In this work we introduce the notion of weak quasigroups, that are quasigroup operations defined almost everywhere on some set. Then we prove that the topological entropy and the ergodic period of an invertible expansive ergodically-supported dynamical system with the shadowing property (X,T ) establishes a sufficient criterion for the existence of quasigroup operations defined almost everywher...

E-mail: [email protected], [email protected], [email protected] Abstract In this paper, the theoretical analysis of the throughput of slotted ALOHA DS-CDMA with random TPC in a multi-cell environment is presented. It is found that for the given occurrence rate of original packets, the throughput performance has a discontinuous property and is not necessarily the ...

Shadowing is a method of backward error analysis that plays a important role in hyperbolic dynamics. In this paper, the shadowing by containment framework is revisited, including a new shadowing theorem. This new theorem has several advantages with respect to existing shadowing theorems: It does not require injectivity or differentiability, and its hypothesis can be easily verified using interv...

Although computational techniques have been extensively applied in nonlinear science, the reliability evaluation of numerical results does not grow in the same pace. Hammel et al. (Journal of Complexity, 1987, 3(2), 136–145) have proved a theorem that a pseudo-orbit of a logistic map is shadowed by a true orbit within a distance of 10−8 for 10 iterates. We checked this theorem in a modern compu...

Most ad hoc and sensor network research assumes idealised radio propagation models without considering fading and shadowing effects. Experimental results have shown that many well-designed protocols will fail simply because of fading and shadowing experienced in a realistic wireless environment. While fading and shadowing for radio propagation are well understood in the wireless communication c...

We study the concepts of continuous shadowing and continuous inverse shadowing with respect to various classes of admissible pseudo orbits, and characterize hyperbolicity and structural stability using the notion of continuous inverse shadowing.