Results 1 to 10 of about 86,722,916 (268)

On the approximation to algebraic numbers by algebraic numbers [PDF]

Glasnik matematički, 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 ε, there are infinitely many algebraic numbers α of degree at most n such that |ξ - α| < H(α)-n - 1 + ε, where H(α) denotes the naive height of α.
Yann Bugeaud, Bugeaud, Yann
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On non-conservative perturbations of three-dimensional integrable systems [PDF]

Известия высших учебных заведений: Прикладная нелинейная динамика
At present, non-conservative perturbations of two-dimensional nonlinear Hamiltonian systems have been studied quite fully. The purpose of the study is to generalize this theory to the three-dimensional case, when the unperturbed system is nonlinear ...
Morozov, Kirill Евгеньевич
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STABILITY OF MOTION OF RAILWAY VEHICLES DESCRIBED WITH LAGRANGE EQUATIONS OF THE FIRST KIND

Nauka ta progres transportu, 2018
Purpose. The article aims to estimate the stability of the railway vehicle motion, whose oscillations are described by Lagrange equations of the first kind under the assumption that there are no nonlinearities with discontinuities of the right-hand sides.
A. G. Reidemeister, S. I. Levytska
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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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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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A Hyper-Dual Number Approach to Higher-Order Derivative Computation

Axioms
This paper develops a theoretical framework for the computation of higher-order derivatives based on the algebra of hyper-dual numbers. Extending the classical dual number system, hyper-dual numbers provide a natural and rigorous mechanism for encoding ...
Ji Eun Kim
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On algebraic approximations of certain algebraic numbers

Journal of Number Theory, 2003
The main result of the present paper consists of an effective improvement on Liouville's bound for the approximations by rational numbers to algebraic numbers of a special type. Namely, the author considers \(n\)-th roots of imaginary quadratic irrationals.
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Normal Shock Wave Approximations for Flight at Hypersonic Mach Numbers

Aerospace
Normal 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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APPROXIMATION OF AN ALGEBRAIC NUMBER BY PRODUCTS OF RATIONAL NUMBERS AND UNITS [PDF]

Journal of the Australian Mathematical Society, 2012
AbstractWe relate a previous result of ours on families of Diophantine equations having only trivial solutions with a result on the approximation of an algebraic number by products of rational numbers and units. We compare this approximation with a Liouville type estimate, and with an estimate arising from a lower bound for a linear combination of ...
Levesque, Claude, Waldschmidt, Michel
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Tropical Solution of Discrete Best Approximation Problems

Mathematics
We 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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