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Exceptional solutions frequently increase fragmentation.
For growth estimates of solutions of a non-homogeneous linear differential equation, in general there exist exceptional solutions that are not easy to discuss (see [6], Chapter 8).
While providing important test cases and useful insights, this approach is not sufficiently robust - boundary and other conditions that select such exceptional solutions are not always present in nature.
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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.
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.
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.
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.
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.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com