The standard harmonic balance method consists in expanding the displacement of an oscillator as a Fourier cosine series in time. A key modification is proposed here, in which the conservative force is additionally expanded as a Fourier sine series in space. As a result, the steady-state oscillation frequency can be expressed in terms of a Bessel series, and the sums of many such series are know...

In this article, we study the oscillation of solutions to a nonlinear forced fractional differential equation. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. Based on a transformation of variables and properties of the modified Riemann-liouville derivative, the fractional differential equation is transformed into a second-order ordinary different...

PURPOSE Spirometry is sometimes difficult to perform in elderly patients and in those with severe respiratory distress. The forced-oscillation technique (FOT) is a simple and noninvasive method of measuring respiratory impedance. The aim of this study was to determine if FOT data reflect spirometric indices. PATIENTS AND METHODS Patients underwent both FOT and spirometry procedures prior to i...

BACKGROUND Impedance measurements by the forced pseudo random noise oscillation technique can be used to study the mechanical characteristics of the respiratory system. The objective of this study was to analyse the changes in impedance to a cold air provocation test in patients with asthma, and to correlate these changes with those in the forced expiratory volume in one second (FEV1). METHOD...

where t ≥ t > , n ≥  is a natural number, βi ≥  (i = , , . . . ,n) are constants, r ∈ C([t,∞),R), qj, τj, e ∈ C([t,∞),R), r(t) > , r′(t)≥ , qj(t)≥  (j = , , , . . . ,n), e(t)≤ . We also assume that there exists a function τ ∈ C([t,∞),R) such that τ (t) ≤ τj(t) (j = , , , . . . ,n), τ (t)≤ t, limt→∞ τ (t) =∞, and τ ′(t) > . We consider only those solutions x of equation (....

Respiratory resistance (Rrs) was measured by the forced oscillation technique at 10, 20 and 30 Hz in 54 healthy subjects. The sinusoidal pressure oscillations were applied around the head, rather than at the mouth, so as to minimize transmural pressure across extrathoracic airway walls and the corresponding artefact (Peslin et al., J Appl Physiol, 1985, 59, 1790-1795). The flow (V') and volume ...

Some new criteria have been established for the oscillation of higher-order forced nonlinear differential equation of the form Lnx(t) + q(t)F(x(t)) = e(t) according to the smart choice of a class of new auxiliary functions. No restriction is imposed on the forcing term e(t) as those assumed in [A.G. Kartsatos, Maintenance of oscillations under the effect of a periodic forcing term, Proc. Amer. ...

Oscillation criteria, extended Kamenev and Philos-type oscillation theorems for the nonlinear second order neutral delay differential equation with and without the forced term are given. These results extend and improve the well known results of Grammatikopoulos et. al., Graef et. al., Tanaka for the nonlinear neutral case and the recent results of Dzurina and Mihalikova for the neutral linear ...

The time evolution of quantum meson fields in the O(4) linear sigma model is investigated in a context of the dynamical chiral phase transition. It is shown that amplitudes of quantum pion modes are amplified due to both mechanisms of a parametric resonance and a resonance by the forced oscillation according to the small oscillation of the chiral condensate in the late time of chiral phase tran...