Sentence examples for be an upper gradient from inspiring English sources

If we want equality for every pair (t, s), we need to require the slope to be an upper gradient.

In general, it is not true that the slope is an upper gradient, but we will give conditions to guarantee that it is.

This representation as a (sup ) allows to prove semicontinuity of the slope.4 It is also possible (see [2], for instance) to prove that the slope is an upper gradient.

usual convex combinations (mu _s 1-s mu _s 1-s mu), which is meaningful in the set of probability measures), such that (|nabla ^-F |) is an upper gradient for F and such that (|nabla ^- F|^2) is convex, then for every initial measure (bar{mu }) there exists at most one gradient flow (mu (t)) in the EDE sense for the functional F satisfying (mu (0)=bar{mu }).

On the one hand, functions smooth enough could satisfy the assumptions on the semi-continuity of F and of (|nabla ^-F|) and the fact that (|nabla ^-F|) is an upper gradient independently of convexity; on the other hand the discrete scheme already provides a method, well-posed under much weaker assumptions, to find a limit curve.

Indeed, we have two good points: the slope is automatically l.s.c., and it is automatically an upper gradient.

"It's an upper.

"There's an upper bound.

Now it should be a gradient field.

You want there to be a gradient.

This also indicates that the gradient is an activity gradient, not an expression gradient.