Poincaré’s stated motivations for topology
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DOI: 10.1007/s00407-020-00247-y
Abstract: It is well known that one of Poincaré’s most important contributions to mathematics is the creation of algebraic topology. In this paper, we examine carefully the stated motivations of Poincaré and potential applications he had… read more here.
Keywords: poincar; mathematics; topology; poincar stated ... See more keywords
From Jurisprudence to Mechanics: Jacobi, Reech, and Poincaré on Convention
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DOI: 10.1017/s0269889718000170
Abstract: Argument This paper aims at understanding the concept of convention in mechanics as a notion transferred from the field of jurisprudence. This enables us to clarify it as a new epistemic category having a pertinent… read more here.
Keywords: poincar; convention; mechanics jacobi; jurisprudence mechanics ... See more keywords
The reasonable effectiveness of contours in vision
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DOI: 10.1073/pnas.2215097119
Abstract: In a Matisse cutout, such as “Blue Nude I” (Fig. 1), the limbs appear to have volumes despite clearly being made of flat sheets of uniformly blue paper glued to a flat cream background. The… read more here.
Keywords: information; points surface; viewpoint; poincar ... See more keywords
Quaternion generalization of super-Poincaré group
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DOI: 10.1142/s0217751x19500064
Abstract: Super-Poincaré algebra in [Formula: see text] space–time dimensions has been studied in terms of quaternionic representation of Lorentz group. Starting the connection of quaternion Lorentz group with [Formula: see text] group, the [Formula: see text]… read more here.
Keywords: poincar; super poincar; poincar group; formula see ... See more keywords
Weak Poincaré inequalities for convolution probabilities measures
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DOI: 10.1142/s021902571950019x
Abstract: In this paper, weak Poincaré inequalities are obtained for convolution probabilities with explicit rate functions by constructing suitable Lyapunov functions. Here, one of these Lyapunov functions is introduced for the first time and can be… read more here.
Keywords: poincar; inequalities convolution; weak poincar; convolution probabilities ... See more keywords
Rational first integrals of the Liénard equations: The solution to the Poincaré problem for the Liénard equations.
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DOI: 10.1590/0001-3765202120191139
Abstract: Poincaré in 1891 asked about the necessary and sufficient conditions in order to characterize when a polynomial differential system in the plane has a rational first integral. Here we solve this question for the class… read more here.
Keywords: poincar; equations solution; first integrals; rational first ... See more keywords
The Poincaré Half-Plane for Informationally-Complete POVMs
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DOI: 10.3390/e20010016
Abstract: It has been shown in previous papers that classes of (minimal asymmetric) informationally-complete positive operator valued measures (IC-POVMs) in dimension d can be built using the multiparticle Pauli group acting on appropriate fiducial states. The… read more here.
Keywords: half plane; povms; informationally complete; poincar ... See more keywords
Poincaré and Log–Sobolev Inequalities for Mixtures
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DOI: 10.3390/e21010089
Abstract: This work studies mixtures of probability measures on Rn and gives bounds on the Poincaré and the log–Sobolev constants of two-component mixtures provided that each component satisfies the functional inequality, and both components are close… read more here.
Keywords: log sobolev; sobolev inequalities; poincar; poincar log ... See more keywords