Results 1 to 10 of about 4,951 (270)

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
openaire   +4 more sources

On approximation to real numbers by algebraic numbers [PDF]

Acta Arithmetica, 2000
Define the height \(H(\alpha)\) of an algebraic number \(\alpha\) as the maximum of the absolute values of the coefficients of its irreducible polynomial over \(\mathbb{Z}\). Let \(n\geq 2\) be an integer and let \(\xi\) be a real number which is not an algebraic number of degree \(\leq n\).
openaire   +2 more sources

On simultaneous approximation of algebraic numbers

Mathematika, 2022
Let $Γ\subset \bar{\mathbb Q}^{\times}$ be a finitely generated multiplicative group of algebraic numbers. Let $α_1,\ldots,α_r\in\bar{\mathbb Q}^\times$ be algebraic numbers which are $\mathbb{Q}$-linearly independent and let $ε>0$ be a given real number.
Kumar, Veekesh, Thangadurai, R.
openaire   +2 more sources

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
doaj   +1 more source

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.
openaire   +1 more source

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 =
openaire   +2 more sources

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
doaj   +1 more source

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.
openaire   +1 more source

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
doaj   +1 more source

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
openaire   +3 more sources