Results 21 to 30 of about 4,546 (229)

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
doaj   +1 more source

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

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
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

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 the approximation to algebraic numbers by algebraic numbers

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.
openaire   +3 more sources

A Q‐Learning Algorithm to Solve the Two‐Player Zero‐Sum Game Problem for Nonlinear Systems

International Journal of Adaptive Control and Signal Processing, Volume 39, Issue 3, Page 566-581, March 2025.
A Q‐learning algorithm to solve the two‐player zero‐sum game problem for nonlinear systems. ABSTRACT This paper deals with the two‐player zero‐sum game problem, which is a bounded L2$$ {L}_2 $$‐gain robust control problem. Finding an analytical solution to the complex Hamilton‐Jacobi‐Issacs (HJI) equation is a challenging task.
Afreen Islam, Anthony Siming Chen, Guido Herrmann   +2 more
wiley   +1 more source

Adaptive Observer for Coupled Wave PDE and Infinite ODE With Sampled Data and Unknown Input: Application to Brain Hemodynamics Estimation

International Journal of Adaptive Control and Signal Processing, EarlyView.
This article proposes a convergent adaptive observer for a damped wave PDE and an infinite‐dimensional ODE coupled in cascade using sampled‐in‐space ODE state measurements. The proposed observer estimates the distributed states of the PDE and ODE along with unknown PDE parameters and spatial input.
Zehor Belkhatir, Sarah Mechhoud, Taous‐Meriem Laleg‐Kirati   +2 more
wiley   +1 more source