Sentence examples for simplex satisfying from inspiring English sources

This lemma allows us to apply our combinatorial Lemma 2 to detect a simplex satisfying the assertion of Sperner's lemma.

The barycentric subdivision of S = conv ( X 1, …, X N ) is a collection of finitely many conditional simplexes satisfying the following properties: (i) σ ( ⋃ π ∈ S N C π ) = S.   (ii) C π has dimension N, π ∈ S N.   (iii) C π ∩ C π ¯ is a conditional simplex of dimension r ∈ N and r < N for π, π ¯ ∈ S N, π ≠ π ¯.   (iv) For s = 1, …, N − 1, let B s : = conv ( X 1, …, X s ).

Fair, simple, satisfying.

Hence, (l' overline{sigma})=l overline {sigma})=[n-1]), which proves the existence of a simplex in T satisfying the desired property.

The set of all δ l,l=1,…,L satisfying the UEP constraints forms an L-simplex in L dimension.

It follows that the number of simplices satisfying the claim is odd since σ̅ has no paired simplex (obtainable using the presented procedure of generating sequences of simplices in (T')).

Let (mathcal{A}=A_{1}cdots A_{n+1}) be an n-simplex in (mathbb {R}^{n}), let (A=sum_{i=1}^{n+1}alpha_{i}A_{i}) be a convex combination of the vertices (A_{i}) with coefficients (alpha _{i}) satisfying (0

Let (mathcal{A}=A_{1}cdots A_{n+1}) be an n-simplex in (mathbb {R}^{n}), and let (A=sum_{i=1}^{n+1}alpha_{i}A_{i}) be a convex combination of the vertices (A_{i}) with coefficients (alpha _{i}) satisfying (alpha_{i}>0).

Most satisfying.

How satisfying.

They're completely satisfying.