Sentence examples similar to be replaced by convex from inspiring English sources

(This can be generalized to the multi-dimensional case. Namely, the domains [a1,a2] and [a3,a4] can be replaced by arbitrary convex compact sets in finite-dimensional vector spaces, and derivatives replaced by gradients).

Moreover, our Theorem 3.1 shows that the assumption of the uniformly smooth Banach space X in [[2], Theorem 3.1] can be replaced by the assumption of the uniformly convex Banach space X having a weakly continuous duality map J φ with gauge φ in our Theorem 3.1.

Corollary 7.2, the Marchaud maps F can be replaced by more general upper Carathéodory maps with convex, compact values.

In Theorem 3.14 ( 3.14.5 and 3.14.6), a locally convex space can be replaced by a normed space, without loss of generality (see, [6, Theorem 3.6]).

It turns out that, in the case of a convex domain, condition (6.20) can always be replaced by (6.22).

The strict inequality can be replaced by the large inequality for the smaller class of differentiable pseudoconvex functions (which includes convex functions).

"Convex/Concave," the Eliasson installation, will be replaced by decor by other artists every night.

To be replaced by whom?

He will be replaced by Manny Ramirez.

He will be replaced by Alfredo Figaro.

should be replaced by.