Characteristic Function, Schur Parameters and Pseudocontinuation of Schur functions

In [19] there is an approach to the investigation of the pseudocontinuability of Schur functions in terms of Schur parameters. In particular, there was obtained a criterion for the pseudocontinuability of Schur functions and the Schur parameters of rational Schur functions were described. This approach is based on the description in terms of the Schur parameters of the relative position of the largest shift and the largest coshift in a completely nonunitary contraction. It should be mentioned that these results received a further development in [8, 21-24]. This paper is aimed to give a survey about essential results on this direction. The main object in the approach is based on considering a Schur function as characteristic function of a contraction (see Section 1.2). This enables us outgoing from Schur parameters to construct a model of the corresponding contraction (see Section 2). In this model, the relative position of the largest shift and the largest coshift in a completely nonunitary contraction is described in Section 3 and then, based on this model, to find characteristics which are responsible for the pseudocontinuability of Schur functions (see Sections 4 and 5). The further parts of this paper (see Sections 6-8) admit applications of the above results to the study of properties of Schur functions and questions related with them.Comment: arXiv admin note: text overlap with arXiv:1003.167

Characteristic Function, Schur Interpolation Problem and Darlington Synthesis

In this paper we would like to show the interrelation between the different mathematical theories concerning the Schur interpolation problem, contractions in Hilbert spaces, pseudocontinuation and Darlington synthesis. The main objects of this article are contractive functions holomorphic in the unit disc (Schur functions). Here they are considered, on the one hand, as characteristic functions of contractions in Hilbert spaces and, on the other hand, as transfer functions of open systems

Stellar twins determine the distance of the Pleiades

© 2016 ESO.Since the release of the Hipparcos catalogue in 1997, the distance to the Pleiades open cluster has been heavily debated. The distance obtained from Hipparcos and those by alternative methods differ by 10 to 15%. As accurate stellar distances are key to understanding stellar structure and evolution, this dilemma puts the validity of some stellar evolution models into question. Using our model-independent method to determine parallaxes based on twin stars, we report individual parallaxes of 15 FGK type stars in the Pleiades in anticipation of the astrometric mission Gaia. These parallaxes give a mean cluster parallax of 7.42 ± 0.09 mas,which corresponds to a mean cluster distance of 134.8 ± 1.7 pc. This value agrees with the current results obtained from stellar evolution models

Influence of single- and double-flame spray pyrolysis on the structure of MnOₓ/γ-Al₂O₃ and FeOₓ/γ-Al₂O₃ catalysts and their behaviour in CO removal under lean exhaust gas conditions

MnOx/Al2O3 and FeOx/Al2O3 samples were prepared by two-nozzle flame spray pyrolysis to minimize the formation of composite phases. For this purpose, manganese(ii) naphthenate or iron(ii) naphthenate and aluminium-sec-butylate were sprayed in separate flames and both the structure and the catalytic performance of the materials in CO oxidation were compared to the corresponding single-nozzle flame spray pyrolysis catalysts. Characterization by X-ray diffraction, diffuse reflectance UV-vis spectroscopy and X-ray absorption near-edge structure unravelled that the phases formed in double-flame spray pyrolysis (DFSP) were significantly different from those in single-flame spray pyrolysis; highly dispersed separate entities of manganese/iron oxide and alumina were identified in this case. Despite a slightly lower BET surface area the DFSP prepared samples performed generally better in catalytic CO oxidation than those derived from one single flame. In addition, the manganese-based catalysts were more effective for CO conversion than the corresponding iron-based samples, even at low concentrations

<i>Gaia</i> Data Release 1. Summary of the astrometric, photometric, and survey properties

Context. At about 1000 days after the launch of Gaia we present the first Gaia data release, Gaia DR1, consisting of astrometry and photometry for over 1 billion sources brighter than magnitude 20.7. Aims. A summary of Gaia DR1 is presented along with illustrations of the scientific quality of the data, followed by a discussion of the limitations due to the preliminary nature of this release. Methods. The raw data collected by Gaia during the first 14 months of the mission have been processed by the Gaia Data Processing and Analysis Consortium (DPAC) and turned into an astrometric and photometric catalogue. Results. Gaia DR1 consists of three components: a primary astrometric data set which contains the positions, parallaxes, and mean proper motions for about 2 million of the brightest stars in common with the HIPPARCOS and Tycho-2 catalogues – a realisation of the Tycho-Gaia Astrometric Solution (TGAS) – and a secondary astrometric data set containing the positions for an additional 1.1 billion sources. The second component is the photometric data set, consisting of mean G-band magnitudes for all sources. The G-band light curves and the characteristics of ∼3000 Cepheid and RR-Lyrae stars, observed at high cadence around the south ecliptic pole, form the third component. For the primary astrometric data set the typical uncertainty is about 0.3 mas for the positions and parallaxes, and about 1 mas yr−1 for the proper motions. A systematic component of ∼0.3 mas should be added to the parallax uncertainties. For the subset of ∼94 000 HIPPARCOS stars in the primary data set, the proper motions are much more precise at about 0.06 mas yr−1. For the secondary astrometric data set, the typical uncertainty of the positions is ∼10 mas. The median uncertainties on the mean G-band magnitudes range from the mmag level to ∼0.03 mag over the magnitude range 5 to 20.7. Conclusions. Gaia DR1 is an important milestone ahead of the next Gaia data release, which will feature five-parameter astrometry for all sources. Extensive validation shows that Gaia DR1 represents a major advance in the mapping of the heavens and the availability of basic stellar data that underpin observational astrophysics. Nevertheless, the very preliminary nature of this first Gaia data release does lead to a number of important limitations to the data quality which should be carefully considered before drawing conclusions from the data

