Sentence examples for a singular set of from inspiring English sources

Mr. Gordon-Levitt faced a singular set of challenges on the film, training for weeks to shoot a long zero-gravity sequence that evokes both the Fred Astaire musical "Royal Wedding" and "2001: A Space Odyssey".

An expert possesses knowledge that is usually focused on a singular set of skills for the purpose of achieving success or overcoming an obstacle for a particular activity without working beyond the foundational scope.

By an approximation method, we prove the existence of a minimizer of the relaxed energy of the Hessian energy, and that the minimizer is biharmonic and smooth outside a singular set Σ of finite (m−4 -dimensional Hausdorff m−4 -dimensional

(Hausdorff dimension of singular sets of SOLA) Theorem 16 allows to define SOLA which are initially defined only almost everywhere via convergence outside a singular set (i.e. set of non-Lebesgue points) of Hausdorff dimension not larger than n - p, when p ≤ n.

We prove that, in the optimal transportation problem with general costs and positive continuous densities, the potential function is always of class W2,ploc for any p≥1 outside of a closed singular set of measure zero.

Combined with existing results on the interior partial regularity, this result yields an upper bound on the Hausdorff dimension of a singular set at the boundary.

As an immediately corollary we can derive an estimates of Hausdorff dimension on the possible singular set of a suitable weak solution as in the case of pure fluid.

We show that every weak supersolution of a variable exponent -Laplace equation is lower semicontinuous and that the singular set of such a function is of zero capacity if the exponent is logarithmically Hölder continuous.

This curve avoids the singular set of the surface Fig. 7 A closed geodesic in a maximal Enneper surface in (mathbb {R}^{2,1}), shown in both smaller and larger portions of that surface.

Note that this geodesic also avoids the singular set of the surface Fig. 8 Another closed geodesic in a maximal Enneper surface in (mathbb {R}^{2,1}), again shown in both smaller and larger portions of that surface.

Note again that the geodesic avoids the singular set of the surface.