Qualitative data were coded and analyzed using codes based on the research plan and interview guides focusing on issues of transition preparedness, changes to services, smoothness of transition, lessons learned and relationships between stakeholders.
Themes in the data were initially coded according to key issues in the overarching research protocol that included transition preparedness, changes to services, the smoothness of transition, lessons learned, and relationships between different actors.
Smoothness of the transition probability densities: Due to Assumption (10) the transition probability of two (or more) consecutive steps (psi^{mathrm{w}}_{Delta t}circpsi^{mathrm{w}}_{Delta t}) of our integrator has a smooth density.
Smoothness of the transition is implied by imposing the following constraints for g : g = β 0 + β 1 τ g = β 2 + β 3 (∂ ∂ t g ) = β 1 (∂ ∂ t g ) = β 3. The top two constraints imply continuity between the polynomial curve and the two linear parts, and the bottom two constraints imply smoothness at the points where the polynomial curve connect to the two linear parts.
Therefore, the smoothness of the transitions between the successive steps of the walk sequence is ensured.
Interestingly, the smoothness of gait transitions is accompanied by a gradual shift from inverted-pendulum gait to bouncing gait, resulting in a "paradoxical" inverted-pendulum running in the vicinity of run-walk and walk-run transitions [ 18].
Both properties can be proven in exactly the same way as in [34], Corollary 7.4, thus we only sketch the proof for (X^{mathrm{w}}): (i) Smoothness of the transition probability densities: Due to Assumption (10) the transition probability of two (or more) consecutive steps (psi^{mathrm{w}}_{Delta t}circpsi^{mathrm{w}}_{Delta t}) of our integrator has a smooth density.
To overcome this, a soft thresholding method as defined in Eq. (4) is proposed, where the a sigmoid function (1 1 + exp (− α (Δ y − T p ) ) ) is used to smooth the transition near the boundary of T p and the parameter α controls the smoothness of the transition.
The smoothness of our transition, the civility shown by all the political actors and the statesmanship demonstrated by president Ernesto Zedillo are all reflections of our enormous transformation.
Whether or not Wayne Rooney stays it is the attitude of the players in general that will decide the smoothness of the transition from one Scottish accent to another.
Perhaps the biggest reason for the smoothness of the transition, though, was that Schwarzenegger had won the election so convincingly that no one could quibble about the legitimacy of his right to the office.
