Sentence examples for proof by means of from inspiring English sources

Don Verdean's original archeological passion may be motivated by faith, but it's a faith perverted both by a wrong-headed quest for earthly success and by a fundamental betrayal of faith itself — by asserting that faith is in need of rational proof by means of science and scholarship.

Proof By means of Lemma 3 and the same way, we can prove that (21), (22), and (23) are valid and equivalent.

Although the general problem of finding the shortest proofs by means of cut-introduction is undecidable [5], there are a few preliminary algorithms that introduce simple cuts [10,15,24], and it has been shown that some techniques of machine learning, such as decision tree learning, can be seen as cut-introduction techniques from a proof-theoretical point of view [23].

Thus, to take the prime example, the 'existence' of Euclidean geometry (or more accurately Euclidean geometries) is shown by the consistency proofs given by means of analytic geometry.[9] Thus, the unit of consistency is not the concept nor the individual propositions, but rather the system of axioms as a whole, and different systems necessarily give accounts of different primitives.

Proof is given by means of the Riccati technique and phase plane analysis of a system.

The objectives of this article are to present WaveCat, a recently patented WEC, and its proof of concept by means of an experimental campaign in a large wave tank.

In Section 3, we complete the proof of Theorem 1.1 by means of the Riccati technique.

In Section 3, we give the proof of Theorem 1.3 by means of the Littlewood-Paley theory and the Bony paradifferential calculus.

Then using the same argument as in the proof of Theorem 3.1 by means of (4.3) and the condition (C3) together with the properties of the bifunction F and the function φ, we must have x ∈ MEP ( F, φ ).

The proof is carried out by means of the decay property of the solution operator and a fixed point-contraction mapping argument.

Proof It is easy to show that there exists a real number r 0 > 0 such that u 0 ≥ r 0 v 0 since u 0, v 0 ∈ P ∘, which completes the proof of Corollary 3.2 by means of Corollary 3.1.