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pro vyhledávání: '"Nicolas Dutertre"'
The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory.The volume contains the
Publikováno v:
Bulletin of the Brazilian Mathematical Society, New Series. 54
Let $$X\subset {\mathbb {R}}^n$$ X ⊂ R n be a closed semi-algebraic set, $$F:{\mathbb {R}}^n\rightarrow {\mathbb {R}}$$ F : R n → R be a $${\mathcal {C}}^2$$ C 2 semi-algebraic function and $$f=F_{|X}:X\rightarrow {\mathbb {R}}^n$$ f = F | X : X
Autor:
Nicolas Dutertre, Juan Antonio Pérez
Publikováno v:
Glasgow Mathematical Journal
Glasgow Mathematical Journal, Cambridge University Press (CUP), 2021, pp.1-15. ⟨10.1017/S0017089521000239⟩
Glasgow Mathematical Journal, Cambridge University Press (CUP), 2021, pp.1-15. ⟨10.1017/S0017089521000239⟩
Let $f\,{:}\,(\mathbb R^n,0)\to (\mathbb R,0)$ be an analytic function germ with non-isolated singularities and let $F\,{:}\, (\mathbb{R}^{1+n},0) \to (\mathbb{R},0)$ be a 1-parameter deformation of f. Let $ f_t ^{-1}(0) \cap B_\epsilon^n$ , $0 < \ve
Autor:
Nicolas Dutertre, Vincent Grandjean
Publikováno v:
Asian Journal of Mathematics. 25:815-840
Autor:
Nicolas Dutertre
We prove two principal kinematic formulas for germs of closed definable sets in $\mathbb{R}^n$, that generalize the Cauchy-Crofton formula for the density due to Comte and the infinitesimal linear kinematic formula due to the author. In this setting,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::529869d9fc5d4c80bde8e09ef59cd898
http://arxiv.org/abs/2012.14783
http://arxiv.org/abs/2012.14783
Autor:
Nicolas Dutertre
Publikováno v:
Advances in Geometry
Advances in Geometry, De Gruyter, 2019, 19 (2), pp.205-230. ⟨10.1515/advgeom-2018-0019⟩
Advances in Geometry, 2019, 19 (2), pp.205-230. ⟨10.1515/advgeom-2018-0019⟩
Advances in Geometry, De Gruyter, 2019, 19 (2), pp.205-230. ⟨10.1515/advgeom-2018-0019⟩
Advances in Geometry, 2019, 19 (2), pp.205-230. ⟨10.1515/advgeom-2018-0019⟩
We relate the Lipschitz–Killing measures of a definable set X ⊂ ℝ n in an o-minimal structure to the volumes of generic polar images. For smooth submanifolds of ℝ n , such results were established by Langevin and Shifrin. Then we give infinit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::41733203469763af9ea10c541bc359c3
https://hal.archives-ouvertes.fr/hal-01239927
https://hal.archives-ouvertes.fr/hal-01239927
Autor:
Nicolas Dutertre
Publikováno v:
Journal of Singularities
Journal of Singularities, Worldwide Center of Mathematics, LLC, 2020, Proc. of 15th International Workshop on Singularities, São Carlos, 2018, 22, pp.159-179. ⟨10.5427/jsing.2020.22j⟩
Journal of Singularities, Worldwide Center of Mathematics, LLC, 2020, Proc. of 15th International Workshop on Singularities, São Carlos, 2018, 22, pp.159-179. ⟨10.5427/jsing.2020.22j⟩
International audience; Khimshiashvili proved a topological degree formula for the Eu-ler characteristic of the Milnor fibres of a real function-germ with an isolated singularity. We give two generalizations of this result for non-isolated singularit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ec2fac53662a32ff31bb41d75dd89041
http://arxiv.org/abs/1901.06161
http://arxiv.org/abs/1901.06161
Autor:
Nicolas Dutertre
Publikováno v:
Singularities and Foliations. Geometry, Topology and Applications.Brazil-Mexico Meeting on Singularities,Northeastern Brazilian Meeting on Singularities (2015).
Singularities and Foliations. Geometry, Topology and Applications. Brazil-Mexico Meeting on Singularities, Northeastern Brazilian Meeting on Singularities (2015)., 2018
Springer Proceedings in Mathematics & Statistics ISBN: 9783319736389
Singularities and Foliations. Geometry, Topology and Applications. Brazil-Mexico Meeting on Singularities, Northeastern Brazilian Meeting on Singularities (2015)., 2018
Springer Proceedings in Mathematics & Statistics ISBN: 9783319736389
In this mini-course, we study the topology of real singularities. After recalling basic notions and classical results of differential topology, we present formulas for topological invariants of semi-analytic or semi-algebraic sets due to several auth
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::de24ffaf3c651da3f3e24ea2000c058d
https://hal.archives-ouvertes.fr/hal-01777412
https://hal.archives-ouvertes.fr/hal-01777412
Autor:
Nicolas Dutertre
Publikováno v:
School on Real and Complex Singularities in São Carlos, 2012, R. N. Araújo dos Santos, V. H. Jorge Pérez, T. Nishimura and O. Saeki, eds. (Tokyo: Mathematical Society of Japan, 2016)
School on Real and Complex Singularities in Sao carlos, 2012
School on Real and Complex Singularities in Sao carlos, 2012, 2016
School on Real and Complex Singularities in Sao carlos, 2012
School on Real and Complex Singularities in Sao carlos, 2012, 2016
The aim of these lecture notes is to provide the students with tools and techniques used in the theory of real singularities and to apply them in order to get interesting results on the topology and geometry of real singularities.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c01e1d415498b7ef5eb8f754ad3d7dd6
https://projecteuclid.org/euclid.aspm/1538621979
https://projecteuclid.org/euclid.aspm/1538621979
Autor:
Nicolas Dutertre
Publikováno v:
Geometriae Dedicata. 158:167-189
We prove a formula that relates the Euler–Poincare characteristic of a closed semi-algebraic set to its Lipschitz–Killing curvatures.