We study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of matrices we formulate conditions, sufficient for stability by linear approximation. For non-periodic time scales we use techniques of central upper Lyapunov exponents...

The objective of this work is to investigate the influence of the different time-scale modification (TSM) methods on the quality of the speech stretched up using the designed non-uniform real-time speech time-scale modification algorithm (NU-RTSM). The algorithm provides a combination of the typical TSM algorithm with the vowels, consonants, stutter, transients and silence detectors. Based on the information about the content and...

An algorithm for non-uniform real-time speech stretching is presented. It provides a combination of typical SOLA algorithm (Synchronous Overlap and Add ) with the vowels, consonants and silence detectors. Based on the information about the content and the estimated value of the rate of speech (ROS), the algorithm adapts the scaling factor value. The ability of real-time speech stretching and the resultant quality of voice were...

The Peano Theorem for some functional differential equations on time scale is proved. Assumptions are of Caratheodory type. Two counter examples for false Peano theorems in the literature are presented.