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Literature DB >> 29555808

Hilbert's sixth problem: the endless road to rigour.

Abstract

In this introduction, the essence of the sixth problem is discussed and the content of this issue is introduced.This article is part of the theme issue 'Hilbert's sixth problem'.

Keywords: Hilbert; axiomatizing; continuum mechanics; kinetics; physics; quantum physics

Year: 2018 PMID： 29555808 PMCID： PMC5869544 DOI： 10.1098/rsta.2017.0238

Source DB: PubMed Journal: Philos Trans A Math Phys Eng Sci ISSN： 1364-503X Impact factor: 4.226

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References

14 in total

Review 1. Blessing of dimensionality: mathematical foundations of the statistical physics of data.

Authors: A N Gorban; I Y Tyukin
Journal: Philos Trans A Math Phys Eng Sci Date: 2018-04-28 Impact factor: 4.226

Review 2. On the emergence of the structure of physics.

Authors: S Majid
Journal: Philos Trans A Math Phys Eng Sci Date: 2018-04-28 Impact factor: 4.226

3. Hilbert's sixth problem and the failure of the Boltzmann to Euler limit.

Authors: Marshall Slemrod
Journal: Philos Trans A Math Phys Eng Sci Date: 2018-04-28 Impact factor: 4.226

4. Derivation of regularized Grad's moment system from kinetic equations: modes, ghosts and non-Markov fluxes.

Authors: Ilya Karlin
Journal: Philos Trans A Math Phys Eng Sci Date: 2018-04-28 Impact factor: 4.226

5. Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics.

Authors: Leo Corry
Journal: Philos Trans A Math Phys Eng Sci Date: 2018-04-28 Impact factor: 4.226

6. Boltzmann equation and hydrodynamics beyond Navier-Stokes.

Authors: A V Bobylev
Journal: Philos Trans A Math Phys Eng Sci Date: 2018-04-28 Impact factor: 4.226

Review 7. The solution of the sixth Hilbert problem: the ultimate Galilean revolution.

Authors: Giacomo Mauro D'Ariano
Journal: Philos Trans A Math Phys Eng Sci Date: 2018-04-28 Impact factor: 4.226

Review 8. Quantum probability and Hilbert's sixth problem.

Authors: Luigi Accardi
Journal: Philos Trans A Math Phys Eng Sci Date: 2018-04-28 Impact factor: 4.226

Review 9. From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems.

Authors: Miguel Ángel Lozada Aguilar; Andrei Khrennikov; Klaudia Oleschko
Journal: Philos Trans A Math Phys Eng Sci Date: 2018-04-28 Impact factor: 4.226

10. The quantum N-body problem in the mean-field and semiclassical regime.

Authors: François Golse
Journal: Philos Trans A Math Phys Eng Sci Date: 2018-04-28 Impact factor: 4.226