1,439 research outputs found

    Power system requirements

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    An overview of electrical power requirements for each mission of a baseline and alternate plan for space activities in the 1990-2035 timeframe is presented. The specific missions included low earth orbit (LEO), geosynchronous earth orbit (GEO), lunar, Mars, and asteroid related projects

    Staff Training

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    Conway's Games and Some of their Basic Properties

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    We formulate a few basic concepts of J. H. Conway's theory of games based on his book [6]. This is a first step towards formalizing Conway's theory of numbers into Mizar, which is an approach to proving the existence of a FIELD (i.e., a proper class that satisfies the axioms of a real-closed field) that includes the reals and ordinals, thus providing a uniform, independent and simple approach to these two constructions that does not go via the rational numbers and hence does for example not need the notion of a quotient field. In this first article on Conway's games, we provide a definition of games, their birthdays (or ranks), their trees (a notion which is not in Conway's book, but is useful as a tool), their negates and their signs, together with some elementary properties of these notions. If one is interested only in Conway's numbers, it would have been easier to define them directly, but going via the notion of a game is a more general approach in the sense that a number is a special instance of a game and that there is a rich theory of games that are not numbers. The main obstacle in formulating these topics in Mizar is that all definitions are highly recursive, which is not entirely simple to translate into the Mizar language. For example, according to Conway's definition, a game is an object consisting of left and right options which are themselves games, and this is by definition the only way to construct a game. This cannot directly be translated into Mizar, but a theorem is included in the article which proves that our definition is equivalent to Conway's.Institute of Applied Analysis, University of Ulm, 89069 Ulm, GermanyGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.J. H. Conway. On numbers and games. A K Peters Ltd., Natick, MA, second edition, 2001.Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990

    Penilaian Kinerja Keuangan Koperasi di Kabupaten Pelalawan

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    This paper describe development and financial performance of cooperative in District Pelalawan among 2007 - 2008. Studies on primary and secondary cooperative in 12 sub-districts. Method in this stady use performance measuring of productivity, efficiency, growth, liquidity, and solvability of cooperative. Productivity of cooperative in Pelalawan was highly but efficiency still low. Profit and income were highly, even liquidity of cooperative very high, and solvability was good

    Juxtaposing BTE and ATE – on the role of the European insurance industry in funding civil litigation