Sentence examples for an exceptional solution from inspiring English sources

The plan explicitly states that Greece is in a uniquely grave situation and requires an exceptional solution.

Curved composite concrete-steel I-girder bridges provide an exceptional solution to the problems of urban congestion, traffic, and pollution, but their behavior is quite complex due to the coupled bending and torsion response of the bridges.

For traditional bargaining problem, Nash (1950) indicated that there is an exceptional solution called Nash solution that satisfies invariance quadruple conditions, Pareto optimization, independence of irrelevant alternative, and symmetry.

There will never be a better proof that this method doesn't work than the dot-com crash that resulted from startup ventures raising millions of dollars to build an exceptional solution and take their companies public without sufficient validation, for many, without a single revenue dollar.

According to this view, RNA is an exceptional solution to the problem of molecular information storage but was not the first solution to this problem in a continuum of molecular systems (Cairns-Smith, 1977; Joyce et al., 1987).

This shows that in Theorem 1.2, there exists one possible exceptional solution with σ ( f ) < max { σ ( B ), 1 } + 1.

Hence equation (1.9) possesses at most one exceptional solution f 0 with σ ( f 0 ) < max { σ ( B ), 1 } + 1.

Then σ [ p + 1, q ] ( f ) = σ 3 holds for all solutions of (1.2) with at most one exceptional solution f 0 satisfying σ [ p + 1, q ] ( f 0 ) < σ 3.

satisfy λ ( f ) = σ ( f ) ≥ max { σ ( B ), 1 } + 1. with at most one possible exceptional solution with σ ( f ) < max { σ ( B ), 1 } + 1. Remark 1.2 Under conditions of Theorem 1.1, equation (1.8) has no rational solution.

holds for all solutions satisfying σ [ p + 1, q ] ( f ) = σ 3 with at most one exceptional solution f 0 satisfying σ [ p + 1, q ] ( f 0 ) < σ 3. (ii) For 2 ≤ q = p + 1, σ 3 > 1, by a similar proof to case (i), we draw the conclusions of case (ii).

If σ [ p + 1, q ] ( F ) ≤ σ 3, by the above proof in (3.8 - 3.9 3.8 - 3.9find that all solutions of (1.2) satisfy σ [ p + 1, q ] ( f ) ≤ σ 3. we affirm that (1.2) can only possess at most one exceptional solution findsathatying σ [ p + 1, q ] ( f 0 ) < σ 3.