Sentence examples for a singular set 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".

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.

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.

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.

Open all day, Eau Rouge is a singular setting for watching the karts whip past dioramas of Manhattan shops and landmarks at speeds of up to 40 miles per hour.

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.

If f and g are bounded away from zero and infinity on strictly convex domains Ω and Λ, respectively, and if the cost is quadratic, then away from ∂ the free boundaries of the active regions are shown to be C1,αloc hypersurfaces up to a possible singular set.

Then u is of class (C^{1}) outside a closed singular set (operatorname{Sing} u subsetOmega) of Haar measure 0. Furthermore, for (xi_{0} inOmegabackslash operatorname{Sing}u), the derivative Xu of u has the modulus of continuity (r to M r)) in a neighborhood of (xi_{0} ).

We prove that every positive function in C1(Sn), n⩾6, can be approximated in the C1(Sn) norm by a positive function K∈C1(Sn) such that the conformal scalar curvature equation(0.1 -Δu+n n-2 4u="Kun+2n-2inSnhas a weak positive solution u whose singular set consists of a single point.

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.