Displaying similar documents to “On the index of contact”

Remarks on the generalized index of an analytic improper intersection

Krzysztof Jan Nowak (2003)

Annales Polonici Mathematici

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This article continues the investigation of the analytic intersection algorithm from the perspective of deformation to the normal cone, carried out in the previous papers of the author [7, 8, 9]. The main theorem asserts that, given an analytic set V and a linear subspace S, every collection of hyperplanes, admissible with respect to an algebraic bicone B, realizes the generalized intersection index of V and S. This result is important because the conditions for a collection of hyperplanes...

Relative tangent cone of analytic sets

Danuta Ciesielska (2012)

Annales Polonici Mathematici

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We give a characterization of the relative tangent cone of an analytic curve and an analytic set with an improper isolated intersection. Moreover, we present an effective computation of the intersection multiplicity of a curve and a set with s-metrization.

Smoothing functions and algorithm for nonsymmetric circular cone complementarity problems

Jingyong Tang, Yuefen Chen (2022)

Applications of Mathematics

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There has been much interest in studying symmetric cone complementarity problems. In this paper, we study the circular cone complementarity problem (denoted by CCCP) which is a type of nonsymmetric cone complementarity problem. We first construct two smoothing functions for the CCCP and show that they are all coercive and strong semismooth. Then we propose a smoothing algorithm to solve the CCCP. The proposed algorithm generates an infinite sequence such that the value of the merit function...

Intersection theory and separation exponent in complex analytic geometry

Ewa Cygan (1998)

Annales Polonici Mathematici

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We consider the intersection multiplicity of analytic sets in the general situation. We prove that it is a regular separation exponent for complex analytic sets and so it estimates the Łojasiewicz exponent. We also give some geometric properties of proper projections of analytic sets.

Relative tangent cone of analytic curves

Danuta Ciesielska (1999)

Annales Polonici Mathematici

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The purpose of this paper is to give a characterization of the relative tangent cone of two analytic curves in ℂ m with an isolated intersection.

On real algebraic links in S 3

R. Benedetti, M. Shiota (1998)

Bollettino dell'Unione Matematica Italiana

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Viene presentata una costruzione che, dato un arbitrario nodo L ⊆ S 3 , produce allo stesso tempo: 1) un'applicazione polinomiale f : R 4 , 0 → R 2 , 0 con singolarità (debolmente) isolata in 0 e L come tipo di nodo della singolarità; 2) una risoluzione delle singolarità di f nel senso di Hironaka. Specializzando la costruzione ai nodi fibrati otteniamo una versione debole (a meno di scoppiementi e nella categoria analitica reale) di un reciproco per il teorema di fibrazione di Milnor.