Oscillation of Solutions to Third-Order Nonlinear Neutral Dynamic Equations on Time Scales

In this paper, we are concerned with the oscillation of solutions to a class of third-order nonlinear neutral dynamic equations on time scales. New oscillation criteria are presented by employing the Riccati transformation and integral averaging technique. Two examples are shown to illustrate the conclusions.

Seventy years since the invention of the averaging technique in Neurophysiology: Tribute to George Duncan Dawson

ABSTRACT In 1951, the physiologist George Duncan Dawson presented his work with the averaging of the signal in the evoked potentials (EPs), opening a new stage in the development of clinical neurophysiology. The authors present aspects of Professor Dawson’s biography and a review of his work on the EPs and, mainly, the article reveals the new technique in detail that would allow the growth of the clinical application of the visual, auditory, and somatosensory EPs.

Passing through resonance of the unbalanced rotor with self-balancing device

The slow dynamics of unbalanced rotors with a passive self-balancing system are investigated considering the interaction of the mechanical system with a limited power engine. The slow dynamics equations are obtained using the averaging technique for partially strongly damped systems. Stationary system configurations, different types of nonstationary solutions while passing through resonance, and areas of stability and attraction are investigated.

The Stability Analysis of Periodic Beams Interacting with Periodic Elastic Foundation with the Use of the Tolerance Averaging Technique

In this paper a stability analysis of microperiodic beams resting on the periodic inhomogeneous foundation is carried out. The main issue of this considerations, which is the analytical solution to the governing equations characterised by periodic, highly oscillating and non-continuous coefficients, is overwhelmed by the application of the tolerance averaging technique. As a result of such application, the governing equation is transformed into a form with constant coefficients which can be solved using well-known mathematical methods. In several calculation examples, the convergence of the results of two derived averaged models is examined, as well as the convergence of the lowest value of the critical force parameter derived from the averaged models with the FEM model. The results prove the superiority of the presented analytical solution over the FEM analysis in the optimisation process.

Averaging Indoor Localization System

This chapter aims at improving the accuracy of estimation the localization by using the RSS method to estimate the positions and take into account the effects of both LOS propagation. The proposed system is depending on developing a mathematical model for the noisy VLC positioning system. For improving the results, adopting the KF is combined with the proposed system, which is considered an optimal estimator. The performance of the proposed technique is determined by evaluating the positioning errors in a typical room. Also this chapter develops the accuracy of the positioning system by using different ideas with average techniques. The discussion of the results for averaging technique is displayed.

Trial applications at gymnasiums of in-situ sound absorption measurement method by ensemble averaging technique

The authors have been published a series of papers on a measurement method for sound absorption characteristics of materials using ensemble averaging technique, i.e., EA method. The papers' results included measurement mechanisms, measurement uncertainty, and so on. Herein, to examine adaptability, especially in in-situ conditions, the EA method is applied to measure absorption characteristics of materials installed in two gymnasiums. A glass-wool panel with the dimension of 0.5 m by 0.5 m by 0.05 m and with the density of 32 kg m^-3 was brought around and measured to check the measurement consistency. Several measurements were conducted during badminton plays were undergoing. Measured sound absorption coefficients revealed that most results agree well with those measured in reverberation rooms. Certain improvement is necessary for the specimen brought to the in-situ measurement to keep the consistency. The inconsistency is considered to originate from unstable conditions between the specimen and floor.

Important Criteria for Asymptotic Properties of Nonlinear Differential Equations

In this article, we prove some new oscillation theorems for fourth-order differential equations. New oscillation results are established that complement related contributions to the subject. We use the Riccati technique and the integral averaging technique to prove our results. As proof of the effectiveness of the new criteria, we offer more than one practical example.