1,721,331 research outputs found
Intrinsic harmonicity of morse functions
No full textConsider a real-valued Morse function f on a C^2 closed connected n-dimensional manifold M. It is proved that a suitable Riemannian metric exists on M, such that f is harmonic outside the set of critical points off of index 0 and n. The proof is based on a result of Calabi [1], providing a criterion for a closed one-form on a closed connected manifold to be harmonic with respect to some Riemannian metric
Metrological Characterization of a Contactless Smart Thrust and Speed Sensor for Linear Induction Motors Testing
No full textNo embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit
No full textThe Hausdorff distance, the Gromov–Hausdorff, the Fréchet and the natural pseudodistance are instances of dissimilarity measures widely used in shape comparison. We show that they share the property of being defined as inf_ρ F(ρ) where F is a suitable functional and ρ varies in a set of correspondences containing the set of homeomorphisms. Our main result states that the set of homeomorphisms cannot be enlarged to a metric space K, in such a way that the composition in K (extending the composition of homeomorphisms) passes to the limit and, at the same time, K is compact
Single Chip Microcontrollers for Measurements on Rotating Electrical Machines
No full textInternational Conference on Electrical Machine
Erratum: Persistent Betti numbers for a noise tolerant shape-based approach to image retrieval (Pattern Recognition Letters (2013) 34 (1320-1321))
No full text
Uniqueness of models in persistent homology: the case of curves
No full textWe consider generic curves in R^2, i.e. generic C^1 functions f : S^1 → R^2. We analyze these curves through the persistent homology groups of a filtration induced on S^1 by f. In particular, we consider the question whether these persistent homology groups uniquely characterize f, at least up to reparameterizations of S^1. We give a partially positive answer to this question. More precisely, we prove that f = g ◦ h, where h : S^1 → S^1 is a C^1-diffeomorphism, if and only if the persistent homology groups of s ◦ f and s ◦g coincide, for every s belonging to the group S_2 generated by reflections in the coordinate axes. Moreover, for a smaller set of generic functions, we show that f and g are close to each other in the max-norm (up to re-parameterizations) if and only if, for every s ∈ S_2, the persistent Betti number functions of s ◦ f and s ◦ g are close to each other, with respect to a suitable distance
Size Functions and Morphological Transformations
No full textIn this paper changes of size functions under morphological transformations are studied. Some inequalities concerning size functions of a subset of the Euclidean plane, its dilation by an open disk and its skeleton are proved. Such inequalities prove the stability of size functions with respect to these morphological transformations and give a new approach for computation in Size Theory
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