14,803 research outputs found

    Orthogonal polarity graphs and Sidon sets

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    Determining the maximum number of edges in an nn-vertex C4C_4-free graph is a well-studied problem that dates back to a paper of Erd\H{o}s from 1938. One of the most important families of C4C_4-free graphs are the Erd\H{o}s-R\'enyi orthogonal polarity graphs. We show that the Cayley sum graph constructed using a Bose-Chowla Sidon set is isomorphic to a large induced subgraph of the Erd\H{o}s-R\'enyi orthogonal polarity graph. Using this isomorphism we prove that the Petersen graph is a subgraph of every sufficiently large Erd\H{o}s-R\'enyi orthogonal polarity graph.Comment: The authors would like to thank Jason Williford for noticing an error in the proof of Theorem 1.2 in the previous version. This error has now been correcte

    Hardy inequalities for fractional integrals on general domains

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    We prove a sharp Hardy inequality for fractional integrals for functions that are supported on a general domain. The constant is the same as the one for the half-space and hence our result settles a recent conjecture of Bogdan and Dyda.Comment: LaTeX, 9 pages, a number of errors have been fixed and the bibliography has been update

    The flow behaviour of inorganic - wood fibre slurries in pressurised pipes

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    Understanding the flow behaviour of inorganic-wood fibre slurries is important for developing new process equipment for the cement fibreboard industry. Little is reported in the technical literature and generally slurry flow knowledge is limited to a few engineers within the industry. Pipe friction loss characteristics and the settling behaviour of inorganic-wood fibre slurries were studied and data were obtained in pressurised horizontal pipes ranging from 25 to100mm diameter at flow velocities up to 8m/s. The inorganic solids studied were cement and fine silica of size range 10 to 150 m. Solids concentrations ranged from 5-20% and fibre concentrations from 0- 2%. Wood pulp fibre suspensions at low fibre concentrations form a structured carrier medium with the ability to support fine particulate solids. Unlike fibre-free suspensions, no permanent stationary deposit formed and therefore no minimum settling velocity exists. At low flow rates particles are trapped in the fibre plug and the friction loss is above water. At high flow rates the particles are still supported but the fibres dislodged from the central plug core damp turbulence and friction losses for the cement-silica-fibre system are less than water (drag reduction). The overall flow behaviour is similar to and consistent with previous data reported for coal-fibre slurries. Fibre concentration has a significant affect on the onset of drag reduction and friction loss increases with fibre concentration as with conventional fibre suspensions. Pipe diameter has a minimal effect on the onset of drag reduction but friction loss decreases with diameter as with conventional fluids

    Value Creation or Destruction: The Role of Private label in UK Grocery Category Management Decisions

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    Category management is a collaborative approach between food manufacturers and retailers to manage product categories rather than individual brands. It operates at both strategic and operational levels and seeks to create value ultimately for the consumer. The paper contributes to the literature and practice. It uses a qualitative interview study of twenty five senior practitioners and explores the role of private label products within UK grocery categories as consumers continue to switch due to lower prices and comparable quality to the traditional brands. The research also examines how private label manufacturers can create value within the category management relationship and how they can aspire to category captainship if they generate retailer specific and differentiated category strategies. The paper accepts its limitations and explains how further research in this important field of retailing is necessary to update the literature and help practitioners navigate their way through turbulent sector change

    Why forums? An empirical analysis into the facilitating factors of carding forums

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    Over the last decade, the nature of cybercrime has transformed from naive vandalism to profit-driven, leading to the emergence of a global underground economy. A noticeable trend which has surfaced in this economy is the repeated use of forums to operate online stolen data markets. Using interaction data from three prominent carding forums: Shadowcrew, Cardersmarket and Darkmarket, this study sets out to understand why forums are repeatedly chosen to operate online stolen data markets despite numerous successful infiltrations by law enforcement in the past. Drawing on theories from criminology, social psychology, economics and network science, this study has identified four fundamental socio-economic mechanisms offered by carding forums: (1) formal control and coordination; (2) social networking; (3) identity uncertainty mitigation; (4) quality uncertainty mitigation. Together, they give rise to a sophisticated underground market regulatory system that facilitates underground trading over the Internet and thus drives the expansion of the underground economy

    Enhancements in reservoir flood risk mapping: example application for Ulley

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    In July 2007, at Ulley Reservoir, South Yorkshire, a catastrophic dam failure was narrowly avoided due to emergency preventative actions. During the event, a number of homes were evacuated and roads were closed for precautionary measures. Within very close proximity of the reservoir lies the town of Rotherham, the busy M1 motorway and a trunk freight railway line. The incident highlights the need for detailed flood risk and hazard modelling to improve management of the risk and better incident planning.Hazards and population vary in both time and space, but when traditionally modelling flood risk, the population are invariably located within the residential housing stock. This paper innovatively combines flood inundation and spatio-temporal population modelling for better estimates of the population potentially at risk. This is demonstrated though application to Ulley for the most probable worst case failure scenario should the preventative measures not have been undertaken and the dam have failed.This paper proposes an enhanced flood risk assessment in three stages: (i) probabilistic modelling of a failure scenario using embankment breach models; (ii) hydrodynamic inundation modelling for assessment of flood water spreading, depths and velocities; (iii) spatio-temporal population modelling to assess the risk to the population likely to be present. The combination with spatio-temporal population outputs aims to demonstrate the enhancements achievable in reservoir flood risk mapping when vulnerable populations are concerned
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