For the progressively mild trajectory, the predicted value underestimated the observed value at months 8 and 1 and overestimated the observed value at months 5, 4, and 3.
Over half the participants in the two mildest clusters in the original study (recovering: 59%; 95% CI 44% to 74%; persistent mild pain: 56%; 95% CI 40%to7373%) stayed in the most comparable trajectory at 7 years, and most who changed moved to the other mild trajectory.
Then, under conditions (i - iv), there exi - iv mild soluthere( u ∗, ω ∗ ) of problexists1) such that j ( u ∗ ) = mildx ∈ solution) j ( x ), where S ( u 0 ) is the set of all mild trajectories of the system (4.1) with the initial value u 0. Proof Under the hypotheses (i)-(iv), the set S ( u 0 ) ≠ ∅ ; see the proof above.
We use this decomposition result to show that under mild regularity conditions, trajectory preserving maps between single-input affine control systems also lift trajectories.
This tight linkage between hospital admission and disability severity was particularly evident for the progressively mild and catastrophic trajectories, for which the two plots were nearly superimposed.
The continuous counterpart of this definition has been studied extensively [5], and under mild conditions the generic trajectory of a continuous cooperative system is guaranteed to converge towards the set of equilibria.
We prove that if the mappings F [0,T]×E→E and B [0,T]×E→L(H,E) satisfy suitable Lipschitz conditions and u0 is F0-measurable and bounded, then this problem has a unique mild solution, which has trajectories in Cλ([0,T] D((−A)θ))) provided λ⩾0 and θ⩾0 satisfy λ+θ<12.
This study examined childhood antecedents and developmental outcomes associated with trajectories of mild and harsh parental physical discipline.
Autoimmune diseases tend to be unpredictable disorders that can take a variety of different trajectories, from mild and slow to devastating and fast.
The models were performed (3,280 data points) to identify the socio-demographic and clinical factors that affected the long-term trajectories of mild AD patients.
After worms were placed at the starting point and allowed to crawl for one hour, we counted the number of worms that moved continuously only in a loopy pattern (strong), exhibited both normal and loopy patterns (the latter covering ≥30% of the full tracks) (mild) and exhibited normal trajectories (<30% of loopy tracks) (normal).
