Ta Lê Loi (1994)
Annales Polonici Mathematici
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We prove that every set definable in the structure can be decomposed into finitely many connected analytic manifolds each of which is also definable in this structure.
Ta Loi (1996)
Banach Center Publications
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The aim of this paper is to prove that every subset of definable from addition, multiplication and exponentiation admits a stratification satisfying Whitney’s conditions a) and b).
Krzysztof Kurdyka (1991)
Annales Polonici Mathematici
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We construct an arc-analytic function (i.e. a function analytic on each analytic arc) whose graph is not subanalytic.
Krzysztof Kurdyka (1994)
Annales Polonici Mathematici
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We construct an arc-analytic function (i.e. analytic on every real-analytic arc) in ℝ² which is analytic outside a nondiscrete subset of ℝ².
Isabelle Bonnard, Federica Pieroni (2004)
Revista Matemática Complutense
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We present a characterization of sums of signs of global analytic functions on a real analytic manifold M of dimension two. Unlike the algebraic case, obstructions at infinity are not relevant: a function is a sum of signs on M if and only if this is true on each compact subset of M. This characterization gives a necessary and sufficient condition for an analytically constructible function, i.e. a linear combination with integer coefficients of Euler characteristic of fibers of proper...
Zhang, Pingping (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Nishiwaki, Junichi, Owa, Shigeyoshi (2007)
Acta Universitatis Apulensis. Mathematics - Informatics
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Khan, Mumtaz Ahmad, Najmi, M. (2002)
Novi Sad Journal of Mathematics
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A. Alexandrou Himonas (1998)
Annales Polonici Mathematici
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We discuss the open problem of analytic hypoellipticity for sums of squares of vector fields, including some recent partial results and a conjecture of Treves.
Åhag, Per, Czyż, Rafał, Lodin, Sam, Wikström, Frank (2007)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Khodr Shamseddine, Martin Berz (2005)
Annales mathématiques Blaise Pascal
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A detailed study of power series on the Levi-Civita fields is presented. After reviewing two types of convergence on those fields, including convergence criteria for power series, we study some analytical properties of power series. We show that within their domain of convergence, power series are infinitely often differentiable and re-expandable around any point within the radius of convergence from the origin. Then we study a large class of functions that are given locally by power...
Sławomir Rams (2000)
Annales Polonici Mathematici
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We prove that the generalized index of intersection of an analytic set with a closed submanifold (Thm. 4.3) and the intersection product of analytic cycles (Thm. 5.4), which are defined in [T₂], are intrinsic. We define the intersection product of analytic cycles on a reduced analytic space (Def. 5.8) and prove a relation of its degree and the exponent of proper separation (Thm. 6.3).
Krasiński, Tadeusz (2001)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Hussain, Saquib (2009)
Acta Universitatis Apulensis. Mathematics - Informatics
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