Sentence examples for shrinking gradient from inspiring English sources

For example, there exist complete noncompact Riemannian manifolds which satisfy (mathrm{Ric}_{f}=lambda g) for some positive constant λ (which is called the shrinking gradient Ricci soliton), but not for (mathrm{Ric}_{f}^{m}=lambda g).

The similar method applies to gradient shrinking Ricci soliton, which is similar to non-compact manifold with non-negative Ricci curvature in many ways.

The control of the stress influences on the free-standing sensor bridge due to shrinking mismatch, TCE mismatch, density gradients and deformation during the lamination is investigated using design of experiments (DoE), resulting in an adapted design and fabrication process.

3. It helps to prove, in some cases, that noncompact shrinking breathers of Ricci flow are gradient shrinking solitons.

Compared with GC3 gradients (fig. 5 A4– B3), GC1 and GC2 gradients are shrunk, noisy, and less distinct whereas the resulting GC-content gradients are distinct and regular albeit less deep than GC3 gradients.

For (kappa>0, kappa= 0, operatorname{or } kappa< 0), the gradient Ricci soliton ((M, langle,rangle, e^{-f},dnu, kappa)) is called shrinking, steady, or expanding, respectively.

It is shrinking.

The population is shrinking.

The permafrost is shrinking.

Elsewhere, forests are shrinking.

Some industries are shrinking.