Agler-Commutant Lifting on an Annulus

This note presents a commutant lifting theorem (CLT) of Agler type for the annulus \({\mathbb A}\) . Here the relevant set of test functions are the minimal inner functions on \({\mathbb A}\) —those analytic functions on \({\mathbb A}\) which are unimodular on the boundary and have exactly two zeros in \({\mathbb A}\) —and the model space is determined by a distinguished member of the Sarason family of kernels over \({\mathbb A}\) . The ideas and constructions borrow freely from the CLT of Ball et al. (Indiana Univ Math J 48(2):653–675, 1999) and Archer (Unitary dilations of commuting contractions. PhD thesis, University of Newcastle, 2004) for the polydisc, and Ambrozie and Eschmeier (A commutant lifting theorem on analytic polyhedra. Topological algebras, their applications, and related topics, 83108, Banach Center Publications, vol 67. Polish Academy of Sciences, Warsaw, 2005) for the ball in \({\mathbb C^n}\) , as well as generalizations of the de Branges–Rovnyak construction like found in Agler (On the representation of certain holomorphic functions defined on a polydisc. Topics in operator theory: Ernst D. Hellinger memorial volume, operator theory: advances and applications, vol 48. Birkhäuser, Basel, pp 47–66, 1990) and Ambrozie et al. (J Oper Theory 47(2):287–302, 2002). It offers a template for extending the result in McCullough and Sultanic (Complex Anal Oper Theory 1(4):581–620, 2007) to infinitely many test functions. Among the needed new ingredients is the formulation of the factorization implicit in the statement of the results in Ball et al. (Indiana Univ Math J 48(2):653–675, 1999) and Archer (Unitary dilations of commuting contractions. PhD thesis, University of Newcastle, 2004) and McCullough and Sultanic (Complex Anal Oper Theory 1(4):581–620, 2007) in terms of certain functional Hilbert spaces of Hilbert space valued functions.     

Rapid and implicit effects of color category on visual search

Many studies suggest that the color category influences visual perception. It is also well known that oculomotor control and visual attention are closely linked. In order to clarify temporal characteristics of color categorization, we investigated eye movements during color visual search. Eight color disks were presented briefly for 20–320 ms, and the subject was instructed to gaze at a target shown prior to the trial. We found that the color category of the target modulated eye movements significantly when the stimulus was displayed for more than 40 ms and the categorization could be completed within 80 ms. With the 20 ms presentation, the search performance was at a chance level, however, the first saccadic latency suggested that the color category had an effect on visual attention. These results suggest that color categorization affects the guidance of visual attention rapidly and implicitly.     

Biological monitoring of solar UV radiation at 17 sites in Asia, Europe and South America from 1999 to 2004

A small and robust dosimeter for determining the biologically effective dose of ambient UV radiation has been developed using UV-sensitive mutant spores of Bacillus subtilis strain TKJ6312. A membrane filter with four spots of the spores was snapped to a slide mount. The slide was wrapped and covered with two or more layers of polyethylene sheet to protect the sample from rain and snow and to reduce monthly-cumulative doses within the measurable range. From 1999, monthly data were collected at 17 sites for more than 1 year, and data for 4 to 6 consecutive years were obtained from 12 sites. Yearly total values of the spore inactivation dose (SID) ranged from 3200 at subarctic Oulu to 96000 at tropical Denpasar, and the mean yearly values of SID exhibited an exponential dependence on latitude in both hemispheres with a doubling for about every 14 degrees of change. During the observation period, increasing trends of UV doses have been observed at all sites with more than 5 years of data available. Year-to-year variations at high and middle latitude sites are considered due mostly to climatic variation. At three tropical sites, negative correlations between the yearly doses and the column ozone amounts were observed. The results verified the applicability of spore dosimetry for global and long-time monitoring of solar UV radiation, in particular at tropical sites where no monitoring is taking place.     

Low-Loss Y-Branch Waveguides Designed by Wavefront Matching Method

In this paper, we describe the procedure for designing low-loss Y-branch waveguides by the wavefront matching (WFM) method, and report experimental results as proof of concept. The designed Y-branches were fabricated using silica-based planar lightwave circuit (PLC) technology. A Y-branch fabricated with a 0.45%-Delta waveguide exhibited a low excess loss of less than 0.2 dB over a wide wavelength range of 1250 to 1650 nm. In addition, we demonstrate that the WFM-designed Y-branches enable us to provide compact 1 times 32 splitters with an average insertion loss of 16.0 dB at a wavelength of 1550 nm. In addition, we present some experimental results obtained using samples with different Delta values, and show that our design method is more efficient for a higher Delta waveguide suitable for functional PLC devices.     

Large reduction of singlemode-fibre coupling loss in 1.5% Δplanar lightwave circuits using spot-size converters

Reduction of singlemode fibre coupling loss in 1.5% Δ planar lightwave circuits from 1.8 to 0.2 dB/point is achieved using simple vertically and laterally tapered spot-size converters. These spot-size converters were used to realise an arrayed-waveguide grating with a very low insertion loss of 0.7 dB     

General formula describing drift of interferometer fiber-optic gyrodue to Faraday effect: reduction of the drift in twin-depo-I-FOG

The drift of an interferometric fiber-optic gyro (I-FOG) by the magnetic field through the Faraday effect is generally formulated. By the derived formula, the drift reduction mechanism in the interferometric fiber-optic gyro using ordinary single-mode fiber as a sensing coil and two depolarizers (twin-depo-I-FOG) is clarified, as well as that in the interferometric fiber-optic gyro using polarization maintaining fiber (PM-I-FOG). Degradation factors in the practical twin-depo-I-FOG are evaluated by using the derived equation, and methods for further drift reduction are discussed     

Distributed fiber-optic stress sensor by synthesis of the optical coherence function

A distributed fiber-optic stress sensor by synthesis of the optical coherence function is proposed. This system can obtain polarization coupling distribution in a polarization maintaining fiber due to lateral stress, using neither mechanical moving parts nor further calculations. In experiments, the spatial resolution of about 9 m and the measurable range of about 1040 m are demonstrated.     

Pushing the Lewis Acidity Boundaries of Boron Compounds With Non‐Planar Triarylboranes Derived from Triptycenes

Bending the planar trigonal boron center of triphenylborane by connecting its aryl rings with carbon or phosphorus linkers gave access to a series of 9‐boratriptycene derivatives with unprecedented structures and reactivities. NMR spectroscopy and X‐ray diffraction of the Lewis adducts of these non‐planar boron Lewis acids with weak Lewis base revealed particularly strong covalent bond formation. The first Lewis adduct of a trivalent boron compounds with the Tf₂N^? anion illustrates the unrivaled Lewis acidity of these species. Increasing the pyramidalization of the boron center and using a cationic phosphonium linker resulted in an exceptional enhancement of Lewis acidity. Introduction of a phosphorus and a boron atom at each edge of a triptycene framework, allowed access to new bifunctional Lewis acid‐base 9‐phospha‐10‐boratriptycenes featuring promising reactivity for the activation of carbon‐halogen bonds.     

An unstructured finite‐volume method for coupled models of suspended sediment and bed load transport in shallow‐water flows

The aim of this work is to develop a well‐balanced finite‐volume method for the accurate numerical solution of the equations governing suspended sediment and bed load transport in two‐dimensional shallow‐water flows. The modelling system consists of three coupled model components: (i) the shallow‐water equations for the hydrodynamical model; (ii) a transport equation for the dispersion of suspended sediments; and (iii) an Exner equation for the morphodynamics. These coupled models form a hyperbolic system of conservation laws with source terms. The proposed finite‐volume method consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms. The gradient fluxes are discretized using a modified Roe's scheme using the sign of the Jacobian matrix in the coupled system. A well‐balanced discretization is used for the treatment of source terms. In this paper, we also employ an adaptive procedure in the finite‐volume method by monitoring the concentration of suspended sediments in the computational domain during its transport process. The method uses unstructured meshes and incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep sediment concentrations and bed load gradients that may form in the approximate solutions. Details are given on the implementation of the method, and numerical results are presented for two idealized test cases, which demonstrate the accuracy and robustness of the method and its applicability in predicting dam‐break flows over erodible sediment beds. The method is also applied to a sediment transport problem in the Nador lagoon.Copyright © 2013 John Wiley & Sons, Ltd.     

One-pot synthesis to engineer a Co-KIT-6 catalyst for the ring opening of methylcyclopentane

Co-KIT-6 mesoporous materials with Ia3d symmetry and Si/Co ratios of 50, 25, and 10 were prepared using hydrothermal one-pot synthesis. The Co-KIT-6 mesoporous materials were characterized by X-ray diffraction, N₂ adsorption–desorption isotherms, scanning electron microscopy, transmission electron microscopy, Fourier transform infrared, and X-ray photoelectron spectroscopy. The physicochemical characterization results show that all of the samples have well-ordered cubic mesostructures and that the structural integrity is preserved for n_Si/n_Co ratios as high as 10. It was found that most of the cobalt ions exist as isolated framework species, but for Co-KIT-6 with an n_Si/n_Co ratio of 10, the presence of extra-framework species/small cobalt oxide clusters cannot be excluded. The ability of these catalysts was tested by examining the conversion of the reaction of methylcyclopentane with hydrogen at atmospheric pressure and temperatures between 200 and 450 °C. The catalytic results show that their catalytic activity increases significantly with increasing cobalt content. The active sites, tetrahedrally coordinated Co and isolated atomic Co sites, were responsible for the endocyclic CC bond rupture between substituted secondary–tertiary carbon atoms, whereas the small clusters serve as active sites for the successive CC bond rupture. The ring-opening selectivity can be improved by increasing the density of isolated cobalt atom sites at low reaction temperatures.