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Generalized method of averaging and the Von Zeipel method
Thermophysics Specialist Conference, 1965Abstract The generalized method of averaging is applied to a perturbed vector system of differential equations of the appropriate form, where there are several “rapidly rotating” phases. It is assumed that no resonances occur, and the averaged equations are derived through the second order in the perturbation parameter. The arbitrariness which arises
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Stability of Processes. Averaging Method
1998In the preceding sections we studied the stability of the zero equilibrium x = 0 of the system whose CLP is given by (3.1). However, the technique developed there enables us to investigate the stability of an arbitrary solution (a process) of the system $$ \frac{{dx}}{{dt}} = Ax + bf + q\left( t \right),\sigma = {c^*}x + \psi \left( t \right),f = M\
Arkadii Kh. Gelig, Alexander N. Churilov
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Significance of averaging method signal denoising
2017 International Conference on Robotics, Automation and Sciences (ICORAS), 2017Biosignals originates from living beings carries significant information. Current noise filters can easily remove noise that usually accompanies with biosignals during acquisition. Nonetheless, small signals such as electroencephalography (EEG) which have the amplitude of in microvolts (μV) requires complex filters.
Izadora binti Mustaffa +2 more
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Asymptotic decomposition method as development of bogoliubov averaging method
Nonlinear Analysis: Theory, Methods & Applications, 1997The author discusses differential equations of the standard form \[ {dx\over dt}= \varepsilon X(t, x),\quad x(t_0)= x_0,\tag{1} \] with \(t\in\mathbb{R}\), \(x\in \mathbb{R}^n\), \(X: \mathbb{R}\times \mathbb{R}^n\to \mathbb{R}^n\), and \(\varepsilon\) a small positive parameter.
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1990
In this chapter we shall consider again equations containing a small parameter e. The approximation method leads generally to asymptotic series as opposed to the convergent series studied in the preceding chapter; see section 9.2 for the basic concepts and more discussion in Sanders and Verhulst (1985), chapter 2.
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In this chapter we shall consider again equations containing a small parameter e. The approximation method leads generally to asymptotic series as opposed to the convergent series studied in the preceding chapter; see section 9.2 for the basic concepts and more discussion in Sanders and Verhulst (1985), chapter 2.
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IRE Transactions on Circuit Theory, 1960
The method of averaging of van der Pol was devised to obtain periodic and almost periodic solutions of quasi-linear systems of differential equations. A theorem is stated for a particular case where this method has been justified mathematically and an example is given to illustrate the results.
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The method of averaging of van der Pol was devised to obtain periodic and almost periodic solutions of quasi-linear systems of differential equations. A theorem is stated for a particular case where this method has been justified mathematically and an example is given to illustrate the results.
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A High Order Generalized Method of Averaging
SIAM Journal on Applied Mathematics, 1982We develop a high order generalized perturbation technique that extends the Krylov–Bogoliubov–Mitropolsky method of averaging to vector systems written in normal form with multiple angular components. An algorithm is presented that iteratively gives the terms in the asymptotic approximation.
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Verification of the Lebesgue averaging method
Mathematical Models and Computer Simulations, 2016This work is devoted to the study of the accuracy of the Lebesgue averaging method for the spectra of resonance radiation in solving the transport equation. The method is tested for the problem of the thermal radiation transfer in the Earth atmosphere.
A. V. Shilkov, M. N. Gerthev
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The Average Response Method of Scaling
Journal of Educational Statistics, 1990The average response method (ARM) of scaling nonbinary data was developed to scale the data from the assessments of writing conducted by the National Assessment of Educational Progress (NAEP). The ARM applies linear models and multiple imputations technologies to characterize the predictive distribution of the person-level average of ratings over a ...
Albert E. Beaton, Eugene G. Johnson
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Method of Averaging and the Quantum Anharmonic Oscillator
Physical Review Letters, 1985The Krylov-Bogoliubov method of averaging is applied to the time-dependent quantum anharmonic oscillator. A regular perturbation expansion contains secular terms. The averaging approximation does not, and as a result has a validity over larger time intervals.
, Ben Lemlih A, , Ellison
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