On the tangency of sets in generalized metric spaces for certain functions of the class
T. Konik (1991)
Matematički Vesnik
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T. Konik (1991)
Matematički Vesnik
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Jacek Chądzyński, Tadeusz Krasiński (1997)
Annales Polonici Mathematici
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We show that for a polynomial mapping the Łojasiewicz exponent of F is attained on the set .
Artūras Dubickas (2012)
Annales Polonici Mathematici
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Let P be a unimodular polynomial of degree d-1. Then the height H(P²) of its square is at least √(d/2) and the product L(P²)H(P²), where L denotes the length of a polynomial, is at least d². We show that for any ε > 0 and any d ≥ d(ε) there exists a polynomial P with ±1 coefficients of degree d-1 such that H(P²) < (2+ε)√(dlogd) and L(P²)H(P²)< (16/3+ε)d²log d. A similar result is obtained for the series with ±1 coefficients. Let be the mth coefficient of the square f(x)² of...
Didier D&#039;Acunto, Krzysztof Kurdyka (2005)
Annales Polonici Mathematici
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Let f: ℝⁿ → ℝ be a polynomial function of degree d with f(0) = 0 and ∇f(0) = 0. Łojasiewicz’s gradient inequality states that there exist C > 0 and ϱ ∈ (0,1) such that in a neighbourhood of the origin. We prove that the smallest such exponent ϱ is not greater than with .
Romain Tessera (2007)
Bulletin de la Société Mathématique de France
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Let be a compactly generated locally compact group and let be a compact generating set. We prove that if has polynomial growth, then is a Følner sequence and we give a polynomial estimate of the rate of decay of Our proof uses only two ingredients: the doubling property and a weak geodesic property that we call Property (M). As a matter of fact, the result remains true in a wide class of doubling metric measured spaces including manifolds and graphs. As an application, we obtain...
Bartłomiej Bzdęga (2016)
Acta Arithmetica
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We prove that for every ε > 0 and every nonnegative integer w there exist primes such that for the height of the cyclotomic polynomial is at least , where and is a constant depending only on w; furthermore . In our construction we can have for all i = 1,...,w and any function h: ℝ₊ → ℝ₊.
Nguyen Van Chau, Carlos Gutierrez (2006)
Annales Polonici Mathematici
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We consider nonsingular polynomial maps F = (P,Q): ℝ² → ℝ² under the following regularity condition at infinity : There does not exist a sequence of complex singular points of F such that the imaginary parts tend to (0,0), the real parts tend to ∞ and . It is shown that F is a global diffeomorphism of ℝ² if it satisfies Condition and if, in addition, the restriction of F to every real level set is proper for values of |c| large enough.
Olli Tapiola (2016)
Colloquium Mathematicae
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With the help of recent adjacent dyadic constructions by Hytönen and the author, we give an alternative proof of results of Lechner, Müller and Passenbrunner about the -boundedness of shift operators acting on functions where 1 < p < ∞, X is a metric space and E is a UMD space.
Ivan Lončar (2017)
Archivum Mathematicum
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For metrizable continua, there exists the well-known notion of a Whitney map. If is a nonempty, compact, and metric space, then any Whitney map for any closed subset of can be extended to a Whitney map for [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.
Andreas Fischer, Murray Marshall (2013)
Annales de la faculté des sciences de Toulouse Mathématiques
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We study the extensibility of piecewise polynomial functions defined on closed subsets of to all of . The compact subsets of on which every piecewise polynomial function is extensible to can be characterized in terms of local quasi-convexity if they are definable in an o-minimal expansion of . Even the noncompact closed definable subsets can be characterized if semialgebraic function germs at infinity are dense in the Hardy field of definable germs. We also present a piecewise...
Richard J. Gardner, Daniel Hug, Wolfgang Weil (2013)
Journal of the European Mathematical Society
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An investigation is launched into the fundamental characteristics of operations on and between sets, with a focus on compact convex sets and star sets (compact sets star-shaped with respect to the origin) in -dimensional Euclidean space . It is proved that if , with three trivial exceptions, an operation between origin-symmetric compact convex sets is continuous in the Hausdorff metric, covariant, and associative if and only if it is addition for some . It is also demonstrated...
J. Musiałek (1969)
Annales Polonici Mathematici
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M. K. Aouf (1988)
Matematički Vesnik
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Swami Jnanananda (1936)
Časopis pro pěstování matematiky a fysiky
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K. Orlov (1981)
Matematički Vesnik
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Stephan Baier (2005)
Acta Arithmetica
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M. K. Sen (1971)
Annales Polonici Mathematici
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P. Srivastava, K. K. Azad (1981)
Matematički Vesnik
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Ralph McKenzie (1971)
Colloquium Mathematicae
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Janusz Matkowski (1989)
Annales Polonici Mathematici
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Stephan Baier (2004)
Acta Arithmetica
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A. Szymański (1977)
Colloquium Mathematicae
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Philippe Clément, Wolfgang Desch (2008)
Studia Mathematica
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Let , be complete separable metric spaces. Denote by (X) the space of probability measures on X, by the p-Wasserstein metric with some p ∈ [1,∞), and by the space of probability measures on X with finite Wasserstein distance from any point measure. Let , , be a Borel map such that f is a contraction from into . Let ν₁,ν₂ be probability measures on Ω with finite. On X we consider the subordinated measures . Then . As an application we show that the solution measures ...