Sentence examples for be the standard simplex from inspiring English sources

be the standard simplex of order whose vertices are all vertices of.

Lemma 4.8 Let Y be a compact set of a topological space, and let Δ n = e 0 e 1 ⋯ e n be the standard simplex.

Definition 4.1 Let Y be a compact set of a topological space, let Δ n = e 0 e 1 ⋯ e n be the standard simplex, and let q : Δ n ↦ 2 Y be a multi-valued mapping.

Example 4.7 Let ( Y, C ) be an abstract convexity space, let { y 0, y 1, …, y n } be a finite subset of ( Y, C ), and let Δ n = e 0 e 1 ⋯ e n be the standard simplex.

Let N = { 0, 1, 2, …, n }, Δ n = e 0 e 1 ⋯ e n be the standard simplex of dimension n, where { e 0, e 1, …, e n } is the canonical basis of R n + 1, and for J ⊂ N, let Δ J = co { e j : j ∈ J } be a face of  Δ n.

Let be the standard -dimensional simplex in with vertices.

Let (delta_{n}) be the standard n-dimensional simplex with vertices ({e_{0},e_{1},ldots,e_{n}}) and for each (Isubseteq{0,1,ldots,n}), let (delta_{vert Ivert -1}) denote the simplex with vertices ({e_{j}:jin I}), where (vert Ivert ) denotes the cardinality of I. Let E be a simply-connected m-dimensional manifold.

The total χ, given NMZ = NDZ = 1000, is broken down into the MZ and the DZ contributions, respectively The 68 df model is the standard AE simplex with occasion-specific variances σ[at] = 0 & σ[et] = 0.

The approach was compared to the standard Simplex square residual minimization of EIS data.

Here, Δ n = co { e i } i = 0 n is the standard n-simplex, and Δ J is the face of Δ n corresponding to J ∈ 〈 A 〉 ; that is, if A = { a 0, a 1, …, a n } and J = { a i 0, a i 1, …, a i k } ⊂ A, then Δ J = co { e i 0, e i 1, …, e i k }.

We chose ρ = .80, so that 20%% of the phenotypic variance is occasion-specific in the standard simplex.