Generalised golden ratios over integer alphabets

It is a well known result that for β ∈ (1,1+√52) and x ∈ (0,1β−1) there exists uncountably many (ǫi)∞i=1 ∈ {0,1}N such that x = P∞i=1ǫiβ−i. When β ∈ (1+√52,2] there exists x ∈ (0,1β−1) for which there exists a unique (ǫi)∞i=1 ∈ {0,1}N such that x=P∞i=1ǫiβ−i. In this paper we consider the more general case when our sequences are elements of {0, . . . , m}N. We show that an analogue of the golden ratio exists and give an explicit formula for it.

The Golden Age returns: Virgil's fourth Eclogue in the political panegyric of the Italian courts

E. H. Gombrich and others have analysed the uses made of language and imagery from Virgil's famous fourth Eclogue in panegyrical writing by partisans of the Medici dynasty in Florence. This study examines the appropriation of the theme of the returning Golden Age and related motifs from the fourth Eclogue in other Italian courts during the same period, by supporters of the Visconti and Sforza of Milan, the Gonzaga of Mantua, Leonello d'Este and his successors in Ferrara, and the Bentivoglio of Bologna, among others. The deployment of this Virgilian material in political panegyric is seen to be a central element in the self-definition and self-promotion of dynastic rulers throughout the peninsula.

The rise of the Golden Dawn in Greece

This report focuses on the rise of the Golden Dawn in the context of economic, social and political crisis, as well as the fascist character of the party.

'To move or not to move': Reflections on the resettlement of artisanal miners in the western region of Ghana

This article critically reflects upon the shortcomings of the 'Prestea Action Plan', an ambitious initiative undertaken to facilitate the resettlement of artisanal miners operating in the Western Region of Ghana. The aim of the exercise was to identify viable areas for the thousands of operators who were working illegally in the town of Prestea, an area under concession to the US-based multinational, Golden Star Resources Ltd. At the time of its launch, it was one of the few support initiatives to target artisanal miners, whose claims to land are generally not recognized by governments. It was a particularly significant exercise in Ghana because it suggested that the authorities, who traditionally have exercised a policy of non-negotiation with such groups, had finally recognized that dialogue was needed if the growing rift between the country's indigenous artisanal miners, foreign mining companies and government bodies was to be bridged. It soon emerged, however, that despite its commendable policy objectives, the Plan was fundamentally flawed-problems which would undermine the entire exercise.

Field evaluation of systemic inducing resistance chemicals at different growth stages for the control of apple (Venturia inaequalis) and pear (Venturia pirina) scab

Two field trials were conducted using established apple (Malus cv. Golden Delicious) and pear (Pyrus communis 'Williams' Bon Chretien') to assess the efficacy of three commercially available systemic inducing resistance (SIR) products, Messenger (a.i. Harpin protein), Phoenix (a.i. Potassium phosphite) and Rigel (a.i. Salicylic acid derivative) applied at four different growth stages of tree development (bud break, green cluster, 90% petal fall, early fruitlet) against the foliar pathogens Venturia inaequalis and Venturia pirina which cause apple and pear scab respectively. A conventional synthetic fungicide (penconazole) used within the UK for apple and pear scab control was included for comparison. Little efficacy as scab protectants was demonstrated when each SIR product and penconazole was applied at only two growth stages (bud break, green cluster). However when the above compounds were applied at three or more growth stages efficacy as scab protectants was confirmed. The synthetic fungicide penconazole provided greatest protection against apple and pear scab in both the 2006 and 2007 field trials. There was little difference in the magnitude of scab protection conferred by each SIR agent. Results suggest application of at least three sprays during bud break to early fruitlet formation with an appropriate SIR agent may provide a useful addition to existing methods of apple and pear scab management under field conditions. (C) 2009 Published by Elsevier Ltd.

