Sentence examples for define the cone from inspiring English sources

Define the cone, where.

Define the cone by (3.3).

For each, define the cone by (4.4).

Define the cone as in (2.5).

Define the cone P' ⊂ E by.

Define the cone as follows: (4.1).

Furthermore, we also define the normal cone N C u of C at u as follows: N C u = { z ∈ H : 〈 z, v − u 〉 ≤ 0, ∀ v ∈ C }.

Furthermore, we also define the normal cone (N_{C}u) of C at u as follows: N_{C}u=bigl{ zin H: langle z, v-urangleleq0, forall vin Cbigr}.

Accordingly, we define the normal cone of K at x by polarity with T K (x) as follows: N K ( x ) : = { ξ : ⟨ ξ, v ⟩ ≤ 0, ∀ v ∈ T K ( x ) }. Definition 2.7.

Let us define the tvs-cone metric with d : X × X → E, by d x, y)(t):= |x − y|e t.

Then for all (xin H), there exist (yinmathcal{K}) and (zinmathcal{K}^) such that x = y+z quad textit{and}quad langle y,zrangle= 0. Let us define the following cones and afterwards prove some invariance properties of them.