Sentence examples for underlying space from inspiring English sources

We fix as an underlying space a (non-compact) Riemannian manifold X and an intensity measure σ on it.

In fact, we have that If, the notion of -boundedness is strictly stronger than boundedness unless the underlying space is isomorphic to a Hilbert space [5, Proposition 1.17].

Identification of least-cost paths, rooted in ecological and behavioral mechanisms underlying space use, can identify realistic putative corridors for focused implementation of control measures for introduced species in ecologically sensitive areas.

It was assumed, with anticipation that there is frequently such a thing in nature, that a transformation T relates members of the series by successively transforming an underlying space of points ω according to a rule.

The rule states that the kth member of the time series is a function of an initial point ω that has migrated in the underlying space Xk = X Tkω).

When the underlying space is obvious from the context, we will usually write instead of.

Importantly, this can be realised without special emphasis on the linear structure of the underlying space.

Note that the underlying space in Theorem 1.3 is a finite-dimensional space (mathbb{R}^{N}).

In other results, the underlying space is more general; see, e.g., [5 8].

The underlying space of Theorem 2 is a generalized metric space.

We think that the basic mechanisms underlying space-induced bifurcations are simple enough that they should still be effective in other systems, in particular, in transcriptional regulation networks comprising larger numbers of gene types or positive regulation (activators).