Results 21 to 30 of about 158,055 (244)
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
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
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
core +1 more source
Simultaneous approximation of a real number by all conjugates of an algebraic number
, 2007 Using a method of H. Davenport and W. M. Schmidt, we show that, for each positive integer n, the ratio 2/n is the optimal exponent of simultaneous approximation to real irrational numbers 1) by all conjugates of algebraic numbers of degree n, and 2) by ...
Alain, Guillaume
core +1 more source
On Approximation constants for Liouville numbers [PDF]
, 2015 We investigate some Diophantine approximation constants related to the simultaneous approximation of $(\zeta,\zeta^{2},\ldots,\zeta^{k})$ for Liouville numbers $\zeta$. For a certain class of Liouville numbers including the famous representative $\sum_{n\
Jarník +7 more
core +3 more sources
Simultaneous rational approximations to algebraic numbers [PDF]
Bulletin of the American Mathematical Society, 1961 Let \(\beta_1, \beta_2, \dots,\beta_n\) be linearly independent numbers of a real algebraic number field of degree \(n+1\). By a study of the units of the field it is shown how to obtain all integral solutions of the set of inequalities: \[ q_0>0, \quad\gcd(q_0,q_1,\dots,q_n)=1,\quad | \beta_j/\beta_0-q_j/q_0| < Cq_0^{-1-1/n} \] for fixed \(C\).
openaire +3 more sources
A Hyper-Dual Number Approach to Higher-Order Derivative Computation
AxiomsThis 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
doaj +1 more source
Exponents of Diophantine Approximation and Sturmian Continued Fractions [PDF]
, 2004 Let x be a real number and let n be a positive integer. We define four exponents of Diophantine approximation, which complement the exponents w_n(x) and w_n^*(x) defined by Mahler and Koksma.
Bugeaud, Yann, Laurent, Michel
core +5 more sources
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
core +2 more sources
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
doaj +1 more source