Stability properties of an inverse parabolic problem with unknown boundaries

We treat the stability issue for an inverse problem arising from nondestructive evaluation by thermal imaging. We consider the determination of an unknown portion of the boundary of a thermic conducting body by overdetermined boundary data for a parabolic initial-boundary value problem.We obtain that when the unknown part of the boundary is a priori known to be smooth, the data are as regular as possible and all possible measurements are taken into account, the problem is exponentially ill-posed. Then, we prove that a single measurement with some a priori information on the unknown part of the boundary and minimal assumptions on the data, in particular on the thermal conductivity, is enough to have stable determination of the unknown boundary. Given the exponential illposedness, the stability estimate obtained is optimal

Investigations of the Morphology of Dust Shells of Comet C/2001 Q4 (NEAT)

The morphology of the dust fans and shells in the images of comet C/2001 Q4 (NEAT) showed significant changes between 2004 April and June due to rapid changes in the Earth viewing and solar illumination geometry. We model the trajectories of dust grains ejected from distributed sources on the comet to explain the observed dust morphology in the images obtained on 2004 April 16, May 12, 16, and 21, and June 3. From the fit to the observations we derive the direction of the rotation pole of the nucleus as αp = 270° ± 10° and δp = 15° ± 10°. The derived latitudes of the sources vary between -85° and +80°. Six of the sources are found to lie on a single meridian within ±25°. Using theoretical production rates of water from these sources, reported water production rates, and the archived visual light curve of the comet, we estimate the total active area on the comet to be 38.7 ± 5.8 km2 near perihelion. The fractional active area on the comet is 12% ± 2% or 25% ± 4% at perihelion, corresponding to a nuclear radius of 5 or 3.5 km, respectively. The large outgassing areas estimated in the present work can be attributed to the fact that comet 2001Q4 is a comet from the Oort Cloud visiting the inner solar system for the first time

Characterization of a MEMS-based pulse-shaping device inthedeep ultraviolet

We describe the implementation and characterization of a micro-mirror-array set-up based on Micro-Electro-Mechanical System (MEMS) technology for femtosecond pulse shaping in the deep UV. We demonstrate its capability of re-compressing spectrally broadened UV pulses with a closed-loop approach based on a genetic algorithm. A single-shot synchronization scheme, taking advantage of the limited duty cycle of the device and allowing on-line correction of the signal, is described. The second dimension of the MEMS chip can be used to partially reduce the spatial chirp of the bea

Analysis of an Inverse Problem Arising in Photolithography

We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship between the target shape and the unknown is modeled through diffractive optics. We develop a variational formulation that is well-posed and propose an approximation that can be shown to have convergence properties. The approximate problem can serve as a foundation to numerical methods.Comment: 28 pages, 1 figur

Discriminability of tryptophan containing dipeptides using quantum control

We show that the coherent manipulation of molecular wavepackets in the excited states of trp-containing dipeptides allows efficient discrimination among them. Optimal dynamic discrimination fails, however, for some dipeptide couples. When considering the limited spectral resources at play (3nm bandwidth at 266nm), we discuss the concept of discriminability, which appears uncorrelated to both static spectra and relaxation lifetime

PO-0803: Validation of a pre-treatment delivery quality assurance method for the CyberKnife Synchrony System

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Solar supergranulation revealed by granule tracking

Context: Supergranulation is a pattern of the velocity field at the surface of the Sun, which has been known about for more than fifty years, however, no satisfactory explanation of its origin has been proposed. Aims: New observational constraints are therefore needed to guide theoretical approaches which hesitate between scenarios that either invoke a large-scale instability of the surface turbulent convection or a direct forcing by buoyancy. Method: Using the 14-Mpixel CALAS camera at the Pic-du-Midi observatory, we obtained a 7.5h-long sequence of high resolution images with unprecedented field size. Tracking granules, we have determined the velocity field at the Sun's surface in great detail from a scale of 2.5Mm up to 250Mm. Results: The kinetic energy density spectrum shows that supergranulation peaks at 36Mm and spans on scales ranging between 20Mm and 75Mm. The decrease of supergranular flows in the small scales is close to a $k^{-2}$-power law, steeper than the equipartition Kolmogorov one. The probability distribution function of the divergence field shows the signature of intermittency of the supergranulation and thus its turbulent nature.Comment: 4 pages, accepted in Astronomy and Astrophysics (Letters

Strategic responses to global challenges: The case of European banking, 1973–2000

In applying a strategy, structure, ownership and performance (SSOP) framework to three major clearing banks (ABN AMRO, UBS, Barclays), this article debates whether the conclusions generated by Whittington and Mayer about European manufacturing industry can be applied to the financial services sector. While European integration plays a key role in determining strategy, it is clear that global factors were far more important in determining management actions, leading to significant differences in structural adaptation. The article also debates whether this has led to improved performance, given the problems experienced with both geographical dispersion and diversification, bringing into question the quality of decision-making over the long term

Reassessing the cardiac box: A comprehensive evaluation of the relationship between thoracic gunshot wounds and cardiac injury

Background: High energy missiles can cause cardiac injury regardless of entrance site. This study assesses the adequacy of the anatomic borders of the current “cardiac box” to predict cardiac injury. Methods: Retrospective autopsy review was performed to identify patients with penetrating torso gunshot wounds 2011-2013. Using a circumferential grid system around the thorax, logistic regression analysis was performed to detect differences in rates of cardiac injury from entrance/exit wounds in the “cardiac box” vs. the same for entrance/exit wounds outside the box. Analysis was repeated to identify regions to compare risk of cardiac injury between the current cardiac box and other regions of the thorax. Results: Over the study period, 263 patients (89% male, mean age = 34 years, median injuries/person = 2) sustained 735 wounds [80% gunshot wounds (GSWs], and 239 patients with 620 GSWs were identified for study. Of these, 95 (34%) injured the heart. Of the 257 GSWs entering the cardiac box, 31% caused cardiac injury while 21% GSWs outside the cardiac box (n = 67) penetrated the heart, suggesting that the current “cardiac box” is a poor predictor of cardiac injury relative to the thoracic non-"cardiac box" regions [Relative Risk (RR) 0.96; p=0.82]. The regions from the anterior to posterior midline of the left thorax provided the highest positive predictive value (41%) with high sensitivity (90%) while minimizing false positives making this region the most statistically significant discriminator of cardiac injury (RR 2.9; p=0.01). Conclusion: For GSWs, the current cardiac box is inadequate to discriminate whether a gunshot wound will cause a cardiac injury. As expected, entrance wounds nearest to the heart are the most likely to result in cardiac injury, but, from a clinical standpoint, it is best to think outside the “box” for GSWs to the thorax