Sentence examples for proceeds we used from inspiring English sources

To test this hypothesis and to characterize the spatial velocity with which the reaction proceeds, we used an agarose stamp that was inked with the phosphopeptide to pattern a maleimide-terminated monolayer with a parallel set of striped regions that presented the peptide.

Before proceeding, we use the following change of variables: varphi bigl(R_{0}^bigr)^{2}times R rightarrow bigl(R_{0}^bigr)^{2}times R,qquad varphi x,y,t)=biggl(K bar{x},Khrbar{y},frac{A+x^{n}}{r}bar{t}biggr) and rewriting x̄, ȳ, t̄ as x, y, t, we obtain the equivalent form of the system (1.3) textstylebegin{cases} dot{x}(t)=x 1-x)(A+x^{n})-x^{n}y, dot{y}(t)=x 1-x{n}-C(A+x^{n} -x^{n}y

Next, we can exploit the fact that s ( x ) = σ o, j 2 + αx + β x 2. To proceed, we use the linear Taylor approximations: s ( ΔtE ) ≈ s ( y min ) + 1 2 1 + 2 β y min / α α ΔtE − y min s y min near α ΔtE = y min s ( y max ) + 1 2 1 + 2 β y max / α α ΔtE − y max s ( y max ) near α ΔtE = y max.

To proceed, we use the local false discovery rate strategy, which consists in assessing the posterior probability that S n is under H0 (Efron et al. 2001).

To proceed we use Lindstedt's method which is a technique for uniformly approximating periodic solutions to ODEs when regular perturbation approaches fail.

To proceed further, we use a mathematical technique called the change of variable is used to get the more simplified version of (9), specifically, putting z = wδ in (9) gives us.

This paper proceeds in the order we used to develop the model: 1) we discuss the assumptions, 2) we present the model (created in an Excel© spreadsheet, see Additional File 1), 3) we discuss the results, and, finally, 4) we discuss implications and conclusions.

To proceed with the analysis, we used a model with a compound symmetry structure.

Note that this is the only literature source we used before proceeding to the literature analysis and verification in Step V.

We used the precede-proceed model for the needs assessment.

To proceed we now use the statistics of the input field.