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Scandinavian Journal of Medicine &Science in Sports, Volume 33, Issue 2, Page 178-188, February 2023., 2023 To benefit from virtual reality (VR) as a complementary tool for training, coaches must determine the proper tools and variables for tracking sports performance. We explored the basketball shooting at several scales (basket‐ball, ball‐player, and player systems) by monitoring success‐rate, and ball and body kinematics.
Pooya Soltani, Antoine H. P. Morice
wiley +1 more source
Some counterexamples to Alt–Caffarelli–Friedman monotonicity formulas in Carnot groups [PDF]
Annali di Matematica Pura ed ApplicataIn this paper we continue the analysis of an Alt–Caffarelli–Friedman (ACF) monotonicity formula in Carnot groups of step $$s >1$$ s > 1 confirming the existence of counterexamples to the monotone increasing behavior.
Fausto Ferrari, Davide Giovagnoli
semanticscholar +1 more source
Rigidity of 2-Step Carnot Groups [PDF]
The Journal of Geometric Analysis, 2017 Except for minor polishing this version is enriched with two appendices concerning pseudo H-type algebras with J^2-condition. In Appendix A we relate these algebras to division algebras and their split versions.
Mauricio Godoy Molina +3 more
openaire +3 more sources
Hilbert-Haar coordinates and Miranda's theorem in Lie groups
Bruno Pini Mathematical Analysis Seminar, 2020 We study the interior regularity of solutions to a class of quasilinear equations of non-degenerate p-Laplacian type on Lie groups that admit a system of Hilbert-Haar coordinates. These are coordinates with respect to which every linear function has zero
András Domokos, Juan J. Manfredi
doaj +1 more source
Structure of porous sets in Carnot groups [PDF]
Illinois Journal of Mathematics, 2017 23 ...
Pinamonti A., Speight G.
openaire +4 more sources
Harnack inequality for fractional sub-Laplacians in Carnot groups [PDF]
, 2013 In this paper we prove an invariant Harnack inequality on Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" formulation of a technique recently introduced by Caffarelli and Silvestre ...
A Bonfiglioli +31 more
core +1 more source
On Viscosity and Equivalent Notions of Solutions for Anisotropic Geometric Equations
Abstract and Applied Analysis, 2020 We prove that viscosity solutions of geometric equations in step two Carnot groups can be equivalently reformulated by restricting the set of test functions at the singular points.
Cecilia De Zan, Pierpaolo Soravia
doaj +1 more source
Pliability, or the whitney extension theorem for curves in carnot groups [PDF]
, 2016 The Whitney extension theorem is a classical result in analysis giving a necessary and sufficient condition for a function defined on a closed set to be extendable to the whole space with a given class of regularity.
Juillet, Nicolas, Sigalotti, Mario
core +5 more sources
Heat and entropy flows in Carnot groups [PDF]
Revista Matemática Iberoamericana, 2019 We prove the correspondence between the solutions of the sub-elliptic heat equation in a Carnot group \mathbb G and the gradient flows of the relative entropy functional in the Wasserstein space of probability measures on \mathbb G ...
Ambrosio L., Stefani G.
openaire +3 more sources
A reverse coarea-type inequality in Carnot groups
Annales de l'Institut Fourier, 2022 . We prove a coarea-type inequality for a continuously Pansu differentiable function acting between two Carnot groups endowed with homogeneous distances. We assume that the level sets of the function are uniformly lower Ahlfors regular and that the Pansu ...
Francesca Corni
semanticscholar +1 more source