Sentence examples similar to if there exists precisely from inspiring English sources
If, there exists satisfying.
(3) If, there exists satisfying.
More precisely, if there exists (lim_{nrightarrowinfty}n^{kappa}(x_{n}-x_{n+1})=l), with (kappa>1), then (lim_{nrightarrowinfty}n^{kappa-1}x_{n}=frac{l}{kappa-1}).
More precisely, one has that (Gamma ) is amenable if and only if there exists a net ({Gamma _i}_{i in I}) of non-empty finite subsets with begin{aligned} lim _ifrac{|gamma Gamma _i cup Gamma _i|}{|Gamma _i|}=1, quad text {for any } gamma in Gamma, end{aligned}where (|cdot |) denotes the cardinality of the subset.
Somewhat more precisely, a problem \(X\) is said to admit a brute force solution if there exists a feasibly decidable relation \(R_X\) and a family of uniformly defined finite sets \(S_x\) such that \(x \in X\) if and only if there exists a feasibly sized witness \ y \in S_x\) such that \(R_X x,y)\).
More precisely, it is shown that the problem admits a solution if and only if there exists (u_{0}in H_{0}^{1}(Omega)) such that (int_{Omega}hu_{0}^{1-alpha},mathrm{d}x<infty).
More precisely, we say that X* is a uniformly weak sharp minima of VIP if there exists α > 0 such that − F ( x ) + α B ⊂ ∩ x ∈ X * ( T X ( x ) ∩ N X * ( x ) ) 0, ∀ x ∈ X *. (3.7).
If there exists a conference graph on 2m−1 vertices, then there exists a regular Hadamard matrix of order 4m2.
However, so far one does not even know if there exists a fourth nontrivial solution.
If there exists such that if (2.12).
