Algebras generated by two bounded holomorphic functions

We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, of which one is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension of such algebras. The conditions are expressed in terms of the inner part of a function which is explicitly derived from each pair of generators. Our results are based on identifying z-invariant subspaces included in the closure of the algebra. Versions of these results for the case of the disk algebra are given.Comment: 22 pages ; a number of minor mistakes have been corrected, and some points clarified. Conditionally accepted by Journal d'Analyse Mathematiqu

High-dimensional simplexes for supermetric search

In a metric space, triangle inequality implies that, for any three objects, a triangle with edge lengths corresponding to their pairwise distances can be formed. The n-point property is a generalisation of this where, for any (n+1) objects in the space, there exists an n-dimensional simplex whose edge lengths correspond to the distances among the objects. In general, metric spaces do not have this property; however in 1953, Blumenthal showed that any semi-metric space which is isometrically embeddable in a Hilbert space also has the n-point property. We have previously called such spaces supermetric spaces, and have shown that many metric spaces are also supermetric, including Euclidean, Cosine, Jensen-Shannon and Triangular spaces of any dimension. Here we show how such simplexes can be constructed from only their edge lengths, and we show how the geometry of the simplexes can be used to determine lower and upper bounds on unknown distances within the original space. By increasing the number of dimensions, these bounds converge to the true distance. Finally we show that for any Hilbert-embeddable space, it is possible to construct Euclidean spaces of arbitrary dimensions, from which these lower and upper bounds of the original space can be determined. These spaces may be much cheaper to query than the original. For similarity search, the engineering tradeoffs are good: we show significant reductions in data size and metric cost with little loss of accuracy, leading to a significant overall improvement in exact search performance

A simple analytical model for dark matter halo structure and adiabatic contraction

A simple analytical model for describing inner parts of dark matter halo is considered. It is assumed that dark matter density is power-law. The model deals with dark matter distribution function in phase space of adiabatic invariants (radial action and angular momentum). Two variants are considered for the angular part of the distribution function: narrow and broad distribution. The model allows to describe explicitly the process of adiabatic contraction of halo due to change of gravitational potential caused by condensation of baryonic matter in the centre. The modification of dark matter density in the centre is calculated, and is it shown that the standard algorithm of adiabatic contraction calculation overestimates the compressed halo density, especially in the case of strong radial anisotropy.Comment: 5 pages, 3 figures. v3 - major improvements, another halo model introduced, discussion extende

Spatially resolved XMM-Newton analysis and a model of the nonthermal emission of MSH 15-52

We present an X-ray analysis and a model of the nonthermal emission of the pulsar wind nebula (PWN) MSH15-52. We analyzed XMM-Newton data to obtain the spatially resolved spectral parameters around the pulsar PSRB1509-58. A steepening of the fitted power-law spectra and decrease in the surface brightness is observed with increasing distance from the pulsar. In the second part of this paper, we introduce a model for the nonthermal emission, based on assuming the ideal magnetohydrodynamic limit. This model is used to constrain the parameters of the termination shock and the bulk velocity of the leptons in the PWN. Our model is able to reproduce the spatial variation of the X-ray spectra. The parameter ranges that we found agree well with the parameter estimates found by other authors with different approaches. In the last part of this paper, we calculate the inverse Compton emission from our model and compare it to the emission detected with the H.E.S.S. telescope system. Our model is able to reproduce the flux level observed with H.E.S.S., but not the spectral shape of the observed TeV {\gamma}-ray emission.Comment: Accepted for publication in A&A, 9 pages, 15 figure

Relative spins and excitation energies of superdeformed bands in 190Hg: Further evidence for octupole vibration

An experiment using the Eurogam Phase II gamma-ray spectrometer confirms the existence of an excited superdeformed (SD) band in 190Hg and its very unusual decay into the lowest SD band over 3-4 transitions. The energies and dipole character of the transitions linking the two SD bands have been firmly established. Comparisons with RPA calculations indicate that the excited SD band can be interpreted as an octupole-vibrational structure.Comment: 12 pages, latex, 4 figures available via WWW at http://www.phy.anl.gov/bgo/bc/hg190_nucl_ex.htm

Partitioning of on-demand electron pairs

We demonstrate the high fidelity splitting of electron pairs emitted on demand from a dynamic quantum dot by an electronic beam splitter. The fidelity of pair splitting is inferred from the coincidence of arrival in two detector paths probed by a measurement of the partitioning noise. The emission characteristic of the on-demand electron source is tunable from electrons being partitioned equally and independently to electron pairs being split with a fidelity of 90%. For low beam splitter transmittance we further find evidence of pair bunching violating statistical expectations for independent fermions

