Minor stars in plane graphs with minimum degree five

The weight of a subgraph $H$ in $G$ is the sum of the degrees in $G$ of vertices of $H$. The {\em height} of a subgraph $H$ in $G$ is the maximum degree of vertices of $H$ in $G$. A star in a given graph is minor if its center has degree at most five in the given graph. Lebesgue (1940) gave an approximate description of minor $5$-stars in the class of normal plane maps with minimum degree five. In this paper, we give two descriptions of minor $5$-stars in plane graphs with minimum degree five. By these descriptions, we can extend several results and give some new results on the weight and height for some special plane graphs with minimum degree five.Comment: 11 pages, 3 figure

Characterization of coal products from high temperature processing of Usibelli low-rank coals

This research project was conducted in association with Gilbert/Commonwealth Inc. as part of an overall techno-economic assessment of high temperature drying of low-rank coals. This report discusses the characteristics of the dried/pyrolyzed products of two high temperature, evaporative processes and the dried product from a hydrothermal process. The long term goal of this and other coal drying studies conducted at MIRL, was to define drying technologies that have significant and real potential to competitively move Alaska's, low-rank coals (LRCs) into the export, steam coal market of the Pacific Rim. In 1990, Japan imported 33 million metric tons (mt) of steam coal with an additional 39 million mt imported by other Far East nations(2). Australia dominates the export steam coal market to these Pacific Rim countries and exported 48 million mt in 1990 and an additional 61 million mt of metallurgical coal(2). The worldwide steam coal export market has been expanding rapidly, from 20 million mt in 1973 to 150 million mt in 1989, and is expected to double to nearly 300 million mt by the end of the century(3). Could Alaska capture only 3% of the projected new world steam coal market, which is not an unreasonable expectation, the value of the state's coal exports would soar from nominally $28 million per year to over$100 million per year. However, without development of economical methods for drying/stabilizing Alaskan LRCs, the only increase in export of Alaskan coals may be from the few "higher rank" coals within a "reasonable" transport range of the existing Alaska rail system or tidewater. Presently the coal from the Usibelli Coal Mine is the only low-rank coal exported internationally as a steam coal; primarily for its blending properties with other coal to improve combustion. But for Alaskan low-rank coals to truly stand on their own merits, economical drying processes must be developed that produce a physically and chemically stable dried product. The technologies that have the most potential for increasing the use of Alaskan coals are those that can reduce the moisture content of these coals economically, and produce a fuel that is accepted in the international market place. Drying technologies will no doubt differ, depending on the end use of the fuel; be it dried lump coal, briquettes or pellets for pulverized coal or stoker applications, or concentrated coal-water fuels made from hot water dried LRCs. There are a number of developing processes that may work with Alaskan coals. Some drying processes, however, have been plagued by the production of excessive amounts of coal fines, Since the demand for Alaskan coal is currently limited to lump size coal, large quantities of fines are a definite liability. In this study, two high temperature drying/pyrolysis processes and one hydrothermal process were investigated. The high temperature drying/pyrolysis processes were conducted at (1) the Western Research Institute, (WRI) an affiliate of the University of Wyoming Research Corporation, Laramie, WY, and (2) Coal Technology Corporation (CTC) of Brisol, VA. Hydrothermal processing was conducted at MIRL, University of Alaska Fairbanks. A summary of these processes and the products they produced follows.The University of Alaska also provided matching funds for this project, which was a portion of a larger study that leveraged U.S. Department of Energy funds

A generalization of a result of Häggkvist and Nicoghossian

Using a variation of the Bondy-Chvátal closure theorem the following result is proved: If G is a 2-connected graph with n vertices and connectivity κ such that d(x) + d(y) + d(z) ≥ n + κ for any triple of independent vertices x, y, z, then G is hamiltonian

When-To-Post on Social Networks

For many users on social networks, one of the goals when broadcasting content is to reach a large audience. The probability of receiving reactions to a message differs for each user and depends on various factors, such as location, daily and weekly behavior patterns and the visibility of the message. While previous work has focused on overall network dynamics and message flow cascades, the problem of recommending personalized posting times has remained an underexplored topic of research. In this study, we formulate a when-to-post problem, where the objective is to find the best times for a user to post on social networks in order to maximize the probability of audience responses. To understand the complexity of the problem, we examine user behavior in terms of post-to-reaction times, and compare cross-network and cross-city weekly reaction behavior for users in different cities, on both Twitter and Facebook. We perform this analysis on over a billion posted messages and observed reactions, and propose multiple approaches for generating personalized posting schedules. We empirically assess these schedules on a sampled user set of 0.5 million active users and more than 25 million messages observed over a 56 day period. We show that users see a reaction gain of up to 17% on Facebook and 4% on Twitter when the recommended posting times are used. We open the dataset used in this study, which includes timestamps for over 144 million posts and over 1.1 billion reactions. The personalized schedules derived here are used in a fully deployed production system to recommend posting times for millions of users every day.Comment: 10 pages, to appear in KDD201

Sensitivity of Capital Stock and Multifactor Productivity Estimates to Depreciation Assumptions: A Canada-U.S. Comparison

This article provides consistent estimates for capital stock and multifactor productivity (MFP) for Canada and the United States across major industries for the 1987-2007 period. For this purpose, capital stock estimates are developed for Canadian and U.S. industries using the same asset depreciation rates (either from the U.S. Bureau of Economic Analysis or from Statistics Canada) for the two countries. The results show that on an hours worked basis Canadian industries invest more in total capital than their U.S. counterparts. This situation reflects much greater investment in structures, with less in machinery and equipment (including information and communications technologies). The results imply that all of the Canada-U.S. labour productivity gap arises from the multifactor productivity gap.multifactor productivity, capital stock, depreciation rate, labour productivity