Diagonal series of rational functions (several variables)

Sławomir Cynk; Piotr Tworzewski

Displaying similar documents to “Diagonal series of rational functions (several variables)”

Diagonal series of rational functions

Sławomir Cynk, Piotr Tworzewski (1991)

Annales Polonici Mathematici

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Some representations of Nash functions on continua in ℂ as integrals of rational functions of two complex variables are presented. As a simple consequence we get close relations between Nash functions and diagonal series of rational functions.

Rational solutions of the Sasano system of type $A_{5}^{(2)}$ .

Matsuda, Kazuhide (2011)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Collective Operations on Number-Membered Sets

Artur Korniłowicz (2009)

Formalized Mathematics

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The article starts with definitions of sets of opposite and inverse numbers of a given number membered set. Next, collective addition, subtraction, multiplication and division of two sets are defined. Complex numbers cases and extended real numbers ones are introduced separately and unified for reals. Shortcuts for singletons cases are also defined.

The growth of regular functions on algebraic sets

A. Strzeboński (1991)

Annales Polonici Mathematici

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We are concerned with the set of all growth exponents of regular functions on an algebraic subset V of $ℂ^{n}$ . We show that its elements form an increasing sequence of rational numbers and we study the dependence of its structure on the geometric properties of V.

On branches at infinity of a pencil of polynomials in two complex variables

T. Krasiński (1991)

Annales Polonici Mathematici

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Let F ∈ ℂ[x,y]. Some theorems on the dependence of branches at infinity of the pencil of polynomials f(x,y) - λ, λ ∈ ℂ, on the parameter λ are given.

New examples of effective formulas for holomorphically contractible functions

Marek Jarnicki, Peter Pflug (1999)

Studia Mathematica

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Let $G \subset ℂ^{n}$ and $B \subset ℂ^{m}$ be domains and let Φ:G → B be a surjective holomorphic mapping. We characterize some cases in which invariant functions and pseudometrics on G can be effectively expressed in terms of the corresponding functions and pseudometrics on B.

On the existence of universal rational structures for groups.

Grigorenko, O.V., Roman'kov, V.A. (2007)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

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Epsilon systems on geometric crystals of type $A_{n}$ .

Nakashima, Toshiki (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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On functions satisfying more than one equation of Schiffer type

J. Macura, J. Śladkowska (1993)

Annales Polonici Mathematici

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The paper concerns properties of holomorphic functions satisfying more than one equation of Schiffer type ( $D_{n}$ -equation). Such equations are satisfied, in particular, by functions that are extremal (in various classes of univalent functions) with respect to functionals depending on a finite number of coefficients.

On the restricted Waring problem over $_{2^{n}} [t]$

Luis Gallardo (2000)

Acta Arithmetica

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1. Introduction. The Waring problem for polynomial cubes over a finite field F of characteristic 2 consists in finding the minimal integer m ≥ 0 such that every sum of cubes in F[t] is a sum of m cubes. It is known that for F distinct from ₂, ₄, $_{16}$ , each polynomial in F[t] is a sum of three cubes of polynomials (see [3]). If a polynomial P ∈ F[t] is a sum of n cubes of polynomials in F[t] such that each cube A³ appearing in the decomposition has degree < deg(P)+3, we say that P is...

Rational interpolation: analytical solution.

Cherednichenko, V.G. (2002)

Sibirskij Matematicheskij Zhurnal

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Linear isometries of finite codimensions on Banach algebras of holomorphic functions.

Hatori, Osamu, Kasuga, Kazuhiro (2009)

Banach Journal of Mathematical Analysis [electronic only]

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On ergodicity of some cylinder flows

Krzysztof Frączek (2000)

Fundamenta Mathematicae

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We study ergodicity of cylinder flows of the form $T_{f} : T \times ℝ \to T \times ℝ$ , $T_{f} (x, y) = (x + α, y + f (x))$ , where $f : T \to ℝ$ is a measurable cocycle with zero integral. We show a new class of smooth ergodic cocycles. Let k be a natural number and let f be a function such that $D^{k} f$ is piecewise absolutely continuous (but not continuous) with zero sum of jumps. We show that if the points of discontinuity of $D^{k} f$ have some good properties, then $T_{f}$ is ergodic. Moreover, there exists $ε_{f} > 0$ such that if $v : T \to ℝ$ is a function with zero integral such that $D^{k} v$ is of bounded...

Analytic determinacy and 0# A forcing-free proof of Harrington’s theorem

Ramez Sami (1999)

Fundamenta Mathematicae

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We prove the following theorem: Given a⊆ω and $1 \leq α < ω_{1}^{C K}$ , if for some $η < ℵ_{1}$ and all u ∈ WO of length η, a is $Σ_{α}^{0} (u)$ , then a is $Σ_{α}^{0}$ . We use this result to give a new, forcing-free, proof of Leo Harrington’s theorem: $Σ_{1}^{1}$ -Turing-determinacy implies the existence of $0$ .

Corrigendum to the paper "Constants for lower bounds for linear forms in the logarithms of algebraic numbers II. The homogeneous rational case" (Acta Arith. 55 (1990), 15-22)

Josef Blass, A. M. W. Glass, David K. Manski, David B. Meronk (1993)

Acta Arithmetica

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Entropy and growth of expanding periodic orbits for one-dimensional maps

A. Katok, A. Mezhirov (1998)

Fundamenta Mathematicae

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Let f be a continuous map of the circle $S^{1}$ or the interval I into itself, piecewise $C^{1}$ , piecewise monotone with finitely many intervals of monotonicity and having positive entropy h. For any ε > 0 we prove the existence of at least $e^{(h - ε) n_{k}}$ periodic points of period $n_{k}$ with large derivative along the period, $| {(f^{n_{k}})}^{'} | > e^{(h - ε) n_{k}}$ for some subsequence $n_{k}$ of natural numbers. For a strictly monotone map f without critical points we show the existence of at least $(1 - ε) e^{h n}$ such points.

Growth of the product $\prod_{j = 1}^{n} (1 - x^{a_{j}})$

J. P. Bell, P. B. Borwein, L. B. Richmond (1998)

Acta Arithmetica

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We estimate the maximum of $\prod_{j = 1}^{n} | 1 - x^{a_{j}} |$ on the unit circle where 1 ≤ a₁ ≤ a₂ ≤ ... is a sequence of integers. We show that when $a_{j}$ is $j^{k}$ or when $a_{j}$ is a quadratic in j that takes on positive integer values, the maximum grows as exp(cn), where c is a positive constant. This complements results of Sudler and Wright that show exponential growth when $a_{j}$ is j. In contrast we show, under fairly general conditions, that the maximum is less than $2^{n} / n^{r}$ , where r is an arbitrary positive number. One consequence...