Results 21 to 30 of about 157,707 (146)
Thue's Fundamentaltheorem, I: The General Case
, 2010 In this paper, Thue's Fundamentaltheorem is analysed. We show that it includes, and often strengthens, known effective irrationality measures obtained via the so-called hypergeometric method as well as showing that it can be applied to previously ...
Voutier, Paul
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The Polyhedron-Hitting Problem [PDF]
, 2014 We consider polyhedral versions of Kannan and Lipton's Orbit Problem (STOC '80 and JACM '86)---determining whether a target polyhedron V may be reached from a starting point x under repeated applications of a linear transformation A in an ambient vector ...
Chonev, Ventsislav +2 more
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Normal Shock Wave Approximations for Flight at Hypersonic Mach Numbers
AerospaceNormal shock pressure ratios in equilibrium air for Mach numbers up to 30 and altitudes to 300,000 feet are shown to be correlated by a simple power law which provides an accuracy of ±2%, thereby permitting direct calculation of corresponding enthalpy ...
Pasquale M. Sforza
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On the approximation of algebraic numbers by algebraic integers [PDF]
Journal of the Australian Mathematical Society, 1963 In his Topics in Number Theory, vol. 2, chapter 2 (Reading, Mass., 1956) W. J. LeVeque proved an important generalisation of Roth's theorem (K. F. Roth, Mathematika 2,1955, 1—20).Let ξ be a fixed algebraic number, σ a positive constant, and K an algebraic number field of degree n.
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Tropical Solution of Discrete Best Approximation Problems
MathematicsWe consider discrete best approximation problems in the setting of tropical algebra, which is concerned with the theory and application of algebraic systems with idempotent operations. Given a set of input–output pairs of an unknown function defined on a
Nikolai Krivulin
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On the approximation to algebraic numbers by algebraic numbers
Glasnik Matematicki, 2009 Let n be a positive integer. Let ξ be an algebraic real number of degree greater than n. It follows from a deep result of W. M. Schmidt that, for every positive real number e, there are infinitely many algebraic numbers α of degree at most n such that |ξ−α| < H(α)−n−1+e, where H(α) denotes the naive height of α. We sharpen this result by replacing e by
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On the approximation of π by special algebraic numbers [PDF]
Glasgow Mathematical Journal, 1980 Suppose that m0 is an integer, m0≥3, ρ = exp(2πi/m0), K = ℚ(ρ, i), v denotes the degree of K, ξ∈K has degree N over ℚ. The length, where is the (irreducible) minimal polynomial for with ξ relatively prime integer coefficients. Feldman [2, p. 49] proved that there is an absolute constant c0>0 such thatFrom [2, p. 49, Notes 1 and 2] we know that v =
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Chromatic homotopy theory is asymptotically algebraic
, 2019 Inspired by the Ax--Kochen isomorphism theorem, we develop a notion of categorical ultraproducts to capture the generic behavior of an infinite collection of mathematical objects.
Barthel, Tobias +2 more
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On approximation of real numbers by real algebraic numbers [PDF]
Acta Arithmetica, 1999 Let \(\mathbb A_n\) be the set of real algebraic numbers of degree \(n\) and \(H(\alpha)\) be the height of \(\alpha\in \mathbb A_n\). A `best possible' regular system \((\mathbb A_n,N)\), where \(N(\alpha)= (H(\alpha)/ (1+|\alpha|)^n)^{n+1}\), is obtained for approximating real numbers by numbers \(\alpha\) in \(A_n\).
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Diophantine approximation of Mahler numbers
, 2015 Suppose that $F(x)\in\mathbb{Z}[[x]]$ is a Mahler function and that $1/b$ is in the radius of convergence of $F(x)$. In this paper, we consider the approximation of $F(1/b)$ by algebraic numbers.
Bell, Jason +2 more
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