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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
- 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)

- Adrian Lewis, J Bolte, A Daniilidis, A Ioffe, C H J Pang, M Shiota
- 2007

Modern variational analysis provides a sophisticated unification of convex and smooth optimization theory, achieving striking generality but at the expense of possible pathology. The general theory must handle highly irregular and oscillatory functions and sets, and yet, on the other hand, a rich family of concrete instances involve no such pathology. In… (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)

More than half a century ago R. Thom asserted in an unpublished manuscript that, generically, vector fields on compact connected smooth manifolds without boundary can admit only trivial continuous first integrals.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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