Sentence examples for bound of the functional from inspiring English sources

A lower bound of the functional range for slip resistance under the soapsuds-covered wet condition was estimated from the requirement of DFC > 0.4 at Ra ≅ 17 μm.

Choosing ε < p ( p + 1 ) 2, we obtain the lower bound of the functional E E ( u ) ≥ − 1 p ( p + 1 ) A ε, q − q, which implies I q ≥ − 1 p ( p + 1 ) A ε, q − q > − ∞. (ii) Let { u n } be a minimizing sequence for the problem ( I q ).

We also obtain the different upper bound of the subcritical functionals.

The obtained condition shows potential advantages over the existing ones since no useful item is ignored throughout the estimate of upper bound of the derivative of Lyapunov functional.

A new Lyapunov functional is constructed and a tighter upper bound of the derivative of the Lyapunov functional is derived by applying a convex polyhedron method.

Second, novel integral inequalities were proposed to obtain a tighter upper bound of the integrals occurring in the time-derivative of the Lyapunov-Krasovskii functional.

On one hand, a modified Lyapunov-Krasovskii functional is constructed which takes information of the lower bound of the time-varying delay into account.

More information about the lower bound of the (h_{1}(t)) and (h_{2}(t)) is sufficiently used in the Lyapunov functional (7).

In order to obtain the asymptotic upper bound of the solution to the recurrence equation (1), Schellekens introduced a special class of functionals known as improvers.

By the continuity of on, the above inequality means that there exists a lower bound of values of functional.

Under the soapsuds-covered wet condition, floors with 50 μm in Ra roughness scale seemed to represent an upper bound in the functional range of floor surface roughness for slip resistance because further increase of surface roughness provided no additional benefit.