From numerical calculations of ion trajectories in a quadrupole field, upper bounds on the initial displacement and radial velocity for zero initial phase have been obtained for. 100 % ion transmission inthe resolution range nz/Am = IOO1000. An empirical expression relating the maximum possible resolution as a function of initial velocity and position involving a position-velocity interaction t...

In this report, we consider longitudinal dynamics of a vehicle and prove that its longitudinal position and velocity are order preserving with respect to the driver’s (or automatic controller’s) input. We also prove that the position is strictly order preserving with respect to the constant term of the acceleration replaced with a linear function of the position and the velocity. This estimatio...