We give the equations governing the shear evolution in Bianchi spacetimes for general f(R)-theories of gravity. We consider the case of R-gravity and perform a detailed analysis of the dynamics in Bianchi I cosmologies which exhibit local rotational symmetry. We find exact solutions and study their behaviour and stability in terms of the values of the parameter n. In particular, we found a set ...

The notion of input-to-state stability (ISS) has proved to be useful in nonlinear systems analysis. This paper discusses a dual notion, output-to-state stability (OSS). A characterization is provided in terms of a dissipation inequality involving storage (Lyapunov) functions. Combining ISS and OSS there results the notion of input/output-to-state stability (IOSS), which is also studied and rela...

This paper presents an invariant image watermarking scheme by introducing the Polar Harmonic Transform (PHT), which is a recently developed orthogonal moment method. Similar to Zernike moment (ZM) and pseudo-Zernike moment (PZM) approaches, PHT is defined on a circular domain. The magnitudes of PHTs are invariant to image rotation and scaling. Furthermore, the PHTs are free of numerical instabi...

Received Okt 2, 2014 Revised Nov 1, 2014 Accepted Nov 23, 2014 In this paper, a generalization to nonlinear systems is proposed and applied to the motordynamic, rotor model and stator model in DC motor equation. We argue that Ulam-Hyers stability concept is quite significant in design problems and in design analysis for the class of DC motor’s parameters. We prove the stability of nonlinear par...

The theory of the coagulation of particles in laminar shear flow was applied in a study of the aggregation of red blood cells. The theory predicts that in a system of initially dispersed particles the total particle concentration would decay (because of aggregation) logarithmically with time with the decay rate, depending on the adhesiveness of the particles. The applicability of this theory wa...