Zobrazeno 1 - 10
of 79
pro vyhledávání: '"Matthias Aschenbrenner"'
Publikováno v:
Revista de la Unión Matemática Argentina. :1-10
Liouville closed $H$-fields are ordered differential fields whose ordering and derivation interact in a natural way and where every linear differential equation of order $1$ has a nontrivial solution. (The introduction gives a precise definition.) Fo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b94f914b38a39bbb79ca2c4292f9d07a
https://doi.org/10.33044/revuma.2892
https://doi.org/10.33044/revuma.2892
Publikováno v:
Revista Matemática Iberoamericana. 35:1027-1052
In 1934, H. Whitney asked how one can determine whether a real-valued function on a closed subset of Rn is the restriction of a Cm-function on Rn. A complete answer to this question was found much later by C. Fefferman in the early 2000s. Here, we wo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::695f349779115b69fb96ccd0dc2eefff
https://doi.org/10.4171/rmi/1077
https://doi.org/10.4171/rmi/1077
Every discrete definable subset of a closed asymptotic couple with ordered scalar field $\boldsymbol k$ is shown to be contained in a finite-dimensional $\boldsymbol k$-linear subspace of that couple. It follows that the differential-valued field $\m
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::90cdcd7f2e18643659287f841d7fe78a
Publikováno v:
Journal of the European Mathematical Society
Journal of the European Mathematical Society, European Mathematical Society, 2019, 21 (4), pp.1179-1199. ⟨10.4171/jems/858⟩
Journal of the European Mathematical Society, European Mathematical Society, 2019, 21 (4), pp.1179-1199. ⟨10.4171/jems/858⟩
We show that the natural embedding of the differential field of transseries into Conway's field of surreal numbers with the Berarducci-Mantova derivation is an elementary embedding. We also prove that any Hardy field embeds into the field of surreals
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::79ca5a3bb4a6d30a98fea67729ba898b
https://doi.org/10.4171/jems/858
https://doi.org/10.4171/jems/858
Publikováno v:
Proceedings of the London Mathematical Society. 117:376-406
We show that every valued differential field has an immediate strict extension that is spherically complete. We also discuss the issue of uniqueness up to isomorphism of such an extension.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2d5b5805e9e47512576e556760ab162e
https://doi.org/10.1112/plms.12128
https://doi.org/10.1112/plms.12128
Publikováno v:
2017, ⟨10.1090/conm/697/14044⟩
Let $\mathbb T$ be the differential field of transseries. We establish some basic properties of the dimension of a definable subset of ${\mathbb T}^n$, also in relation to its codimension in the ambient space ${\mathbb T}^n$. The case of dimension $0
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::043a360ac496c8c8df8cd80c373bc016
https://doi.org/10.1090/conm/697/14044
https://doi.org/10.1090/conm/697/14044
Publikováno v:
International Congress of Mathematicians 2018
International Congress of Mathematicians 2018, Aug 2018, Rio de Janeiro, France. pp.1-23, ⟨10.1142/9789813272880_0042⟩
International Congress of Mathematicians 2018, Aug 2018, Rio de Janeiro, France. pp.1-23, ⟨10.1142/9789813272880_0042⟩
Germs of real-valued functions, surreal numbers, and transseries are three ways to enrich the real continuum by infinitesimal and infinite quantities. Each of these comes with naturally interacting notions of ordering and derivative. The category of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::92997c336c41fc4a4df9ccb371b17bc2
https://hal.archives-ouvertes.fr/hal-02350415
https://hal.archives-ouvertes.fr/hal-02350415
Publikováno v:
Transactions of the American Mathematical Society. 368:5889-5949
We recast the problem of calculating Vapnik-Chervonenkis (VC) density into one of counting types, and thereby calculate bounds (often optimal) on the VC density for some weakly o-minimal, weakly quasi-o-minimal, and P P -minimal theories.
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https://explore.openaire.eu/search/publication?articleId=doi_________::9e6be105cba2414ca4176c92dc5d9c53
https://doi.org/10.1090/tran/6659
https://doi.org/10.1090/tran/6659
Publikováno v:
Advances in Geometry. 15:293-313
We establish versions of Michael’s Selection Theorem and Tietze’s Extension Theorem in the category of semilinear maps.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cea17c13e2870a3ba9c1dee5144eadd3
https://doi.org/10.1515/advgeom-2015-0018
https://doi.org/10.1515/advgeom-2015-0018
Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variab