Sentence examples for extended formula from inspiring English sources

In specific apps, like the calculator, additional functions may appear on the sides of the device, like the extended formula set for scientific calculator mode.

For regions with more than one SNP in LD, we used the extended formula: λ k = ∑ j p k j r k j 2 (∑   j p k j r k j ) 2 where p k j is the frequency of haplotype j for the multi-locus region k and r k j is the corresponding risk estimate.

We calculated population attributable risk proportions (PAR) using the extended formula for multi-category exposure, in this case the socioeconomic quintiles [ 20]: (1) PAR= ∑ i = 0 k P i R R i − 1 1 + ∑ i = 0 k P i R R i − 1 Subscript i refers to the i th exposure level (Q2, Q3, Q4 and Q5).

The correctness of these extended formulae is verified by comparing them with available ones in the literature, and the importance of these formulae is on their direct application in the three-dimensional dislocation dynamics simulation involving interface or surface.

For this reason, we will extend formula (3) rather than (2).

We extend formula (2.1) of [8] to (2.13) in this paper.

Observe that both corollaries extend formula (3) by choosing (f=psi_{m}) and (p=q=1) in Corollary 2.2, and (f=psi_{m}) and (j=1) in Corollary 2.3.

It was shown in [54] that under natural assumptions it is impossible to extend formula (3.9.1) to the class of all continuously differentiable functions.

(2) We remove the hypothesis T with bounded range and obtain the same result by the different method from [8].   (3) We extend formula (2.1) of [8] to (2.13) in this paper.

The derivation of the generalized Goertzel algorithm is analog to the technique presented in Section 2. Compared to that, however, we extend formula (22) at the very beginning by unity in the form of e j2 π k N N ⋅ e - j 2 π k N N = 1 for  k ∈ ℝ, (23).

Synthesizing Formulas (1) and (2) and two vectors extends Formula (1) to the following form: (3) S p = C p + ∑ g ∈ G (p ) β p g Φ g.