Sentence examples for point in the proof of from inspiring English sources

The key point in the proof of (i) is to obtain λ 1 < 0 by contradiction.

The critical point in the proof of this result is the production of elements in the intersection of three Schubert varieties.

Since the key point in the proof of Theorem 3.2.1 is the center manifold function, we introduce an approximation formula of the center manifold function derived in [16].

Beside the choice of operator (25), which is naturally imposed, a crucial point in the proof of Theorem 2 is the choice of constant q in (23) to get the contractivity of the operator.

We characterize the exact observability of this system only in terms of C and of the spectral elements of the operator A. The starting point in the proof of this result is a Hautus-type test, recently obtained in Burq and Zworski (J. Amer. Soc. 17 (2004) 443 471) and Miller (J. Funct. Anal. 218 (20052005) 425 444).

The key point in the proof of this lemma is the observation that, as a consequence of (6.5), the real tangential Hessian of any defining function for a domain as in Lemma 3 is positive definite when restricted to the complex tangent space T w C ( b D ) (viewed as a vector space over the real numbers).

This fact is used at important points in the proof of the following result.

Now, we state the crucial points in the proof of our theorems.

The crucial point in the proofs of Theorems 5 and 6 is to prove that the Krein integral K[ f]<∞ by Condition L and the moment condition.

It is worth mentioning that the key point in the proofs of Theorems C and D is the q-integration by parts formula: int_{0}^{b}f(t)D_{q}g(t),d_{q}t= (fg) (b -lim_{ntoinfty }(fg) b -lim_{ntoinfty- int_{0} fg}D_{q}f(t) g(qt),d_{q}t.

Let ({x_{k}}_{kinmathbb{Z}}) be the sequence of points defined in the proof of Theorem 3.1.