Degrees of Polynomial Solutions of a Class of Riccati - tipe Differential Equations*.
Mira Bhargava (1964)
Collectanea Mathematica
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Mira Bhargava (1964)
Collectanea Mathematica
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H. Kaufman, Mira Bhargava (1965)
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Christoph Schwarzweller, Artur Korniłowicz (2016)
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In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic polynomials we present the canonical embedding of R into R[X] and deal with both unit and irreducible elements. We also define polynomial GCDs and show that for fields F and irreducible polynomials p the field F[X]/ is isomorphic to the field of polynomials with degree smaller than the one of p.
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.
Toufik Zaïmi (2011)
Publications de l'Institut Mathématique
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J. Siciak (1971)
Annales Polonici Mathematici
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R. Ger (1971)
Annales Polonici Mathematici
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Jason Lucier (2006)
Acta Arithmetica
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Krzysztof Woźniakowski (2001)
Studia Mathematica
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We show that in the space C[-1,1] there exists an orthogonal algebraic polynomial basis with optimal growth of degrees of the polynomials.
Norbert Hegyvári, François Hennecart (2009)
Acta Arithmetica
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Umberto Zannier (2007)
Acta Arithmetica
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Luís R. A. Finotti (2009)
Acta Arithmetica
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I. R. Shafarevich (1999)
The Teaching of Mathematics
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Chistov, A.L. (2005)
Zapiski Nauchnykh Seminarov POMI
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C. Fong, G. Lumer, E. Nordgren, H. Radjavi, P. Rosenthal (1995)
Studia Mathematica
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We prove that a function f is a polynomial if G◦f is a polynomial for every bounded linear functional G. We also show that an operator-valued function is a polynomial if it is locally a polynomial.
Shih Ping Tung (2006)
Acta Arithmetica
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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.
Nguyen Van Chau (2008)
Annales Polonici Mathematici
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A non-zero constant Jacobian polynomial map F=(P,Q):ℂ² → ℂ² has a polynomial inverse if the component P is a simple polynomial, i.e. its regular extension to a morphism p:X → ℙ¹ in a compactification X of ℂ² has the following property: the restriction of p to each irreducible component C of the compactification divisor D = X-ℂ² is of degree 0 or 1.
Jacek Chądzyński, Tadeusz Krasiński (1992)
Annales Polonici Mathematici
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A complete characterization of the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² is given. Moreover, a characterization of a component of a polynomial automorphism of ℂ² (in terms of the Łojasiewicz exponent at infinity) is given.
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.