Sentence examples for proof of continuity from inspiring English sources
A proof of continuity between the two models (for oblate and prolate voids) is provided.
Since (Phi^{prime}) is a mapping of type ((S_)), by Lemma 3.5, the proof of continuity of the inverse operator ((Phi^{prime})^{-1}) is obvious.
end{aligned} Equation (3.12) allows us to finish the proof of continuity in time, that is, (theta t,x inmathcal{C}(0,infty; F_{p,q}^{s})).
The inequality is obtained by using the majorizing measure, ν n 0 , defined in the proof of continuity of stationary distribution.
Indeed, it led us to introduce the notion of "last reset" time and, at some point in the proof (see, e.g., Equation (39)), obliged us to consider several situations (e.g., τ k ( t, ω ) ≥ t − m or τ k ( t, ω ′ ) ≥ t − m versus τ k ( t, ω ) < t − m and τ k ( t, ω ′ ) < t − m in the proof of continuity, Section 6).
From the latter and estimate (16) we conclude that ϰ ( k, r ) | D − k f ( x ) | ⩽ 2 r ∥ f ∥ L ∞ ( G ) k h k + ∥ r − 1 − k χ ( 0, r h ) ∥ E 1 ⋅ ∥ f ( r ) ∥ E k r k, which proves the existence and uniform boundedness of derivative D − k f ( x ) at an arbitrary point x ∈ G. Now, we turn to the proof of continuity of D − k f on G. Let x ∈ G be an arbitrary point.
The proof of complete continuity of (mathcal {K}_{2}) is similar to the proof of complete continuity of (mathcal {K}_{1}), so we omit the details.
The proof of Jewish continuity was right in the Chabad building, where the sound of morning play could be heard.
Though few other scenarios exist in our 21st-century society in which proof of bloodline continuity is necessary, one is still crucial - the British monarchy.
The death of Osama bin Laden, in a raid that operationalized Bush's famous "dead or alive" dictum, offered the most visible proof of this continuity.
And because such testing provides positive proof of family continuity, it has become indispensable in inheritance disputes and in cases of disputed paternity, for example when the child support agency needs to determine liability.
