Sentence examples for core proof from inspiring English sources

The core proof of  [14] then uses the observation from  [49] that the so-called total error is contracted in each step of the adaptive loop in the sense of (3.4) Δ ℓ + 1 ≤ κ Δ ℓ for  Δ ℓ ≔ ‖ ∇ (u − U (T ℓ ) ) ‖ L 2 2 + γ osc (T ℓ ; U (T ℓ ) ) 2 with some ℓ -independent constants 0 < κ < 1 and γ > 0.

Here is (the core of) a proof of it: Suppose that one comes to know left-cancellation by following this sequence of steps.

At the core of our proof is finding specially designed Hamiltonian cycles in 2-dimensional and heavily pruned 3-dimensional tori, irrespective of the actual networks G and H we happen to be working with.

The core of the proof is a new notion of k-gradation for P and Q, whose existence (even in an arbitrary metric space) is proved using the Knaster–Tarski fixed point theorem, by a method introduced by Reem and Reich for a slightly different purpose.

end{aligned}From this formula it is clear that the core of the proof is to provide estimates independent of the volume of E for the potential begin{aligned} int _Efrac{xcdot p}{sqrt{1- xcdot p}{sqrt{1- xcdotl H}^{n-1} end{aligned} (5.40)and for its maximum with respect to p. This requires some technically involved ideas and strategies.

This method starts with a wire skeleton covered with a core of fire-proof material such as clay or plaster that forms the rough shape of the final sculpture.

The setting has been transformed, but a core within remains unaltered, proof that it is easier to transform buildings than lives.

Equality proof the core competencies and make them transparent to all employees to reduce the chances of disadvantaging any one group.

That Ralph Lauren should seek to focus on its core lines is further proof too that high-end retailers see more potential in the upper end of the market, rather than on the high street.

The syntactic study of these notions, especially of consistency, which became a core part of Hilbertian "proof theory" is not present in Dedekind's work.

The core part of the proof of [[3], Theorem 2.1] is to show that { T i x } is Cauchy.