Displaying similar documents to “On the Euler characteristic of fibres of real polynomial maps”

On Kelvin type transformation for Weinstein operator

Martina Šimůnková (2001)

Commentationes Mathematicae Universitatis Carolinae

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The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator W k : = Δ + k x n x n on n is proved. In this note there is shown that in the cases k 0 , k 2 no other transforms of this kind exist and for case k = 2 , all such transforms are described.

On Garcia numbers.

Brunotte, Horst (2009)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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Distances on the tropical line determined by two points

María Jesús de la Puente (2014)

Kybernetika

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Let p ' and q ' be points in n . Write p ' q ' if p ' - q ' is a multiple of ( 1 , ... , 1 ) . Two different points p and q in n / uniquely determine a tropical line L ( p , q ) passing through them and stable under small perturbations. This line is a balanced unrooted semi-labeled tree on n leaves. It is also a metric graph. If some representatives p ' and q ' of p and q are the first and second columns of some real normal idempotent order n matrix A , we prove that the tree L ( p , q ) is described by a matrix F , easily obtained from A . We also...

On infinite composition of affine mappings

László Máté (1999)

Fundamenta Mathematicae

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 Let F i = 1 , . . . , N be affine mappings of n . It is well known that if there exists j ≤ 1 such that for every σ 1 , . . . , σ j 1 , . . . , N the composition (1) F σ 1 . . . F σ j is a contraction, then for any infinite sequence σ 1 , σ 2 , . . . 1 , . . . , N and any z n , the sequence (2) F σ 1 . . . F σ n ( z ) is convergent and the limit is independent of z. We prove the following converse result: If (2) is convergent for any z n and any σ = σ 1 , σ 2 , . . . belonging to some subshift Σ of N symbols (and the limit is independent of z), then there exists j ≥ 1 such that for every σ = σ 1 , σ 2 , . . . Σ the composition (1) is a contraction....

Guidance properties of a cylindrical defocusing waveguide

Oldřich John, Charles A. Stuart (1994)

Commentationes Mathematicae Universitatis Carolinae

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We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification...