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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A note on elliptic functions and approximation by algebraic numbers of bounded degree. [PDF]
, 1983 Let p be a Weierstrass elliptic function with algebraic invariants g2 and g3. By a counterexample it is shown that lower bounds for the simultaneous approximation of p(a), b and p(ab) by algebraic numbers of bounded degree cannot be given without and ...
Bijlsma, Alex +3 more
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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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Continued fractions for some transcendental numbers [PDF]
, 2015 We consider series of the form $p/q + \sum_{j=2}^\infty 1/x_j$, where $x_1=q$ and the integer sequence $x_n$ satisfies a certain non-autonomous recurrence of second order, which entails that $x_n|x_{n+1}$ for n?1.
Andrew N. W. Hone, Hone, Andrew N.W.
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Approximation of complex algebraic numbers by algebraic numbers of bounded degree [PDF]
, 2007 We investigate how well complex algebraic numbers can be approximated by algebraic numbers of degree at most n. We also investigate how well complex algebraic numbers can be approximated by algebraic integers of degree at most n+1.
Bugeaud, Yann, Evertse, Jan-Hendrik
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The successive minima in the geometry of numbers and the distinction between algebraic and transcendental numbers [PDF]
, 1986 This paper discusses an application of Minkowski's theory of the successive minima in the geometry of numbers to the problem of the approximation of an algebraic or transcendental number a by algebraic numbers. I consider for simplicity only real numbers
Kurt Mahler, Mahler, Kurt
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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 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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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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Diophantine Approximation with Algebraic Points of Bounded Degree [PDF]
, 2000 In this paper, we extend Schmidt's subspace theorem to the approximation of algebraic numbers by algebraic points of bounded ...
Wang, Julie Tzu-Yueh, Ru, Min
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