High-K isomers in 176^{176}W and mechanisms of K-violation

An isomer, with t1/2 = 35 +- 10 ns and J, Kpi = 14, 14+, has been observed in the nucleus 176W using the reaction 150Nd(30Si,4n) at a beam energy of 133 MeV. The isomer exhibits an unusual pattern of decay in which the _majority_ of the flux proceeds directly to states with =0, bypassing available levels of intermediate K. This severe breakdown of normal K-selection rules in 176W is compared with recent observations of K-violation in neighboring nuclei, within the framework of proposed theoretical approaches. The available data on these K-violating decays seem to have a consistent explanation in models of K-mixing which include large-amplitude fluctuations of the nuclear shape

On the Spectral Index of Distant Radio Galaxies

The problems of using the spectral index of radio galaxies in various tests, in particular, in selecting distant radio sources are considered. The history of the question of choosing a criterion of searching for distant radio galaxies based on the spectral index is presented. For a new catalog of 2442 radio galaxies constructed from NED, SDSS, and CATS data, an analytical form of the sp ectral index.redshift relation has been determined for the first time. The spectral index.angular size and spectral index.flux density diagrams have also been constructed. Peculiarities of the distribution of sources on these diagrams are discussed.Comment: 7 pages,5 figure

Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides

All-optical signal processing is envisioned as an approach to dramatically decrease power consumption and speed up performance of next-generation optical telecommunications networks. Nonlinear optical effects, such as four-wave mixing (FWM) and parametric gain, have long been explored to realize all-optical functions in glass fibers. An alternative approach is to employ nanoscale engineering of silicon waveguides to enhance the optical nonlinearities by up to five orders of magnitude, enabling integrated chip-scale all-optical signal processing. Previously, strong two-photon absorption (TPA) of the telecom-band pump has been a fundamental and unavoidable obstacle, limiting parametric gain to values on the order of a few dB. Here we demonstrate a silicon nanophotonic optical parametric amplifier exhibiting gain as large as 25.4 dB, by operating the pump in the mid-IR near one-half the band-gap energy (E~0.55eV, lambda~2200nm), at which parasitic TPA-related absorption vanishes. This gain is high enough to compensate all insertion losses, resulting in 13 dB net off-chip amplification. Furthermore, dispersion engineering dramatically increases the gain bandwidth to more than 220 nm, all realized using an ultra-compact 4 mm silicon chip. Beyond its significant relevance to all-optical signal processing, the broadband parametric gain also facilitates the simultaneous generation of multiple on-chip mid-IR sources through cascaded FWM, covering a 500 nm spectral range. Together, these results provide a foundation for the construction of silicon-based room-temperature mid-IR light sources including tunable chip-scale parametric oscillators, optical frequency combs, and supercontinuum generators

Chemical evolution of the Galactic bulge as traced by microlensed dwarf and subgiant stars. Detailed abundance analysis of OGLE-2008-BLG-209S

AIMS. Our aims are twofold. First we aim to evaluate the robustness and accuracy of stellar parameters and detailed elemental abundances that can be derived from high-resolution spectroscopic observations of microlensed dwarf and subgiant stars. We then aim to use microlensed dwarf and subgiant stars to investigate the abundance structure and chemical evolution of the Milky Way Bulge. [ABRIDGED] METHODS. We present a detailed elemental abundance analysis of OGLE-2008-BLG-209S, the source star of a new microlensing event towards the Bulge, for which we obtained a high-resolution spectrum with the MIKE spectrograph on the Magellan Clay telescope. We have performed four different analyses of OGLE-2008-BLG-209S. [ABRIDGED] We have also re-analysed three previous microlensed dwarf stars OGLE-2006-BLG-265S, MOA-2006-BLG-099S, and OGLE-2007-BLG-349S with the same method. This homogeneous data set, although small, enables a direct comparison between the different stellar populations. RESULTS. We find that OGLE-2008-BLG-209S is a subgiant star that has a metallicity of [Fe/H] ~-0.33. It possesses [alpha/Fe] enhancements similar to what is found for Bulge giant stars at the same metallicity, and what also is found for nearby thick disc stars at the same metallicity. In contrast, the previous three microlensing dwarf stars have very high metallicities, [Fe/H]>+0.4, and more solar-like abundance ratios, i.e. [alpha/Fe]~0. The decrease in the [alpha/Fe] ratio with [Fe/H] is the typical signature of enrichment from low and intermediate mass stars. We furthermore find that the results for the four Bulge stars, in combination with results from studies of giant stars in the Bulge, seem to favour a secular formation scenario for the Bulge.Comment: Accepted for publication in A&A, 17 pages, online table will be available in published version, or by contacting the first autho