Sets of Minimal Capacity and Extremal Domains

Let f be a function meromorphic in a neighborhood of infinity. The central problem in the present investigation is to find the largest domain D \subset C to which the function f can be extended in a meromorphic and singlevalued manner. 'Large' means here that the complement C\D is minimal with respect to (logarithmic) capacity. Such extremal domains play an important role in Pad'e approximation. In the paper a unique existence theorem for extremal domains and their complementary sets of minimal capacity is proved. The topological structure of sets of minimal capacity is studied, and analytic tools for their characterization are presented; most notable are here quadratic differentials and a specific symmetry property of the Green function in the extremal domain. A local condition for the minimality of the capacity is formulated and studied. Geometric estimates for sets of minimal capacity are given. Basic ideas are illustrated by several concrete examples, which are also used in a discussion of the principal differences between the extremality problem under investigation and some classical problems from geometric function theory that possess many similarities, which for instance is the case for Chebotarev's Problem

Design and Fabrication of Components with Optimized Lattice Microstructures

The design and fabrication of components with optimized lattice microstructures is a new approach to creating lightweight high-performance objects. This paper introduces a unique and complete integration of design and fabrication leading to the creation of structural components with complex composite microstructures. Rather than a solid cast component with optimized outer shape this new approach leads to a component with an inner skeleton or microstructure maximizing one or more properties such as the stiffness-to-weight ratio. Three dimensional gradient materials are a natural outcome of this approach. An introduction to the design optimization and hybrid fabrication approach will be provided in addition to research progress and challenges through Spring 2004.Mechanical Engineerin

Using neural networks for high-speed blood cell classification in a holographic-microscopy flow-cytometry system

High-throughput cell sorting with flow cytometers is an important tool in modern clinical cell studies. Most cytometers use biomarkers that selectively bind to the cell, but induce significant changes in morphology and inner cell processes leading sometimes to its death. This makes label-based cell sorting schemes unsuitable for further investigation. We propose a label-free technique that uses a digital inline holographic microscopy for cell imaging and an integrated, optical neural network for high-speed classification. The perspective of dense integration makes it attractive to ultrafast, large-scale cell sorting. Network simulations for a ternary classification task (monocytes/granulocytes/lymphocytes) resulted in 89% accuracy

The support of the logarithmic equilibrium measure on sets of revolution in R3\R^3

For surfaces of revolution $B$ in $\R^3$, we investigate the limit distribution of minimum energy point masses on $B$ that interact according to the logarithmic potential $\log (1/r)$, where $r$ is the Euclidean distance between points. We show that such limit distributions are supported only on the ``out-most'' portion of the surface (e.g., for a torus, only on that portion of the surface with positive curvature). Our analysis proceeds by reducing the problem to the complex plane where a non-singular potential kernel arises whose level lines are ellipses

A Solid State Pulsed Coagulating Diathermy Instrument

Solid state pulsed coagulating diathermy instrumen

The 2006 hot phase of Romano's star (GR 290) in M33

Understanding the nature of the instabilities of LBVs is important to understand the late evolutionary stages of very massive stars. We investigate the long term, S Dor-type variability of the luminous blue variable GR290 (Romano's star) in M33, and its 2006 minimum phase. New spectroscopic and photometric data taken in November and December 2006 were employed in conjunction with already published data on GR290 to derive the physical structure of GR290 in different phases and the time scale of the variability. We find that by the end of 2006, GR 290 had reached the deepest visual minimum so far recorded. Its present spectrum resembles closely that of the Of/WN9 stars, and is the hottest so far recorded in this star (and in any LBV as well), while its visual brightness decreased by about 1.4 mag. This first spectroscopic record of GR290 during a minimum phase confirms that, similarly to AG Car and other LBVs, the star is subject to ample S Dor-type variations, being hotter at minimum, suggesting that the variations take place at constant bolometric luminosity.Comment: 4 figures, 1 table, accepted for publication in A&A Letter

SN 2005 gj: Evidence for LBV supernovae progenitors?

There has been mounting observational evidence in favour of Luminous Blue Variables (LBVs) being the direct progenitors of supernovae. Here we present possibly the most convincing evidence yet for such progenitors. We find multiple absorption component P-Cygni profiles of hydrogen and helium in the spectrum of SN 2005gj, which we interpret as being an imprint of the progenitors mass-loss history. Such profiles have previously only been detected in Luminous Blue Variables. This striking resemblance of the profiles, along with wind velocities and periods consistent with LBV's leads us to connect SN 2005gj to an LBV progenitor.Comment: Accepted as a letter to A&A, 4 pages,3 figure

The variable stellar wind of Rigel probed at high spatial and spectral resolution

We present a spatially resolved, high-spectral resolution (R=12000) K-band temporal monitoring of Rigel using AMBER at the VLTI. Rigel was observed in the Bracket Gamma line and its nearby continuum in 2006-2007, and 2009-2010. These unprecedented observations were complemented by contemporaneous optical high-resolution spectroscopy. We analyse the near-IR spectra and visibilities with the 1D non-LTE radiative-transfer code CMFGEN. The differential and closure phase signal exhibit asymmetries that are interpreted as perturbations of the wind. A systematic visibility decrease is observed across the Bracket Gamma. During the 2006-2007 period the Bracket Gamma and likely the continuum forming regions were larger than in the 2009-2010 epoch. Using CMFGEN, we infer a mass-loss rate change of about 20% between the two epochs. We further find time variations in the differential visibilities and phases. The 2006-2007 period is characterized by noticeable variations of the differential visibilities in Doppler position and width and by weak variations in differential and closure phase. The 2009-2010 period is much more quiet with virtually no detectable variations in the dispersed visibilities but a strong S-shape signal is observed in differential phase coinciding with a strong ejection event discernible in the optical spectra. The differential phase signal that is sometimes detected is reminiscent of the signal computed from hydrodynamical models of corotating interaction regions. For some epochs the temporal evolution of the signal suggests the rotation of the circumstellar structures.Comment: Paper accepted in the A&A journa