On the positive half-trajectory of system denoted by (g(p,T^), T^= 0,+infty)), let ({0leq{t_{1}}<{t_{2}}<cdots<{t_{n}}<cdots} ) be a time series such that (lim_{nrightarrow+infty}t_{n}=+infty).
Then we show that there is no positive half-trajectory close to E 0 in S △ if R 0 > 1. Lemma 3.3 The two stable manifolds of saddle E 0 are not in S △ if R 0 > 1. Proof Suppose there is a stable manifold L P + in S △, then the L P − stay in the S △ or traverse through S △.
If (g=alpha g_1^r) where (alpha ne 0) and (g_1=0implies nabla g_1ne 0), the generalized Hamiltonian trajectories are just (ordinary) Hamiltonian trajectories of (g_1) and (mathcal {K}^pm (x,upxi )) are just half-trajectories.16.16
Subsequently, only an active tree is built until it is time to kick the fixed particles at which point they are drifted through the remaining half of their trajectory.
To account for this fact in a heuristic way, straight lines were fitted to the first and second half of the trajectory, allowing for some overlap.
However, in over half of the trajectories individual enzymes form interactions with the cellulose substrate.
We set aside half of the trajectories as the training dataset for model construction and the other half as the test dataset D′ for checking the quality of the model constructed.
The weight w (k, h ) between k and h is the product of (i) the minimum centrosome separation distance in the first half of the trajectories and (ii) the absolute difference in radii averaged over time.
Four years ago, polls showed that eighty-three per cent of Afghans held a favorable view of the United States; today, only half do, and the trajectory is downward.
In this paper, we focus on data from the latter half of the VISIONS trajectory when the rocket traversed the polar cap region.
We build a single second very active tree when the number of particles on a rung drop below a certain threshold (5% seems to be a good value).5 The inactive particles are drifted half-way along their trajectory and a fixed tree built as shown in Figure 3.
