Clinical testing of the forced oscillation test (FOT) yielded criteria for bronchial obstruction: an increase in viscous respiratory resistance (VRR) (Rfo, Rin, Rex); the frequency dependence of VRR. The study of VRR promoted detection of bronchial malpatency in additional 20% of pulmonary tuberculosis patients who had no lung ventilation disorders, as evidenced by spirometry.
It is easy to notice the great recent development in the oscillation theory of neutral differential equations. The primary aim of this work is to extend this development to neutral differential equations of mixed type (including both delay and advanced terms). In this work, we consider the second-order non-canonical neutral differential equations of mixed type and establish a new single-condition criterion for the oscillation of all solutions. By using a different approach and many techniques, we obtain improved oscillation criteria that are easy to apply on different models of equations.
Abstract
We consider explicit sufficient conditions for all solutions of a first-order linear difference equation with several variable delays and non-negative coefficients to be oscillatory.
The conditions have the form of inequalities bounding below the upper and lower limits of the sums of coefficients over a subset of the discrete semiaxis.
Our main results are oscillation tests based on a new principle for composing the estimated sums of coefficients.
We also give some results in the form of examples, including a counterexample to a wrong oscillation test cited in several recent papers.
Validation of an Oscillation Test for the Sonographic Assessment of Fetal-Type Posterior Cerebral Artery Variants in Migraine Patients with Visual Aura
