Sentence examples for alternate proof 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].
A very interesting alternate proof to a theorem very close to Kato is due to Vakulenko [660].
Teufel [641] has an alternate proof for this Avron Elgart result and he has a book [642] on the subject.
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).
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].
In Section 3, alternate and easy proofs of results [[13], Lemmas 2.1, 2.10] are discussed.
All students registered in an insurance-required program are enrolled in the University Student Health Insurance Plan (U-SHIP), administered by UnitedHealthcare StudentResources, unless they waive coverage by providing proof of alternate comparable coverage.
Quasitriangular Hopf algebras (quantum groups), "braided monoidal category," such as Kuperberg's proof of the alternating sign conjecture, deformations of the Weyl character formula, and knot invariants such as the Jones polynomial.
