper we find conditions which guarantee that a given flow $\Phi$ on a compact metric space $X$ admits a Lyapunov one-form $\omega$ lying in a prescribed \v{C}ech cohomology class $\xi\in \check H^1(X;\R)$. These conditions are formulated in terms of the restriction of $\xi$ to the chain recurrent set of $\Phi$. The result of the paper may be viewed as a generalization of a well-known theorem of C. Conley about the existence of Lyapunov functions.Comment: 27 pages, 3 figures. This revised version incorporates a few minor improvement

Gamma-Ray Burst Polarization: Limits from RHESSI Measurements

Using the RHESSI satellite as a Compton polarimeter, a recent study claimed that the prompt emission of GRB021206 was almost fully linearly polarized. This was challenged by a subsequent reanalysis. We present an novel approach, applying our method to the same data. We identify Compton scattering candidates by carefully filtering events in energy, time, and scattering geometry. Our polarization search is based on time dependent scattering rates in perpendicular directions, thus optimally excluding systematic errors. We perform simulations to obtain the instrument's polarimetric sensitivity, and these simulations include photon polarization. For GRB021206, we formally find a linear polarization degree of 41% (+57% -44%), concluding that the data quality is insufficient to constrain the polarization degree in this case. We further applied our analysis to GRB030519B and found again a null result.Comment: 39 pages, 11 figures, accepted for publication by the Astrophysical Journa

Spectral Analysis of GRBs Measured by RHESSI

The Ge spectrometer of the RHESSI satellite is sensitive to Gamma Ray Bursts (GRBs) from about 40 keV up to 17 MeV, thus ideally complementing the Swift/BAT instrument whose sensitivity decreases above 150 keV. We present preliminary results of spectral fits of RHESSI GRB data. After describing our method, the RHESSI results are discussed and compared with Swift and Konus.Comment: 4 pages, 4 figures, conference proceedings, 'Swift and GRBs: Unveiling the Relativistic Universe', San Servolo, Venice, 5-9 June 2006, to appear in Il Nouvo Ciment

Dentine decalcification and smear layer removal by different ethylenediaminetetraacetic acid and 1-hydroxyethane-1,1-diphosphonic acid species

AIM To compare solutions of di- and tetrasodium ethylenediaminetetraacetic acid (EDTA) and 1-hydroxyethane-1,1-diphosphonic acid (HEDP) regarding their ability to solubilize calcium from dentine and remove smear layer. METHODOLOGY Solutions with a molarity corresponding to that of 17% Na EDTA (pH adjusted to 8.5) were prepared by dissolving Na and Na salts of HEDP (etidronate), or Na EDTA in deionized water. Standardized root dentine discs covered by a smear layer were prepared from human third molars. These discs (n = 10 per group) were immersed in test solutions or phosphate-buffered saline for 1 min. The dissolved Ca was determined by atomic absorption spectroscopy, apparently opened dentinal tubules by laser scanning microscopy and automated image analysis. Ca values were compared between groups by parametric, tubular areas by nonparametric methods, α = 0.05. RESULTS Solutions prepared from the tetrasodium salts were alkaline (pH 11.3-11.4), whilst counterparts made from the disodium salts were acidic. The EDTA solutions dissolved more calcium than the HEDP counterparts (P < 0.05); solutions prepared with the disodium salts dissolved more calcium than those made from the tetrasodium salts (P < 0.05). There was a high correlation between dissolved calcium and the apparently opened tubular areas (Spearman's ρ = 0.81). Differences between groups regarding opened tubules were similar to those observed regarding the Ca values, with a slightly reduced discerning power due to high variance. CONCLUSION Calcium chelation and thus smear layer removal by EDTA and HEDP are influenced by pH

Generation of three-dimensional prototype models based on cone beam computed tomography

Purpose: The purpose of this study was to generate three-dimensional models based on digital volumetric data that can be used in basic and advanced education. Methods: Four sets of digital volumetric data were established by cone beam computed tomography (CBCT) (Accuitomo, J. Morita, Kyoto, Japan). Datasets were exported as Dicom formats and imported into Mimics and Magic software programs to separate the different tissues such as nerve, tooth and bone. These data were transferred to a Polyjet 3D Printing machine (Eden 330, Object, Israel) to generate the models. Results: Three-dimensional prototype models of certain limited anatomical structures as acquired volumetrically were fabricated. Conclusions: Generating three-dimensional models based on CBCT datasets is possible. Automated routine fabrication of these models, with the given infrastructure, is too time-consuming and therefore too expensiv

Nonsolar astronomy with the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI)

The Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) is a NASA Small Explorer satellite designed to study hard x-ray and gamma-ray emission from solar flares. In addition, its high-resolution array of germanium detectors can see photons from high-energy sources throughout the Universe. Here we discuss the various algorithms necessary to extract spectra, lightcurves, and other information about cosmic gamma-ray bursts, pulsars, and other astrophysical phenomena using an unpointed, spinning array of detectors. We show some preliminary results and discuss our plans for future analyses. All RHESSI data are public, and scientists interested in participating should contact the principal author

Polarization from GRB021206: No constraints from reanalysis of RHESSI data

The determination of a polarization signal in Gamma Ray Bursts (GRBs) would give new information about their nature and mechanism. Using the RHESSI satellite as a Compton polarimeter, Coburn W. and Boggs S. E. (Nature, 423 (2003) 415) reported that GRB021206 was highly linearly polarized. This was contradicted by Rutledge R. E. and Fox D. B. (Mon. Not. R. Astron. Soc., 350 (2004) 1288) who found about 10 times less scattering events suitable for measuring polarization. Applying our own method to thesamedata weconfirm them uch lower number of suitable scattering events. But we obtain three times smaller errors by using better selection criteria. Comparison with our Monte Carlo simulations shows that from the RHESSI data of GRB021206 we cannot distinguish between no and full polarization within less than 2 standard deviations. We also applied our method to other GRBs observed by RHESSI. This shows that the probability to observe a GRB suitable for polarization search with such an instrument is small

Phase detection at the quantum limit with multi-photon Mach-Zehnder interferometry

We study a Mach-Zehnder interferometer fed by a coherent state in one input port and vacuum in the other. We explore a Bayesian phase estimation strategy to demonstrate that it is possible to achieve the standard quantum limit independently from the true value of the phase shift and specific assumptions on the noise of the interferometer. We have been able to implement the protocol using parallel operation of two photon-number-resolving detectors and multiphoton coincidence logic electronics at the output ports of a weakly-illuminated Mach-Zehnder interferometer. This protocol is unbiased and saturates the Cramer-Rao phase uncertainty bound and, therefore, is an optimal phase estimation strategy.Comment: 4 pages, 5 figures replaced fig. 1 to correct graphics bu