Sentence examples for argument we used from inspiring English sources

The proof follows from similar steps in [11] and combines the argument we used in the above lemmas.

The argument we used to construct (hat {{e}}) shows that the upper bound on the coefficient is (left (frac {w check {{omega }}}{p}right)^{-1/check {{omega }}}).

Instead, we will mention here that exactly the same argument we used for Theorem 1.3 yields also the classical fixed point theorem of Browder, Gohde, and Kirk concerning the nonexpansive maps.

Thus by iterating the argument we used in the previous example (where we had (Ww subset wmathcal A w oplus xmathcal A w)), we can show begin{aligned} dim (W {mathcal F}) ge dim ( W w cdot {mathcal F}_0 ) ge 3 dim ( W w ) > frac{6}{5} dim (W).

In this respect the "aversion for reciprocity" argument we used in the discussion before may just be reversed by using a notion of "preference for the self-supporting", which is exactly the consequence of the priming of money according to Vohs et al. [33].

To further strengthen this argument, we used the BODIPY-cyclopamine, a fluorescent cyclopamine derivative, assay.

Since primitive recursion only allows us to recurse on the first argument, we use two steps to define the exponential function: Finally we can define \(E x,y) = R(\eta y),\eta(x))\) by composition.

When talking about argument, we use war metaphors.

In the above argument, we use the perturbation ({{tilde{Phi }}}=c|x-y|^alpha + frac{epsilon }{2}|x-y|^2) of the function (Phi =c|x-y|^alpha ).

With this argument, we use a computational modeling approach combined with in vivo electrophysiological data obtained from an experimental model of status epilepticus to infer about changes that may lead to a seizure.

In this argument, we use the recoil shear rate v ∼ cut as a measure proportional to tissue stress.