Sentence examples for using the quantitative deformation from inspiring English sources

Using the quantitative deformation lemma and topological degree theory, we prove that (I' u)=0).

Using the quantitative deformation lemma [30], Lemma 2.3, we prove that (J' u)=0).

The book [16] contains the first application of this methodology, using the quantitative deformation lemma in [25].

The two extreme deformation conditions shown in Fig. 4 were used to extract the quantitative deformation parameters: the image of the stable non-deformed cornea (reference condition), shown in red; and the image of the maximum transient deformed cornea, overlapped in green.

Specifically, we establish an existence result of positive solutions using fixed point index theory and an existence result of nodal solutions via the quantitative deformation lemma.

In order to prove Theorem 1.4, we need to show (I' u_{0})=0) by the quantitative deformation lemma.

Quantitative analysis of the reaction products is made possible by using the methyl deformation band at 1377 cm−1 as internal standard.

The quantitative maps were masked to remove background noise, warped into standard Montreal Neurological Institute space using the segmentation deformation fields, and then smoothed using an 8-mm full-width at half maximum Gaussian kernel.

Using the DARTEL extension, deformation parameters were extracted for normalization of functional images (Ashburner, 2007).

These maps were normalized to MNI space using the affine and diffeomorphic deformations calculated above.

PHEMA polymers (also previously conditioned) were analysed using the material pocket accessory in deformation mode.