Evaluation of film forming polymers to control apple scab (Venturia inaequalis (Cooke) G. Wint.) under laboratory and field conditions

A detached leaf bioassay was used to determine the influence of several film forming polymers and a conventional triazole fungicide on apple scab (Venturia inaequalis (Cooke) G. Wint.) development under laboratory in vitro conditions, supported by two field trials using established apple cv. Golden Delicious to further assess the efficacy of foliar applied film forming polymers as scab protectant compounds. All film forming polymers used in this investigation (Bond, Designer, Nu-Film P, Spray Gard, Moisturin, Companion PCT12) inhibited germination of conidia, subsequent formation of appressoria and reduced leaf scab severity using a detached leaf bioassay. Regardless of treatment, there were no obvious trends in the percentage of conidia with one to four appressoria 5 days after inoculation. The synthetic fungicide penconazole resulted in the greatest levels of germination inhibition, appressorium development and least leaf scab severity. Under field conditions, scab severity on leaves and fruit of apple cv. Golden Delicious treated with a film forming polymer (Bond, Spray Gard, Moisturin) was less than on untreated controls. However, greatest protection in both field trials was provided by the synthetic fungicide penconazole. Higher chlorophyll fluorescence Fv/Fm emissions in polymer and penconazole treated trees indicated less damage to the leaf photosynthetic system as a result of fungal invasion. In addition, higher SPAD values as measures of leaf chlorophyll content were recorded in polymer and penconazole treated trees. Application of a film forming polymer or penconazole resulted in a higher apple yield per tree at harvest in both the 2005 and 2006 field trials compared to untreated controls. Results suggest application of an appropriate film forming polymer may provide a useful addition to existing methods of apple scab management. (C) 2008 Elsevier Ltd. All rights reserved.

Is it functional?

This report describes the first scientific meeting of the British Society for Proteome Research (BSPR), which was organised jointly with the European Bioinformatics Institute (EBI) and held in July 2004. The focus of the conference was functional proteomics with an emphasis on possible clinical application. The main subjects described here are: the need to simplify samples, the use of biological fluids verses tissue, consideration of biological and experimental variation and the creation of databases to achieve menaingful functional analysis.

Evaluation of data for atmospheric models: master equation/RRKM calculations on the combination reaction, BrO+NO2 -> BrONO2, a conundrum

Experimental data for the title reaction were modeled using master equation (ME)/RRKM methods based on the Multiwell suite of programs. The starting point for the exercise was the empirical fitting provided by the NASA (Sander, S. P.; Finlayson-Pitts, B. J.; Friedl, R. R.; Golden, D. M.; Huie, R. E.; Kolb, C. E.; Kurylo, M. J.; Molina, M. J.; Moortgat, G. K.; Orkin, V. L.; Ravishankara, A. R. Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies, Evaluation Number 15; Jet Propulsion Laboratory: Pasadena, California, 2006)(1) and IUPAC (Atkinson, R.; Baulch, D. L.; Cox, R. A.: R. F. Hampson, J.; Kerr, J. A.; Rossi, M. J.; Troe, J. J. Phys. Chem. Ref. Data. 2000, 29, 167) 2 data evaluation panels, which represents the data in the experimental pressure ranges rather well. Despite the availability of quite reliable parameters for these calculations (molecular vibrational frequencies (Parthiban, S.; Lee, T. J. J. Chem. Phys. 2000, 113, 145)3 and a. value (Orlando, J. J.; Tyndall, G. S. J. Phys. Chem. 1996, 100,. 19398)4 of the bond dissociation energy, D-298(BrO-NO2) = 118 kJ mol(-1), corresponding to Delta H-0(circle) = 114.3 kJ mol(-1) at 0 K) and the use of RRKM/ME methods, fitting calculations to the reported data or the empirical equations was anything but straightforward. Using these molecular parameters resulted in a discrepancy between the calculations and the database of rate constants of a factor of ca. 4 at, or close to, the low-pressure limit. Agreement between calculation and experiment could be achieved in two ways, either by increasing Delta H-0(circle) to an unrealistically high value (149.3 kJ mol(-1)) or by increasing , the average energy transferred in a downward collision, to an unusually large value (> 5000 cm(-1)). The discrepancy could also be reduced by making all overall rotations fully active. The system was relatively insensitive to changing the moments of inertia in the transition state to increase the centrifugal effect. The possibility of involvement of BrOONO was tested and cannot account for the difficulties of fitting the data.

