Displaying similar documents to “Smooth Cantor functions”

On first integrals for polynomial differential equations on the line

Henryk Żołądek (1993)

Studia Mathematica

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We show that any equation dy/dx = P(x,y) with P a polynomial has a global (on ℝ²) smooth first integral nonconstant on any open domain. We also present an example of an equation without an analytic primitive first integral.

On perturbations of pluriregular sets generated by sequences of polynomial maps

Maciej Klimek (2003)

Annales Polonici Mathematici

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It is shown that an infinite sequence of polynomial mappings of several complex variables, with suitable growth restrictions, determines a filled-in Julia set which is pluriregular. Such sets depend continuously and analytically on the generating sequences, in the sense of pluripotential theory and the theory of set-valued analytic functions, respectively.

The determinant of oriented rotants

Adam H. Piwocki (2007)

Colloquium Mathematicae

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We study the determinant of pairs of rotants of Anstee, Przytycki and Rolfsen. We consider various notions of rotant orientations.

Observability of control systems for polynomial inputs and genericity

Philippe Jouan (2001)

Applicationes Mathematicae

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We consider smooth single-input, two-output systems on a compact manifold X. We show that the set of systems that are observable for any polynomial input whose degree is less than or equal to a given bound contains an open and dense subset of the set of smooth systems.

On the zeros of polynomials and analytic functions

Roshan Lal, Susheel Kumar, Sunil Hans (2011)

Annales UMCS, Mathematica

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For a polynomial of degree n, we have obtained some results, which generalize and improve upon the earlier well known results (under certain conditions). A similar result is also obtained for analytic function.

On ramification locus of a polynomial mapping

Zbigniew Jelonek (2003)

Banach Center Publications

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Let X be a smooth algebraic hypersurface in ℂⁿ. There is a proper polynomial mapping F: ℂⁿ → ℂⁿ, such that the set of ramification values of F contains the hypersurface X.

Separating polynomials on Banach spaces.

R. Gonzalo, J. A. Jaramillo (1997)

Extracta Mathematicae

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In this paper we survey some recent results concerning separating polynomials on real Banach spaces. By this we mean a polynomial which separates the origin from the unit sphere of the space, thus providing an analog of the separating quadratic form on Hilbert space.

Combinatorial Nullstellensatz approach to polynomial expansion

Fedor Petrov (2014)

Acta Arithmetica

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Applying techniques similar to Combinatorial Nullstellensatz we prove a lower estimate of |f(A,B)| for finite subsets A, B of a field, and a polynomial f(x,y) of the form f(x,y) = g(x) + yh(x), where the degree of g is greater than that of h.