Sentence examples for using the equivalence of from inspiring English sources

Using the equivalence of the K-functional and the Ditzian-Totik modulus we get the desired estimate.

The tCO2e are directly estimated from the toe using the equivalence of 0.345 toe per tCO2e [31].

Integrating this over ((t_{2}, t)) and using the equivalence of ({mathcal {F}}(t)) and (E t)) again, we obtain (2.10).

Using the equivalence of the item response theory and binary factor analysis frameworks when modeling dichotomous item responses, this study introduces a structural equation modeling (SEM) approach that is capable of estimating various types of position effects.

Remark 2.1 Very recently, using the equivalence of the three basic metrics, Samet et al. [19] show that many of the coupled fixed point theorems are immediate consequences of well-known fixed point theorems in the literature.

Dividing by (|theta-theta_{h}|_{1,Omega}) and using the equivalence of the norms (|cdot|_) and (|cdot|_{1,Omega}), we reduce (40) to begin{aligned}& |theta-theta_{h}|_{1,Omega}leq C bigl[{|theta- eta_{h}|_+sqrt {lambda t^{-2}}|omega- upsilon_{h}|_{1,Omega}} bigr],quad eta_{h} in H_{h}, upsilon_{h} in W_{h}.

The fuel consumption is estimated from the running kilometers considering: an average consumption value of 0.25 0.35 l/km in 2003 and 1997 [26, 29, 30], and using the equivalences of 41.87 petajoules per mtoe and 38.66 megajoules per liter of diesel [31].

where in the last inequality we use the equivalence of all norms on the finite dimensional subspace Y k.

Also, we will use the equivalence of the MDMR test statistic to the sum of squared case control dissimilarities.

Using the equivalence P=D of primal and dual optimum values it follows that the inequalities in (13) must hold as equalities.

Besides the equivalence classes of ℱ-random variables, we also use the equivalence classes of ℱ-measurable sets.