Light-induced off-flavor development in cloudy apple juice

Cloudy apple juice has been found to develop off-flavors during storage in daylight. The development of off-flavors and volatile compounds was monitored in reconstituted juice prepared from 'Golden Delicious' and 'Fuji' apple concentrates stored in glass bottles under fluorescent light (3000 Ix, 8 degrees C). A strong metallic off-flavor was formed by photooxidation. A major contributor to the off-flavor was identified as 1-octen-3-one by gas chromatography-olfactometry. In addition, six volatile compounds, pentanal, 2-methyl-1-penten-3-one, hexanal, (E)-2-heptenal, 6-methyl-5-hepten-2-one, and (E)-2octenal, increased significantly after light exposure and could contribute to the off-flavor. Except for pentanal and hexanal, these volatiles were found only after light exposure. Higher levels of volatiles were observed in juice from 'Golden Delicious' apples than in juice from 'Fuji' apples, and this difference was consistent with higher levels of suspended solids. When the suspended solids were removed by centrifugation, the development of volatiles on exposure to light was reduced significantly.

Synthesis of broadband anti-reflection coatings for spaceflight infrared optics

A synthesis method is outlined for the design of broadband anti-reflection coatings for use in spaceborne infrared optics. The Golden Section optimisation routine is used to make a search, using designated non-absorptive dielectric thin film combinations, for the coating design which fulfils the required spectral requirements using the least number of layers and different materials. Three examples are given of coatings designed by this method : (I) 1µm to 12µm anti-reflection coating on Zinc Sulphide using Zinc Sulphide and Yttrium Fluoride thin film materials. (ii) 2µm to 14µm anti-reflection coating on Germanium using Germanium and Ytterbium Fluoride thin film materials. (iii) 6µm to 17µm anti-reflection coating on Germanium using Lead Telluride, Zinc Selenide and Barium Fluoride. The measured spectral performance of the manufactured 6µm to 17µm coating on Germanium is given. This is the anti-reflection coating for the germanium optics in the NASA Cassini Orbiter CIRS instrument.

Synthesis of infrared filters for use in spaceflight systems

Progress is reported in the development of a new synthesis method for the design of filters and coatings for use in spaceborne infrared optics. This method uses the Golden Section optimization routine to make a search, using designated dielectric thin film combinations, for the coating design which fulfills the required spectral requirements. The final design is that which uses the least number of layers for the given thin film materials in the starting design. This synthesis method has successfully been used to design broadband anti-reflection coatings on infrared substrates. The 6 micrometers to 18 micrometers anti-reflection coating for the germanium optics of the HIRDLS instrument, to be flown on the NASA EOS-Chem satellite, is given as an example. By correctly defining the target function to describe any specific type of filter in the optimization part of the method, this synthesis method may be used to design general filters for use in spaceborne infrared optics.

Forecasting the future: an overview of the strategic planning of the Bournemouth and Poole conurbation

An important part of strategic planning’s purpose should be to attempt to forecast the future, not simply to belatedly respond to events, or accept the future as inevitable. This paper puts forward a conceptual approach for seeking to achieve these aims and uses the Bournemouth and Poole area in Dorset as a vehicle for applying the basic methodology. The area has been chosen because of the significant issues that it currently faces in planning terms; and its future development possibilities. In order that alternative future choices for the area – different ‘developmental trajectories’ – can be evaluated, they must be carefully and logically constructed. Four Futures for Bournemouth/Poole have been put forward; they are titled and colour-coded: Future One is Maximising Growth – Golden Prospect which seeks to achieve the highest level of economic prosperity of the area; Future Two is Incremental Growth – Solid Silver which attempts to facilitate a steady, continuing, controlled pattern of the development for the area; Future Three is Steady State – Cobalt Blue which suggests that people in the area could be more concerned with preserving their quality of life in terms of their leisure and recreation rather than increasing wealth; Future Four is Environment First – Jade Green which makes the area’s environmental protection its top priority even at the possible expense of economic prosperity. The scenarios proposed here are not sacrosanct. Nor are they simply confined to the Bournemouth and Poole area. In theory, suitably modified, they could use in a variety of different contexts. Consideration of the scenarios – wherever located - might then generate other, additional scenarios. These are called hybrids, alloys and amalgams. Likewise it might identify some of them as inappropriate or impossible. Most likely, careful consideration of the scenarios will suggest hybrid scenarios, in which features from different scenarios are combined to produce alternative or additional futures for consideration. The real issue then becomes how best to fashion such a future for the particular area under consideration