Sentence examples for an alternate proof of from inspiring English sources

As a corollary, an alternate proof of a theorem of Bade is obtained.

Jecko [284] has an alternate proof of Theorem 19.9.

This yields an alternate proof of this fact from [2].

However, an alternate proof of the same result, which is much easier than that given by Ali et al. [13], is presented below.

An alternate proof of (18) is provided as Appendix A. In this section, we first introduce the theoretical upper bound by employing the Hadamard inequality (18).

We stress that the following result applies, in particular, also to the continuous formulation (2) and provides an alternate proof for the existence and uniqueness of a solution of the Johnson Nédélec FEM BEM coupling.

Teufel [641] has an alternate proof for this Avron Elgart result and he has a book [642] on the subject.

For the lowest-order case p = 1, an alternate proof is found in  [33, Section 4], where R (T, T ^ ) = ω (T ; T ∖ T ^ ) are the refined elements plus one additional layer of elements, see  (5.19).

Against Fichte's attempts at system-building, Schlegel proposes a notion of what he calls an alternating proof (Wechselerweis): "In my system the ultimate principle [der letzte Grund] is actually a reciprocal proof [Wechselerweis].

Schlegel himself describes his philosophical approach as resembling both a circle and epic poetry because it must forever "begin in the middle": "Philosophy must have at its basis not only an alternating proof [Wechselbeweis] but also an alternating concept [Wechselbegriff].

A very interesting alternate proof to a theorem very close to Kato is due to Vakulenko [660].