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It is confirmed that the Forming Limit Diagram (FLD) and the FLSD are two mathematically equivalent representations of forming limits in strain-space and stress-space, respectively.
Compared with other reliability methods, the first-order reliability method (FORM) is consistent for different but mathematically equivalent limit state functions.
Schrödinger soon demonstrated that the different formulations were mathematically equivalent, though the physical significance of this equivalence remained unclear.
As explained in 'Materials and methods', the models in Figure 2B,C can be treated as mathematically equivalent.
The Tychonic and Copernican systems are mathematically equivalent.
The axiom of choice has many mathematically equivalent formulations, some of which were not immediately realized to be equivalent.
5. We don't appreciate that what's mathematically equivalent isn't psychologically so.
(Note that this is mathematically equivalent to including a linear time trend variable in the model).
It was soon proved that the two formulations were mathematically equivalent.
Heisenberg called Schrodinger's theory "disgusting" -- but both versions of quantum mechanics were soon found to be mathematically equivalent.
1926 Schrodinger finds the mathematical equation for the wave interpretation, and proves that wave and matrix mechanics are mathematically equivalent".
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