Displaying similar documents to “On the extendability of quadratic polynomial mappings of the plane”

Quadratic mappings and configuration spaces

Gia Giorgadze (2003)

Banach Center Publications

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We discuss some approaches to the topological study of real quadratic mappings. Two effective methods of computing the Euler characteristics of fibers are presented which enable one to obtain comprehensive results for quadratic mappings with two-dimensional fibers. As an illustration we obtain a complete topological classification of configuration spaces of planar pentagons.

Intersect a quartic to extract its roots

Raghavendra G. Kulkarni (2017)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this note we present a new method for determining the roots of a quartic polynomial, wherein the curve of the given quartic polynomial is intersected by the curve of a quadratic polynomial (which has two unknown coefficients) at its root point; so the root satisfies both the quartic and the quadratic equations. Elimination of the root term from the two equations leads to an expression in the two unknowns of quadratic polynomial. In addition, we introduce another expression in one...

On the complexification of real-analytic polynomial mappings of ℝ²

Ewa Ligocka (2006)

Annales Polonici Mathematici

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We give a simple algebraic condition on the leading homogeneous term of a polynomial mapping from ℝ² into ℝ² which is equivalent to the fact that the complexification of this mapping can be extended to a polynomial endomorphism of ℂℙ². We also prove that this extension acts on ℂℙ²∖ℂ² as a quotient of finite Blaschke products.

Infinitesimal generators for a class of polynomial processes

Włodzimierz Bryc, Jacek Wesołowski (2015)

Studia Mathematica

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We study the infinitesimal generators of evolutions of linear mappings on the space of polynomials, which correspond to a special class of Markov processes with polynomial regressions called quadratic harnesses. We relate the infinitesimal generator to the unique solution of a certain commutation equation, and we use the commutation equation to find an explicit formula for the infinitesimal generator of free quadratic harnesses.