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We establish the following result: if the graph of a (nonsmooth) real-extended-valued function f : R n → R ∪ {+∞} is closed and admits a Whitney stratification, then the norm of the gradient of f at x ∈ dom f relative to the stratum containing x bounds from below all norms of Clarke subgradients of f at x. As a consequence, we obtain some Morse-Sard type… (More)

- Goulwen Fichou, Masahiro Shiota, MASAHIRO SHIOTA
- 2008

By Hironaka Desingularization Theorem, any real analytic function has only normal crossing singularities after a suitable modification. We focus on the analytic equivalence of such functions with only normal crossing singularities. We prove that for such functions C ∞ right equivalence implies analytic equivalence. We prove moreover that the cardinality of… (More)

This is a survey on the history of and the solutions to the basic global problems on Nash functions, which have been only recently solved, namely: separation, extension, global equations, Artin-Mazur description and idempotency, also noetherianness. We discuss all of them in the various possible contexts, from manifolds over the reals to real spectra of… (More)

Proefschrift voorgelegd tot het behalen van de graad van doctor in de wetenschappen, richting informatica aan de transnationale Universiteit Limburg te verdedigen door Preface First of all, I would like to thank Jan Van den Bussche for his support during the last four years. His never ending enthusiasm and advice made this dissertation possible. His… (More)

- GOULWEN FICHOU, MASAHIRO SHIOTA
- 2013

A blow-analytic homeomorphism is an arc-analytic subanalytic home-omorphism, 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, giving a positive and a negative answer depending of the topol-ogy involved. We generalise the result to spaces… (More)

- GOULWEN FICHOU, MASAHIRO SHIOTA
- 2008

Approximation of real analytic functions by Nash functions is a classical topic in real geometry. In this paper, we focus on the Nash approximation of an analytic desingularization of a Nash function germ obtained by a sequence of blowings-up along smooth analytic centers. We apply the result to prove that Nash function germs that are analytically… (More)

More than half a century ago R. Thom asserted in an unpublished manuscript that, generically, vector fields on compact connected smooth manifolds without boundary can admit only trivial continuous first integrals. Though somehow unprecise for what concerns the interpretation of the word " generically " , this statement is ostensibly true and is nowadays… (More)

- F. Acquistapace, F. Broglia, M. Shiota
- 2003

We prove a Lojasiewicz inequality for global semianalytic sets that implies the usual Hörmander's form. Some consequences are deduced on the finiteness property and separation for global semianalytic sets.

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