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A Note on Polyhedral Banach Spaces [PDF]
Proceedings of the American Mathematical Society, 1972 We give a sufficient condition for an infinitedimensional Banach space X to be polyhedral. If X
Gleit, Alan, McGuigan, Robert
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Boundaries and Polyhedral Banach Spaces [PDF]
Proceedings of the American Mathematical Society, 2015 We show that if X X and Y Y are Banach spaces, where Y Y is separable and polyhedral, and if T : X → Y T:X\to Y is a bounded linear operator such that T ∗ ( Y ∗ )
S Troyanski
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Loop Spaces of Polyhedral Products Associated With the Polyhedral Join Product
Proceedings of the Edinburgh Mathematical SocietyAbstract We provide a homotopy equivalence for the loop space of the polyhedral product associated with a simplicial complex formed via the polyhedral join operation, and give sufficient conditions under which this loop space is a finite-type product of spheres and loops on spheres.
Eldridge, Briony
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On Linear Spaces of Polyhedral Meshes [PDF]
IEEE Transactions on Visualization and Computer Graphics, 2015 Polyhedral meshes (PM) - meshes having planar faces - have enjoyed a rise in popularity in recent years due to their importance in architectural and industrial design. However, they are also notoriously difficult to generate and manipulate. Previous methods start with a smooth surface and then apply elaborate meshing schemes to create polyhedral meshes
Renjie Chen, Craig Gotsman
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Convex Analysis on Polyhedral Spaces [PDF]
Mathematische Zeitschrift, 2022 AbstractWe introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.
Martín Sombra
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Local Characterization of Polyhedral Spaces [PDF]
Geometriae Dedicata, 2015 We show that a compact length space is polyhedral if a small spherical neighborhood of any point is conic.
Nina D Lebedeva, Anton Petrunin
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Best Approximation in Polyhedral Banach Spaces
Journal of Approximation Theory, 2011 The authors study conditions under which the metric projection of a polyhedral Banach space \(X\) onto a closed subspace \(Y\) is Hausdorff lower or upper semicontinuous. The paper is organized as follows. Section 0 is an introduction. Section 1 contains notation concerning Banach spaces, followed by definitions and preliminary facts on polyhedral ...
Libor Vesely +2 more
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Integrating geometries of ReLU feedforward neural networks
Frontiers in Big Data, 2023 This paper investigates the integration of multiple geometries present within a ReLU-based neural network. A ReLU neural network determines a piecewise affine linear continuous map, M, from an input space ℝm to an output space ℝn.
Yajing Liu +3 more
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Tropicalization of the universal Jacobian [PDF]
Épijournal de Géométrie Algébrique, 2022 In this article we provide a stack-theoretic framework to study the universal tropical Jacobian over the moduli space of tropical curves. We develop two approaches to the process of tropicalization of the universal compactified Jacobian over the moduli ...
Margarida Melo +3 more
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$k$-smoothness on polyhedral Banach spaces [PDF]
Colloquium Mathematicum, 2022 11 ...
Dey, Subhrajit +2 more
openaire +2 more sources