On the Euler characteristic of fibres of real polynomial maps

Adam Parusiński; Zbigniew Szafraniec

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

Similarity:

The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator $W_{k} : = Δ + \frac{k}{x_{n}} \frac{\partial}{\partial x_{n}}$ on $ℝ^{n}$ is proved. In this note there is shown that in the cases $k \neq 0$ , $k \neq 2$ 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]

Similarity:

Distances on the tropical line determined by two points

María Jesús de la Puente (2014)

Kybernetika

Similarity:

Let $p^{'}$ and $q^{'}$ be points in $ℝ^{n}$ . Write $p^{'} \sim q^{'}$ if $p^{'} - q^{'}$ is a multiple of $(1, ..., 1)$ . Two different points $p$ and $q$ in $ℝ^{n} / \sim$ 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

Similarity:

Let $F_{i} = 1, . . ., N$ be affine mappings of $ℝ^{n}$ . It is well known that if there exists j ≤ 1 such that for every $σ_{1}, . . ., σ_{j} \in 1, . . ., N$ the composition (1) $F_{σ 1} \circ . . . \circ F_{σ_{j}}$ is a contraction, then for any infinite sequence $σ_{1}, σ_{2}, . . . \in 1, . . ., N$ and any $z \in ℝ^{n}$ , the sequence (2) $F_{σ 1} \circ . . . \circ F_{σ_{n}} (z)$ is convergent and the limit is independent of z. We prove the following converse result: If (2) is convergent for any $z \in ℝ^{n}$ 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 $σ = σ_{1}, σ_{2}, . . . \in Σ$ the composition (1) is a contraction....

Guidance properties of a cylindrical defocusing waveguide

Oldřich John, Charles A. Stuart (1994)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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...

On the roots of polynomials over division algebras.

Topuridze, N. (2003)

Georgian Mathematical Journal

Similarity:

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

Similarity:

1. Introduction. Let p be a prime number and $ℤ_{p}$ the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, $k_{\infty}$ a $ℤ_{p}$ -extension of k, $k_{n}$ the nth layer of $k_{\infty} / k$ , and $A_{n}$ the p-Sylow subgroup of the ideal class group of $k_{n}$ . Iwasawa proved the following well-known theorem about the order $A_{n}$ of $A_{n}$ : Theorem A (Iwasawa). Let $k_{\infty} / k$ be a $ℤ_{p}$ -extension and $A_{n}$ the p-Sylow subgroup of the ideal class group of $k_{n}$ , where $k_{n}$ is the $n$ th layer of $k_{\infty} / k$ . Then there exist integers $λ = λ (k_{\infty} / k) \geq 0$ , $μ = μ (k_{\infty} / k) \geq 0$ , $ν = ν (k_{\infty} / k)$ , and n₀ ≥ 0...