Stability of solutions of linear difference equations with periodic coefficients

This paper represents the last technical contribution of Professor Patrick Parks before his untimely death in February 1995. The remaining authors of the paper, which was subsequently completed, wish to dedicate the article to Patrick. A frequency criterion for the stability of solutions of linear difference equations with periodic coefficients is established. The stability criterion is based on a consideration of the behaviour of a frequency hodograph with respect to the origin of coordinates in the complex plane. The formulation of this criterion does not depend on the order of the difference equation.

Identification and minimization of IIR tap coefficients for the cancellation of complex multipath in terrestrial television

By using a deterministic approach, an exact form for the synchronous detected video signal under a ghosted condition is presented. Information regarding the phase quadrature-induced ghost component derived from the quadrature forming nature of the vestigial sideband (VSB) filter is obtained by crosscorrelating the detected video with the ghost cancel reference (GCR) signal. As a result, the minimum number of taps required to correctly remove all the ghost components is subsequently presented. The results are applied to both National Television System Committee (NTSC) and phase alternate line (PAL) television.

Use of the statistical properties of the wavelet-transform coefficients for optimization of integration time in Fourier transform spectrometry

We show that an analysis of the mean and variance of discrete wavelet coefficients of coaveraged time-domain interferograms can be used as a specification for determining when to stop coaveraging. We also show that, if a prediction model built in the wavelet domain is used to determine the composition of unknown samples, a stopping criterion for the coaveraging process can be developed with respect to the uncertainty tolerated in the prediction.

Preparation of (–)-epigallocatechin gallate from commercial green tea by caffeine precipitation and solvent partition

A method has been developed which enables the easy and inexpensive preparation of gram quantities of (–)-epigallocatechin gallate from green tea (Camellia sinensis). A decaffeinated aqueous brew of commercial green tea is treated with caffeine (30 m ). The precipitate is redissolved after decaffeination with chloroform and further purified by solvent partition with ethyl hexanoate and propyl acetate. Commercial leaf (25 g) yields 400 mg (–)-epigallocatechin gallate at better than 80% purity, as judged by reversed phase HPLC.

Asymptotic expansions for Taylor coefficients of the composition of two functions

We give an asymptotic expansion for the Taylor coe±cients of L(P(z)) where L(z) is analytic in the open unit disc whose Taylor coe±cients vary `smoothly' and P(z) is a probability generating function. We show how this result applies to a variety of problems, amongst them obtaining the asymptotics of Bernoulli transforms and weighted renewal sequences.

Alternating sums of binomial coefficients with unit fraction arithmetic sequence coefficients

Expressions for finite sums involving the binomial coefficients with unit fraction coefficients whose denominators form an arithmetic sequence are determined.

Arboreal thorn-dwelling ants use domatia morphology to partition nest sites on the savanna ant-plant, Vachellia erioloba

Nest site selection in arboreal, domatia-dwelling ants, particularly those coexisting on a single host plant, is little understood. To examine this phenomenon we studied the African savannah tree Vachellia erioloba, which hosts ants in swollen-thorn domatia. We found four ant species from different genera (Cataulacus intrudens, Tapinoma subtile, Tetraponera ambigua and an unidentified Crematogaster species). In contrast to other African ant plants, many V. erioloba trees (41 % in our survey) were simultaneously co-occupied by more than one ant species. Our study provides quantitative field data describing: (1) aspects of tree and domatia morphology relevant to supporting a community of mutualist ants, (2) how ant species occupancy varies with domatia morphology and (3) how ant colony size varies with domatia size and species. We found that Crematogaster sp. occupy the largest thorns, followed by C. intrudens, with T. subtile in the smallest thorns. Thorn age, as well as nest entrance hole size correlated closely with ant species occupant. These differing occupancy patterns may help to explain the unusual coexistence of three ant species on individual myrmecophytic trees. In all three common ant species, colony size, as measured by total number of ants, increased with domatia size. Additionally, domatia volume and species identity interact to predict ant numbers, suggesting differing responses between species to increased availability of nesting space. The proportion of total ants in nests that were immatures varied with thorn volume and species, highlighting the importance of domatia morphology in influencing colony structure.

