After motivating why the study of asymptotically flat spaces is important in loop quantum gravity, we review the extension of the standard framework of this theory to the asymptotically flat sector detailed in [1]. In particular, we provide a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. States in these Hilbert spaces can be int...

In this paper, we study asymptotic stability properties of risk-sensitive filters with respect to their initial conditions. In particular, we consider a linear time-invariant systems with initial conditions that are not necessarily Gaussian. We show that in the case of Gaussian initial conditions, the optimal risksensitive filter asymptotically converges to any suboptimal filter initialized wit...

In this note we prove a theorem on non-vacuum initial data for general relativity. The result presents a “rigidity phenomenon” for the extrinsic curvature, caused by the nonpositive scalar curvature. More precisely, we state that in the case of asymptotically flat non-vacuum initial data if the metric has everywhere non-positive scalar curvature then the extrinsic curvature cannot be compactly ...

In chaos synchronization, the main goal is to design such controller(s) that synchronizes the states of master and slave system asymptotically globally. This paper studied and investigated the synchronization problem of two identical Chen, and identical Tigan chaotic systems and two non-identical Chen and Tigan chaotic systems using Non-linear active control algorithm. In this study, based on L...

We study the late time evolution of flat and negatively curved FRW models with a perfect fluid matter source and a scalar field having an arbitrary non-negative potential function V (φ). We prove using a dynamical systems approach four general results for a large class of non-negative potentials which show that almost always the universe ever expands. In particular, for potentials having a loca...