Under standard Lipschitz conditions, trajectories of systems described by ordinary differential equations are well defined in both forward and reverse time. (The flow map is invertible.) However for hybrid systems, uniqueness of trajectories in forward time does not guarantee flow-map invertibility, allowing non-uniqueness in reverse time. The paper establishes a necessary and sufficient condit...

We examine the time reversal symmetry of quantum measurement sequences by introducing a forward and backward Janus sequence of measurements. If the forward sequence of measurements creates a sequence of quantum states in time, starting from an initial state and ending in a final state, then the backward sequence begins with the time-reversed final state, exactly retraces the intermediate states...

urban expansion and agriculture intensification are relevant drivers in land degradation (ld)processes in europe due to net loss of land, soil sealing, landscape fragmentation and other negative effects on the environment. this paper explores changes (or “trajectories” of change) in land use and cover (lulc) and their relationship with the consumption of soils in emilia-romagna (northern italy)...

canola genotypes reaction to stopping irrigation was surveyed. this experiment was carried out as a split plot randomized block design whit three replications in the safiabad argicultural research center for two years. main plot was considered of different levels of stopping  irrigation (stopping irrigation at the ending flowering, poding, 10%  and 30% ripening of pods in main stem ) and sub pl...

We calculated Eq. (4) by using the Runge-Kutta method. The attractors obtained by the simulations are shown in Fig. 3(a). We can confirm the generation of periodic and chaotic attractors. In order to investigate the attractors in van der Pol oscillator under noisy parametric excitation in detail, we consider the Poincaré map. The result of the Poincaré map are shown in Fig. 3(b). We can see tha...