Sentence examples for boundary contraction from inspiring English sources

Unusually, segregation of larger atomic size Zn leads to grain boundary contraction.

We first prove the existence and uniqueness of the local solution for the free boundary problem by the contraction mapping theorem, then we show that the solution can be expanded to all time using suitable estimates.

This switches the right contact boundary from expansion to contraction.

Instead, we use a modified version of the Laplacian contraction, and these boundary points contract normally along the inward curvature flow in normal directions as inner points.

In addition, the mismatch of pixel values at ROI boundaries changes during the cardiomyocyte contraction making it impossible to compensate such boundary effects, for example, by varying the signal length.

The micro fractures are mainly interlayer fractures, grain boundary fractures and organic matter contraction fractures.

Hence, by the Banach contraction mapping principle, boundary value problems (1.1) and (1.2) have a unique solution on [ 0, 1 ].

By (26), we get K < 1, which implies that T is a contraction, therefore the boundary value problem given in (5) has a unique solution.

Two-stage length changes of UFG Al were observed which are explained by counteracting effects of expansion due to grain boundary segregation of Ga and contraction due to precipitation and recrystallization.

Hence, by the Banach contraction mapping principle the boundary value problem (1.1)–(1.2) has a unique positive solution on ([0,1]).

Boundary stresses are due to hinge contraction and to the resistance of extracellular matrix attachments to the cuticle.