Sentence examples for following formulations from inspiring English sources

The two following formulations are designed to overcome this limitation.

Then, in virtue of (3.20), we have the following formulations for any matrices,, with appropriate dimensions: (3.21).

Notice that the matrix V is represented as (1) rather than V = W H commonly used in NMF-related literatures to make the derivatives of following formulations more readable without loss of generality.

For this purpose, the following formulations are presented: Min Z = ∑ j 1 - ρ j u j + ∑ k ∑ j ∑ i C i a ij X ik 1 - Y jk + ∑ k ∑ j ∑ i U ij X ik Y jk 1 - a ij + ∑ k ∑ j ∑ i h i a ij X ik Y jk n p i Open image in new window (1).

The following formulations show how to generate the initial chromosomes in each group: Deviation: Chr g, c [p] = random[σmin, σmax], where  p = 2,  4, …, 2 n ; g = 1,  2, …, P s i z e ; c = 1,  2, …, N C, (15).

The following formulations assume an underlying mean treatment effect, coming from a population of treatment effects.

The following formulation appears as the first entry in Martin Gardner's "The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems".

Therefore it forms the following formulation: (21).

For simplicity, the index is omitted in the following formulation.

This can be done by the following formulation, frac{d{rho}^K}{d{ A}^K}=0 (7).

The following formulation provided for PC with priority for a predefined service level (named ɛ).