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Below is the modified Navier Stokes equation in cylindrical coordinate: u ∂ u ∂ x + v ∂ u ∂ v ρ = − ∂ p ∂ x + 1 r ∂ ∂ r μr ∂ u ∂ r − ρg.

Below is the derivation of the equation for fluorescence intensity as a function of solution composition for FCA titrations.

The D w matrix given below is the watermarked D matrix given in Equation (2).

Below are the proposed chemical equations for H2 evolution.

Below are the ordinary differential equations for the network of regulatory influences shown in Fig. 2. <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0014752.e001.PNG" class= inline-graphic"/> To keep the model simple and minimal, we kept the number of parameters which characterize the interactions to the minimum.

Below are the limitations of using Equation 3: (a) The angle of incidence of beam radiation is 0° ≤ θ < 90°.

As a result, a placebo factor (PLAC), as defined by the equation below, was included in the differential equation to account for the effect of lifestyle intervention or placebo on HbA1c levels.

The parameter C in the equations below is a normalizing constant, and "unweighted" refers to the fact that these probability density functions do not incorporate the probability of detection in a GWAS.

The dephosphorylation of phosphorylated CheY by CheZ (represented by F C in Figure  1C and by Z in the equation below) is given by, (6) Z + C P ↔ K ZC Z C P → k ZC Z + C, where K ZC and k ZC are the dissociation constant and the catalytic constant of CheZ, respectively.

Below are area equations for a few common shapes: Circle: π(r 2 — r is the distance from the exact center of the circle to its edge (or its "radius").

The equation below is a means to manipulate among joint, conditional and marginal probabilities.

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