<p style='text-indent:20px;'>Given an undirected measurement graph <inline-formula><tex-math id="M1">\begin{document}$ G = ([n], E) $\end{document}</tex-math></inline-formula>, the classical angular synchronization problem consists of recovering unknown angles id="M2">\begin{document}$ \theta_1, \dots, \theta_n $\end{document}</tex-math></inline-formula...

<p style='text-indent:20px;'>We study the Maslov-type index theory under a special Lagrangian boundary condition, namely <inline-formula><tex-math id="M2">\begin{document}$ (P,L_0) $\end{document}</tex-math></inline-formula> which comes naturally in of brake orbits id="M3">\begin{document}$ P $\end{document}</tex-math></inline-formula>-invariant Hami...

In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub-$ sigma_Theta $-algebra having finite atoms is defined and then   the ergodic properties of relative  semi-dynamical systems are investigated.  Also,  a relative version of Kolmogorov-Sinai theorem  is given. Finally, it is proved  that the relative entropy of a...