Sentence examples for the earlier proof from inspiring English sources

The rest of the proof is similar to the earlier proof.

The earlier proof of this result presented in the literature was based on an incomplete expression for the elastic strain energy.

Our proofs are based on the properties of reproducing kernels, and they do not involve the use of biharmonic Green functions as had some of the earlier proofs.

Then x p q − x 0 ∈ W. Now observe that if for ( k, l ) ∈ I r s, x k l − x 0 ∈ W, then x k l − x p q = x k l − x 0 + x 0 − x p q ∈ W + W ⊂ V ⊂ U. Hence, as in the earlier proofs, we can prove that K ⊂ { ( r, s ) ∈ N × N : 1 h r s | { ( k, l ) ∈ I r s : x k l − x p q ∉ W } | < δ }, which consequently implies that ( x k l ) is I θ r, s -statistically τ-Cauchy.

Was Sputnik 2 the early proof?

Let's check out the early proof.

Its printed edition was "edited" and "commented" on by Fielding's pseudonym H. Scriblerus Secundus who pretends not to be the original author, and it contains a frontispiece by Hogarth, which serves as the earliest proof of a relationship between Fielding and Hogarth.

Behind her, in boxes, are the early proofs of her 15th book.

Historically, the eclipses of Jupiter's Galilean moons are important, for they provided one of the earliest proofs of the finite speed of light.

Even the early proof-of-concept and pilot work may provide help to millions or save lives — it's not every day a company is founded that can say that.

We note that the earliest proofs of N-body asymptotic completeness for (text {0}(|x|^{-1-epsilon })) potentials (at least when (N ge 4)) were by Sigal Soffer [564, 565] and then by Graf [196] and Dereziński [115].