Sphere packings revisited

AbstractIn this paper we survey most of the recent and often surprising results on packings of congruent spheres in d-dimensional spaces of constant curvature. The topics discussed are as follows:–Hadwiger numbers of convex bodies and kissing numbers of spheres;–touching numbers of convex bodies;–Newton numbers of convex bodies;–one-sided Hadwiger and kissing numbers;–contact graphs of finite packings and the combinatorial Kepler problem;–isoperimetric problems for Voronoi cells, the strong dodecahedral conjecture and the truncated octahedral conjecture;–the strong Kepler conjecture;–bounds on the density of sphere packings in higher dimensions;–solidity and uniform stability.Each topic is discussed in details along with some of the “most wanted” research problems

Degradation studies of synthetic food colouring matters

The heat and light stabilities of the 16 UK-permitted synthetic food colouring matters were investigated in aqueous solution. A specially constructed light box was used to provide exaggerated lighting conditions with fan-cooling of the samples. Comparison of stability has been made on the basis of the shape of the entire decay curve rather than by simple comparison of loss after a fixed degradation period. Indigo carmine and erythrosine showed little light stability, while ponceau 4R, chocolate brown HT and brown FK all showed fairly mediocre stability. The thermal stabilities of chocolate brown HT, ponceau 4R and, most especially, indigo carmine, all proved poor. A new polarographic peak which appeared during the thermal degradation of red 2G was shown to be due to the deacetylation product, red lOB. Identification was made by polarographic and chromatographic (hplc) comparison with a red lOB standard. A method for the analysis of red 2G and red lOB present in the same solution was developed using differential pulse polarography. This method included the use of tetrapheny1phosphonium chloride to produce a differential shift 1n the E 1/2 values of the respective colouring matters, and so increase the resolution of their polarographic peaks. Hplc analysis was conducted using reversed-phase ion-pair chromatography. A temperature control system was devised for the hplc column (water jacket) which was shown to improve the resolution and reproducibility of retention of the chromatographic peaks. An eluent comprising 63/37/0.25 v/v/w methano1/water/cetrimide, an SAS-Hypersil packing and thermos tatting at 40°C were found to be suitable for most of the thermal degradation solutions. A series of 13 chromatograms of thermally degraded solutions were produced under these conditions for comparative purposes. An unexpectedly large number of decay product chromatographic peaks were observed for some food colours. Whereas thermally degraded ponceau 4R only showed four peaks, most colours showed up to about ten peaks, and a few, e.g. amaranth, green S and sunset yellow FCF showed a dozen or more. Tentative identifications were made of some products from azo colours by reference to standard phenols and aromatic amines. Growth curves were plotted by hplc for a number of the products from the thermal degradation of yellow 2G. Polarographic and/or chromatographic evidence clearly showed that the thermal degradations of yellow 2G and of red 2G were not single step, single pathway processes. The large number of products observed by hplc indicate that this is true of most of the colours. Moreover, thermal degradation pathways need not be the same as photodegradation pathways. This has been shown simply for ponceau 4R by comparison of UV spectra. Qualitative analysis linked to hplc was also investigated. The construction of UV spectra of decay products by repeated chromatography at different detection wavelengths proved to be quite straightforward. It was found that the use of diazotisation as a pre-column reaction for the differentiation of aromatic amines from phenolic analogues was not suitable: the acidic and strongly ionic conditions employed for diazotisation disrupted the chromatographic ion-pair mechanism beyond correction. Use of fluorescamine proved rapid and simple for sulphanilic acid, but no significant reaction occurred in the aase of naphthionic acid. A method was devised for the analysis of phenol-4-sulphonic acid and sulphanilic acid when chromatographically unresolved by comparison of peak absorbance at two wavelengths. Finally, preliminary work was carried out to find how the dependence of retention on eluent composition was affected by the presence of specific functional groups in the analyte. This was seen as of particular application where functional group (e.g. carboxylate) analysis was required for decay products present in low concentration

Core-Shell Columns in High-Performance Liquid Chromatography: Food Analysis Applications

Theincreased separation efficiency provided by the newtechnology of column packed with core-shell particles in high-performance liquid chromatography (HPLC) has resulted in their widespread diffusion in several analytical fields: from pharmaceutical, biological, environmental, and toxicological.The present paper presents their most recent applications in food analysis.Their use has proved to be particularly advantageous for the determination of compounds at trace levels or when a large amount of samples must be analyzed fast using reliable and solvent-saving apparatus. The literature hereby described shows how the outstanding performances provided by core-shell particles column on a traditional HPLC instruments are comparable to those obtained with a costly UHPLC instrumentation, making this novel column a promising key tool in food analysis

The Glance of an Observer on the War of Brands of Food Products

The present work proposes a model to compare means of many constructs that evaluate competitiveness of brands of the Brazilian chilled and frozen food industry. Such a model is based on a nomological network, which was built over the concepts pointed by [4] [13] [8], and [7] by the NUME – Marketing and Strategy Research Center of the Federal University of Minas Gerais - research group. Besides the validation of the new research instrument for gauging and generalization, it will be made an evaluation of brands - the ones well-positioned at the market - using the comparison of the indexes and averages of the nomological chain built for the companies, in relation to the following concepts: Tangibility (perception of packings, flavors and smells); Reliability in the Brand; Satisfaction; Loyalty; Image of the Brand; Perceived Value and Functional Conflict

D4.3 Final report on compilation of key organic market data

The OrganicDataNetwork survey on organic market data has made available, for the first time, the organic market data per product group and sales channels that are available for Europe; however, a range of challenges were encountered

CROSS-BORDER TRADE & SUPPLY CHAIN LINKAGES REPORT. InterTradeIreland, 2017

This paper examines the patterns of cross-border trade on the island of Ireland, focusing on the role of supply chain links, measured by the extent of trade in intermediate products and the contribution to overall trade of two-way trading firms (those simultaneously importing and exporting). We use detailed firm-level trade records to examine the composition, specialisation and dynamism of trading firms. This data is provided by the Central Statistics Office (CSO) and is based on detailed statistics on merchandise exports and imports of manufacturing firms. A number of case studies on specific firms are also included to illustrate the empirical patterns. The analysis is motivated by the key role that trade plays in overall economic performance across both parts of the island and, in the more immediate policy context of potential changes in the trading environment posed by the UK exit from the EU, by the importance of understanding and quantifying the cross-border linkages both in terms of direct trade in final products and also in firms’ supply chains