680,920 research outputs found

    On moving averages

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    We show that the moving arithmetic average is closely connected to a Gauss-Seidel type fixed point method studied by Bauschke, Wang and Wylie, and which was observed to converge only numerically. Our analysis establishes a rigorous proof of convergence of their algorithm in a special case; moreover, limit is explicitly identified. Moving averages in Banach spaces and Kolmogorov means are also studied. Furthermore, we consider moving proximal averages and epi-averages of convex functions

    Moving across Spaces

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    Integrating Multiple 3D Views through Frame-of-reference Interaction

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    Frame-of-reference interaction consists of a unified set of 3D interaction techniques for exploratory navigation of large virtual spaces in nonimmersive environments. It is based on a conceptual framework that considers navigation from a cognitive perspective, as a way of facilitating changes in user attention from one reference frame to another, rather than from the mechanical perspective of moving a camera between different points of interest. All of our techniques link multiple frames of reference in some meaningful way. Some techniques link multiple windows within a zooming environment while others allow seamless changes of user focus between static objects, moving objects, and groups of moving objects. We present our techniques as they are implemented in GeoZui3D, a geographic visualization system for ocean data

    Quantization of systems with internal degrees of freedom in two-dimensional manifolds

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    Presented is a primary step towards quantization of infinitesimal rigid body moving in a two-dimensional manifold. The special stress is laid on spaces of constant curvature like the two-dimensional sphere and pseudosphere (Lobatschevski space). Also two-dimensional torus is briefly discussed as an interesting algebraic manifold.Comment: 19 page
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