منابع مشابه
Local topological algebraicity of analytic function germs
T. Mostowski showed that every (real or complex) germ of an analytic set is homeomorphic to the germ of an algebraic set. In this paper we show that every (real or complex) analytic function germ, defined on a possibly singular analytic space, is topologically equivalent to a polynomial function germ defined on an affine algebraic variety.
متن کاملTable of integrals of squared Jacobian elliptic functions and reductions of related hypergeometric R-functions
Any product of real powers of Jacobian elliptic functions can be written in the form csm1 (u, k) ds2 (u, k) nsm3 (u, k). If all three m’s are even integers, the indefinite integral of this product with respect to u is a constant times a multivariate hypergeometric function R−a(b1, b2, b3; x, y, z) with halfodd-integral b’s and −a + b1 + b2 + b3 = 1, showing it to be an incomplete elliptic integ...
متن کاملEquivalence Relations for Two Variable Real Analytic Function Germs
For two variable real analytic function germs we compare the blowanalytic equivalence in the sense of Kuo to the other natural equivalence relations. Our main theorem states that C equivalent germs are blow-analytically equivalent. This gives a negative answer to a conjecture of Kuo. In the proof we show that the Puiseux pairs of real Newton-Puiseux roots are preserved by the C equivalence of f...
متن کاملOn the real algebra of quasianalytic function germs
Given a quasianalytic system Q = (Qn)n∈N of sheaves, denote by Qn the local ring of Q-analytic function germs at 0 ∈ Rn. This paper introduces the concepts of Lojasiewicz radical and geometric spectrum SpegQn ⊂ SperQn. Via the Lojasiewicz inequality, a version of the Nullstellensatz for Qn is given. We establish a quasianalytic version of the Artin–Lang property for Qn. Finally, we prove, by me...
متن کاملBlow-analytic Equivalence of Two Variable Real Analytic Function Germs
Blow-analytic equivalence is a notion for real analytic function germs, introduced by Tzee-Char Kuo in order to develop the real analytic equisingularity theory. In this paper we give several complete characterisations of blow-analytic equivalence in the two dimensional case in terms of the minimal resolutions, the real tree model for the arrangement of Newton-Puiseux roots, and the cascade blo...
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ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2017
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2017.v13.n4.a5