Sentence examples for a proof for the from inspiring English sources

The decreased relative viscosity upon acidification was a proof for the wrapping phenomenon in the biopolymer mixture.

The four-dimensional case was proved in 1982, and in 2003, a Russian mathematician, Grigori Perelman, completed a proof for the thorniest case, of three dimensions.

This paper presents a proof for the semiglobal asymptotic stabilization of stirred jacketed chemical reactors under PID control, which is based on results from nonlinear singularly perturbed systems.

We offer a proof for the counting bound to hold in a connectivity ATR sense, and illustrate trends with cubic and lattice networks.

The dual program is monotonic and sub-modular, providing stronger results, including a proof for the sufficiency of one-shot deviations.

We also give a proof for the convergence of such schemes, by combining the stability results of this paper with the corresponding properties of consistency.

For these, students may rightfully ask for a justification, or a proof, for why the result is true.

In case the renormalized amplitudes are finite it is a proof for RGE invariance of the ordinary DR ¯ scheme.

Proof: It is enough to have a proof for a single column appended from the right.

Proof: Again, it is enough to have a proof for a single column added from the right.

(iii) We present a proof for a fixed 1 < p < ∞ (the case p = 1 follows analogously).