Sentence examples for existence interval from inspiring English sources

Let be the solution of system (1.4) with initial values, and let be the maximal existence interval of the solution.

Our proof of the uniqueness does not depend on the size of the time existence interval [ 0, T 0 ].

The maximum principle leads to (0< u(cdot, t)< 1) for all t in the existence interval.

By the maximum principle, we can obtain (0< u(cdot, t)< 1) for all t in the existence interval.

The solution ((P t),S t),I t))^{T}) of (2.5) with initial function (phigeqmathbf{0}) is nonnegative on its existence interval.

Then the comparison principle leads to (P t geq0) for (tgeq t_{1}), in contradiction with (P t)<0), (tin(t_{1},t_{0})), that is, (P t ge0) if (P 0 geq0), also on its maximal existence interval.

At α = ∞, branch lengths become hard constraints, and proteins between which the existence intervals do not overlap are not allowed to interact; this αalso prohibits the formation of blocking loops.

Here, α δ is a function that assigns a cost to a pair of nodes { u, v} that is proportional to the distance between the existence intervals of these nodes (and is 0 if they overlap).

Let u 0 ( x ), u 1 ( x ) ∈ H 2 be given and u ( x, t ) be a weak solution of problem (1.1 - 1.2 1.1 - 1.2imal existence time interval [ 0, T 0 ), T 0 ≤ + ∞. Assume that the initial data satisfy (3.1).

The existence of interval cancers may influence both patients' and health professionals' perceptions and trust in the benefit of the screening programme, and may make it necessary to give specific information on the uncertainties involved.

On the issue of the balance between benefits and risks, our group underlined the importance of revising the information given to women so as to integrate the context of uncertainty, particularly the uncertainty tied to overdiagnosis and the existence of interval cancers.