Sentence examples for some vin from inspiring English sources
By Lemma 2.6 there exists a convergence subsequence ({v_{n}}) of ({u_{n}}) such that (Delta!mbox!lim v_{n}=v) for some (vin K).
Plurisubharmonic functions satisfying (2.3) are precisely of the form begin{aligned} psi =-log (-v) end{aligned}for some (vin PSH^- Omega )).
Since S is compact, we can suppose that along a subsequence (v_{n} rightarrow v), as (nrightarrowinfty), for some (vin S).
By Lemma 2.6 there exists a convergent subsequence ({v_{n}}) of ({u_{n}}) such that (Delta!mbox!lim v_{n}=v) for some (vin K).
(3.6) By the boundedness of ({v_{n} }), passing to a subsequence, if necessary, we may assume that (v_{n} to v) with (| v|=1) in E for some (vin E).
From Lemma 2.5, setting (lambda_{n}:=frac{1}{theta_{n}}) where (theta_{n} rightarrow0) as (nrightarrowinfty), (z=Jv) for some (vin E), and (y_{n}:= (J+frac{1}{theta_{n}}A )^{-1}z), we obtain begin{aligned} &Ay_{n}=theta_{n}(Jv-Jy_{n}), &y_{n}rightarrow y^in A^{-1}0, end{aligned} (2.7) where (A Erightarrow E^) is maximal monotone.
Therefore, ({T^{n}z}_{n=1}^{infty}) is a Cauchy sequence in K and hence converges to some point (vin K).
A set (Dsubseteq V(G)) is a distance k-dominating set of G if for every vertex (uin V(G setminus D), (d_{G} u,v leq k) for some vertex (vin D), where k is a positive integer.
For (kin N^), a set (Dsubseteq V(G)) is a distance k-dominating set of G if, for every vertex (uin V(G setminus D), (d_{G} u,v leq k) for some vertex (vin D).
Be it a stately $1,000 bottle of the inimitable Black Bowmore, the smoothest, smokiest single malt that will ever slide over your lips, be it the last surviving jeroboam of '45 Haut-Brion or some other vin de sicle, this fatuous, Babbitt-brained caveat must, by law, appear somewhere on its illustrious surface.
Then, for any (epsilon>0), there exists some point (vin V) with F v leqinf_{V}F+epsilon,qquad F w geq F v -epsilon d(v,w) quadtextit {F v -epsilonn V. We are in a position to show the existence of a second vositive solution for (1.1).
