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pro vyhledávání: '"Shiota, Masahiro"'
As well-known, the $C^\infty$ stability of proper $C^\infty$ maps is characterized by the infinitesimal $C^\infty$ stability. In the present paper we study the counterpart in real analytic context. In particular, we show that the infinitesimal $C^\om
Externí odkaz:
http://arxiv.org/abs/2406.18106
Autor:
Shiota, Masahiro
Consider the semialgebraic structure over the real field. More generally, let an ominimal structure be over a real closed field. We show that a definable metric space X with a definable metric d is embedded into a Euclidean space so that its closure
Externí odkaz:
http://arxiv.org/abs/1701.03858
Publikováno v:
Can. Math. Bull. 59 (2016) 760-768
We propose a version of the classical Artin approximation which allows to perturb the variables of the approximated solution. Namely, it is possible to approximate a formal solution of a Nash equation by a Nash solution in a compatible way with a giv
Externí odkaz:
http://arxiv.org/abs/1511.01262
Autor:
Ohmoto, Toru, Shiota, Masahiro
Publikováno v:
Journal of Topology, vol 10 (3) (2017), 765-775
We show that every semialgebraic set admits a semialgebraic triangulation such that each closed simplex is $C^1$ differentiable. As an application, we give a straightforward definition of the integration $\int_X \omega$ over a compact semialgebraic s
Externí odkaz:
http://arxiv.org/abs/1505.03970
Autor:
Fichou, Goulwen, Shiota, Masahiro
Given a real polynomial function and a point in its zero locus, we defined a set consisting of algebraic real Puiseux series naturally attached to these data. We prove that this set determines the topology and the geometry of the real Milnor fibre of
Externí odkaz:
http://arxiv.org/abs/1404.3509
Autor:
Maříková, Jana, Shiota, Masahiro
We introduce a non real-valued measure on the definable sets contained in the finite part of a cartesian power of an o-minimal field $R$. The measure takes values in an ordered semiring, the Dedekind completion of a quotient of $R$. We show that ever
Externí odkaz:
http://arxiv.org/abs/1402.4787
Autor:
Shiota, Masahiro
Hilbert initiated the standpoint in foundations of mathematics. From this standpoint, we allow only a finite number of repetitions of elementary operations when we construct objects and morphisms. When we start from a subset of a Euclidean space. The
Externí odkaz:
http://arxiv.org/abs/1310.5489
Autor:
Fichou, Goulwen, Shiota, Masahiro
A blow-analytic homeomorphism is an arc-analytic subanalytic homeomorphism, and therefore it induces a bijective mapping between spaces of analytic arcs. We tackle the question of the continuity of this induced mapping between the spaces of arcs, giv
Externí odkaz:
http://arxiv.org/abs/1201.2775
Autor:
Fichou, Goulwen, Shiota, Masahiro
The Euler characteristic of the link of a real algebraic variety is an interesting topological invariant in order to discuss local topological properties. We prove in the paper that an invariant stronger than the Euler Characteristic is well defined
Externí odkaz:
http://arxiv.org/abs/1201.0684
Autor:
Shiota, Masahiro
In [5] I solved the Thom's conjecture that a proper Thom map is triangulable. In this paper I drop the properness condition in the semialgebraic case and, moreover, in the definable case in an o-minimal structure.
Externí odkaz:
http://arxiv.org/abs/1006.4719