Sentence examples for instead of the relation from inspiring English sources

Therefore, instead of the relation, we can write f(theta)=sum^{infty}_{n=0}D_{n} cosbiggl n-frac{beta}{2}biggr)theta.

Let us notice that the difference of the expressions (E_{2}) and (E'_{2}) is only in the fact that we need to take into account the relation sum_{j=s}^{infty} bigl(V_{j}^{-frac{p'}{p}}-V_{j+1}^{-frac {p'}{p}} bigr)=V_{s}^{-frac{p'}{p}}-V_{infty}^{-frac{p'}{p}} instead of the relation (22).

Another approach towards estimating the extent of mismatches is to directly estimate the efficiency of matching in the economy instead of estimating the relation between the unemployment rate and measures of mismatches.

If instead refinements of the relation 'part of' are disallowed, all consistent atomic RCC8 relations can be convexly realized in 3D.

The discussion here, talking instead of the propositional relation being interpreted as ascribing the property of swimming to Dara, echoes Soames' [2010] (discussed below) way of stating what is essentially the same point.

(See also the suggestion in Sainsbury (2010 82 3) that Lewis could have accommodated a plurality of possible Holmes-candidates by refusing to identify Holmes with any of them, instead modeling the relation between talk of Holmes and talk of these possible Holmes-candidates on the model of the notion of precisification used in Lewis's semantics of vagueness).

The experimental results suggest that the incremental stress strain relation for the transition loading path within the so-called yield surface from one yield state to another may be related to the displacement increments that correspond to the change of microscopic folding mechanisms instead of the usual elastic relation according to the classical plasticity theory.

The grey-rough approximation is based on an interval coincidence relation and an interval inclusion relation instead of an equivalence relation and an indiscernibility relation in Pawlak's model.

For instance, if the wind shear factor is 1/4 instead of the used 1/7, the relation global warming potential per kWh ranges from 5.4 to 23 g CO2-eq./kWh instead of 9.5 to 29.7 g CO2-eq./kWh, since more wind energy can be captured at higher wind shear factors and hub heights.

These senses are "abstract" individuals and relations, instead of the ordinary individuals and relations discussed thus far.

As for the lack of the positive implicature, since the focus associate in 53 is degrees instead of superiority relation (cf. 49), the participants in the conversation do not need to assume that the standard has the positive sense to make sentences informative19.