Sentence examples for formulate below from inspiring English sources

The definitions and theorems we formulate below carry over to continuous transformations without further ado, and where this is not the case we explicitly say so and treat the two cases separately.

The objective function is formulated below.

The optimization problem is formulated below.

Similar reduction is demonstrated for IGP formulated below.

The corresponding decision list coloring problem is formulated below.

On the basis of the above consideration, Model-2 is formulated below.

The total reception power consumption of node i is the sum of all power consumed to receive data from other nodes, as formulated below, where λ is a constant coefficient: {P}_{ri=}{displaystyle sum lambda cdot {r}_{ki}.} (7).

The order decision under case B(I) is formulated below X_{text{B(I)}}^{text{WHP}} = left{ {begin{array}{*{20}l} D hfill & {{text{for }}p > w} hfill 0 hfill & {text{else}} hfill end{array} } right.

The proof of Proposition 3.1 is based on Lemma 3.2 formulated below, which provides an estimate for the sequence of functions α m, m ≥ 0, given by the formula α m ( t ) : = ( 1 − t − t 0 p ) ∫ t 0 t α m − 1 ( s ) d s + t − t 0 p ∫ t t 0 + p α m − 1 ( s ) d s, (3.12).

Hence, as the order decision under case B II) includes the solution of case B(I), the overall order decision under the WHP contract is formulated below X^{text{WHP}} = left{ {begin{array}{ll} {X_{text{B II)}}^{text{WHP}} } hfill & {{text{for }}p > w} hfill 0 hfill & {text{else}} hfill end{array} } right.

The masking threshold M[k, n] formulated below M [ k, n ] = E [ k, n ] 10 m [ k ] 10 (32). is calculated by weighting the excitation patterns E[k, n] with the masking offset m[k] as given in m [ k ] = 3. 0 0. 25 ⋅ k ⋅ Δ z for  k ⋅ Δ z ≤ 12 for  k ⋅ Δ z > 12.