Sentence examples for length space from inspiring English sources

This method is proven to be asymptotically optimal among brute-force strategies in terms of proof length, space and time [4].

We give sufficient conditions for a measured length space (X,ν,ν) to admit local and global Poincaré inequalities, along with a Sobolev inequality.

A space (X, d) is said to be a length space if for every x and y we have begin{aligned} d x,y)=inf {{{mathrm{Length}}} omega ),omegaga in mathrm {AC}(X),omegaa (0)=x,omegaa (1)=y}.

In the case that the low-regularity Riemannian metric induces a complete length space, we demonstrate essential self-adjointness of the operator and its higher powers up to the regularity of its coefficients.

A metric space ( X, d ) is a length space if any two points of X are joined by a rectifiable path (that is, a path of finite length) and the distance between any two points of X is taken to be the infimum of the lengths of all rectifiable paths joining them.

A metric space is said to be a length space if any two points of are joined by a rectifiable path (i.e., a path of finite length), and the distance between any two points of is taken to be the infimum of the lengths of all rectifiable paths joining them.

We then prove a Sobolev inequality for measured length spaces with N-Ricci curvature bounded below by K>0.

Our proof holds on non-smooth structures, such as length spaces, and provides a universal control of the constants.

The effects of parameters such as soil density, reinforcement length, spacing and stiffness on the seismic response of the model walls were studied.

Metal-assisted wet chemical etching is advantageous for achieving SiNWs with controlled diameter, length, spacing, and density, avoiding expensive and low-throughput usual lithographic processes [13].

Specifically, the impact of certain detailed fracture characteristics, such as density, mean length, spacing, connectivity and matrix permeability on the flow was measured.