Sentence examples for exists bar from inspiring English sources

Specifically, if (P > frac {E_{s}}{T_{s}}), then for almost every energy harvesting sample path, there exists (bar {K} < infty ) such that (K leq bar {K} < infty ) as N→∞.

If M i is upper bounded, that is, there exists (bar {M}) such that k m =0 for all (m > bar {M}), then K is finite and (3) is true.

There exists (bar {theta }_{H}) such that if (theta _{H} > bar {theta }_{H}), (frac {partial bar {gamma }}{partial P} ge 0), and if (theta _{H} < bar {theta }_{H}), (frac {partial bar {gamma }}{partial P} le 0).

This means that for almost every energy harvesting sample path, there exists (bar {N} < infty ) such that Q(n T s )≥E s, (forall n > bar {N}), or there exists a time threshold after which the best-effort sensing policy will be exactly the same as the uniform sensing policy.

We consider ({mathcal {P}}={mathcal {P}}_{textbf {D}}) as in Example 3, but now we choose D in a way to allow for a degenerate case, where there exists (bar {Q}in {mathcal {P}}) such that the canonical process is constantly equal to its initial value.

Now by assumption (bar {{q}}(cdot) > tilde {{q}}(cdot)) on [0,γ ⋆) and (bar {{q}}(cdot) - tilde {{q}}(cdot)) is continuous with respect to γ, there exists (bar {gamma } < gamma ^{star }) such that (bar {{q}}(cdot) ; - ; epsilon (cdot) < tilde {{q}}(cdot) < bar {{q}}(cdot) ) on ([ bar {gamma }, gamma ^{star })).

Then, from the local existence results, there exists (bar{T}'>bar{T}) such that (2.5) and (2.6) hold for (T=bar{T}'), which contradicts (3.1).

If (|omega -1 | < alpha) as in Propositions 4.1 and 4.2, then there exists (bar{R} > 0) such that ω can be an eigenvalue of the problem left { textstylebegin{array}{l} Delta_{mathbf{g}}v + omega p u_{R}^{p-1}v=0 quad textit{in }A_{R}, v=0 quad textit{on }partial A_{R}, end{array}displaystyle right.

Hence, there exists (bar{z}in G(bar {x} cap -E)) such that (z^{x} cap -Eleq0).

As (K_{2}) is usc at ((bar{x}, bar{lambda})) and (K_{2}(bar{x}, bar {lambda})) is compact, there exists (bar{y}in K_{2}(bar{x}, bar {lambda})) such that y_{n_{k}} rightarrow bar{y} quadmbox{as } krightarrow infty (mbox{taking a subsequence if necessary}).

Since E is complete, using Proposition 2.3, (E = bigcap_{i} E_{i}), therefore there exists (bar{x} in E) such that (xi_{n}^{i}rightarrow bar{x} in E).