Sentence examples for this note is to prove from inspiring English sources

The aim of this note is to prove that Theorems 1.1, 1.2 and 1.3 are equivalent.

The purpose of this note is to prove a global inverse function for homogeneous mappings on R n.

The aim of this note is to prove refinements of the latter two asymptotic relations where α=α(n)→0 and β=β(n)→0 as n→∞, and to prove similar results for two-sided confidence intervals and for the power function when testing corresponding hypotheses.

The aim of this note is to prove an analogous Hardy-type inequality on a half-space for Kohn's sub-Laplacian in Heisenberg groups H n. It has been proved by D'Ambrosio ([11], Theorem 3.3) that for u ∈ C 0 ∞ ( H n ), the following holds: ∫ H n | ∇ H u | 2 d x d t ≥ ( n − 1 ) 2 ∫ H n u 2 | x | 2 d x d t, (1.3).

The Supreme Court has noted how hard it is to prove this kind of mental condition beyond a reasonable doubt.

The aim of this short note is to further prove the Smith approximation (S ( x ) ) is an upper one.

Every genealogist needs a first-class filing system and One Note is proving a credible competitor to the popular Evernote app.

He noted, however, that it is difficult to prove that compensation is unreasonable unless it is far outside norms.

This was noted in [6] and is easy to prove using Fourier transforms or finite field theory.

More important to note is that this result proves that the correctness of the protocol is guaranteed when using nodes in different modes in the presence of mobility.

Note that it is sufficient to prove only Eq. (87), as Eq. (88) follows by the symmetry of the expressions.