Results 1 - 10 of 3,296

POLYNOMIAL MAPS OF AFFINE QUADRICS

by R. M. W. Wood
"... Since the article [3] on polynomial maps of spheres appeared about 25 years ago, there have been a number of papers on the theory of rational maps of real varieties (see the references in [2], for example) which have many interesting things to say about the representation of homotopy classes by alge ..."
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Since the article [3] on polynomial maps of spheres appeared about 25 years ago, there have been a number of papers on the theory of rational maps of real varieties (see the references in [2], for example) which have many interesting things to say about the representation of homotopy classes

Unfolding polynomial maps at infinity

by Walter D. Neumann, Paul Norbury
"... Let f: C n → C be a polynomial map. The polynomial describes a family of complex affine hypersurfaces f −1 (c), c ∈ C. The family is locally trivial, so the hypersurfaces have constant topology, except at finitely many irregular fibers f −1 (c) whose topology may differ from the generic or regular f ..."
Abstract - Cited by 10 (3 self) - Add to MetaCart
Let f: C n → C be a polynomial map. The polynomial describes a family of complex affine hypersurfaces f −1 (c), c ∈ C. The family is locally trivial, so the hypersurfaces have constant topology, except at finitely many irregular fibers f −1 (c) whose topology may differ from the generic or regular

Moduli space of polynomial maps

by Toshi Sugiyama
"... In the study of the dynamics of a polynomial map $f $ , the eigenvalues of the fixed points of $f $ play a very important role to characterize the original map $f $. In this paper, we shall study how many affine conjugacy classes of polynomial maps are there when the eigenvalues of their fixed point ..."
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In the study of the dynamics of a polynomial map $f $ , the eigenvalues of the fixed points of $f $ play a very important role to characterize the original map $f $. In this paper, we shall study how many affine conjugacy classes of polynomial maps are there when the eigenvalues of their fixed

NONCOMMUTATIVE POLYNOMIAL MAPS

by Andre ́ Leroy
"... Polynomial maps attached to polynomials of an Ore extension are naturally defined. In this setting we show the importance of pseudo-linear transformations and give some applications. In particular, factorizations of polynomials in an Ore extension over a finite field Fq[t; θ], where θ is the Frobeni ..."
Abstract - Cited by 3 (0 self) - Add to MetaCart
Polynomial maps attached to polynomials of an Ore extension are naturally defined. In this setting we show the importance of pseudo-linear transformations and give some applications. In particular, factorizations of polynomials in an Ore extension over a finite field Fq[t; θ], where θ

POLYNOMIAL MAP SYMPLECTIC ALGORITHM

by Govindan Rangarajan , 2002
"... Long-term stability studies of nonlinear Hamiltonian systems require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the symplectic map representing the Hamiltonian system is refactorized using polynomial symplectic ..."
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Long-term stability studies of nonlinear Hamiltonian systems require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the symplectic map representing the Hamiltonian system is refactorized using polynomial symplectic

On Approximating the Entropy of Polynomial Mappings

by Zeev Dvir, Dan Gutfreund, Guy N. Rothblum, Salil Vadhan - ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 160 (2010) , 2010
"... We investigate the complexity of the following computational problem: Polynomial Entropy Approximation (PEA): Given a low-degree polynomial mapping p: F n → F m, where F is a finite field, approximate the output entropy H(p(Un)), where Un is the uniform distribution on F n and H may be any of severa ..."
Abstract - Cited by 10 (0 self) - Add to MetaCart
We investigate the complexity of the following computational problem: Polynomial Entropy Approximation (PEA): Given a low-degree polynomial mapping p: F n → F m, where F is a finite field, approximate the output entropy H(p(Un)), where Un is the uniform distribution on F n and H may be any

Relative cohomology of polynomial mappings

by unknown authors , 2008
"... Let F be a polynomial mapping from C n to C q with n> q. We study the De Rham cohomology of its fibres and its relative cohomology groups, by introducing a special fibre F −1 (∞) ”at infinity ” and its cohomology. Let us fix a weighted homogeneous degree on C[x1,...,xn] with strictly positive wei ..."
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Let F be a polynomial mapping from C n to C q with n> q. We study the De Rham cohomology of its fibres and its relative cohomology groups, by introducing a special fibre F −1 (∞) ”at infinity ” and its cohomology. Let us fix a weighted homogeneous degree on C[x1,...,xn] with strictly positive

Generalizations of Chebyshev polynomials and Polynomial Mappings

by Yang Chen, James Griffin, Mourad E H Ismail , 2004
"... In this paper we show how polynomial mappings of degree K from a union of disjoint intervals onto [−1, 1] generate a countable number of special cases of generalizations of Chebyshev polynomials. We also derive a new expression for these generalized Chebyshev polynomials for any genus g, from which ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
In this paper we show how polynomial mappings of degree K from a union of disjoint intervals onto [−1, 1] generate a countable number of special cases of generalizations of Chebyshev polynomials. We also derive a new expression for these generalized Chebyshev polynomials for any genus g, from which

An Inequality for Polynomial Mappings

by Arkadiusz P̷loski - Bull. Ac. Pol.: Math , 1992
"... Abstract. We give an estimate of the growth of a polynonial mapping of C n. 1. Main result. Let F = (F1,...,Fn) : Cn → Cn be a polynomial mapping. We put d(F) = #F −1 (w) for almost all w ∈ Cn and call d(F) the geometric degree of F. Let di = deg Fi for i = 1,...,n. Then 0 ≤ d(F) ≤ ∏n i=1 di if Fi ..."
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Abstract. We give an estimate of the growth of a polynonial mapping of C n. 1. Main result. Let F = (F1,...,Fn) : Cn → Cn be a polynomial mapping. We put d(F) = #F −1 (w) for almost all w ∈ Cn and call d(F) the geometric degree of F. Let di = deg Fi for i = 1,...,n. Then 0 ≤ d(F) ≤ ∏n i=1 di

ON RAMIFICATION LOCUS OF A POLYNOMIAL MAPPING

by Zbigniew Jelonek , 2004
"... Let X be a smooth algebraic hypersurface in Cn: There is a proper polynomial mapping F: Cn! Cn, such that the set of ramication values of F contains the hypersurface X. ..."
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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 ramication values of F contains the hypersurface X.
Results 1 - 10 of 3,296