11 resultados para First Integrals

em Boston University Digital Common


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The future of theology libraries is far from clear. Since the nineteenth century, theology libraries have evolved to support the work of theological education. This article briefly reviews the development of theology libraries in North America and examines the contextual changes impacting theology libraries today. Three significant factors that will shape theology libraries in the coming decade are collaborative models of pedagogy and scholarship, globalization and rapid changes in information technology, and changes in the nature of scholarly publishing including the digitization of information. A large body of research is available to assist those responsible for guiding the direction of theology libraries in the next decade, but there are significant gaps in what we know about the impact of technology on how people use information that must be filled in order to provide a solid foundation for planning.

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The print copy of this sermon is held by Pitts Theology Library. The Pitts Theology Library's digital copy was produced as part of the ATLA/ATS Cooperative Digital Resources Initiative (CDRI), funded by the Luce Foundation. Reproduction note: Electronic reproduction. Atlanta, Georgia : Pitts Theology Library, Emory University, 2003. (Thanksgiving Day Sermons, ATLA Cooperative Digital Resources Initiative, CDRI). Joint CDRI project by: Andover-Harvard Library (Harvard Divinity School), Pitts Theology Library (Emory University), and Princeton Theological Seminary Libraries.

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http://www.archive.org/details/memorialvolumeof00andeuoft

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http://www.archive.org/details/firsttenannualre00amerrich

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http://www.archive.org/details/memorialvolumeof00andeiala

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We prove that first order logic is strictly weaker than fixed point logic over every infinite classes of finite ordered structures with unary relations: Over these classes there is always an inductive unary relation which cannot be defined by a first-order formula, even when every inductive sentence (i.e., closed formula) can be expressed in first-order over this particular class. Our proof first establishes a property valid for every unary relation definable by first-order logic over these classes which is peculiar to classes of ordered structures with unary relations. In a second step we show that this property itself can be expressed in fixed point logic and can be used to construct a non-elementary unary relation.

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We give an explicit and easy-to-verify characterization for subsets in finite total orders (infinitely many of them in general) to be uniformly definable by a first-order formula. From this characterization we derive immediately that Beth's definability theorem does not hold in any class of finite total orders, as well as that McColm's first conjecture is true for all classes of finite total orders. Another consequence is a natural 0-1 law for definable subsets on finite total orders expressed as a statement about the possible densities of first-order definable subsets.

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Understanding and modeling the factors that underlie the growth and evolution of network topologies are basic questions that impact capacity planning, forecasting, and protocol research. Early topology generation work focused on generating network-wide connectivity maps, either at the AS-level or the router-level, typically with an eye towards reproducing abstract properties of observed topologies. But recently, advocates of an alternative "first-principles" approach question the feasibility of realizing representative topologies with simple generative models that do not explicitly incorporate real-world constraints, such as the relative costs of router configurations, into the model. Our work synthesizes these two lines by designing a topology generation mechanism that incorporates first-principles constraints. Our goal is more modest than that of constructing an Internet-wide topology: we aim to generate representative topologies for single ISPs. However, our methods also go well beyond previous work, as we annotate these topologies with representative capacity and latency information. Taking only demand for network services over a given region as input, we propose a natural cost model for building and interconnecting PoPs and formulate the resulting optimization problem faced by an ISP. We devise hill-climbing heuristics for this problem and demonstrate that the solutions we obtain are quantitatively similar to those in measured router-level ISP topologies, with respect to both topological properties and fault-tolerance.