Bollène-2002 experiment: radar quantitative precipitation estimation in the Cévennes–Vivarais region, France

The Bollène-2002 Experiment was aimed at developing the use of a radar volume-scanning strategy for conducting radar rainfall estimations in the mountainous regions of France. A developmental radar processing system, called Traitements Régionalisés et Adaptatifs de Données Radar pour l’Hydrologie (Regionalized and Adaptive Radar Data Processing for Hydrological Applications), has been built and several algorithms were specifically produced as part of this project. These algorithms include 1) a clutter identification technique based on the pulse-to-pulse variability of reflectivity Z for noncoherent radar, 2) a coupled procedure for determining a rain partition between convective and widespread rainfall R and the associated normalized vertical profiles of reflectivity, and 3) a method for calculating reflectivity at ground level from reflectivities measured aloft. Several radar processing strategies, including nonadaptive, time-adaptive, and space–time-adaptive variants, have been implemented to assess the performance of these new algorithms. Reference rainfall data were derived from a careful analysis of rain gauge datasets furnished by the Cévennes–Vivarais Mediterranean Hydrometeorological Observatory. The assessment criteria for five intense and long-lasting Mediterranean rain events have proven that good quantitative precipitation estimates can be obtained from radar data alone within 100-km range by using well-sited, well-maintained radar systems and sophisticated, physically based data-processing systems. The basic requirements entail performing accurate electronic calibration and stability verification, determining the radar detection domain, achieving efficient clutter elimination, and capturing the vertical structure(s) of reflectivity for the target event. Radar performance was shown to depend on type of rainfall, with better results obtained with deep convective rain systems (Nash coefficients of roughly 0.90 for point radar–rain gauge comparisons at the event time step), as opposed to shallow convective and frontal rain systems (Nash coefficients in the 0.6–0.8 range). In comparison with time-adaptive strategies, the space–time-adaptive strategy yields a very significant reduction in the radar–rain gauge bias while the level of scatter remains basically unchanged. Because the Z–R relationships have not been optimized in this study, results are attributed to an improved processing of spatial variations in the vertical profile of reflectivity. The two main recommendations for future work consist of adapting the rain separation method for radar network operations and documenting Z–R relationships conditional on rainfall type.

Determination of the embedded thermo-optical expansion coefficients of PbTe and ZnSe thin film infrared multilayers

This paper reports the first derived thermo-optical properties for vacuum deposited infrared thin films embedded in multilayers. These properties were extracted from the temperature-dependence of manufactured narrow bandpass filters across the 4-17 µm mid-infrared wavelength region. Using a repository of spaceflight multi-cavity bandpass filters, the thermo-optical expansion coefficients of PbTe and ZnSe were determined across an elevated temperature range 20-160 ºC. Embedded ZnSe films showed thermo-optical properties similar to reported bulk values, whilst the embedded PbTe films of lower optical density, deviate from reference literature sources. Detailed knowledge of derived coefficients is essential to the multilayer design of temperature-invariant narrow bandpass filters for use in non-cooled infrared detection systems. We further present manufacture of the first reported temperature-invariant multi-cavity narrow bandpass filter utilizing PbS chalcogenide layer material.

Intensities and self-broadening coefficients of the strongest water vapour lines in the 2.7 and 6.25μm absorption bands

Intensities and self-broadening coefficients are presented for about 460 of the strongest water vapour lines in the spectral regions 1400–1840 cm−1 and 3440–3970 cm−1 at room temperature, obtained from rather unique measurements using a 5-mm-path-length cell. The retrieved spectral line parameters are compared with those in the HITRAN database ver. 2008 and 2012 and with recent ab-initio calculations. Both the retrieved intensities and half-widths are on average in reasonable agreement with those in HITRAN-2012. Maximum systematic differences do not exceed 4% for intensities (1600 cm−1 band) and 7% for self-broadening coefficients (3600 cm−1 band). For many lines however significant disagreements were detected with the HITRAN-2012 data, exceeding the average uncertainty of the retrieval. In addition, water vapour line parameters for 5300 cm−1 (1.9 μm) band reported by us in 2005 were also compared with HITRAN-2012, and show average differences of 4–5% for both intensities and half-widths.