A spectral element approach for the stability analysis of time-periodic delay equations with multiple delays

This paper describes a general spectral element approach to study the stability of multiple time delay systems (MTDS). We show, for the first time, how this approach can be applied to periodic MTDS where the delays and the period are incommensurate. In contrast to prior works on MTDS, the spectral element approach is applicable to both autonomous as well as non-autonomous MTDS. Both MTDS of first order or higher can be obtained and systems with or without damping can be investigated. Since the spectral element approach uses efficient interpolation and a set of well-distributed interpolation points, the size of the matrices necessary for convergence is kept small. Further, since the spectral element approach is a semi-analytical procedure, it avoids the need to use tedious time marching algorithms to explore the stability behavior of the system.     

Response behavior of bi-stable point wave energy absorbers under harmonic wave excitations

Nonlinear Dynamics - To expand the narrow response bandwidth of linear point wave energy absorbers (PWAs), a few research studies have recently proposed incorporating a bi-stable restoring force in...     

Assessing Logo programming among Jordanian seventh grade students through turtle geometry

The present study is concerned with assessing Logo programming experiences among seventh grade students. A formal multiple-choice test and five performance tasks were used to collect data. The results provided that students’ performance was better than the expected score by the probabilistic laws, and a very low correlation between their Logo programming performance and school mathematics achievement was revealed. Most of the made misconceptions were due to geometrical aspects rather than Logo primitives, and were concentrated on the angle of rotation, the angle of complete rotation and the angle of regular polygon. In addition, students’ problem-solving ability was limited while conducting some Logo programming tasks, and acceptable in others. In regard to the results, it is recommended that teaching Logo programming should be used in different contexts that enhance students’ learning, and develop problem-solving processes.