Sentence examples for exists a selection from inspiring English sources

Let be any element, then there exists a selection such that (5.60).

Then is said to be a -multivalued weakly Picard operator (briefly -MWP operator) if and only if there exists a selection of such that for all.

Then, T is said to be a ψ-multivalued weakly Picard operator (briefly ψ-MWP operator) if and only if ψ : ℝ+→ ℝ+ is a continuous in t = 0 and increasing function such that ψ(0) = 0, and there exists a selection t∞ of T∞ such that d ( x, t ∞ ( x, y ) ) ≤ ψ ( d ( x, y ) ), f o r a l l ( x, y ) ∈ G r a p h ( T ).

As alluded to earlier, there exists a selection bias, whereby only patients and loved ones who are strong enough emotionally and psychologically to discuss these personal issues will participate.

We do acknowledge the possibility that there exists a selection bias amongst our referrals and therefore we may be presenting an over-estimate of the true rate of re-coarctation.

Proposed by Seligmann and Pollock, this hypothesis posits that there exists a selection for off-frame stop codons (OSCs) to counteract the possible deleterious effects of translational frameshifts, including the waste of resources and potential cytotoxicity.

There may also exist a selection bias in favor of young and highly productive researchers who would not have been hired if they had had a lower level of productivity.

Furthermore, owing to the retrospective nature of this analysis, there may exist a selection bias where those patients who underwent a more extensive lymphadenectomy may have had less comorbidity, as well as having tumours with more favourable prognostic features.

Notably, because the fat specimen chosen at 50 μm distance was less than the mean diameter of the adipocytes, there may be exist a selection bias that some measured adipocytes were repeatedly calculated.

Observe that the measurability of the operator (PcolonOmegatimes multimap C [0,a],mathbb {R}^{n})) says that for any measurable (xicolonOmegato mathbb {R}^{n}), in view of the Kuratowski-Ryll-Nardzewski selection theorem, there exists a measurable selection (etacolonOmegatimes mathbb {R}^{n}to C [0,a],mathbb {R}^{n})) such that (eta omega,x subset P omega,xi omega))).

[12]Let M, V : Ω → CB X) be two measurable set-valued mappings, ϵ > 0 be a constant and x : Ω → X be a measurable selection of M. Then there exists a measurable selection y : Ω → X of V such that, for any t ∈ Ω, x ( t ) - y ( t ) ≤ ( 1 + ∈ ) Ĥ ( M ( t ), V ( t ) ).