Formal asymptotic analysis of phase field models for voids is crucial for proving thermodynamic and mathematical consistency of the models and for determining their parameters from sharp-interface counterpart.
Minkowski's geometric ideas provided a powerful tool for checking the mathematical consistency of special relativity and for calculating its experimental consequences.
Thus, the mathematical consistency of the inverse problem formulation has been guaranteed.
It is shown, how this parameter can be determined for general triaxial stress states, and conditions are derived for mathematical consistency.
When such a series of distances and angles returns to its point of beginning or begins and ends at stations of superior (more accurate) control, it can be checked and the small errors of measurement adjusted for mathematical consistency.
One of the peculiar features of string theory is that it requires extra dimensions of spacetime for its mathematical consistency.
Also, the property derivatives are validated and verified for thermodynamic and mathematical consistency.
For sure, there's lots of mathematical consistency and compatibility with established laws, but should a theory that makes no predictions be regarded as scientific?
It is always constrained by the straitjacket of mathematical consistency and compatibility with established laws.
"For the first 25 years, the thinking has been that superstring theory is so difficult to see experimentally that you have to figure it out by its own mathematical consistency and beauty," Dr. Lykken said.
