Sentence examples for using this relation we from inspiring English sources

By using this relation, we will give the explicit forms of the Green functions.

Using this relation we prove general results on uniqueness and convergence for subcritical Gaussian multiplicative chaos that hold for Gaussian fields with arbitrary covariance kernels.

Using this relation, we divide ({mathcal F}{mathcal S}({s_0,s_1})) into the disjoint equivalence classes.

Using this relation we have ξ 15=1, that is ξ is the primitive 15th root of unity.

Using this relation, we can compute all the distinct powers of α in G F(212), see Table 4 (it is clear that α has order 45).

Using this relation, we can rewrite the canonical conjugate momentum p in terms of x and ẋ, and we obtain this diagram for different values of ω. Figure 5 The contour plot for conjugate momentum p. A contour plot is a graphical technique for representing a three-dimensional surface by plotting constant z slices, called contours, on a two-dimensional format.

By using this relation in inequality (26), we get the required result.

Using this relation, with VSW/Vsc ~ 1.17, we estimated the wave frequency in the SW rest frame as f r = 1 - V SW / V sc f ~ - 0.17 f (6).

These considerations link the PEP formation rate, F2, to the PPi concentration, (10) F 2 = α PPi Using this relation in Eq. (8), we see that product inhibition of RP by [PPi] leads to the following connection between the systems output F2 and the RP phosphate rate: (11) V p (ADP ) = V p 0 (ADP ) ∕ (1 + F 2 ∕ F 0 ) Where F0 = α Ki,PPi.

Essentially we should be able to construct qualitatively, the features of the phase diagram using this relation.

Using this relation, properties can be assigned to an object.