2,426,136 research outputs found

    Map Collection - Accession 1535

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    The Map Collection consists of various maps from around the world and contains original maps and reproductions of historical maps. This collection focuses on maps from the Southern United States and South Carolina and North Carolina in particular, but also contain maps featuring Africa, Alabama, Arkansas, Asia, Central America, Europe, Florida, Georgia, Global, Holy Land, Kentucky, Louisiana, Mississippi, North America, South America, Tennessee, United States, Virginia, and World War II as well.https://digitalcommons.winthrop.edu/manuscriptcollection_findingaids/2577/thumbnail.jp

    Change of the plane of oscillation of a Foucault pendulum from simple pictures

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    The change of the plane of oscillation of a Foucault pendulum is calculated without using equations of motion, the Gauss-Bonnet theorem, parallel transport, or assumptions that are difficult to explain.Comment: 5 pages, 4 figure

    Working With Administration: Getting and Keeping Support for Professional Development Programs

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    Outline Positioning Your Office: The Real Organization Chart Seven Competencies Required of Faculty Developers Seven Competencies Required of Administrator

    Phantom maps and chromatic phantom maps

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    In the first part, we determine conditions on spectra X and Y under which either every map from X to Y is phantom, or no nonzero maps are. We also address the question of whether such all or nothing behaviour is preserved when X is replaced with V smash X for V finite. In the second part, we introduce chromatic phantom maps. A map is n-phantom if it is null when restricted to finite spectra of type at least n. We define divisibility and finite type conditions which are suitable for studying n-phantom maps. We show that the duality functor W_{n-1} defined by Mahowald and Rezk is the analog of Brown-Comenetz duality for chromatic phantom maps, and give conditions under which the natural map Y --> W_{n-1}^2 Y is an isomorphism.Comment: 18 page

    Maps conjugating holomorphic maps in C^n

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    If f is a bijection from C^n onto a complex manifold M, which conjugates every holomorphic map in C^n to an endomorphism in M, then we prove that f is necessarily biholomorphic or antibiholomorphic. This extends a result of A. Hinkkanen to higher dimensions. As a corollary, we prove that if there is an epimorphism from the semigroup of all holomorphic endomorphisms of C^n to the semigroup of holomorphic endomorphisms in M, or an epimorphism in the opposite direction for a doubly-transitive M, then it is given by conjugation by some biholomorphic or antibiholomorphic map. We show also that there are two unbounded domains in C^n with isomorphic endomorphism semigroups but which are neither biholomorphically nor antibiholomorphically equivalent.Comment: 10 page

    Skinning maps

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    Let M be a hyperbolic 3-manifold with nonempty totally geodesic boundary. We prove that there are upper and lower bounds on the diameter of the skinning map of M that depend only on the volume of the hyperbolic structure with totally geodesic boundary, answering a question of Y. Minsky. This is proven via a filling theorem, which states that as one performs higher and higher Dehn fillings, the skinning maps converge uniformly on all of Teichmuller space. We also exhibit manifolds with totally geodesic boundaries whose skinning maps have diameter tending to infinity, as well as manifolds whose skinning maps have diameter tending to zero (the latter are due to K. Bromberg and the author). In the final section, we give a proof of Thurston's Bounded Image Theorem.Comment: 50 pages, 4 figures. v3. Major revision incorporating referees' comments. To appear in the Duke Mathematical Journal. v2. Cosmetic changes, minor corrections, inclusion of theorem with K. Bromber
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