Sentence examples for bounded in the case from inspiring English sources

He was able to prove that (||u(t)||_2) (which is bounded in the case (-Delta +V) is bounded below) doesn't grow worse than (|t|^3) and then push through a variant of the Chernoff Nelson argument (since a (|t|^3) bound can eliminate exponential growth).

{ g y n } is bounded in the case ( f, S ) satisfies the (E.A -property, { f y n } is boundE.A -propertye ( g, T ) satisfies (E.A)-property.

{ g y n } is bounded in the case ( f, S ) satisfies the (E.A -property, or.

This, together with ((H_{7})), means that (Omega_{1}) is bounded in the case (p>2) and, similarly, for (1 < p leq2).

Therefore (H x,y)) is also bounded in the case (2) since (x^{alpha- lambda+1)}leq1) for (x^{alpha- lambda+1

{ g y n } is bounded in the case ( f, S ) satisfies the (E.A -property, { f y n } is boundE.A -propertye ( g, T ) satisfies the (E.A)-property, then the pairs ( f, S ) and ( g, T ) have a point of coincidence in X.

From the two scenarios, we can conclude that the relative position errors are kept bounded by the inter-agent ranging, while the absolute position errors (relative starting location) are bounded in the best case (stationary agents) and that the error growth is reduced by a factor of 1 / N in the worst case.

The difference between agents trajectories can be bounded in this case and bounds on the state disagreement are derived.

In order to implement the set aggregation service described above, the peers first reconcile their sets using an efficient set reconciliation protocol that is not fault-tolerant but where the complexity is bounded even in the case of failures.

This paper proposes a new adaptive control scheme for non-linear systems containing time-varying uncertainties with unknown bounded in special case in which the uncertainties vary exponentially with time.

end{cases} It is shown in [13] that the smallest local maxima (m_{n} (bar{U} ) ) are bounded (in contrast to the case of the Chebyshev nodes T) by m_{n} (bar{U} )< 1.57079ldots.