Sentence examples for relative boundary of from inspiring English sources

and are said to commute weakly [12] if for all, where denotes the relative boundary of with respect to.

For a set X ⊂ R n, ∂ ( X ) denotes its boundary (or relative boundary of the closure of X if X is convex).

First, we are going to characterize the behavior of z near the (relative) boundary of its domain, which is crucial for the theorem to follow.

T and t are said to be weakly commuting if t(∂ K T x)) ⊆ T(t(x))) for all x ∈ K, where ∂ K A denotes the relative boundary of A ⊆ K.

For a set (Xsubsetmathbb{R}^{n}), (partial({X})), intX, and convX denote its boundary (or relative boundary of the closure of X if X is convex), interior (or relative interior if X is convex), and convex hull, respectively.

For r > 0, let K r = {u ∈ K : ||u|| < r}, and ∂K r = {u ∈ K : ||u|| = r}, which is the relative boundary of K r in K. To prove our result, we need the following fixed point index theorem of cone mapping.

Thus, the (relative) boundary (partial(S)) of S contains no ((n-2))-face (sigma') of a simplex (sigmain T) such that (l sigma')=[n-1]).

Definition 1 Let ℰ be a closed subset of X and let Q be a submanifold of X with relative boundary ∂Q.

Let S, Q be closed subsets of a Banach space X, Q with relative boundary ∂Q.

Therefore, it comprises increasingly lean modalities of knowledge and knowledge representations media and the relative boundaries and relationships between them.

It is well known that energy minima in the conduction band of silicon are located nearby X-points symmetrelativerelatove thethe boundary of the Brillouin zone.