Sentence examples for expanding the expression from inspiring English sources

The affine formulation (6) (resp. (6) and (10)) can then be derived by simply expanding the expression (16) (and (17)) in terms of the subdomains Ω l and the different entries of K i j l.

Expanding the expression of displacements in the region of anchor-grouting into a Maclaurin series, and utilizing the cumulative displacement curve of the surrounding rock through observation, a theoretical model is set up.

There is no simple analytic solution to Equation 3 but assuming | s| < 1, we can obtain an approximate solution by expanding the expression in powers of s ^.

A caveat is that the number of loci required can be quite large if the fraction of missing data is large or the number of taxa large (when p << 1 and or q << 1, the lower bound on number of loci k scales as 1/(p q) (expanding the expression Theorem 2 part (ii) in a Taylor series approximation)).

The pressure change can be estimated by expanding the expression for small volume changes: (12) Δ P A = (V i (t d ) A 0, i ) β + β Δ V i A 0, i (V i (t d ) A 0, i ) β − 1 − (V i (t d ) A 0, i ) β (13) Δ P A = β Δ V i A 0, i (V i (t d ) A 0, i ) β − 1 By comparing this last equation to Eq. (6) we obtain a relation between both compliance parameters.

With this adjustment and assuming K is constant, after combining eqns (3) and (4), expanding the expressions for n and n′ using eqns (1) and (5), and simplifying, yields: (6) With this formulation, values of the ratio >1 indicate that the temporal method has greater precision, while the LD method is more precise when the ratio <1.

Using this fact, we can expand the expression ( 1 − ( w − z w ) ρ + 1 ) − α − 1 in power series.

Further, we expanded the expression analysis of AP2/ERF genes using the gene expression database SRA (ERA047687) submitted by Brown et al [ 34].

Our studies expand the expression of spastin to human fibroblasts, hiPSCs and astrocytes and indicate that the M87 isoforms of spastin are expressed in diverse human cell types.

When we expanded the expression of TAβ42 to include all clock neurons, by using tim,repo-gal80, the flies became behaviourally arrhythmic.

cDNA samples derived from three additional time points (D0, D7 and D9 after treatment) were included to expand the expression pattern data for these genes.