Figures 19 and 20 show the average destination regularity value for every subject in the GPS dataset for every weekday, and Fig. 21 shows the average and standard deviation for length difference regularity for the same subjects of the GPS dataset.
It is shown in [15,16] that for sufficiently regular initial values the regularity of the solution to the KdV equation is not diminished as it is evolved in time (although this does not rule out the appearance of high frequency oscillations).
These results concern, inter alia, infinite products, nonexpansive mappings, approximate fixed points, contractive mappings, bounded linear regularity, set-valued mappings, holomorphic mappings and weak ergodic theorems.
We obtain the local well-posedness for the Cauchy problem with low regularity initial value data by the Fourier restriction norm method.
Such a point, indicated with a rectangle point in Fig. 7, is supposed to provide, in terms of accuracy and regularity, the value of the parameter corresponding to the most balanced perturbed solution of the inverse problem.
The regularity of the value function and the optimal dividend policy are studied as well.
However, when following this approach, it is more difficult to obtain the desired regularity of the value function.
These so called distance estimates have wide-spread application in state constrained optimal control, including justifying the use of the Maximum Principle in normal form and establishing regularity properties of value functions.
One measure of geometric order, the nearest neighbor regularity index, showed similar values for double and single cones (Figure 5B and data not shown).
Increased LLEs reflect increased sensitivity to initial conditions and characterize unpredictable variations, whereas low values indicate regularity [ 21].