A new Late Agenian (MN2a, Early Miocene) fossil assemblage from Wallenried (Molasse Basin, Canton Fribourg, Switzerland)

Excavations of two fossiliferous layers in the Wallenried sand- and marl pit produced a very diversified vertebrate fauna. New material allows the reassessment of the taxonomic position of the ruminant taxa Andegameryx andegaviensis and endemic Friburgomeryx wallenriedensis. An emended diagnosis for the second species is provided and additional material of large and small mammals, as well as ectothermic vertebrates, is described. The recorded Lagomorpha show interesting morphological deviations from other Central European material, and probably represent a unique transitional assemblage with a co-occurrence of Titanomys, Lagopsis and Prolagus. Rodentia and Eulipotyphla belong to typical and well-known species of the Agenian of the Swiss Molasse Basin. Abundant small mammal teeth have allowed us to pinpoint the biostratigraphic age of Wallenried to late MN2a. The biostratigraphic age conforms to data derived from the charophyte assemblages and confirms the oldest occurrence of venomous snake fangs. The palaeoenvironmental context is quite complex. Sedimentary structures and fauna (fishes, frogs, salamanders, ostracods) are characteristic for a humid, lacustrine environment within a flood plain system

Survival and long-term maintenance of tertiary trees in the Iberian Peninsula during the Pleistocene. First record of Aesculus L.

The Italian and Balkan peninsulas have been places traditionally highlighted as Pleistocene glacial refuges. The Iberian Peninsula, however, has been a focus of controversy between geobotanists and palaeobotanists as a result of its exclusion from this category on different occasions. In the current paper, we synthesise geological, molecular, palaeobotanical and geobotanical data that show the importance of the Iberian Peninsula in the Western Mediterranean as a refugium area. The presence of Aesculus aff. hippocastanum L. at the Iberian site at Cal Guardiola (Tarrasa, Barcelona, NE Spain) in the Lower– Middle Pleistocene transition helps to consolidate the remarkable role of the Iberian Peninsula in the survival of tertiary species during the Pleistocene. The palaeodistribution of the genus in Europe highlights a model of area abandonment for a widely-distributed species in the Miocene and Pliocene, leading to a diminished and fragmentary presence in the Pleistocene and Holocene on the southern Mediterranean peninsulas. Aesculus fossils are not uncommon within the series of Tertiary taxa. Many appear in the Pliocene and suffer a radical impoverishment in the Lower–Middle Pleistocene transition. Nonetheless some of these tertiary taxa persisted throughout the Pleistocene and Holocene up to the present in the Iberian Peninsula. Locating these refuge areas on the Peninsula is not an easy task, although areas characterised by a sustained level of humidity must have played an predominant role

Real-Time Nanoparticle–Cell Interactions in Physiological Media by Atomic Force Microscopy

Particle–cell interactions in physiological media are important in determining the fate and transport of nanoparticles and biological responses to them. In this work, these interactions are assessed in real time using a novel atomic force microscopy (AFM) based platform. Industry-relevant CeO2 and Fe2O3 engineered nanoparticles (ENPs) of two primary particle sizes were synthesized by the flame spray pyrolysis (FSP) based Harvard Versatile Engineering Nanomaterials Generation System (Harvard VENGES) and used in this study. The ENPs were attached on AFM tips, and the atomic force between the tip and lung epithelia cells (A549), adhered on a substrate, was measured in biological media, with and without the presence of serum proteins. Two metrics were used to assess the nanoparticle cell: the detachment force required to separate the ENP from the cell and the number of bonds formed between the cell and the ENPs. The results indicate that these atomic level ENP–cell interaction forces strongly depend on the physiological media. The presence of serum proteins reduced both the detachment force and the number of bonds by approximately 50% indicating the important role of the protein corona on the particle cell interactions. Additionally, it was shown that particle to cell interactions were size and material dependent